High Performance Loudspeakers: Optimising High Fidelity Loudspeaker Systems [7. ed.] 9781118413531

Table of contents :
Cover
High Performance Loudspeakers:

Optimising High Fidelity Loudspeaker Systems
© 2018
Contents
Preface to the First Edition
Prefaceto the Fifth Edition
Prefaceto the Sixth Edition
Prefaceto the Seventh Edition
Acknowledgements
1 General Review
2 Developments in Loudspeaker System Design
3 Theoretical Aspects of Diaphragm Radiators
4 Transducers Diaphragms and Loudspeaker Technologies
5 Low‐Frequency System Analysis: Room Environments
and 2π Half Space Radiation
6 Horn and Other Loading Variations
7 Moving‐Coil Direct‐Radiator Drivers
8 Systems and Crossovers
9 The Enclosure
10 Loudspeaker Assessment
Index

Citation preview

High Performance Loudspeakers

High Performance Loudspeakers Optimising High Fidelity Loudspeaker Systems

Martin Colloms

Colloms Electroacoustics UK

Paul Darlington SoundChip UK

Seventh Edition

This edition first published 2018 © 2018 John Wiley & Sons Ltd Edition History John Wiley & Sons (5e,1997) John Wiley & Sons (6e, 2013) All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions. The right of Martin Colloms to be identified as the author of this work has been asserted in accordance with law. Registered Offices John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK Editorial Office The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com. Wiley also publishes its books in a variety of electronic formats and by print‐on‐demand. Some content that appears in standard print versions of this book may not be available in other formats. Limit of Liability/Disclaimer of Warranty While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. Library of Congress Cataloging‐in‐Publication Data Names: Colloms, Martin, author. | Darlington, Paul, author. Title: High performance loudspeakers / by Martin Colloms and Paul Darlington. Description: 7th edition. | Hoboken, NJ : John Wiley & Sons, 2018. | Includes bibliographical references and index. | Identifiers: LCCN 2018005470 (print) | LCCN 2018012066 (ebook) | ISBN 9781118706268 (pdf ) | ISBN 9781118706251 (epub) | ISBN 9781118413531 (pbk.) Subjects: LCSH: Loudspeakers. Classification: LCC TK5983 (ebook) | LCC TK5983 .C64 2018 (print) | DDC 621.382/84–dc23 LC record available at https://lccn.loc.gov/2018005470 Cover Design: C. Wallace Cover Images: Courtesy of Bang & Olufsen Mediacenter Set in 10/12pt Warnock by SPi Global, Pondicherry, India 10 9 8 7 6 5 4 3 2 1

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Contents Preface to the First Edition  xix Preface to the Fifth Edition  xxi Preface to the Sixth Edition  xxiii Preface to the Seventh Edition  xxv Acknowledgements  xxvii 1 General Review  1 1.1 ­Early Loudspeakers  1 1.1.1 The Elements of the Ubiquitous Cone Loudspeaker  2 1.1.2 Loudspeaker Types and Technologies  4 1.2 ­Audible Frequency Range and Wavelength  4 1.2.1 Horn Loading and Efficiency  5 1.2.2 Moving‐Coil Longevity and Advantages  5 1.2.3 Loudspeaker Design Is Not an Exact Science  6 1.2.4 Passing Technologies and Fashions  7 1.2.5 An Emerging Consensus for Performance  7 1.2.6 Those Electroacoustic Fundamentals Were in Place  9 1.3 ­The BBC Contribution  12 1.3.1 A Step Change for Reduced Colouration and Improved Response Accuracy  12 1.4 ­Emerging Standards  13 1.4.1 Diaphragms: Materials and Consistency  16 1.5 ­Influence of Improved Low‐Frequency Analysis  17 1.5.1 Crossover Developments and Active Designs  19 1.5.2 Home Theatre Systems: Dolby Atmos  21 1.6 ­Changes in UK Lifestyle are Affecting Domestic Audio Systems  22 1.7 ­High‐End Stereo Audio  23 1.8 ­Sound Docks  23 1.8.1 ­Sound Quality Issues for Docks  24 1.8.2 Sound Bars for Flat‐Screen Displays  26 1.9 ­Headphones  27 1.10 ­Advances in Pro Audio  27 2 Developments in Loudspeaker System Design  31 2.1 ­Developments in Loudspeaker System Design  31 2.1.1 Assessing Sound Quality: Frequency Balance  32

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2.1.2 Driver and Crossover Advances  33 2.1.3 Transparency and Noise Masking  34 2.2 ­Limits to Performance  37 2.3 ­The Stereo Illusion: ‘3D Sound’  38 2.4 ­Sensitivity and Impedance  40 2.4.1 Stealing Sensitivity From Impedance  40 2.5 ­Enclosures  41 2.5.1 Materials 42 2.5.2 Enclosure Support  43 2.5.3 Enclosure Shape  43 2.6 ­Drive Units  44 2.6.1 Diaphragm Materials  44 2.6.2 High‐Frequency Diaphragms  46 2.7 ­The Room  47 2.7.1 Loudspeaker Positioning  47 2.7.2 A Period of Consolidation  48 Theoretical Aspects of Diaphragm Radiators  51 3.1 ­Radiation From Simple Sources  51 3.1.1 The deciBel  53 3.1.2 The Monopole  53 3.1.3 The Doublet or Dipole  54 3.1.4 Directivity and Directivity Index  55 3.1.5 Near and Far Field  55 3.1.6 Modelling Complex Sources  56 3.2 ­Electromechanics of a Hypothetical Moving‐Coil Loudspeaker  57 3.2.1 Voltage Drive  61 3.2.2 Air Load on a Loudspeaker  62 3.2.3 Electrical Input Impedance  66 3.3 ­Radiated Pressure  67 3.3.1 Radiated Power  70 3.3.2 Sensitivity and Efficiency  71 3.3.3 Acoustic Backload  72 3.4 ­Relating the TwoPort Model to Low‐Frequency Analogous Circuits  74 3.5 ­Higher Modes of the Loudspeaker Diaphragm  77 3.5.1 Radiation From Large Diaphragms  79 3.5.2 The Distributed Mode Loudspeaker  82

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4

Transducers Diaphragms and Loudspeaker Technologies  87

4.1 ­Dome Radiators  87 4.1.1 Phase Loss: On Axis  88 4.1.2 Breakup Modes  89 4.1.3 Rocking 91 4.1.4 Dome Radiator, First Breakup  92 4.2 ­Velocity of Sound In a Diaphragm  93 4.3 ­Compensation of Dome Characteristics  95 4.4 ­Cone Behaviour  95

Contents

4.5 ­Cone Parameters  96 4.5.1 Klippel Analysis and Test  97 4.5.2 Comsol Multiphysics Software  97 4.5.3 Transmission‐Line Cone Analogy  98 4.5.4 Termination  99 4.5.5 The Perfectly Homogeneous Cone  99 4.5.6 Normal or Straight‐Sided Cones  99 4.5.7 Sub‐Harmonics and Rocking  103 4.5.8 Cone Material Damping  104 4.6 ­Cone Shape  104 4.6.1 Straight‐Sided or True Cones  104 4.6.2 A Natural Cone Angle  105 4.6.3 Cone Thickness and Resonance Control  105 4.6.4 Curved Profiles  107 4.6.5 Early Analysis of a Straight‐Sided Cone  108 4.6.6 Radiation From Practical Diaphragms  110 4.7 ­Motor Systems  112 4.7.1 Magnetic Circuits and Motor Coils  112 4.8 ­Moving‐Coil Motor Linearity  115 4.8.1 Instability  116 4.8.2 Distortion Compensation  117 4.8.3 Combined Suspension and Motor Design  118 4.8.4 Coil Inductance and Its Suppression  118 4.8.5 Dual‐Coil LF Unit for Response Extension  119 4.9 ­Effect of Magnetic Field Strength Variation on Loudspeaker Pressure Response  119 4.10 ­Magnet Systems  120 4.10.1 Magnet Design  121 4.10.2 Neodymium Alloy Magnets  124 4.10.3 FEA Applied to Magnets  125 4.10.4 Magnetic Shielding  126 4.11 ­Film Transducers, Magnetic and Electrostatic  126 4.11.1 Sheathed Electrode Design  130 4.11.2 Alternative Forms of Film Transducer  133 4.11.3 Larger Film Diaphragm Transducers  134 4.11.4 The True Ribbon  138 4.11.5 A Stabilized Ribbon for MF‐HF Duty  138 4.11.6 Ribbon Developments  141 4.11.7 Air‐Motion Transformer  141 4.11.8 Piezoelectric and High‐Polymer Transducers  142 4.12 ­Bending Radiators, DML, Distributed Mode and BMR: The Balanced Mode Radiator  144 5

Low‐Frequency System Analysis: Room Environments and 2π Half Space Radiation  157

5.1 ­General Considerations  157 5.1.1 Loudspeaker Interaction with Rooms  158

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5.1.2 5.1.3 5.1.4 5.1.5 5.1.6 5.1.7 5.1.8 5.1.9

Dipole, Monopole Low‐Frequency Sources  160 Dipoles Versus Monopoles in the Listening Room  160 Room Interaction with Radiation Behaviour  161 Room Compensation  162 Room Equalization, Dereverberation  163 Low‐Frequency Room Compensation Using Traps  164 Effectiveness of Low‐Frequency Room Compensators  164 Loudspeaker–Room Equalization Using Measurement of Acoustical Impedance  164 5.2 ­Room Interaction, The Broader Picture  165 5.3 ­Optimum System Design for Low Subjective Colouration  167 5.3.1 LF Response Limitation Due to Room Size  167 5.3.2 Integrated Room‐Speaker Design  168 5.3.3 Some Room Acoustic Subtleties  169 5.3.4 Exploitation of Boundary Effects  171 5.3.5 Loudspeaker Placement  173 5.3.6 Wilson Placement Method  174 5.3.7 Wall‐Mounted Speakers with Free‐Space Listeners  176 5.3.8 ‘Free‐Space’ Loudspeaker Placement  177 5.3.9 Comparisons of Anechoic and In‐Room Responses  178 5.4 ­LF System Analysis  181 5.4.1 Fundamental Performance Limitation  182 5.4.2 Magnitude of kn, the Efficiency Constant  183 5.4.3 High‐Pass Filter Analogy  183 5.4.4 Infrasonic Overload  184 5.4.5 Subjective Considerations, Transient Response and Timing  184 5.4.6 Low‐Frequency Group Delay  186 5.4.7 High Acoustic Outputs, LF  189 5.4.8 Air Non‐Linearity  189 5.4.9 Compact Enclosures  190 5.4.10 Virtual Loudspeaker Enclosure Volume  190 5.4.11 Low‐Frequency Sensitivity of the Ear  191 5.4.12 Assessment of Low‐Frequency Responses  192 5.4.13 Programme Spectral Content  193 5.4.14 Damping 193 5.4.15 The Lumped Parameter Approximation  194 5.4.16 Low‐Frequency Parameters: Accuracy  194 5.5 ­Viewpoint—What Is an Optimal Low‐Frequency Q Factor for a System?  195 5.5.1 Adaptable Low‐Frequency Design  195 5.5.2 Large‐Signal Distortion and Loudspeaker Alignments  197 5.6 ­Closed‐Box System  198 5.6.1 Analysis  198 5.6.2 Response Shape  200 5.6.3 Enclosure Volume and Efficiency  202 5.6.4 Box Filling or Damping  203 5.6.5 Design Example  203 5.6.6 Constant Pressure Chamber (‘Isobarik’)  205

Contents

5.6.7 Resistive Chamber Coupling  206 5.7 ­Reflex or Vented Enclosures  207 5.7.1 Transient Response  208 5.7.2 Exploring Enclosure Tuning Variations  208 5.7.3 Reflex Enclosure Analysis  211 5.7.4 Design Example Vented Box  212 5.7.5 Vented‐Box Distortion Audibility  214 5.7.6 Enclosure Ducts  216 5.7.7 Complications Arising From Twin Bass Units  217 5.7.8 Multiple Ports and Resonance Distribution  218 5.7.9 Port Length  218 5.7.10 Port Shape  218 5.7.11 Port Location  219 5.7.12 Box Filling  219 5.7.13 Port Modes and Port Output Measurement  220 5.7.14 Port Modes Used Constructively  221 5.7.15 Acoustic Resistance Vents or Ports  221 5.7.16 The ABR: Auxiliary Bass Radiator  221 5.7.17 Some Examples of Tailored LF Alignments, Comparing Closed, IB and Vented Alternatives  222 5.7.18 A Note on the Interaction of Crossover Networks with Low‐Frequency Alignments  224 5.8 ­Band‐Pass Designs and LF Equalization  224 5.8.1 Enclosure Loading  225 5.8.2 Sound‐Quality Aspects for Band‐Pass Enclosure Stability  226 5.8.3 Odd‐Order Alignments, IB and Reflex  230 5.8.4 LF Alignments with Electronic Equalization  230 5.8.5 Designing with ‘Excessive’ Bl  231 5.8.6 An Active Biquadratic Filter for Equalizing Over‐Damped Loudspeakers  232 5.8.7 Motional Feedback  233 5.8.8 Acoustic Adjustability of Loudspeakers  234 5.8.9 Comparison of Second‐, Fourth‐, and Sixth‐Order Systems Including Equalization  236 5.9 ­Longevity, Reliability, Tolerances, Climate  237 5.9.1 The Running‐In Phenomenon  239 5.9.2 Driver Build Information, Gaps and Tolerances  240 5.9.3 Tolerancing  241 5.9.4 Effects of Parameter Variation  242 5.10 ­Transmission‐Line Enclosures  243 5.10.1 Quarter‐Wave ‘Line’ Loading  245 5.10.2 Pipes and Lines: An Overview  246 5.11 ­Sub‐Woofers and Extended Low‐Frequency Design  249 5.11.1 Absolute Phase  251 5.11.2 Pros and Cons of Sub‐Woofers: The Extension of the Low‐Frequency Range  251 5.11.2.1 Pros 251 5.11.2.2 Cons 252

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5.11.3 5.11.4 5.11.5 5.11.6

Design Details: Sub‐Woofers  253 Passive Sub‐Woofer Design Aspects  253 Active Sub‐Woofer Design Aspects  254 Sub‐Woofer Amplifiers  255

Horn and Other Loading Variations  261 6.1 ­Introduction  261 6.1.1 Improved Acoustic Matching  261 6.1.2 Horns and Waveguides  262 6.1.3 Waveguides  263 6.1.4 Efficiency  264 6.1.5 Bandwidth, Frequency Range  264 6.1.6 Position  265 6.1.7 Propagation Delay  265 6.1.8 Folded Horns  265 6.1.9 Horn Shape  265 6.1.10 Directivity 267 6.1.11 Upper‐Range Problems  267 6.1.12 Commercial Horn Systems  267 6.2 ­Line Source Loudspeakers  269 6.2.1 Near‐Field and Far‐Field Comparisons of Line Radiation  270 6.2.2 A: Sealed Back Line  271 6.2.3 B: Open Line (Dipole)  272 6.3 ­The Moving‐Coil Spaced Dipole  275 6.4 ­Bi‐Polar Speakers  276

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7 Moving‐Coil Direct‐Radiator Drivers  279 7.1 ­Moving‐Coil Motor System  279 7.1.1 Diaphragm or Sound Radiating Element  280 7.1.2 Surround or Outer Support  281 7.1.3 Suspension or Inner Support (Spider)  281 7.1.4 Motor Coil or Voice Coil, VC  281 7.1.5 Magnet  281 7.1.6 Chassis (or Supporting Basket or Frame)  281 7.1.7 Dust Cap or Centre Dome  281 7.1.8 Phase Plate  282 7.1.9 Non‐Uniform Windings  282 7.1.10 Low Electrical Conductivity Poles  283 7.2 ­Low Frequencies, Bass Units  283 7.2.1 SWL, Sound Power (Acoustic Watts)  284 7.2.2 Diaphragm Materials (LF)  284 7.2.3 Material Properties  289 7.2.4 Diaphragm Shape  291 7.2.5 Surrounds  292 7.2.6 Subjective Effect of Bass Driver Suspension Hysteresis: Pace and Rhythm  293

Contents

7.2.7 Suspensions (LF)  295 7.2.8 Double Suspensions (LF)  296 7.2.9 Motor Coil and Magnet Assembly (LF): Power and Bandwidth  296 7.2.10 Designing With Very High Bl Drivers  298 7.2.11 Power Dissipation (LF)  298 7.2.12 Compression 299 7.2.13 Ferrofluids 301 7.2.14 Winding Techniques (LF)  302 7.2.15 Linearity and Magnets (LF)  303 7.2.16 Demagnetization (LF)  304 7.2.17 The Dust or Centre Cap (LF)  305 7.2.18 Mass Control Ring (LF)  305 7.2.19 Chassis (LF)  305 7.3 ­LF/MF Units  306 7.3.1 Diaphragms (LF/MF)  306 7.3.2 Metal Cones  307 7.3.3 Suspension and Surrounds (LF/MF)  308 7.3.4 Motor Coil (LF/MF)  308 7.4 ­MF, Mid‐Frequency Units  309 7.4.1 Diaphragm (MF)  309 7.4.2 Phase Plug  310 7.4.3 Domes (MF)  310 7.4.4 Cones (MF)  313 7.4.5 Suspensions (MF)  315 7.4.6 Surround (MF)  316 7.4.7 Motor Systems (MF)  316 7.5 ­High‐Frequency Units  317 7.5.1 Dome Diaphragms (HF)  318 7.5.2 Drive Units: Beryllium and Diamond (HF)  322 7.5.3 Motor Systems (HF)  324 7.5.4 Ultrasonic Driver, Dual Coil  325 7.6 ­Full‐Range Units  326 7.6.1 Full‐Range Drive Unit  326 7.6.2 A Full‐Range Moving‐Coil Tensioned Film Panel Transducer  328 7.6.3 ICT—The Inductively Coupled Transducer  329 7.6.4 Dual Concentric Drivers  331 7.7 ­Dynamics and Engineering  333 7.7.1 Modulation of Motor‐Coil Inductance with Position in the Magnetic Gap  334 7.7.2 Modulation Effects Due to Common Baffle  334 7.7.3 Effect of Flux Density on Modulation and Dynamics  335 7.7.4 Effect of Bass Alignment on Dynamics  335 7.7.5 Doppler Modulation  335 7.7.6 Low‐Frequency Alignment Variation with Dynamics  336 7.7.7 Temperature Effects  336 7.7.8 Mechanical Vibration  337

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8 Systems and Crossovers  339 8.1 ­Passive Loudspeaker System Design  342 8.1.1 8Ω Versus 4Ω Rated Speaker Impedance  343 8.1.2 Factors Affecting the Choice of Drive Units  345 8.1.3 Low‐Frequency Drivers  346 8.1.4 Mid‐Frequency Drivers  346 8.1.5 High‐Frequency Drivers  346 8.1.6 Sensitivity Matching  347 8.1.7 Auto‐Transformer Level Matching for Drivers  347 8.2 ­‘Two‐and‐a‐Half‐Way’ System Design  348 8.3 ­The Crossover Network and Target Function  349 8.3.1 First‐Order Crossovers  350 8.3.2 Second‐Order Networks  350 8.3.3 Higher‐Order Networks  352 8.3.4 Energy Contour Plots  355 8.3.5 High‐Frequency Units Operating to Lower Frequencies  355 8.3.6 Mis‐Termination  355 8.3.7 Non‐Time Coincident Drivers and the Effect of Distance  360 8.3.8 Compensation for Driver Impedance, Motional and Electrical  362 8.3.9 Low‐Order Crossover Considerations  364 8.3.10 External Crossover Location  367 8.3.11 D’Appolito Configuration  367 8.3.12 Open or Top Location for an HF Unit  369 8.3.13 High‐Order Crossover Considerations  369 8.3.14 Notched Crossover Networks  371 8.3.15 Amplitude Response Equalization  371 8.3.16 Computer‐Aided Crossover Design  374 8.3.17 Acoustic Centre and Delay  376 8.3.18 Passive Delay  378 8.3.19 Series Connected Crossovers  380 8.4 ­Crossover Component Considerations  380 8.4.1 Inductors  381 8.4.2 Cored Inductors  381 8.4.3 Capacitors  382 8.4.4 Crossover Circuit Geometry and Printed Circuit Board Design  383 8.4.5 Subtle Aspects of Crossover Component Behavior  384 8.4.6 Capacitor Sound Quality  386 8.4.7 Resistors  387 8.4.8 Inductors  387 8.4.9 Inductor Cores: Distortion  388 8.4.10 Bypass Capacitors  390 8.4.11 Wiring 392 8.5 ­General Design Considerations, Voicing and Balancing  392 8.5.1 Test Sound Levels: Checking Quality Over a Range of Sound Levels  393 8.5.2 Test Location  394 8.5.3 Loudspeaker System Design: Some Practical Aspects for Crossover Tuning and Voicing  394

Contents

8.5.4 8.5.5

The Difficulties Associated with CAD, Computer‐Aided Design  399 Practical Example of a Two‐Way Crossover at 2.2kHz; Subjective Effect of a Given High‐Pass Crossover Alignment  400 8.5.6 Multiple Driver Combinations: Series and Parallel, Voltage Sensitivity and Impedance  400 8.5.7 A Practical Crossover Example  401 8.5.8 Some Commercial System Examples  404 8.6 ­The Amplifier–Loudspeaker Interface  407 8.6.1 Speaker Performance: Influence of Valve/Tube Amplification  409 8.6.2 Bi‐Wiring and Multi‐Wiring  409 8.6.3 Polyamplification  410 8.6.4 Speaker Cable Practice  411 8.6.5 Cable Design and Sound  411 8.6.6 Effect of Damping Factor on Speaker Low‐Frequency Alignment  412 8.6.7 Cable Design Factors  413 8.6.8 Electromagnetic Screening Loudspeaker and Cable, EMC Effects  414 8.6.9 The Sound of Metal Conductors  415 8.7 ­Active Loudspeakers  416 8.7.1 Electronic Filter Crossovers  418 8.7.2 Second‐Order Low‐Pass Filters  419 8.7.3 High‐Pass Filters  419 8.7.4 First‐Order Low‐Pass Filters  420 8.7.5 Higher Orders  420 8.7.6 Driving Impedance and Noise  420 8.7.7 Equalization for Driver Sensitivity and/or Network Losses  422 8.7.8 Correction for Rising Driver Axial Response  422 8.7.9 Correction for Premature Driver Roll‐Off  423 8.7.10 Other Irregularities  424 8.7.11 Crossover Calculations  427 8.7.12 Leap Crossover Synthesis  429 8.7.13 AST 429 8.7.14 Higher‐Order Filters by Direct Synthesis  432 8.7.15 Gain Limitation in Active‐Filter Amplifiers  433 8.7.16 A Low‐Cost Example  434 8.7.17 Loudspeaker System Alignment and Service  435 8.7.18 Maintenance and Repair  436 8.8 ­Current Drive  436 8.8.1 Hybrid System Design: Mixing Cones with Panels  439 8.9 ­Digital Loudspeakers  440 8.9.1 Hybrid Digital Loudspeaker Driver  440 8.9.2 Smart Digital Loudspeaker  440 8.9.3 Digital Loudspeaker Arrays  442 8.9.4 Active Transducers (AT)  442 8.9.5 Crossover Systems in Digital Loudspeakers  442 8.9.6 DSP Potential  444 8.9.7 Control of the Room–Speaker Interface  444 8.9.8 Control of Loudspeaker Characteristics  444

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8.9.9 Phase and Frequency Response  445 8.9.10 The Impulse Response Objective  445 8.9.11 DSP Feedforward Correction for Manufactured Loudspeaker Systems  446 8.9.12 Digital Active Loudspeakers  448 8.9.13 Digital Speaker System Design  448 8.9.14 Filter Order for the DSP  449 8.9.15 DAC Resolution: Dynamic Range  449 8.10 ­Digital Active System Details  450 8.10.1 Volume Control  450 8.11 ­DSP Crossover Filter Order  450 8.11.1 Performance 451 8.11.2 DSP Speaker Dynamic Range Considerations  452 8.11.3 An Interesting ‘Digital Loudspeaker’ Example by 1 Ltd of Cambridge, UK; the Sound Projector  453 8.11.4 Wireless Connectivity  454 The Enclosure  457 9.1 ­Enclosure Materials  458 9.1.1 Wood and Wood‐Based Composition Panels  458 9.1.2 Other Constructions  460 9.1.3 Mixed Materials  463 9.2 ­Enclosure Resonances  463 9.3 ­Magnitude of Undamped Panel Output  465 9.3.1 Analysis of Enclosures and Panel Resonance  468 9.3.2 Variation of Young’s Modulus with Frequency  468 9.3.3 Coincidence Frequency  468 9.4 ­Audibility of Resonances  469 9.5 ­Resonance Control, Damping Materials and Bracing  470 9.5.1 Placement of Damping Pads  472 9.5.2 Bracing  472 9.5.3 Curved Walls  475 9.6 ­Internal Enclosure Modes  476 9.6.1 Suppression of Internal Standing‐Wave Modes  478 9.6.2 Optimum Placement of Absorbent  479 9.7 ­Driver‐Cone, Transmission of Internal Resonances  480 9.7.1 Effect of Filling on Frequency Response and Sound Quality  482 9.8 ­Cabinet Construction  483 9.8.1 Cabinet Size  483 9.8.2 Corner Joints  485 9.8.3 Front Grilles  486 9.8.4 The Matrix Enclosure  488 9.8.5 Low‐Mass Enclosures  489 9.8.6 Driver Decoupling  491 9.8.7 Push‐Pull Driver Mounting  492 9.8.8 The Separated Box Enclosure  493 9.9 ­Diffraction and Cabinet Shape  493

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9.9.1 Common Rectangular Enclosures  494 9.9.2 The 6 dB Pressure Response Step  495 9.9.3 Enclosure Diffraction  499 9.10 ­Loudspeaker Design Software  499 9.11 ­Importance of Effective Driver Mounting Methods  501 9.11.1 Modelling Diffraction  504 9.12 ­Drive‐Unit Mounting: Clamped or Decoupled?  505 9.12.1 Sources of Unwanted Vibration and Resonance  505 9.12.1.1 Driver Fixing  505 9.12.1.2 Other Sources of Stray Resonance  506 9.13 ­Open Baffles: Dipoles  506 9.14 ­Loudspeaker Supports and Placement  507 9.14.1 Wall Placement  508 9.14.2 Floor Stands  508 10 Loudspeaker Assessment  513 10.1 ­Loudspeaker Specifications Standards and Distortions  515 10.1.1 Amplitude/Frequency Response  515 10.1.2 Ultrasonic Perception, Beyond 20 kHz  519 10.1.3 Directivity (AKA Dispersion)  521 10.1.4 Audibility of Response Irregularities  522 10.1.5 Non‐Linear Distortion  525 10.2 FM: Frequency‐Modulation Distortion  532 10.2.1 Transient Response Decay Rates and Colouration  534 10.2.2 Phase  536 10.2.3 Absolute Phase  537 10.2.4 Direct Versus Reverberant Sound Balance  539 10.2.5 Impedance (as Seen By an Amplifier at the Loudspeaker Terminals)  540 10.2.6 Dynamic Impedance and Peak Current Demand  541 10.2.7 Power Capacity  542 10.2.8 Compression and Dynamics  544 10.3 ­Measurement and Evaluation: Introduction  545 10.3.1 Objective, Instrument‐Based Measurements  546 10.4 ­Objective Measurements: Amplitude/Frequency Responses (4π, Full Anechoic)  554 10.4.1 Sine Excitation  554 10.4.2 Off‐Axis Responses  557 10.5 ­Random Noise Excitation  558 10.5.1 Impulse Excitation and Decay Resonances  561 10.5.2 TDS Time Delay Spectrometry  564 10.5.3 Gated Measurement  567 10.5.4 MLSSA, an MLS Measuring System  569 10.5.5 Waterfall Presentation and Excess Phase  570 10.5.6 Audio Precision  574 10.5.7 Reciprocity Method for Measurement at Low Frequencies  574 10.5.8 Harmonic and Intermodulation Distortion  575

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Contents

10.5.9 10.5.10 10.5.11 10.5.12 10.5.13 10.5.14 10.5.15 10.5.16 10.5.17 10.5.18

Dynamic or Pulsed Distortion Testing  577 Doppler Distortion  577 Intermodulation Distortion and Multi‐Tone Signals  577 Phase Response  580 Minimum Phase  581 Square Wave and Impulse Response  581 Tone‐Burst Response  581 Sensitivity Voltage and Power, Efficiency and Sound Power Output  582 Power Rating  582 AES Recommended Practice for Professional Audio—Subjective Evaluation of Speakers AES20—1996  583 10.5.19 Laser Measurements  584 10.5.20 Electrical Impedance  584 10.5.21 Computer‐Controlled Testing  588 10.5.22 Driver Parameters  591 10.5.23 Suspension Compliance, CMS (N/m)  592 10.5.24 Moving Mass, MD (kg)  593 10.5.25 DC Resistance (Motor/Voice Coil), Rc (Ohms)  593 10.5.26 Coil Inductance, lc (Henrys)  593 10.5.27 Mechanical Resistance RMS (of Suspension Components) and QM  593 10.5.28 Electrical ‘Q’ Factor, QE (Assuming Zero Generator Impedance)  594 10.5.29 Total ‘Q’ Factor, QT  594 10.5.30 Flux Density, B  594 10.5.31 Cone Area, SD (Square Metres)  594 10.5.32 Force Factor, Bl (N/A)  594 10.5.33 Developments in Driver Evaluation: Errors Arise From T‐S Results at Low Power  595 10.5.34 Distortion AM and FM  595 10.5.35 Jordan on T‐S Parameters  598 10.5.36 Voice Coil Temperature Variations  599 10.5.37 Rub and Buzz  599 10.5.38 Excursion Limits: X Max  600 10.6 ­Subjective Evaluation  600 10.6.1 Perception of Loudness: Loudspeaker Sensitivity  600 10.6.2 Live Versus Recorded Comparisons  601 10.6.3 Stereo Image: Focus, Width, Depth  602 10.6.4 Loudspeaker Standards  603 10.6.5 Stereo Image Depth  604 10.6.6 Ambience and Scale  606 10.6.7 Extended Low‐Frequency Response  607 10.6.8 Salava and Low‐Frequency Reproduction  608 10.6.9 Perception at Low Frequencies and Group Delay  608 10.6.10 Tonal Balance, Timbre and Spatiality  609 10.6.11 Rooms, Timbre, Frequency Response and Directivity  610 10.6.12 Micro‐Voicing Experiments, Psychoacoustic Effects  612 10.6.13 The Listening Room Environment  613 10.6.14 Ideal Listening Rooms  615

Contents

10.6.15 Positioning of Loudspeakers  616 10.6.16 Listening Panel  617 10.6.17 Programme Material  617 10.6.18 Analogue and Digital Programme and Its Effect on Listening Tests  618 10.6.19 Loudness for Subjective Testing  619 10.6.20 Duration 619 10.6.21 Test Procedures  619 10.6.22 A/B Paired Comparisons and Live Sounds  620 10.6.23 Single Presentation Methods  621 10.6.24 Definitions: Spatial Quality  621 10.6.25 Definitions: Sound Quality (Toole)  622 10.6.26 Scaling Considerations  624 10.6.27 The Results and Their Analysis  625 10.6.28 ITU Standards  626 10.6.29 Psychological Factors  627 10.6.30 The High End: ‘High‐Fidelity’ Sound Quality  628 Index  635

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Preface to the First Edition A high‐quality loudspeaker is required to reproduce sound with sufficient fidelity to satisfy a critical audience when fed from an accurate electrical signal. It is immaterial whether the listeners are numbered in thousands or comprise only a few individuals: loudspeaker systems can be designed to cater for both situations without compromising the basic standard of performance. There are, thus, numerous applications for high‐quality loudspeakers. For example, broadcast and recording engineers rely heavily on monitor loudspeakers in order to critically analyse the quality of the programme they are producing. Other applications range in scope from the rock festival to the concert and opera hall, and in size from a theatre auditorium to an ordinary living room. Reinforcement loudspeakers are commonly used for sound amplification in live performances today, and while specialized systems are employed for instruments such as an electric guitar, other wider range sounds such as voice and woodwind require high‐performance speakers with a capability to allow the reproduced level to match that of the accompanying brass or a modern drum kit. Theatres and opera houses often use systems for off‐stage sound effects, and most of today’s star performers would be unable to reach a large audience without the aid of a microphone and sound reinforcement. Special techniques are, however, required to attain the acoustic outputs necessary to satisfy a large stadium audience, and high‐efficiency, stacked, horn‐loaded, directional arrays are commonly employed for this purpose. The author’s aim is to provide an up‐to‐date analysis and review of high‐performance loudspeaker techniques. Although it is not intended to be an exhaustive work, reference has been made in the text to original research material including the most important modern work in the field. Precedence is accorded to the moving coil drive unit, as this is by far the most widely used, although some coverage is also given to other viable if less common devices. In addition to the fundamentals—relevant acoustic theory, transducer design, enclosures, acoustic loading, and so on—space is also accorded to developments in electronic crossover design and active speaker systems, as well as to the latest measurement techniques and such controversial questions as linear phase. By using the references supplied, the book can be used as the basis for further research, and as such, not only high‐fidelity enthusiasts should find it of interest, but also students studying such subjects as electronics, electroacoustics, broadcasting and recording. Even the design engineer and technical author may find it a useful appraisal of current techniques and a convenient source of subject references. Martin Colloms

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­Preface to the Fifth Edition For the fifth edition, my title High Performance Loudspeakers has joined the technical publisher John Wiley. My initial concern about the transfer was replaced by increasing confidence. The Wiley UK team backed my proposals to substantially expand the text as well as bring the format and layout up to date. Finally, through economies of scale it was planned to significantly reduce the cover price, making the work accessible to a far wider readership. Many revisions have made the book as up to date as possible, while continuing with that vital critical viewpoint when covering new developments and technologies. Every existing chapter has seen revision and expansion. Building on the previous editions, the first chapter has been expanded adding an overview of modern design trends and practice. Almost as soon as this edition was released to the typesetters a new loudspeaker development was announced in London under the NXT brand, patents applied for by New Transducers Ltd. Covering non‐pistonic, vibrating acoustic panels, there is significant theory to match the wide variety of applications. Press attendance at the launch broke all records with the consensus view that this was an important development in the evolution of the loudspeaker. Accordingly, a major section has been included on this technology. A new chapter appears covering ‘home theatre systems’, taking account of their special acoustic requirements, Dolby PRO‐LOGIC, THX and the more recent AC‐3, DTS and MPEG digital discrete, multi‐channel systems. The review of computer‐aided design has been extended, covering both hardware and software systems and including the new generation of low‐cost audio instrumentation. Complementing the necessarily academic nature of the theoretical aspects of speaker engineering, there is also a new section which gives much practical advice for real world speaker system design; it has been dubbed ‘hot tips’. In ‘Systems and Crossovers’ new topics include 2 ½–way system design, external crossovers, D’Appolito types, a distortion analysis of inductors, digital active loudspeakers and low‐order system design. There has been a major expansion of the section on sub‐woofers, also with relevance to home theatres where subs are almost mandatory. Subjective aspects of bass response are explored together with newly expanded sets of boundary matched low‐frequency alignments.

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Speaker placement techniques, multiple driver and port combinations plus adjustable low frequency design are also covered. In ‘drivers’, there are extensions to include both the metal cone driver and its resonance control. Design considerations for better dynamic performance are explored, both for overall build and for enclosure construction. On measurement issues there are more data on absolute phase and the effect of phase on energy decay waterfall displays. Aspects of running in, quality control and ageing are all considered, together with the effects of tolerances on system performance. Many new diagrams and illustrations have been included involving an overall 25% expansion for this new edition. The front cover features the Nautilus speaker, designed by Laurence Dickie and has been reproduced with the kind permission of B&W Loudspeakers Ltd. Many thanks to all of those who have continued to provide constructive criticism and support for High Performance Loudspeakers. Martin Colloms

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­Preface to the Sixth Edition With my enthusiasm for all aspects of loudspeaker engineering and design undiminished since the publication of the fifth edition, I have found that this still burgeoning industry has provided a wealth of material, which has made the preparation of this sixth edition well worthwhile. This time, I have been joined by contributing author Dr Paul Darlington, who was inspired to create a radically new approach to explaining and modelling of the fundamentals of sound radiation. This ground‐breaking thinking is presented in a new chapter that supersedes the older material; this was based on Beranek, which is still classic source material but undeniably half a century old. Paul’s approach leads to an elegant equivalent, elegantly leading to the familiar electrical circuit analogues still so useful for low‐frequency system analysis. He has also contributed an excellent glossary. Since the last edition, the PC has played an increasingly important role at the loudspeaker engineer’s workstation—indeed, in some labs, they are one and the same. The variety, maturity and often moderate cost of sophisticated design analysis software forms one‐half of a PC partnership, while effective acoustic measuring systems provide the other. The latter may frequently be enabled by means of a book‐sized signal conditioning interface to a PC database or, in some cases, by simply employing an on‐board soundcard in conjunction with suitable control software. It has never been so easy to acquire such sophisticated design and measurement tools, and a number of them are introduced and discussed. Additional highlights include the commercial introduction of pure diamond tweeters, as well as numerous developments in the field of digital loudspeakers for the extension of home theatre coverage, the latter including multi‐channel music reproduction as well as 5.1 and 7.1 theatre systems. Over 300 new source references in the loudspeaker field have been assessed and, where relevant, their significant content has been accounted for in this new edition. Fortuitous timing allowed the inclusion of a new theoretical development in the field of non‐diffuse, coherent bending wave speakers, dubbed BMR or balanced‐mode radiator. This technology employs a fascinating blend of pistonic and practical bending diaphragm behaviour, leading to full bandwidth, wide directivity devices, rectangular and circular. The listening environment is studied further, in particular, the interactions of different types of speakers, including the low‐frequency cardioid, as well as new findings on ideal room proportions. Likewise, for loudspeaker enclosures, the discussion of diffraction behaviour has been expanded while important developments in the analysis of pipe and line loading

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are included. Developments in directivity control are noted, including LaCarruba’s acoustic lens, while a number of research findings concerning perception and ­psycho‐acoustics have been employed to update the text. There is barely a single page of the previous edition that has not benefited from the incorporation of new material for the sixth edition. Many thanks to all those who have supported and advised us in the making of the past and the present editions. I hope the industry will find the sixth edition every bit as useful and informative as its predecessors. Martin Colloms

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­Preface to the Seventh Edition Audio engineers may view loudspeakers as acoustical machinery and design and build them on that basis but they remain somewhat imperfect reproducers of speech and music. If you know and love music, then the design of fine loudspeakers must also be guided by the quality of the musical experiences they create. The science must serve the art. Some design engineers imagine that the necessary content of electroacoustics, done diligently by the book, will be sufficient to complete the task. While a reference quality ‘monitor’ speaker of this type may be highly competent, both mechanically and acoustically, and certainly be informative of program content fed to it, it still may not fully inspire the listener with the quality of its performance when judged musically. Those elusive connections which need to be made in the mind, to help create a sense of involving sound quality, depend on the subtle balancing of complex imperfections. The potential sound quality of a resulting loudspeaker design must also be served by similarly capable recording and reproducing electronics and, not least, reference quality programme. High performance loudspeakers begin with a good listening system and high-quality music material. The science and electroacoustic engineering should be applied in combination with subjective development, so delivering loudspeaker designs of significant technical accuracy, also capable of robust and satisfying musical performances. This seventh edition is threaded with a review of the technologies and principles within, which is included to help the keen designer create loudspeakers which are musically satisfying. Martin Colloms

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Acknowledgements There are many that I need to thank, for help and encouragement for those stages along the way to this seventh edition. So many early loudspeaker enthusiasts owe Gilbert Briggs, expert and manufacturer, a great debt. They remember his witty, accessible style and enthusiasm for the subject; his many compact books suffused with years of experience from his own company, Wharfedale, which connected so many amateurs with the craft. I also owe much to Laurie Fincham, KEF who embraced a modern approach to system design which previously was largely regarded as a black art. He researched the fundamentals behind the control of impulse behaviour and colouration and has been unstintingly generous with his time and wise counsel. Spencer Hughes taught me by example where his fine ear and painstaking development led to the lowest coloration cone driver I have ever heard, key to the highly successful BC1 loudspeaker. And while we did not always see eye to eye, Raymond Cooke, founder of KEF, proved supportive behind the scenes, coming to the rescue of my first commercial loudspeaker design by second‐sourcing a failing driver supply. He also established the KEFTOPICS series of notes which for me, at an early stage, illuminated the future of well founded electroacoustical engineering. Ted (E J) Jordan propelled me head first into loudspeaker engineering when I was a student at the Regent St Poly (now Westminster University) and I had already built system examples using his then revolutionary, full‐range anodised aluminium drive unit. Ted’s own book Loudspeakers prompted me to write the first edition of High Performance Loudspeakers a decade later. In the early 1970s John Bartlett, founder of the AudioT Hi Fi retail chain, recruited a happy band of science undergraduates, including myself, to work as part time salesmen at weekends. Effectively this constituted a high‐end audio club within the business; we could sample all kinds of exotic products and explore how high‐end audio systems could be best configured. I had also begun to write and review product for Haymarket publications, also thanks to a lead from John. That early foundation in audio, plus a fascination with sound engineering, led me in 1972 to accept an invitation to join and invest in a nascent loudspeaker company as R&D Director. Mike Beeny, ex‐Audio T, took Sales Director and Mo Iqbal took Managing. With an equal capital investment of just £300 each, and after some discussion, we decided to name it Monitor Audio LTD. We rented production space in Teversham, Cambridge, and under Mo’s direction we turned around goods‐in to finished product in record times. Despite my inexperience, this gave me the freedom to design any kind of loudspeaker I liked. At Monitor I received valuable lessons in commercial life, promotion, exports, audio shows, dealers and not least, some modest experience in design, mass production and quality control.

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Acknowledgements

I also thank John Bowers, co‐founder of B&W, for his generosity and kindness in helping Monitor Audio through difficult times engulfing the UK economy, this during the government enforced 3‐day week. John authorised the supply of the vital OEM mid range driver used for the powerful three‐way MA3 and he shares credit for his improvement of the sound quality and industrial design of UK loudspeaker systems. Peter Walker, despite being one of my fiercest critics, for my audacity in daring to describe amplifier sound quality differences, is lauded for his monumental contributions to audio, especially for the full range electrostatic loudspeaker. 50 years on, it remains a true reference example for extremely low coloration and time coherence. On many occasions I thought I had hit the mark for timbre and colouration, only to be brought down to earth upon revisiting his electrostatic. Those golden years for loudspeaker manufacturers gave rise to decades worth of AES papers covering every aspect of loudspeaker theory, voicing and measurement from Benson and Thiele onwards, not to omit Dick Small. Many of these contributions are referenced in this book. In particular, Floyd Toole provided valued teaching on the language of coloration on listening, and the interaction of loudspeakers with real rooms. Thanks are due to Siegfried Linkwitz for his fine work on those beloved Hewlett Packard spectrum analysers and his free thinking and fresh approach to sound field perception, loudspeaker measurement and system design. Dr John Dibb is mentioned for his detailed research on diaphragm behaviour at B&W and his commitment to my crazy Silver Signature project, which explored the behaviour of metals on conductor sound quality. I am grateful to the tireless John Borwick for his invitation to contribute a chapter to his Loudspeaker and Headphone Handbook. Called the ‘Amplifier Loudspeaker Interface’, it included some controversial aspects of audio cable performance. Also thanks to audio enthusiast Peter Maguire for his patient guidance, helping me understand much of the mysteries of patents, and facilitating numerous loudspeaker related patent applications. Henry Azima and Dr Neil Harris, co‐patentees, supported the distributed mode ‘DM’ panel‐form project, and greatly helped bring it to fruition. Subsequently, Dr Graham Bank provided explanations for some particularly complex ideas which resulted in his co‐invention, with Dr Harris, of the full‐range, balanced vibration mode, radiating diaphragm (BMR). Dudley Harwood of the BBC led his research team into new territory for dramatically lowered colouration and greater consistency for loudspeaker systems. He gave a seminal, yet almost impromptu lecture on loudspeakers at the London AES 50th convention 1975 which I found greatly influential. Also, Wolfgang Klippel whose almost tireless research into drivers and their evaluation led to important findings on how drivers and loudspeaker systems behave. And there are still more to mention and thank. Roy George, who by example demonstrated the importance of broad band vibration control to help define leading edge timing for audio systems, including loudspeakers. Stan Kelly, a great teacher and innovative engineer. Paul Klipsch, particularly for exemplifying the relationship between efficiency, distortion and musical dynamics. Franco Serblin, founder of Sonus Faber, who demonstrated how musical sensibility, subtle driver and system integration, could be applied to advance the loudspeaker system design art.

Acknowledgements

Dick Shahinian for persevering with the idea of acoustically illuminating the room space uniformly with frequency and letting the ear/brain sort out the relationship between direct and reflected sound. James, Jimmy Moir of the IEE, that frisky self, who kindly sponsored me for my application for Chartered Engineer when my only significant qualification, aside for some varied industrial training, was the recently published first edition of this book. John Vanderkooy and Stan Lipshitz, for whom acoustical research was a team hobby, and who brought many insights to the subject. More recently, discussions with Yair Tamman have been most helpful and encouraging, in furthering the art of transparency and still lower loudspeaker distortion and coloration, while at the same time advancing enhancing the exposition of natural musical timing. David Wilson’s fearless ambition and imagination must be noted, showing just how high you can reach with largely commercial drive units employed in moving coil system design. (Note: many recent Wilson systems now use proprietary drivers.) The writing team of Newell and Holland (‘Loudspeakers’) have been influential for their work on group delay and its effect on reproduced musical timing, of particular interest as so few sound reproducers seem to possess a sufficiency of this quality. To John Atkinson (Stereophile Editor) who almost single handedly maintains the tradition for comprehensive measurement of loudspeaker system examples for published review, holding manufacturers to account. And Paul Messenger, friend first and editor of my many published reviews. For decades audio electronics designer, engineer and friend Chris Bryant has encouraged and supported my endeavours and is much valued as my fiercest critic, helping to keep me on the road to best practice for pace, rhythm, dynamics and timing, both for designs and for the performance of complete audio reproducing systems. And not least, those editors and reviewers consulted in confidence by John Wiley as to whether a seventh edition would be worthwhile, were critical, certainly, but also supportive and encouraging. And finally, my co‐author Paul Darlington, for writing Chapter 3, covering the theory of acoustics and transducers.

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1 General Review Speech and music is noise with meaning. The recording and reproduction of sound is imperfect, and the imperfections in these processes reduce meaning and add noise. The art of the loudspeaker designer is the employment of science to help increase meaning for reproduced sound. An understanding and familiarity with music and live sound is fundamental for a reasoned application of acoustical engineering to the still‐imperfect process of loudspeaker design. Great advances have been made with materials technology, refined acoustical modeling, electrical theory and design software, all these helping to manipulate, control and balance all the factors involved in the engineering and construction, but there remains a substantial human component, namely the subjective judgment of reproduced sound quality, which is a skill the loudspeaker designer must acquire. Some design engineers may view speakers as acoustical machinery, and thus design and build them as such. Conversely, loudspeakers must be considered as imperfect reproducers of speech and music. If you know and love music, then the machinery design part of loudspeakers should be guided by a continual assessment of the quality of the musical experiences that they create. Here science must serve art. Reference ‘monitor’ speakers may be designed which are highly competent mechanically and acoustically, are usefully informative, but which may not fully inspire the listener with the quality of their musical performances. Highly qualified and trained engineers may well be responsible for numerous notionally accurate loudspeakers while some engineers are not particularly musical. Often they imagine that application of pure science, ‘done by the book’, will be sufficient to complete the work.

1.1 ­Early Loudspeakers It is some 90 years since the ubiquitous moving‐coil loudspeaker was first developed as we know it, the mass‐controlled, paper cone direct radiator: an electrodynamic transducer which converts electrical current into sound pressure at a useful loudness. In contrast to most other sound transducers it possesses an intrinsically uniform ­frequency response. It is clearly highly reliable in use, and comes with the proven potential for economic manufacture. Before this development there were numerous ‘earphone’ type transducers, moving iron and the like of various kinds for music reproduction, some ‘amplified’ by improved coupling to the air with various early horn configurations. Certainly, somewhat earlier, High Performance Loudspeakers: Optimising High Fidelity Loudspeaker Systems, Seventh Edition. Martin Colloms and Paul Darlington. © 2018 John Wiley & Sons Ltd. Published 2018 by John Wiley & Sons Ltd.

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Figure 1.1  A horn driver from the Pridham Patent, issued 1923, showing a moving coil and an edge clamped planar diaphragm.

primitive forms of moving coil and diaphragm sound signal reproducers had been made. Back in 1874, a U.S. patent for Siemens by Ernst Werner, was one of these, though at that time no electrical audio signals were available to drive it and so it was never heard to reproduce sound, instead emitting pulsed signal noises. And certainly, Peter L Jensen working with Pridham, (Figure 1.1) had developed a significantly powerful horn loaded loudspeaker by 1914, where the transducer employed a 75 mm diameter diaphragm of nickel silver alloy and employed electromagnetic field excitation acting on the moving coil. It was used successfully for large‐scale public addresses for many years. However, the familiar mass‐controlled direct radiator moving‐coil cone loudspeaker, whose principle is so effective that its key elements have remained essentially unchanged to this day, came with ‘the New Hornless Loudspeaker’ of 1925 by Rice and Kellogg of GE (USA). This set the stage for the, low‐resonant frequency, direct radiating type of drive unit we know so well, a driver where a good part of the primary frequency response is intrinsically uniform with frequency, and which also may be acoustically loaded at lower frequencies to usefully extend the working range, by controlling the potential for front (positive) to back (negative) radiation cancellation from this intrinsically dipolar transducer. 1.1.1  The Elements of the Ubiquitous Cone Loudspeaker To build such a transducer, take an affordable magnet and incorporate a simple arrangement of magnetically permeable ‘soft’ iron to help concentrate much of the available magnetic flux into a narrow radial gap using a cylindrical, central magnetic pole. A small light coil, a ‘solenoid’, is wound on a low mass former. This can be a tube of thin card. The assembly is suspended freely in the magnetic gap using a radially corrugated flexible disc or similar, allowing axial motion of a quarter centimeter or so.

General Review

In accordance with Maxwell’s electromagnetic equations, an axial force is generated on the coil when current flows through it. This force is the product of B, the magnetic field strength, l the length of the wire immersed in that flux field and I, the current flowing through the coil. This force coupled relationship is fundamentally linear and consequently there is very little inherent distortion. It is intrinsic for a moving‐coil motor that there is effectively no lower resolution limit for small signals. An infinitely small electrical input will produce an equivalent and essentially infinitely small sound output. Another excellent feature of the moving‐coil transducer, generally taken for granted, is that despite its nature as a moving mechanical device, it is essentially noiseless. It does not grate, scrape or whirr. Apply a sub‐audible 5 Hz sine‐wave current and you can see the coil move, but silently. The moving coil used on its own generates almost zero sound output. Radiated sound level is proportional to the area of air load driven or coupled by the transducer element, and for the coil alone, it comprises a thin ring of negligible radiating area. It is essential to couple this moving element to a larger air load and thus a rigid, light diaphragm, generally of much larger area, is securely bonded to the coil former. Typically, such larger diaphragms have their own flexible outer surround, constituting a second suspension, fixed to an, skeletal, non‐reflective support frame or chassis, the assembly providing the vitally important axial centering of the moving system, which can now be positioned in a close tolerance magnet gap. Such fine tolerance helps increase the magnetic flux density in the gap so maximizing efficiency and thus loudness. We know that flat paper sheet is desirably lightweight, but it is very weak in bending. However, paper is remarkably stiff in tension. To make use of the latter property simply cut out some suitable paper in a useful shape, curl it up into a cone and glue the remaining seam. This simple conical structure exhibits an extraordinary axial stiffness for its mass, a marvellous means of coupling a much larger area of air load to that otherwise near silent moving‐coil motor, so aiding conversion efficiency of force into sound. The coil former is firmly glued to the cone apex. Here acting as an acoustical transformer, the cone or diaphragm matches the much lower acoustical impedance of the air load to the higher driving force impedance of the coil assembly, thus greatly improving the efficiency of energy transfer from electrical power, now providing readily audible sound pressure. This signal path includes the translation of electric audio currents to mechanical forces; these are then coupled to a cone to usefully radiate sound pressure to be heard at a distance. The result is the familiar loudspeaker. This elegant principle has proved highly useful and effective for almost a century, even if in absolute terms the conversion efficiency from input electrical watts to acoustic watts is quite low, typically less than 1%. Fortunately, amplifier watts are easy to come by and our hearing is exquisitely sensitive; in practice one acoustic watt goes a very long way. Include the virtue of very moderate cost, and noting that general purpose loudspeaker drivers may be mass produced like light bulbs, and it is these fundamental strengths that make the moving‐coil principle so very effective, and so very popular. Over 99% of all the loudspeakers ever made have been moving‐coil direct radiators. And the operating principle may be used over a very wide range of applications, from low‐power speech reproducers of just 2.5 octaves bandwidth and a modest 75 dB maximum sound pressure output, built on a frame just 20 mm, to low‐frequency capable monsters of

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600 mm, capable of generating 20 Hz sound waves at body shattering 110 dB pressure levels, still more if acoustically loaded by a horn and/or aided by a local boundary. Humans have sensitive hearing and even a low‐efficiency drive unit, at typically 0.5% for the conversion of electrical to acoustic power, may be more than loud enough for many purposes. Indeed, the vast majority of domestic direct radiating speakers, including hi fi designs, are of similarly low efficiency. An electrical watt converted to sound level by this means will result in an average of 86 dB spl at 1 m, or about 80 dB in‐room for a stereo pair, and in practice this is satisfactorily loud. For comparison, normal speech at 2 meters is about 70 to 73 dBA while shouting might raise 80 dB. Orchestral crescendos might raise 100 dB in room. 1.1.2  Loudspeaker Types and Technologies Most moving‐coil cone loudspeaker drivers manufactured are ‘full range’, nominally covering 150 Hz to 7 kHz, −6 dB, and when provided with a housing or enclosure of some kind are quite satisfactory for general purpose reproduction of speech and music. Where higher standards are required, for example, greater loudness, wider frequency response say 30 Hz to 15 kHz, and with a more consistent off axis directivity, the frequency range is usually subdivided, to be shared amongst different sizes of drivers each suited to specific narrower ranges, such an arrangement forming a speaker system. Specialized smaller drivers intended for higher frequencies, smaller so that the sound radiation angle remains suitably wide, may typically employ a light dome, which may be concave or convex, formed from a variety of materials such as paper, moulded plastic foil, resin doped fabric, metal foil such as aluminium or beryllium, or even vacuum‐ deposited pure diamond. These elements fitted as a cap to a voice coil former. In sizes down to 19 mm effective radiating diameter, and with the use of high technology stiff low mass materials, the frequency range may in some cases extend to well beyond 40 kHz. Such performance helps to ensure good results up to the nominal industry agreed steady state perception limit of 15 to 20 kHz. More recent work on perception suggests discrimination of leading edge transients with a bandwidth extending to 80 kHz, and this constitutes a subtle sound quality issue. The perception of fast rise times[1–3] persists even for older listeners and is not related directly to the well‐known hearing sensitivity limits applying for steady‐state tones. Designing for a greater than nominal 20 kHz bandwidth is worthwhile where the budget permits, and in any case often results in superior subjective performance in the accepted steady state perception range.

1.2 ­Audible Frequency Range and Wavelength By apportioning the accepted audible frequency range to appropriately sized combinations of drivers, these mounted in a suitable baffle or an enclosure, moving‐coil technology can cover a frequency range of 20 Hz to 80 kHz, mathematically a massive ratio of 4000:1. Note that this great span corresponds to radiated acoustic wavelengths extending from 17 metres in the bass to just 4.25 mm in the high treble. Physicists and materials scientists may well sound warnings in respect of such a wide frequency range, highlighting the potential engineering difficulties which may be incurred, for example, where the

General Review

radiation efficiency over frequency is dominated by driver size. The mechanical properties of materials used, their stiffness and damping, will vary considerably over such a wide range. The loudspeaker designer needs to keep this warning concerning materials science in view, seriously consider the properties of materials over frequency and temperature, and try not to attempt the impossible. With some difficulty and considerable expense loudspeaker systems with that 4000:1 frequency range have been designed for costly high‐fidelity installations. Typically, this near 11 octave span may be reached with a set of four moving‐coil drivers, each of appropriate size, scaled for their respective frequency coverage. The most ambitious of these ‘hi fi’, high fidelity loudspeaker examples can cost as much as a high‐performance car, and with still greater sales markup, and yet the humblest moving‐coil drive unit, for example, intended for speech and portable radio application at moderate loudness, may be priced in as little as tens of cents in typical, industrial high‐volume quantities. 1.2.1  Horn Loading and Efficiency When the diaphragm of a moving‐coil driver is loaded by a horn, this coupling a larger area of air load to the diaphragm, the improved acoustical matching will substantially increase the efficiency. This is vitally important for addressing larger audiences at greater sound levels. It is possible to reach a conversion efficiency of almost 50% over narrower frequency ranges with this technique, compared with the typical 1% efficiency for the usual larger size of direct radiating high‐fidelity speaker. With typical horn designs, a fairly easily obtained 40 electrical watts can deliver a seriously intense, very loud, 15 acoustic watts, sufficient to cover very large audiences at realistic volume levels. Horns are inherently directional, considered a disadvantage in some cases for domestic use and nearfield studio monitoring, but conversely, they offer the powerful benefit of beaming the sound more selectively to where it is required. Judged subjectively, domestic listeners also report that perceived musical dynamics are improved for all loudspeakers in proportion to higher effective efficiency, here noting that higher efficiency is a natural attribute of horn loading. Despite potentially greater coloration and a narrower spread of energy into the local acoustic, a greater dynamic headroom is conferred, and the need for less powerful amplifiers are important benefits. 1.2.2  Moving‐Coil Longevity and Advantages Moving‐coil drivers have proved to be remarkably durable with many examples still operating after rather more than half a century of use. We can observe that numerous alternative sound reproducing technologies have been proposed and tried out, such as magnetically driven ribbons, shape changing piezos, electrostatic membrane drive, ionic plasma sources, and ultrasonic demodulation in air. Some of these principles remain in use, if on a small scale. However, like the wheel, the moving‐coil principle remains ubiquitous. And for no better reason that it is economical, durable and effective (see Figure 1.2). At times, it may seem that some new transducer and/or acoustic loading innovation appears in the specialist loudspeaker field, with many of these claimed by their inventors

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Rear suspension

Roll surround

Chassis Coil former Voice coil Magnetic gap Steel pole Magnet Steel pole Vent hole

Figure 1.2  A low distortion bass–mid driver (Vivid) with open multi‐spoke frame and short coil‐long gap construction. Here the coil former is of perforated titanium foil for rigidity and increased power handling. The alloy cone is reinforced by a rigid central dome.

and supporters to supplant the substantially pistonic moving‐coil driver with its generally simple box enclosure. However, no alternative technology has so far emerged to mount a credible value challenge and the moving‐coil principle remains pre‐eminent in terms of effectiveness, economy, wide application, flexibility, and performance potential. While this introductory review concentrates on the moving‐coil principle applied to loudspeakers, this simple mechanism is also widely used in precision actuators, both for the high‐speed focus and the high‐resolution tracking mechanisms for laser optical heads used for video data and compact discs. It is also applied in the most popular form of microphone and not least, for almost all high‐fidelity headphones and earpieces, as well many applications in related communications apparatus. 1.2.3  Loudspeaker Design Is Not an Exact Science Over the last 50 years the growth and worldwide acceptance of the high‐fidelity market, and the manifestly high sound quality standards achieved in recording and broadcast studios, have given great impetus to high‐performance loudspeaker design. Nevertheless, the loudspeaker remains the most argued‐over device in the entire high‐fidelity chain; every aspect of its design and execution has been subject to lengthy and involved discussion, even dispute. Although audio engineers like to deal in facts, much to their dismay, fashion plays a considerable part in the burgeoning consumer market and loudspeakers are not exempt. A designer building to a high standard for bandwidth, linearity, and maximum loudness will likely deliver quite a large object, very probably a floor standing enclosure of 50 to 150 litres enclosure volume. In view of the likely high price, the market demands that elements of design style and finish are to a high standard, commensurate with luxury furniture and related fashion sectors, commonly automotive. While a car may well be designed to a high performance standard technically, it is now expected that an excellent appearance will also be commensurate with the price.

General Review

Likewise, designers of high‐quality speaker systems need to include substantial industrial design input at an early stage, and must carefully consider all elements including colour and finish, for example, piano gloss lacquer and custom veneers and colours. Customers now expect that contemporary luxury standards are met in all aspects of design, build, style and finish. 1.2.4  Passing Technologies and Fashions Concerning less commonly encountered technologies and design approaches, occasionally a design which would otherwise be considered technically ‘unbalanced’, a loudspeaker which a consensus of trained electroacoustic design engineers would consider includes an obvious design weakness or error, will nevertheless find public and even specialist consumer journal review approval. In some cases, such a model may be claimed to have a ‘new and better sound’, perhaps deriving from an alternative bass loading principle, or a new transducer technology, or a reworked sound dispersion method. Unfortunately, for many such products other important aspects of performance may well have been neglected by the designers in their perhaps blinkered efforts to exploit that ‘special’ feature and resulting novel sound. After a cooling‐off period, the market generally regains its senses and a longer‐term consensus concerning reliable opinion for natural sound reproduction obtains. 1.2.5  An Emerging Consensus for Performance Audio professionals are inevitably conditioned by experience and may be suspicious of any change, even for the better. Sound quality judgments which are free of prejudice, made by those who have frequent contact with musicians and live programme sources are more reliable than most. Nevertheless, there has been an encouraging development over recent years, in that a degree of rationalisation for performance standards has occurred, on both the domestic and professional fronts. Audio researchers and designers are beginning to agree on a common standard based on factors such as a natural sounding frequency balance, good uniformity of acoustic output, both on and off axis, together with lower distortion and lowered colouration. This common ground has developed despite dissimilarities of design approach and philosophy. It suggests that a consensus is developing concerning gathered data, objective and subjective, and informal opinion concerning speaker performance and quality. Such a situation presents a dramatic reversal of the state of affairs which prevailed in the 1960s when hi fi was beginning to take off. Then there was a marked divergence of opinion over subjective sound quality, especially from loudspeakers. Indeed, this was so extreme that the line of products from the major manufacturers could be readily identified by a specific ‘in‐house’ sound that pervaded all their designs. In addition, a country or even a region could well be involved, for example, for the United States, ‘West Coast’ or ‘East Coast’ frequency balances. At this period, a typical domestic ‘hi fi’ speaker system comprised a 250 or 300 mm chassis diameter bass‐mid unit, with a light paper cone of fairly high resonance frequency, driven by a 33 or 50 mm diameter voice coil wound on a paper former. A separate 75 or 100 mm paper‐cone tweeter covered the treble range and was often concentrically mounted on the bass unit frame. The drivers were mounted on the inside

7

High Performance Loudspeakers

face of the front panel forming a frontal cavity, the enclosure was likely to have a typical volume of between 60 and 120 litres, and generally employed reflex, that is, vented, low frequency loading. Performances, both for distortion and for colouration, for example, from unnatural ‘ringing’ effects due to in‐band resonances, and for tonal balance or a ‘natural timbre’, generally fell well short of the performance of even low‐cost models today. Measured frequency responses frequently resembled a series of jagged crags accompanied by obvious and obtrusive audible colorations (Figure 1.3). It is fascinating to consider the ‘ideal performance’ that a contemporary speaker designer aimed at achieving in those times. (Table 1.1), even though those typical ‘hi fi’ speakers then on sale, as noted above, fell rather short of this objective This target specification was inherently limited by the level of achievement typically attained by the industry for the time (Table 1.2 and Figure 1.1). The target efficiency/ sensitivity was set at 100 dB SPL for a 1 W input at 1 m relative to a typical commercial system of the day, typically 94 dB/W. Presumably this high value reflected the relatively low power output of contemporary hi fi amplifiers where 10 to 20 W/channel maximum for an 8 ohm load, was commonplace while many failed on 4 ohms loading. Interestingly only mild improvements in response flatness or bandwidth were thought possible due to an acceptance that inherent diaphragm resonances were largely incurable. Commercial speakers of the time typically provided a noted 35 Hz ‘useable’ limit at a substantial 16 dB down, despite their significant size, and a 15 kHz limit frequency typically some 12 dB down, which contrasts with the somewhat more ambitious −10 dB limits which were then suggested for an idealised system. Note that the +, −5 dB

80 Sound pressure (dB)

8

70 60 50 40

20

50

100

200

500 1000

2k 5 k 10 k Frequency Hz

20 k

Figure 1.3  Axial response of a typical early 1960s loudspeaker system. Table 1.1  Idealized loudspeaker system specification, circa 1960. Efficiency (sensitivity)

100 dB at 1 m for 1 W at 1 kHz (8 ohms)

Frequency response Response limits

100–10,000 Hz, ±6 dB; 35 Hz at −10 dB; 15 kHz at −10 dB

Polar response

100–10,000 Hz: better than 6 dB down at a 60° arc limit

Distortion

Less than 10% at 35 Hz, sound level unspecified (likely 1 W input)

Distortion

Less than 2% above 100 Hz (likely 1 W input)

Cabinet volume

60 litres internal

General Review

Table 1.2  Specification of domestic two‐way system, circa 1965. Efficiency

93 dB at 1 m for 1 W at 100 Hz

Frequency response

100 Hz to 10,000 Hz, ±6 dB

35 Hz limit

At −17 dB

15 kHz limit

At −12 dB

Polar response

Less than 6 dB down over a 60° arc, 100 Hz–5 kHz

Distortion

Above 200 Hz, not quoted; at 100 Hz, 4%, at 35 Hz, 10%

Power rating

25 W programme

Cabinet volume

75 litres

amplitude limits which were aimed for, also show relatively little ambition compared with those finer limits now attained with more recent practice. It should be noted that specifying for such a wide tolerance for amplitude not only allows for significant variation in timbre, tonal balance, from sample to sample but also obscures the important question of pair matching. Closer tolerances for amplitude versus frequency are now understood to be vital to greater sample‐to‐sample consistency and thus genuinely higher performance. Closer tolerances are also key to superior stereo image performance, where the quality of virtual image sharpness is now known to be strongly dependant on the accuracy of loudspeaker pair matching. 1.2.6  Those Electroacoustic Fundamentals Were in Place While the performance data of such historic commercial practice looks disappointing now, it is perhaps surprising to note that the basic technology and theory now considered essential to present‐day higher‐quality loudspeaker design was already well known to advanced specialists in the field. Furthermore, such research was well documented in many papers, periodicals and books. Commercial speaker designers were aware of colouration effects which could often be associated with errors in frequency response, and with the connected so called delayed resonances in cones and structures; designers appear to have done little about them, despite the excellent research at the BBC by Shorter that had been conducted almost 20 years earlier concerning audio band resonances, their sources and effects. While extant in the reference literature, many of the now accepted loudspeaker technologies and principles were rarely applied commercially, and the overall approach to design seemed to be a rather haphazard, even amateur exercise. Many loudspeaker companies were small scale, almost garage operations. Perhaps it was felt at the time that there were so many acoustical problems acting in concert that solving just one or two of them would not result in a significant improvement in sound quality. And it may be argued that several hi fi speaker designs remain rather amateur, even now. However, some companies were researching highly advanced technologies, and were also working on more sophisticated designs. Some made it into production, albeit in limited quantities. Hugh Brittain, researching in the 1950s at the GEC Hirst Research Centre at Wembley, designed a 200 mm ‘BCS1851’ aluminum cone, full range driver,

9

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High Performance Loudspeakers

loaded by proprietary ‘Periphonic’ enclosures. Ted Jordan worked with Brittain, and later and went on to develop a whole range of advanced moving‐coil drivers and systems when he moved on to Goodmans Loudspeakers, then located close by in North London. Then, in the mid‐1960s Jordan founded Jordan‐Watts, of ‘JW Module’ fame. The JW module was a highly advanced, futuristic, unit full‐range driver which used a single flared aluminum cone, 100 mm dia see 7.6.1. The assembly was built into a die‐cast, acoustically porous, box‐like frame. The lead out wires were configured as an integral tangential voice coil suspension, made of beryllium copper bars, and the module was designed with integral low‐ frequency damping making it largely uncritical of alignment and enclosure volume. By 1967, K.E.F. Electronics (UK) had released the Carlton, designed largely by company founder Raymond Cooke, this a costly three‐way, closed box, considered well ahead of its time, and fitted with a substantial planar rectangular composite diaphragm bass driver, a polystyrene foam core with reinforcing skins, called the B1814, measuring unsurprisingly, 18 by 14 inches. The diaphragm skins were aluminium foil. The system also incorporated a highly developed mid‐band transducer. This, the M65, covered a 250 Hz to 4 kHz range and employed a 65 mm hemispherical dome formed of a rigid polyester polymer, fitted with an advanced double suspension to control rocking. It was back loaded via the hollow pole piece by an extended transmission line pipe, some 0.8 m long. This was filled with graded density long‐fibre wool for effective back wave absorption and predates the present graded lines used by B&W by some 35 years. The use of an aluminum voice‐coil former provided a high‐power handling capacity (Figure 1.4). Finally, high frequencies were covered by the T27, here with a 19 mm polyester laminate dome, typically operating to 30 kHz; the latter design was so advanced that it continued in production for almost 30 years and was also chosen for the BBC LS 3/5a studio monitor. At that time, very few mid‐range dome drivers were available, the other well‐ established example being that employed in the classic American design, the, AR‐3, designed by co‐founder of Acoustic Research (AR), designer Edgar Villchur, was setting Magnet

Voice coil on aluminium former

63.5 mm

Dome diaphragm

Sulphur filling

Surround

840 mm Long flexible pipe filled with long-hair wool

Figure 1.4  KEF mid‐range dome loudspeaker with absorbent line loading.

General Review

standards for extended, uniform bass from a compact sealed‐box (IB) enclosure, if at necessarily low efficiency. Low impedance and low sensitivity also characterised these models. AR also introduced one of the first types of wide directivity rigid ‘dome’ type units for mid and for treble, these 2‐inch and 3/8‐inch sizes first disclosed in 1958. Villchur is now acknowledged as the leading commercial exponent of the volume compliance dominant sealed box with his original and highly successful AR‐1 ‘acoustic suspension’ speaker. This was a radical commercial development when developed in late 1953, with a patent granted in 1956 (but later revoked), when most loudspeakers were much larger in volume and with generally rather less low‐frequency extension and certainly much less uniform frequency responses. A two‐way design of 40 litres, by today’s standards the original AR‐1 employed an improbably large 8‐inch mid‐treble unit, combined with a 12‐inch long throw, very low resonance bass driver, the alignment dominated by the enclosure air volume stiffness. Efficiency was low while its dynamic range was limited by the relatively small amplifiers of the time. In the late 1950s in the UK a contemporary Goodmans ‘Audiom’ driver had a similarly low free air bass driver resonance at 16 Hz, and was designed for a three cubic foot box for a 50 Hz in‐cabinet resonance. Incidentally Peter Walker, founder of Quad, noted that there were sales of a UK designed ‘acoustic suspension’ loudspeaker in about 1937, coincidentally called the ‘Audiom 8’ and significantly predating the Villchur development. Back in 1967, Bill Hecht patented a 2‐inch soft fabric dome tweeter in the United States, (here with an unusual form of internal suspension), while complaining at the time that the raw fabric diaphragm disappointingly would operate to only a few kHz due to lack of rigidity. But the later addition of a rubberised doping had a surprising effect, resulting in a smooth response to over 12 kHz. Thanks to hysteresis from the doped fabric, this exhibited fortuitous and substantial stiffening with increasing frequency, combined with useful damping. Boston Acoustics used the Hecht design in large quantities while Philips independently produced a 1‐inch doped soft fabric dome in Europe with an integral edge suspension, which was also very widely used and endlessly copied. This development essentially spelled the end for the then ubiquitous cone tweeter with its difficulties of irregularities in frequency response, consistency and directivity, though some designers regretted this transition, hearing some deficiencies in terms of clarity and dynamic expression with many of the soft dome transducer designs. One non‐moving‐coil loudspeaker system surviving the passage of time is the Quad ‘57’ full‐range electrostatic loudspeaker designed by Peter Walker and DTN Williamson, production dating from 1957 and still well regarded for its exceptional naturalness (to which I can testify), and obtainable on the second user market. While it was by no means the first electrostatic speaker, with other examples dating back at least 80 years, its push‐pull, constant charge design helped give unprecedentedly low distortion and conferred great subjective transparency. (The underlying low distortion, constant‐ charge principle had been previously proposed and fully analysed by Hunt.) Accepting that moderate power handling and a low voltage sensitivity are specific limitations, its subjective performance in terms of low distortion, neutral timbre, very low coloration and excellent transient accuracy continues to bear favourable comparison with many current loudspeaker designs. The reputation of its successor, the ESL63, whose original design dates from 1963, has also survived; and it is still in production, (now with a revised model number), but remains largely unchanged. Standards are still set here in

11

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High Performance Loudspeakers

several respects by this near zero moving mass technology. Here the large area, low excursion film diaphragm is just one tenth the thickness of the human hair.

1.3 ­The BBC Contribution By the mid‐1960s, proprietary BBC engineering research for a new generation of monitoring loudspeakers was under way, largely prompted by the considerable inconsistency experienced both with commercial drive units and with complete bought‐in commercial systems which had been chosen for programme quality monitoring work. These new BBC designs incorporated cones of a vacuum formed synthetic co‐polymer (Bextrene) of more consistent performance rather than the usual paper/pulp formulations and this progress, inspired by Shorter’s research, was now well advanced, extensively developed and prototyped by a team primarily led by Dudley Harwood and including electroacoustic engineer Spencer Hughes. This project proved to be of great significance as it was clear that a major improvement in both loudspeaker quality and consistency had been achieved during this development period. The high standards set by these designs, with their well damped, critically shaped polymer cone drivers, in particular the LS5/5 three‐way with a 200 mm mid unit, acted as a great stimulus to the UK hi fi industry. Through attempts to attain this standard at a commercial level numerous new developments and designs appeared, many of these rather more closely related to the BBC originals and some less so. Raymond Cooke, founder of KEF also provided valuable production experience in respect of these new technologies and KEF manufactured a number of BBC monitors both under contract and under license for retail sale. 1.3.1  A Step Change for Reduced Colouration and Improved Response Accuracy Independently, and also designed for commercial sale, ex BBC engineer Spencer Hughes developed a compact two‐way system (BC1) derived from the LS5/5 technology, this for his own new company Spendor, and using his own proprietary highly developed bass‐ mid driver. This derivative proposal for a compact two‐way system had initially been rejected by the BBC. The consumer loudspeaker market in the late sixties was quite conservative. At that time, the favourably reviewed high quality systems were relatively large (60–150 litres), and when this new 40 litre contender, the BC1, of compact dimensions became available it was initially viewed with considerable suspicion. This radical design employed a 200 mm cast alloy chassis, Alnico magnet bass‐mid driver, fitted with a Hughes developed Bextrene co‐polymer bass‐mid diaphragm of critical flare, vibro‐elastically damped with a hand‐applied coating of an aqueous polyvinyl acetate based mix, terminated by a custom surround termination in white PVC, and which driver at least in part, clearly benefited from the prior BBC research. The HF unit was a carefully selected, BBC‐ approved Celestion HF1300 using a 34‐mm acoustically loaded rigid diaphragm. The result, the BC1 compact loudspeaker sounded quite different from the relatively massive and more costly systems available and, in fact was judged rather closer to the sound of live sources than most of its larger and more costly contemporaries, and

General Review

indeed rather close to the highly rated Quad electrostatic. After some acclimatisation some listeners also became aware that the initially perplexing difference between its sound and that expected from regular speakers was in fact due to its rather closer approach to realism, particularly for spectral balance, pair matching, clarity on transients and most especially low coloration, the latter achieved through advanced control of decay resonances. This compact speaker represented a skilled balance of the important parameters responsible for natural sound quality, and yet it took almost a decade for this level of performance to become fully appreciated by the wider industry. Further, when the BBC had occasion to audition this small Spendor they chose to employ it after all, directing Hughes to complete a transformer matched version under BBC auspices, designating it LS3/6a, and which production was then licensed to Rogers. While a few dozen of the official LS3/6a were manufactured, some 2,000 of the more commercially orientated BC1 were supplied to the professional market, including many to the BBC. The BC1 continued in very successful production for many years, reaching 20,000 pairs, and it was later subject to development to improve the power handling, cognisant of rapidly emerging rock music programme demanding more low frequency power. This change aided growing domestic market sales, though the Rogers‐built version held to the official BBC licensed specification. By 1977, Spencer’s former chief Dudley Harwood had left the BBC engineering department to establish Harbeth, and also launched another LS 3/6 sized design, but here with a 25 mm soft‐dome tweeter, and a new design of bass driver fitted with a proprietary, self‐damped, co‐polymer polypropylene cone. This polymer Harwood had jointly patented for loudspeaker application with David Stebbings (BBC) and Joseph Pao (the latter pair going on to found Chartwell, here also to exploit this diaphragm technology). Chartwell also went on to build BBC licensed designs. Many UK speaker designs which followed gained much from the BBC sound quality improvements and consequently showed much reduced coloration and greater consistency. Subsequent and varied polypropylene cone formulations are now used in millions of driver diaphragms around the world.

1.4 ­Emerging Standards The performance of today’s typical high‐quality domestic systems would have been disbelieved in 1960, for they exceed the majority of requirements of that contemporary ideal specification by a handsome margin. The particular model described in the following table is for a compact, so called ‘bookshelf ’ bass reflex design, now widely popular, and intended for free space mounting on a 46 cm high stand, employing a moulded 160 mm diameter polymer‐coned bass–mid‐range unit working in conjunction with a 25 mm diameter soft‐fabric dome tweeter. However, note that for this system (Figure 1.5), the sensitivity/efficiency is a massive 12 dB lower than that 1960s target ideal. This is the inevitable compromise resulting from the requirement for extended bass response from domestically acceptable compact enclosures. Fortunately, over the intervening period much larger and comparatively inexpensive 50 to 150 W amplifiers have become commonplace for matching this low efficiency (Table 1.3). Such low efficiency and sensitivity is the inevitable outcome of the fashionable requirement for wide bandwidth from increasingly compact enclosures, also, to some

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High Performance Loudspeakers

100 Sound pressure (dB)

14

90 80 70 60

20

50

100

200

500 1000 2 k

5k

10 k

20 k

Frequency Hz

Figure 1.5  Typical response curve of good‐quality two‐way domestic system (1 m anechoic). Table 1.3  Typical specification of domestic two‐way loudspeaker system, circa 2014. See Figure 1.5.

Sensitivity

87 dB/W 1 m, 1 W 8 ohm input (85 dB/W for the sealed box alternative)

Frequency response

55 Hz–18 kHz, ±3 dB; 45 Hz, −6 dB

Polar response

Within ±3 dB of axial output over ±30° lateral arc, 50 Hz–15 kHz

Distortion (90 dB)

Less than 0.5% at 100 Hz–10 kHz; less than 5% at 35 Hz

Power rating

100 W peak programme

Volume (internal)

15−20 litres

Impedance

6 ohm nominal, 3.5 ohm minimum

Drivers

160 mm frame diameter, formed polymer bass–mid‐range, 25 mm diameter soft dome tweeter

Maximum level

103 dB @1 m short term

Crossover frequency

2.6−3.3 kHz (typical)

degree, the drive for substantially lower colouration with better control of delayed resonances. This often involves increased diaphragm mass. The tighter tolerance seen for the amplitude response is also important. Together these also qualify a significantly wider frequency response, also serving to illustrate a considerable manufacturing improvement achieved in the uniformity and consistency of sound output with frequency. The standards achieved for distortion and polar, off axis response are also substantially improved, as is the higher power rating of 100 W programme which is 6 dB greater than the typical equivalent for 1965. This is inevitably necessitated by the reduced efficiency of the system as well as the need to cope with considerably higher power output of modern amplifiers, up from the previous 15 W to typically 75 W now. We note that there a few of the larger domestic amplifiers are now capable of 2,000 W/channel into 4‐ohm loads. One consequence of a high‐power requirement arising from low sensitivity may well be a loss of subjective dynamic expression, due in part to the requirement to absorb the increased power and the resulting thermal response. Many of the better system design examples now include a form of waveguide loading (e.g., a shallow horn contour) for the HF unit. This increases efficiency in this driver’s

General Review

lower frequency range but also helps to somewhat narrow the directivity through the crossover region to better match the mid‐range driver output. The result is a smoother power response which also improves sound quality. The shallow horn helps address the usual power peak found near the crossover point for the Mid‐HF. This power step can develop where a wide directivity HF driver takes over from the mid‐range section where the directivity of the larger driver is already narrowing. In the light of the current level of performance for contemporary loudspeaker technology (Table 1.4) then goes on to suggest some idealized specifications for a spectrum of high‐quality domestic loudspeaker systems. Concerning the amplitude/frequency response the close amplitude tolerances suggested have as much to do with the value of consistency as with sound quality per se, and for a given design, note that a given enclosure and driver format may not necessarily deliver a perfect ‘flat response target’ for optimum sound quality, since the latter criterion is also affected by the power response, and by how the speaker system as a whole interacts with the listening environment. There are also several larger and more costly loudspeaker systems of wider bandwidth and higher efficiency, and thus greater maximum output than the examples given below, though these types are made in smaller numbers and suffer a more limited distribution. Somewhat idealized suggested specifications for contemporary loudspeaker systems are as follows:

Table 1.4  Idealised loudspeaker specification.

Axial pressure response

60 Hz–15 kHz, ±2 dB (sine and/or 1/64 octave measuring bandwidth) 100 Hz–10 kHz, ±1 dB (when octave averaged) (or closely compliant with an objective response target)

LF compensation for room gain

Output from 25 Hz to 70 Hz tailored to specified local boundary and to overall room conditions

Off‐axis response (up to 12 kHz)

Within 2 dB of axial output for ±20° vertical and within 3 dB up to ±45° lateral

Harmonic distortion (90 dB)

100 Hz–15 kHz, < 0.3% (with 3rd 200

Boron

2.4

39

16.5

13

>200

Boronized titanium

4.2

25

Carbon fibre composite

0.26

Chipboard (600)

0.6

Copper

8.5

15

Diamond

3.5

100

28.6

Graphite polymer

1.8

7

3.9

6.2

12

Iron

7.9

20

2.5

5

>200

Magnesium

1.8

4.5

2.6

5.8

>200

Paper/pulp (typical)

0.15

0.05

0.33

1.8

10

Paper/phenolic

0.35

0.1

0.285

1.7

15

Plywood

0.78

0.86

1.1

3.3

>50

Polyester film

1.4

0.7

0.5

2.2

>50

Polyethylene

0.94

0.1

0.106

1.0

10

Polyamide film

1.4

0.3

0.22

1.5

>50

Polymethyl pentene (TPX)

0.84

0.28

0.33

1.8

8

Polypropylene homopolymer

1.0

0.23

0.23

1.5

11

Polypropylene co‐polymer

0.91

0.14

0.153

1.2

10

Polypropylene (filled, eg talc)

1.3

0.30

0.23

1.5

10

Polystyrene*

0.95

0.19

0.2

1.5

31

Polystyrene foam

0.01

0.0003

0.030

0.55

8

Polystyrene (foam, alloy foil skinned)

0.027

0.20

7.5

8.6

12

Resin glass fibre composite (honeycomb core)

0.43

1.1

2.55

5.5

15

Titanium

4.5

11.6

2.6

5

>200

6

7.7

>100

1.0

3.8

6.2

>100

0.2

0.33

1.8

50

1.8

4.1

>200

17

>200

recent years have escalated thanks to fragile and exposed metal domes on higher quality loudspeaker systems. Those large shiny tweeter ‘buttons’ are showroom finger magnets. Designers should consider protection, durability and easy repair strategies for such drivers.

Moving‐Coil Direct‐Radiator Drivers

The properties listed in Table 7.2 can only be a guide for drivers since they refer to the properties in sheet form. When made up into practical diaphragm shapes additional factors play their part, such as geometry and self‐damping. The resulting performance cannot be fully determined from the material properties alone. (also note that the ­concept of sonic velocity has limited meaning for composites.) 7.2.4  Diaphragm Shape Some of the effects of diaphragm shape have been discussed in Section  34.1. These ­principles cannot be ignored even for intendedly pistonic bass drivers, and the determination of a suitable profile for a given material and driver size has historically been a matter of trial and error, now greatly accelerated by advances in FEA. The choice of surround is vital and, strictly speaking, the surround is mechanically best considered as a continuation of the diaphragm even though it is generally a separate component formed from a different material. With vacuum‐formed thermoplastic cones, the best results to date have been given by flared, moderately shallow diaphragm profiles. The transition between the neck and the motor‐coil former may form a smooth curve, and to inhibit localized ‘reflex’ bending towards the edge, the tangential angle between the cone rim and front plane should not be much less than 25 degrees. The flare rate, diameter of cone and motor coil, coil mass and cone thickness will all affect the linearity, slope, range and directivity of the pressure response. Even if a bass driver is not intended to operate beyond 400 Hz, it is well worth designing the unit to give a well‐behaved characteristic at least two octaves greater, since this will generally reduce audible colouration and the crossover transition and necessary overlap will be better defined and controlled. Designers often ignore peaks in driver response if they are going to be placed outside the driver’s chosen band‐pass. However for high‐performance systems such peaks may present problems in terms of crossover slope and integration since some response ‘ripples’ are still likely to intrude in the designed frequency response. Such cone resonances, where present, may also be excited by acoustic coupling from an adjacent range driver working higher in the band, and thus be rendered audible despite the crossover rolloff. Most synthetic cones are produced by some kind of suction or vacuum forming process where heated thermoplastic sheet is drawn over a porous cone mould. This process tends to form diaphragms where the thinnest, most stretched section is at the apex, while the thickest ‘least formed’ region is at the rim. Study of cone behaviour indicates that the reverse condition is preferable, for example, a stronger thicker apex section tapering out to a thinner rim. Injection moulding is an increasingly popular alternative and allows more freedom in grading cone thickness over the profile though it does require very close tolerances for the machine and for the tool components in order to achieve the high degree of axi‐symmetric uniformity required. If the cone is not well balanced axially, rocking and related vibration modes may occur. With still more sophisticated vacuum moulding methods, it may also be possible to control the mould temperatures differentially over area for different sectors of the cone former at the moment prior to moulding, such that the apex section does not experience the usual thinning. Recent FEA software can model cone shape and surround behaviour quite well, thus speeding up the design process, especially for the more isotropic v­ acuum moulded designs.

291

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Metal cones, for example, aluminium, are frequency straight‐sided, pushing the first bending mode well beyond the working range, for example, to 2 kHz for a 250 mm frame LF driver intended to operate to 350 Hz. Large centre caps, for example, of carbon fibre composite may be added to control and damp residual modes. 7.2.5 Surrounds This component is important to all drivers but it is most critical in lower frequency applications, where it must perform two roles. First, it must enable the large amplitude linear excursions required at low frequencies, together with a resistance to the considerable differential air pressures experienced, and where necessary, provide effective absorption and termination of energy at the cone edge right through to the mid‐range. It must also support the cone for years without sagging, preventing decentration and catastrophic voice coil scraping. Surrounds may be formed as a series of concentric corrugations, either as an extension of the cone edge often with applied damping or as an additional formed component. These are seen on some very high power and larger public address and studio applications. By contrast, almost all hi fi drivers today employ some form of half‐roll surround of selected composition. These are satisfactorily linear and can also be made to the high compliance values required for low‐resonance sealed‐ cabinet drivers. In addition, they may be formed from a variety of materials, some of which offer excellent termination properties at higher frequencies. The curved shape of a roll surround endows it with a resistance to the high differential pressure between the front and rear sides of a bass driver. Less distortion results from materials that overload gradually, and plastic foams and rubbers are often preferable to treated fabric. Although they are quite heavy, surrounds of moulded neoprene are extensively used with bass drivers (Figure  7.4) while other similar materials such as nitrile modified rubbers are also in use. Preferred suspension materials such as PVC and nitrile rubbers have densities in the 1 to 1.1 × 103 kg m3 range, comparing well with the density of polypropylene and Bextrene cone plastics. Butyl rubber has also proved popular with dense, heavy‐coned pulp cone drivers. For lighter grade cones, foamed polyurethane works well especially with an additional sealing coating, though unless UV stabilized and treated it can degrade prematurely in tropical conditions. Also, adhesive difficulties have been noted both with cone plastics, notably polypropylene, and also surrounds, though in recent years these have been overcome. Favoured joining methods now include RF bonding of surrounds and cones, also with adhesive primers, these and compression heating are preferable to solvent‐based methods, which can result in serious physical distortion of the components and which also may be hazardous to assemblers. Rubber modified methacrylates have justifiably found favour for their durability, bond strength and lower hazard. Metered adhesive application is ideal for bond consistency, also for control of added mass and bonded area. Designers must take into account divergent surround requirements, namely useful dissipation of vibration energy above 150 Hz or so; a profile which allows reasonably linear excursion up to typically 8 mm peak to peak, (much more for powerful sub‐woofer bass units) and a mechanical structure which inhibits self‐resonance. For a particular prototype driver, a response dip occurred at about 600 Hz, whose source was eventually traced to an anti‐resonance in the surround. A flat section had been designed between

Moving‐Coil Direct‐Radiator Drivers

the half‐roll and the cone edge, but another was unintentionally present between the outer ‘roll’ edge and the clamping point on the chassis. The unwanted circuit comprised the ‘roll’ vibrating with the compliance of the two adjacent flat sections. Readjustment of the roll dimension to eliminate the outer flat portion removed the dip. Such ‘­surround response dips’ remain a common design problem. Recent designs have modeled the surround shape to include an additional mass component to help terminate cone‐­ surround modes. The surround must also be regarded as an additional radiating element, in part ­producing an out‐of‐phase component and should, in theory at least, be as narrow as practicable for the required excursion. Another issue is the significant temperature variability of compliance and termination shown by many surround materials, particularly nitrile rubber and PVC. For a given driver compromises may need to be found as between optimum bass excursion and linearity and upper range response uniformity. Hitachi patented a particular type of geometrically pleated surround using a moulding of doped fabric claiming improved excursion linearity and termination. 7.2.6  Subjective Effect of Bass Driver Suspension Hysteresis: Pace and Rhythm The author has undertaken an analysis to investigate a particular aspect of low‐­ frequency sound quality concerning 400 commercial speaker models, correlating a particular factor associated with bass sound quality, and which may be separated from the usual criteria such as low‐frequency bandwidth, and the bass–midrange frequency balance. It can materially affect judgment of bass sound quality aspects. With continuing sound quality improvements for amplification and source material, particularly with digitally derived programme, a more critical awareness of low‐­ frequency quality is developing among reviewers and users. This concerns not just bass response uniformity but also bass dynamics, timing, rhythm and tunefulness. For good tune playing in the bass, the low‐frequency register should ideally be reproduced with the kind of low colouration performance and uniformity that was originally only sought and expected from the mid‐range of high‐quality speaker systems. As regards engineering aspects, obvious influential factors include the use of pistonic bass diaphragms, rigid inert enclosures, an absence of internal standing‐wave modes within the enclosure, and if used, a ducted reflex loading of moderate Q alignment that is itself largely free of secondary resonances and has extended bandwidth. Obviously, the low‐frequency response shape must also be tailored for the expected environmental loading in order to optimize the overall response shape in conjunction with room gain. Lower group delay is an objective here. Attention to these factors alone will not guarantee the valued subjective qualities of expression, good timing, dynamics and rhythm for the bass. In part these aspects can be associated with the mechanical impedance of the suspension of a moving‐coil driver. In this connection two basic kinds of suspension have been identified: those with the soft visco‐elastic, vinyl related surrounds, and those with rubber or foam plastic surrounds. The former are often chosen for a low mechanical Q helping to terminate cone problems but more importantly suffer from a considerable degree of hysteresis. Here the return to the centre zero or rest position is considerably delayed (seconds, minutes or even hours) after a large signal bass excursion has occurred. Some term this behavior as creep.

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Conversely the mechanical response of the second type is largely Hookean, that is, following a simple spring like characteristic and possessing negligible hysteresis. Interestingly, some unpublished engineering work done at KEF correlates well with the following subjective observation, namely that the hysteretic class of surrounds can ­perform well on simple sine‐wave related sounds such as the ‘open’ bass waveforms of acoustic orchestral bass instruments, organ, bass viol, bass drum, but are clearly ‘slower’ and less accurate when reproducing the faster percussive rhythm bass generally ­encountered in modern jazz and popular music. A well damped pedal drum sound can be heard to be subjectively distorted. In such cases the bass may be described as ‘­compressed’, ‘undynamic’, ‘slowed’ and fails to ‘time properly’ with the mid‐range beat. In fact the bass rhythm falls behind the mid‐range timing signature. Conversely, the majority of low hysteresis bass units, when optimally loaded, and, for that matter, large, open‐panel film‐type transducers, have a bass that is fluid and dynamic, holds close rhythmic time with the rest of the frequency range, and sounds naturally upbeat with a suitable quality of programme input. The KEF data on this subject concerned research investigating the lack of correlation between steady state measurements, for example, swept sine wave and those for narrow impulses. This was for frequency responses at low‐frequencies (see Figure 7.8). Which method was correct? In a particular example, the discrepancy was associated with a semi‐random movement of the internal absorbent linings of the tested enclosure. Its movement was uncontrolled on impulse excitation but settled into regular patterns on continuous, slow swept sine‐wave stimulus. This behaviour is analogous to hysteresis in a driver suspension material and further investigation of the fine detail of the impulse response of bass drivers is expected to reveal further information on this subject. Hysteresis has been discussed in connection with plasticized and high‐loss surrounds while, more recently, Bolanos[4] has looked closely at the subject, including investigation of spider ‘creep’, a comparable non‐linearity related to time history. Such behaviour is dispersive in that the distortion products are modulated with frequency, resulting in rather non‐musical, inharmonic effects. Certainly, when subjectively judged, significantly hysteretic suspension systems appear to reproduce a bass rhythm line with poorer sound quality, a blurring of the time signature, revealed when they used in a corresponding speaker design. Many speaker designers have been intuitively aware of the complex subjective sound qualities of various surrounds profiles and materials. There seems to be two identifiable schools of thought. Where a high hysteresis vinyl or similar based surround is judged acceptable, this is usually exploited to produce the finest termination for the diaphragms of reference quality bass–mid‐range drivers. These are fundamental to the design of medium sized two‐way speakers considered to be of monitor standard when judged in terms of frequency balance, accuracy and low mid band colouration. Their customers have generally valued mid‐range quality and accuracy above bass definition and neutral rhythm exposition. On the other hand, the alternative school values bass rhythm highly and, in some cases, will go to almost any lengths to preserve it, preferring high QM, for example, ≥4. The use of emphasised tonal balances, for example, some mid‐range lift, also some ­curtailment of unnecessary low‐frequency extension, and finally choosing unduly low system Q, all of which factors may objectively maintain the rhythm for bass

Moving‐Coil Direct‐Radiator Drivers

percussion sounds. However, the primary sacrifice for two way systems may then in the area of mid‐range colouration, resulting from the deliberate use of low hysteresis, low‐loss rubber or rubber equivalent driver surrounds, perhaps imparting poorer cone mode termination in the mid‐range. One technical solution is to adopt three‐way system design and to use surrounds optimised for the respective driver frequency bands. Another solution is to design self‐ terminating diaphragms for a bass–mid‐driver, so placing less reliance on the terminating function of the surround. Another fairly successful solution was seen in a Celestion 170 mm Cobex cone bass–mid‐driver where the half‐roll surround was split into two parts which were bonded together; it comprised an outer rim of butyl rubber for ­optimum bass articulation and an inner section of more hysteretic vinyl chosen for its diaphragm termination property. Clearly, there is scope for more elaborate designs which integrate diaphragm and the surround termination; variable surround thickness achieved by precision moulding may also be a useful technique. As a rule a numerically lower value for system Qtc and a smooth, even tapered extension to lower frequencies may also be found helpful to rhythm and timing performance, helping to reduce group delay. 7.2.7  Suspensions (LF) The compliance of synthetic surrounds is frequently temperature dependent; PVC compliance may vary by two‐to‐one over a reasonable operating range of 15 to 30°C. Note that a low‐frequency driver will benefit from a reasonably stable fundamental resonance, for example, to maintain alignment for a reflex‐loaded application. If it is temperature sensitive, then the surround should not provide the bulk of the diaphragm restoring stiffness. The latter should then be dependent on the remaining supporting component, namely the inner suspension or ‘spider’. Closed‐box designs are less critical in this respect. Good‐quality suspensions are often manufactured from a polyamide fabric (nylon or polyester) impregnated with a cured, temperature stable epoxy resin. If carefully designed, the suspension can provide a reasonably stable restoring force over the required excursion. The suspension should also be engineered so as to limit gently towards the peak coil displacement allowed by the magnet assembly. This will help control the coil jump‐out effect noted in the section on magnet/coil systems in section 4.8.1. By suitable choice of materials and geometry for the spider, it is also possible to ­characterize the suspension non‐linearity to compensate for the magnetic non‐linearity resulting from large excursions.[5] This is important if an optimal efficiency, short‐coil short‐gap assembly is used, where the coil length is only 5% to 10% greater than the physical magnet gap. Some of the classic BBC Bextrene‐based driver systems employ this technique, but owing to the difficulty of its execution, the newer generation of reflex‐loaded monitors have reverted to a more conventional linear ­suspension and employ a motor coil with an approximately 25% coil overhang. Nevertheless, where possible, the most articulate mid‐range seems to result from smaller diameter and lower mass voice coils. Spiders may have varying corrugation d ­ ensity with radius to adjust the linearity characteristic. Poorly designed suspensions, particularly those which are large and heavy, may ­possess inherent self‐resonances at even a few hundred Hz. Odd spikes in the frequency

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response of the driver may result. Additionally, in a matter of days, poorer quality cotton or linen fabric suspensions fitted to heavy coned bass drivers can take a ‘set’ away from the nominal centre zero coil position particularly under humid conditions and if the units are stored horizontally or even designed to be installed in this orientation. Standard vertical positioning relieves the suspension of an axial bias due to gravity, but the long‐term stability of weakly elastic suspensions is still in doubt. Several speaker systems do employ horizontally mounted drivers and require design thought concerning the long‐term such as a suitable offset or bias included in manufacture. In practice, any type of suspension may develop a degree of off‐centre ‘set’ if stored long enough in unconventional orientations, which is why conventional ‘vertical’ mounting, particularly of heavy coned bass drivers, is strongly recommended. 7.2.8  Double Suspensions (LF) While there is little evidence that moderate degrees of suspension non‐linearity are significantly audible at low frequencies, some manufacturers have attained very low orders of bass distortion by utilizing a double suspension. The corrugation geometry is arranged to be complementary, so making the excursion characteristic for force versus displacement close to identical in both directions. With large drivers intended for high‐power applications residual lateral forces at the voice coil resulting from mild gap tolerances may be sufficient to cause momentary de‐centering and consequent coil grounding. A spaced double suspension may then be used to advantage, resulting in a greatly improved resistance to decentration. Matsushita developed suspension geometry with an improved resistance to lateral decentering forces, comprising a four‐piece box section structure with a motion akin to a pantograph. Rocking modes are strongly resisted, which is vitally important with ­shallow drivers such as the pistonic honeycomb cored, planar diaphragm designs it was designed for. An additional benefit conferred is the improved linearity; for a given size the ‘box’ suspension claimed twice the linear excursion as compared with the usual corrugated cloth type (see Figure 7.6). 7.2.9  Motor Coil and Magnet Assembly (LF): Power and Bandwidth The moving diaphragm, the assembled mass, is something of a fixed quantity for a given unit size, relating to expectations of low frequency response, sensitivity and power ­handling. The motor‐coil diameter and length are generally proportional to the required thermal power handling, and with these two factors determined, the efficiency of the resulting driver is proportional to the square of the magnetic field strength in the gap. The detail design of magnet structure will depend on the acoustic loading and the maximum undistorted output requirement for the system. For example, take the case of a sealed box with a long‐throw 200 mm driver, which is required to develop 96 dB spl from 60 Hz. Suppose the magnetic field strength is sufficient to provide a typical system Qtc of about 0.7. Since a fairly large cone excursion is needed to produce 96 dB at 60 Hz, about ±6 mm peak, a typical 6 mm magnet gap height will require a coil overhang of at least double, resulting in a coil length of approximately 18 mm. Quite low motor efficiency results, as only one third of the power dissipated in the coil acts to provide sound pressure.

Moving‐Coil Direct‐Radiator Drivers

(a)

(b)

DISPLACEMENT (mm)

TITLE LINEAR SUSPENSION LARGE DEFORMATION ANAL YSIS

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FEM PROGRAM SAP7 GEOMETRIC NONLINEAR ANAL YSIS

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MATERIAL LINEAR ISOTROPIC

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5

0

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15

FORCE (N)

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LINEAR SUSPENSION CORRUGATION SUSPENSION

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MATSUSHITA ELECTRIC IND. CORP., LTD. ACOUSTIC RESEARCH LAB.

Figure 7.6  (a) Linear damper (Courtesy Technics); (b) linear suspension, large deformation analysis.

It is worth noting that if the bass response of this system was extended by one octave, that is, to 30 Hz for the same power level, the cone excursion would need to be multiplied by four, to an impractical 50 mm peak to peak. Sound power is proportional to the square of the diaphragm amplitude. An undistorted output down to 30 Hz, −3 dB for this particular design requires that the output would have to be reduced by a massive 12 dB. For an alternative sealed‐box design, for which 96 dB at 30 Hz is required, this could also be achieved within a sensible excursion limit by increasing the diaphragm size, since the sound power radiated is proportional to the square of the product of the ­moving area and excursion. If the same ±6 mm excursion limit is adopted, then the

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diaphragm area must be four times greater to radiate 96 dB at 30 Hz and the required driver would need to be scaled up to a 380 mm version. For sealed‐box designs we need radiating area, excursion and power for extended bass. Helpfully there is something of a get out clause. The power spectrum of music and speech program typically reduces with frequency below 80 Hz and this provides some extra headroom. Reflex or ported loading this a fourth‐order alignment, allows a given driver to ­produce more bass. The peak excursion of the driver at system resonance is reduced by as much four times, which allows the formerly long motor coil of the sealed box ­example to be reduced in length, in turn giving an improvement in efficiency. In fact that resulting increase in Bl factor is in fact essential to control the working Q of the vented system. Typically, a sound power increase of four times (6 dB) is possible with a given driver for reflex as compared with the sealed box, if here allowing for a mild degree of amplitude ripple. This power increase holds true even for the same numeric low‐frequency cut‐off, although in this latter comparison the reflex enclosure is likely to be significantly larger than the sealed‐box equivalent. Taking into account the average spectral energy distribution of programme, a well‐ designed reflex enclosure fitted with a 300 mm or 350 mm bass driver can produce upwards of 115 dB of wide‐band speech and music at 1 m (a factor of 6 dB or so of headroom is assumed from the falling energy in most programme material below 70 Hz. Note that for stage PA and special applications such as sub‐woofers this extra margin cannot be assumed). Still higher sound levels may be attained by multiple arrays of such enclosures and/or by horn loading, although the latter technique is unavoidably bulky at low frequencies and its use is generally restricted to fixed installations such as cinemas and stadia. 7.2.10  Designing With Very High Bl Drivers Keele[6] supplements the work of Vanderkooy et al. for very high Bl drivers, by pointing out that the usual constant voltage model for efficiency, which is based on maximally flat teaching for amplitude response, may be inappropriate in some cases. Given the scope for active bass equalization, and an amplifier with substantial voltage swing, fortunately requiring less current in this situation thanks to the now high but almost purely reactive load impedance arising with excessive Bl, what matters is stated to be electrical power in versus sound power out. Keele used Spice modeling to explore this and the analysis shows that the potential efficiency of high Bl drivers has been substantially underestimated; strongly reinforcing the usefulness of what is effectively a new class of more powerfully augmented, ­electronically boosted low‐frequency alignments. 7.2.11  Power Dissipation (LF) Motor‐coil diameters is roughly associated with cone size and power rating, with 20 to 25 mm coils the rule for small 100 to 170 mm chassis drivers; 25 to 37 mm coils in 200 and 250 mm units and 44 to 100 mm diameters for 250 to 380 mm units. There is

Moving‐Coil Direct‐Radiator Drivers

no particular advantage for large diameter voice coils, except perhaps the argument that a large voice coil on a small cone means that no part of the cone is far from the driving point, which is likely to result in a stiffer structure, unlikely to break up until a higher frequency range is reached. In addition large 75 to 100 mm coils can dissipate up to 200 W and more of continuous thermal power if constructed of suitable high temperature formers such as aluminium foil or selected synthetics, and utilizing matching heat‐cured adhesives. Since most direct radiator loudspeakers are at best only a few percent efficient, the bulk of the input power is dissipated as heat in the motor coil, then conducted by the air gap to the magnet and frame. Surprisingly high‐coil temperatures (up to 200°C) may occur under heavy drive, and even with models designed for domestic use, some manufacturers aim at surviving short‐term temperatures of the order of 250°C. Several factors must be taken into consideration when temperature rises of this magnitude are to be accommodated. The increase in DC resistance is appreciable and will provide some degree of self‐limiting concerning the maximum power drawn from a given source. It will also add a degree of slow time constant compression in the working band, depending on the motor coil. Such compression may unbalance the frequency characteristic of the system. Note that some earlier magnet alloys may begin to demagnetize at higher temperatures, for example, above 120°C. 7.2.12 Compression King describes an example of a 305 mm driver equipped with a 75 mm coil and designed for use with an electric guitar.[7] The coil reached a steady 270°C after four hours running at a voltage level equivalent to 200 W into 6Ω, the latter value the driver’s nominal ‘cold’ specification. The ‘hot’, on‐load impedance was found to be double (note that copper’s resistivity rises by 0.35% per degree centigrade), indicating that the driver was now drawing only 100 W from the source (V2/R) to maintain the elevated temperature. At this power and temperature then was an attendant 3 dB of ‘compression’ a loss of sound level. Here the thermal time constant for the coil was 15 s, this the time for a rated 34% drop in resistance from a higher value. If this LF section was part of a two‐ or three‐way system or array, the frequency response would be flawed as the mid and treble ranges would now be 3 dB too loud, these unlikely to suffer thermal compression. Another example of a powerful bass driver rated at 300 W on music signals of medium term, was fed full power over a 50 Hz to 500 Hz bandwidth and resulted in 7 dB of compression within 25 seconds when using a standard 62 mm diameter coil. When rebuilt with a 100 mm coil, the compression improved to 4.4 dB. Adding a vented magnet gap construction further greatly lowered the coil temperature, here reducing the output loss to a modest 1.9 dB. Note that significant changes in coil resistance Re, from large temperature rises will also result in related errors arising for the designed, tuned LF alignment. Clearly operation which provides an average power much above 75 W would be inappropriate for the above driver example and highlights this often neglected problem which is encountered with high‐power units. There is an empirical 120 dB self‐limiting maximum sound level for a copper coil driver where increases in input power raises the coil temperature sufficiently for the increase in resistance to offset the power increase. The solution here is to use a new

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alloy which despite having lower conductivity than copper, of aluminium with a few percent of magnesium, has a lower thermal coefficient of resistance. This allows a new threshold of 123.3 dB or so to be attained. The best method for cooling a coil is via conduction to the magnet structure. This thermal mass benefits from a large area to dissipate heat. Heat transfer from the coil is aided by a narrow gap clearance, though difficult to achieve with LF drivers as the coil excursion is considerable. However, there are some ways round this particular problem. For example, the magnet gap may be designed longer than the coil so that the latter is always in close proximity to a large mass of metal. Alternatively, the coil may be wound on a large heat‐conducting former, such as anodized aluminium foil, and more recently titanium, helping to spread the heat over a larger area. Thirdly, the magnet/coil structure may be ventilated such that air is continuously pumped through the gap when the unit is under drive, thus providing forced cooling; this artifice is only effective at lower frequencies, for example, below 200 Hz where the cone excursion is appreciable. The magnet structure itself may be fitted with blackened radial fins on the exterior surface to aid heat dissipation. A further problem concerns the effect of conducted heat on the diaphragm. While the high temperature components of the motor‐coil may be designed to withstand the stress, 200°C and more short term, some thermoplastic cones readily soften at around 100°C and a hot coil former will quickly become de‐centred or even detached. Also pulp cones may begin to char at the neck and suffer from premature failure. A solution may be provided by the use of a non‐conducting coil‐former section adjacent to the cone, which isolates the hot section of the coil from the cone (Figure 7.7). Some premature failures had been noted with Nomex formers due to their hygroscopic nature. After a period of disuse, a Nomex‐equipped driver started up at high power may produce rapid moisture outgassing, usually resulting in structural distortion and even bubbles, and may lock the coil in the gap. Kapton, a high‐temperature plastic (also Kaneka Apical and some Far East alternatives), has been brought into use as an alternative despite significant adhesive difficulties when bonding to cones. Hygroscopy is not a problem with these. Substitutes are also being introduced to supplement the Figure 7.7  Example of a high temperature working motor‐coil assembly. The coil is wound on alloy foil, bonded to a ventilated ‘Nomex’ former (high temperature polyamide). Heat‐cured adhesives are employed (Source: Courtesy KEF Audio).

Moving‐Coil Direct‐Radiator Drivers

preferred Kaptontm supply; Kaptontm polyimide film is effective to a high 400° ­centigrade. Suitable coil formers of aluminum and titanium are also found, sometimes slotted to lower the mass. Metal formers conduct heat to the joins for the suspension/spider and to the diaphragm and this needs consideration. 7.2.13 Ferrofluids A development now in common use is a gap retentive fluid which may be applied to the motor of moving‐coil drivers. It consists of a relatively stable, inert organic di‐ester base containing a colloidal, and hence a non‐settling dispersion of ferromagnetic material. The liquid is sufficiently magnetic to conveniently concentrate in the regions of greatest field strength, that is, the gap. It is thus self‐locating upon measured injection into the gap, on either side of the voice coil. It may be obtained in a range of viscosities from 3000 to 50 cp, centipoise, with 100 cp suggested as suitable for low‐frequency drivers to avoid over damping coil motion. Interesting performance gains may result from its application. For LF the primary benefit is greatly improved short‐term power dissipation for the motor‐coil, since the fluid exhibits good thermal conductivity, many times that of the air it replaces. While drivers in low power applications would derive little advantage from its use, the high‐power examples described could gain a short‐term power handling increase of up to three or four times. If additional damping is made a design feature, then the fluid can provide this through choice of a suitable viscosity. Finally, the fluid provides a lowered reluctance path in the coil gap which reduces magnetic fringing and may marginally increase efficiency, perhaps up to 0.75 dB, depending on the driver construction, and may even slightly reduce distortion. Precautions need to be taken with regard to the fluid pumping through the gap with deep excursions, and in some cases pooling outside it. By maintaining lower coil temperatures the fluid can dramatically reduce the short term power compression effect noted earlier in connection with temperature rises. For higher frequency units, some extra centering force may also provided by the tendency for the fluid to try to form a uniform layer around the pole. This may help avoid the need for additional centering, for example, that second suspension or may obviate the rear suspension altogether in a particular low mass mid‐range diaphragm assembly. However, with heavier excursions and higher velocity, the fluid may not flow evenly, resulting in an asymmetric distribution which may impede coil motion and impair excursion linearity. Another consideration is the potential catastrophic failure, the decomposition or evaporation of this hydrocarbon based fluid when overheated. In one investigation,[8] the temperature of a bass driver fitted with a 25 mm motor coil of four layers and with a 20 W input at 25°C, was noted at 185°C after two minutes, a rise of 160°C. Then 0.6 cm3 of Ferrofluid of 2000 cp viscosity, was injected into the gap. Over the same period the temperature now reached 80°C, a rise of 55°C, one‐third that of the untreated gap. The gap intensity was 20 Tm. Where the Ferrofluid viscosity is used to provide additional resistive mechanical damping a potential variation of viscosity with temperature should be borne in mind. It  was noted that for one Ferrofluid damped HF driver, of small thermal capacity, its transient response varied markedly with level. At 0.1 W it operated as designed, but at 3 to 10 W input the motional damping fell off considerably due to the loss in viscosity. Certain Ferrofluid grades have also proved incompatible with some motor‐coil

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adhesives, and also some coil formers can soak up fluid. Finally, the fluid flow under large excursion can result in a back pressure buildup behind the coil, necessitating a rear vent in the magnet, particularly for low frequency units. The fluid medium itself has a long but finite life, which may be 5 to 15 years depending on the materials used for gap and voice coil, the working duty cycle and thermal history for the driver and environmental conditions, including humidity. As it degrades there may be some deterioration, partial loss or evaporation, where some clumping of the magnetic particles may result, altering the performance of the driver. Note that these very fine particles rely on Brownian motion to remain uniformly in suspension. For costly designs the driver gaps may be cleaned out and the fluid recharged in order to extend the service life of the system. For less costly models the driver may be unrepairable and the speaker system will need modification or scrapping. Insidiously the fluid may slowly deteriorate after a period of years, almost unnoticed, until a significant loss in performance is noticed, such as a quieter and thinner sounding treble range. On this basis designers might consider avoiding magnetic fluid and, for that matter, polyurethane foam surrounds as well, the latter frequently degrading totally after a ­decade or less. By contrast many previous generations of loudspeakers built with more conventional materials have been known to operate satisfactorily for several decades, if not more than half a century. 7.2.14  Winding Techniques (LF) Coils may be wound with a variety of conductors, but the most common is enameled copper, with silver used very occasionally for HF units. Anodized aluminium is also used, more especially in HF units where the reduced coil mass and inductance (its higher resistivity results in fewer turns) is beneficial to response extension and to some degree, sensitivity. CCAW is a copper clad aluminum variant to aid soldering the terminations. Ideally, the bulk of the coil should fill the gap to provide maximum utilization of the available magnetic flux. In practice, a clearance must be provided to prevent rubbing as the coil moves, and to allow for changes in the coil‐former profile with age, thermal stress and suspension creep. A further loss occurs due to the wasted space in the winding and the thickness of the former on which it is wound. If a rectangular or even ribbon cross‐section wire is employed, then the space utilization factor may be improved, with a resulting 15% to 20% increase in efficiency. The cost of these flat wire, ‘edge wound’ coils is high and the technique is generally uneconomic except for a few expensive and high performance designs. Alternatively, the wire may be partially deformed either before or after winding to partially ‘square’ the profile and hence reduce the small but inevitably lossy air space (Figure 7.8). At present, the vast majority of motor coils are wound in insulated copper which may also be pre‐coated with a thermosetting adhesive to aid bonding after winding. Most coils are also heat cured after bonding to bake out any solvents or moisture which might cause bubbling or mechanical distortion in service. Most voice coils are two‐layer, though four is quite common and six have been used in some short‐coil, long‐throw LF drivers. The main consideration is mass. If wound in four layers, the long coils required for sealed‐box systems will be sufficiently heavy to curtail the response in the mid‐band to possibly 2 kHz or less, and may also undesirably

Moving‐Coil Direct‐Radiator Drivers

Figure 7.8  Edge wound motor‐coil using ribbon conductors (Source: Courtesy Bose).

increase the mechanical coil mass/cone resonance. In addition, multi‐layer coils have a higher inductance, which further curtails the response, though for LF units this can be an advantage. With the principle dating back over half a century, dual, separated voice coils, wound on one former, have been investigated afresh.[9] Interesting findings show that in ­combination with modern Neodymium magnet designs higher efficiency and greater maximum spl is possible with this type. The efficiency gain is small but real, despite the use of two air gaps in the primary magnetic circuit (Figure 7.9). One benefit is a doubling of emissive surface area for the coil, providing 3 dB more temperature‐limited maximum power. Even better, the upper and lower coils are wound in opposite directions as the upper and lower gap polarizations are also opposite. This has the effect of greatly reducing the self‐inductance of the coil, extending bandwidth and efficiency. Such improvements, combined with flux modulation suppression and peak excursion velocity braking rings, led to an improved generation of JBL sound distribution loudspeakers. 7.2.15  Linearity and Magnets (LF) At low frequencies, for example, below 150 Hz, distortion is primarily a function of acoustic loading and available linear excursion, both mechanical and magnetic. In the mid‐band other factors also assume importance, for example, eddy currents in the poles. Lamination of the pole faces, or the use of a special material of high permeability and low electrical conductivity around the gap, will help control eddy effects. For a typical driver run at average power this may reduce the typical distortion in the 200 Hz to 1 kHz band from 1% or 2% to below 0.25%. This may be audible as improved mid‐range transparency since these distortion products reach beyond the crossover point and will lie in the mid‐range octaves set above the low frequency range. Magnet poles are often operated in saturation since this gives good control of magnet strength variations in production, but by definition, it is also wasteful of flux. Saturation places a limit on the maximum flux density in the gap. The usual mild steel pole and top plate allows maximum values around 1.4 T for a 25 mm pole and 1.7 T for a 50 mm pole.

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Figure 7.9  Dual‐coil motor with neodymium alloy magnet (after Button).

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Steel cylinder

Steel

The incorporation of a higher saturation material for the pole faces such as costly Permendur or alternatively laminated Permalloy, will allow a further gap flux increase, in some cases up to 20 T. Using a costly cobalt steel alloy with a 6.25 mm top plate, a gap flux density of 2.5 T has been obtained. Gap flux values are usually lower than the saturation value for the pole due to flux leakage saturating the base of the pole prematurely. Undercut ‘T’ section poles, used to improve flux linearity, also have the disadvantage of earlier saturation owing to the thinner ‘T’ section steel employed. As discussed in Section  3.8, other factors can help control linearity, including eddy current control rings, shorting out flux modulation. Alnico and neodymium magnets enjoy substantially less flux modulation distortion than ceramics, owing to their high electrical conductivity and much steeper B‐H curve, and this may also contribute to an overall performance gain including reduced third harmonic distortion. 7.2.16  Demagnetization (LF) While the choice of magnet material (Alnico, Alcomax, Magnadur, Ceramag, Neodymium alloys, etc.) is usually dictated by cost for a given pole structure, one point also deserves mention. If a permanent magnet is strongly stressed, either mechanically or magnetically, it tends to lose some magnetic strength. While ceramic and neodymium types are exceedingly difficult to demagnetize, older iron alloy‐based materials are less so. Drivers employing the latter type of magnet may be unsuited to high‐power applications where the peak coil flux is considerable. King cites the example of a bass driver fitted with a long four‐layer coil 37 mm diameter, with an Alnico cup magnet. Twenty‐five watts of drive at 50 Hz resulted in a permanent 2 dB mid‐band efficiency drop. This worst‐case demagnetization effect occurred when driven in the frequency range of greatest excursion, that is, fundamental resonance, particularly evident for  long multi‐layer coils. A two‐layer coil under the same conditions gave only a 0.5 dB loss.[10]

Moving‐Coil Direct‐Radiator Drivers

Neodymium alloy magnets are very resistant to demagnetisation but some of these alloys have quite low Curie points, that is, where self‐demagnetization begins to occur, for example, 140°C or even less. Exceed this thermal limit under a power handling test, and there will be some permanent loss of magnetization and thus of sensitivity. 7.2.17  The Dust or Centre Cap (LF) The dust cap may influence the performance of LF units, though its effects are usually more noticeable at mid frequencies. Functionally it prevents the ingress of dust to the magnet gap and if porous may allow the differential air pressure at the pole to equalize that in front of the diaphragm. This behavior depends on other aspects such as pole venting. Conventional caps are made from treated fabric and may contribute little to the acoustic output. However, a few diaphragms are fitted with rigid caps of pulp/paper or aluminium. A small ventilation hole may be present at the apex. The function of a rigid cap is twofold. The dome structure may be an additional radiating element to extend the frequency range; it may also serve as a stiffening structure helping to reduce cone break up, particularly of those modes which tend to distort the motor coil from a circular to an elliptical shape: this unwanted behaviour has been observed for some powerful sub‐ woofer drivers. In one recent design of LF‐MF driver, here using a formed thermoplastic diaphragm, the usual moulded apex, normally removed from the cone, is intentionally left intact. Here formed with a ledge it provides a rigid foundation for the attachment of the motor‐coil former. This type of construction also seals the magnet gap, and helps to stiffen the cone apex. 7.2.18  Mass Control Ring (LF) Occasionally reference may be found to a mass control ring on an LF driver. This usually comprises a rigid metal ring attached to the diaphragm at the apex which can be used to improve the performance of certain drivers. Suppose an ideal cone for a given design of driver is too light for its required purpose, for example, a wide‐range, low‐resonance application, and mass needs to be added. Increasing the cone mass by simply substituting a thicker material will alter its acoustic properties. Instead, mass is added as a ring weight at the neck. Additionally, the ring may provide some stiffening and in one example, the ring mass is attached via a compliant adhesive and the resulting critical damping is used to control a dominant concentric mode resonance (see Figure 7.3). 7.2.19  Chassis (LF) With motor‐coil/magnet gap clearances of the order of 10 µm, and large LF driver magnets up to 10 kg in weight, a rigid and stable chassis or ‘basket’ is essential both for long‐term stability, and to prevent misalignment due to transport. If properly deployed, both die‐cast alloy and pressed steel are suitable materials for chassis construction. The designer must find a compromise between the maximum window area for the frame webs and the quantity of material needed to provide the required structural strength. Too much material results in reflective cavities behind the cone which may colour the output in the upper range, too little will encourage chassis flexure. Long, thin‐walled

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chassis sections are obviously weak structures and may resonate, in some cases ameliorated with counter layer damping pads. Many units have suffered from such secondary resonances both pressed steel and polymer chassis, usually in the 200 to 500‐Hz range. The magnet mass may resonate with the web elasticity; with such a driver better results have been produced when the matching enclosure is fitted with internal bracing to ­reinforce the driver chassis. The chassis may have a subtle effect on a driver. In one inexpensive system using an established 200 mm pressed‐steel frame, some audible colouration and minor response irregularity was experienced in the 800 Hz to 2 kHz range. Flexure of the front mounting flange was detected and substitution of a new frame with a deeper rolled‐over front flange was found to solve this problem. If the application can justify the expense, then well‐designed die‐cast frames provide the best solution, with better build tolerances, lower colouration, and over longer production runs are usually more economic.

7.3 ­LF/MF Units The majorities of smaller loudspeaker systems today are two‐way, and incorporate a combined bass/mid‐range driver plus a high‐frequency unit: with a crossover point at between 2 and 4 kHz. The main driver must satisfy two possibly conflicting requirements, namely a clean, wide directivity and uniform mid‐band, plus a low distortion bass with adequate power capacity. Only in exceptional cases such as the 305 mm ­polypropylene co‐polymer driver mentioned earlier, can the larger LF units offer good performance in the crucial mid‐band. Even in this instance there is still an inevitable sacrifice in terms of narrowed directivity near the crossover point (approximately 1.7 kHz). The almost universal choice of chassis diameter for a wide‐range driver is 120 to 180 mm. Such a unit offers a unique combination of virtues, which accounts for its wide popularity for medium level domestic applications. If well designed, the bass power is sufficient for most domestic purposes, and an adequate bass output can be achieved in an acceptably small enclosure (8 to 25 litres). The frequency response and directivity may be satisfactorily maintained up to a practical crossover point, typically 2–3 kHz. The sensitivity and power handling are both sufficient for quite demanding use without excessive expenditure on the magnet structure. With careful control of the important design factors, a genuinely good performance may be attained. Active ­systems with synthesized higher order alignments and controlled power limits can be surprisingly capable. 7.3.1  Diaphragms (LF/MF) The extension of the low‐frequency range upwards to meet an HF unit requires that the diaphragm, usually polymer or pulp based, be particularly well controlled and consistent, since it will almost generally be operating in break‐up at the higher working ­frequencies. To attain a satisfactory performance, consistent, uniformly isotropic cone materials are essential. A few exceptions, for example, pistonic types will include very stiff metal foils and composites. Drivers for LF/MF duty range in size from 80 mm to 250 mm although the LF power handling is obviously much reduced with the smaller diaphragms. Many mid‐range

Moving‐Coil Direct‐Radiator Drivers

drivers are in fact often designed to fulfill two purposes: to act either as a true mid‐ range unit in the more elaborate designs, or as a bass/mid unit in the simpler systems. Similarly the larger, wide‐range units (200 mm and above) may also be employed in some more sophisticated systems, even if only for LF duty, where their inherent lower colouration characteristics may still be beneficial to the sound quality of the system as a whole. 7.3.2  Metal Cones Metal cones have been in production for more than half a century and have been used in the UK since 1955 (GEC). Their advantages include durability, resistance to adverse environmental conditions, for example, humidity and temperature, and the exploitation of their inherent stiffness in order to widen the pistonic range of operation. Light metal, or metal alloys of aluminium and magnesium, are substantially stiffer than the usual pulp or plastic material: between 10 and 20 times stiffer. Such greater stiffness places the first bending‐mode resonance of a typical cone profile to between 4 kHz and 8 kHz depending on diameter and material thickness, as compared with the usual break‐up ­frequency, which can be as low as 600 Hz. The bending frequency is essentially proportional to the square root of stiffness, so substantial increases in stiffness are necessary to make a significant further improvement. Working in the mid‐1960s, Jordan extensively researched the design of a full‐ range 170 mm frame driver employing a strongly flared aluminium alloy cone with a nominal range of 50 Hz to 15 kHz. It had heavily resistive edge termination while a large metal dome at the centre dominated the high‐frequency response. Many successful moderate price systems were marketed using this driver—with the sound quality benefiting from the absence of any crossover network. This helped to make up for the somewhat imperfect frequency response and narrowing directivity. Metal cone drivers became popular again in the 1980s and designers had to relearn how to build them. Typically, these later cones are straight sided, of thickness 0.2 to 0.3 mm, formed by drawing or spinning, and are often deeply anodized to form a so‐called ‘ceramic’ (alumina) stiffening layer on each side of the cone. Recently, flared curvatures have been reintroduced which may partially ameliorate the inevitable and severe upper range resonances. Thin shell cones have also been successfully produced by die casting in magnesium alloy. For a 90 mm diameter cone in a 115 mm chassis the cone mass is typically 3–5 g. In the 140 mm cone size for a 160 to 170 mm chassis, it may weigh between 6 g and 12 g. Sensitivity is generally lower by 2 to 3 dB than for pulp or polymer cone equivalents due to the higher mass. LF and MF drivers are now produced where the aluminium diaphragm is almost wholly reduced to the ‘ceramic’ oxide. An 80 mm diameter concave radiator of this type, driven on the first nodal circle remains ‘pistonic’ up to 12 kHz. A similar unit, at 25 mm, is pistonic to 35 kHz. (Thiele Accuton). Characteristically, save radiation size issues, the frequency response remains uniform until the break‐up region is approached. Just prior to resonance there is a dip in output (as with metal dome tweeters). When break up occurs, it can be severe, peaking at 10 dB or 15 dB and may be followed by further ­integer related modes. For a good quality, 110 mm frame, alloy pistonic unit, the break up may occur in the range 6 to 9 kHz, while for a 170 mm framed unit it is typically 5 kHz. Figure 7.10 shows

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Figure 7.10  Comparison of straight‐sided and flared profiles metal cones. Key: ____straight sided cone profile, 170 mm driver, aluminium alloy cone, …… flared alternative (‐‐‐‐‐ near‐field correction).

the improved control of resonance in a well‐behaved metal cone driver when a flared profile is substituted for a straight‐sided form. For severe peaks above the crossover point a parallel trap filter may be added to the network, thus providing better control over the overall axial response (see Figure 8.33b). However, the mode may still be acoustically excited by the nearby output from a wide directivity HF unit. Even with the trap filter the mode may remain subtly audible, here as a loss in HF purity and transparency (if evident in the decay response), often only identified when the issue is fully resolved Nevertheless large commercial quantities of loudspeakers with alloy cones have been sold without significant criticism from the purchasers. 7.3.3  Suspension and Surrounds (LF/MF) Little needs to be said about these two components except that the suspension is generally less influential in the mid‐range as it largely decouples from the moving assembly, while the surround and its terminating impedance becomes more critical as the cone enters its resonant range with bending waves traveling to the edge benefiting from matched termination. 7.3.4  Motor Coil (LF/MF) Whereas a large and heavy coil may be a necessary requirement for an LF unit, a satisfactory extension of response to cover the mid‐range may dictate a compromise whereby the coil is reduced in both mass and inductance. Where this is impossible to effect, in order to maintain adequate LF performance, the costlier solution of a short, light coil immersed in a deep magnet gap can be adopted for good low frequency coil excursion.

Moving‐Coil Direct‐Radiator Drivers

7.4 ­MF, Mid‐Frequency Units True mid‐frequency units are characterized by a relatively high fundamental resonance, 100 to 500 Hz, but ideally set at about 200 Hz, to help resist local acoustic pressure from the low frequency section; this compares to the LF driver natural resonance region of 15 to 60 Hz. The required mid excursion is small, and hence the motor coil and magnet may be optimized for maximum efficiency and linearity. Both dome and cone diaphragms are in common use, the former generally restricted to the upper frequency range (600 Hz to 6 kHz), while the latter may operate from 250 Hz to 5 kHz. These smaller diaphragms are generally less than 160 mm in diameter and typically range from 60 mm to 100 mm. Note that dome units smaller than 44 mm are more correctly classed as ‘lower treble’ drivers rather than mid‐range. The mid‐range, typically given as 250 Hz to 5 kHz, is undoubtedly the most critical from a subjective sound quality viewpoint. This is the region where the ear’s sensitivity and analytical ability are most acute, and it additionally includes the greatest concentration of information in normal programme material. Many brave attempts to produce a high‐performance system have been unsuccessful because the designer has failed to adequately appreciate these facts. Critical listeners may tolerate moderate problems in the LF or HF bands but cannot ignore significant inaccuracies in the mid‐range, whether they are in the form of spectral imbalances, response irregularities, distortion, colouration or any combination of these. For this reason, MF units must be designed with great care and deployed with considerable technical skill and subjective judgment. It has been indicated in Section 6.1 for systems and crossovers that a reasonable response extension beyond the nominal −3  dB band‐pass is desirable to help maintain smooth crossover transitions. Considering our ideal mid band‐pass of 250 Hz to 5 kHz, we should add an octave or more to either extreme, resulting in an ideal overall mid‐driver coverage of 125 Hz to 10 kHz. Where a high‐quality, but moderately sized LF unit is to be used in conjunction with a mid‐range driver, the high‐pass frequency may be lifted to the 600 Hz range or above, then making possible the use of a dome mid unit. There remains, however, some reservation concerning the placement of such a crossover point with its attendant polar and phase anomalies, since these occur in that aurally most sensitive range. An acoustically neutral, low diffraction test enclosure will prove helpful in the research and assessment of mid drivers whose performance may otherwise can get tangled up with the system and enclosure under development. Once the mid unit design has been properly validated then it may be incorporated in the overall project. 7.4.1  Diaphragm (MF) As has been suggested, dome units give their best results in the upper mid‐range while cone units favour the lower mid‐range frequencies. Figure  7.11 shows the theoretical effect of the front cavity of a pistonic cone compared with a planar disc diaphragm. The cone result is characteristic of the geometry. Both characteristics will also be modified by enclosure diffraction and the intrinsic behaviour of the diaphragm.

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0

–10

–20 200

500

1k

2

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Frequency (Hz)

Figure 7.11  Cone cavity acoustic and effect on frequency response compared with a piston.

Advanced composites are increasingly used for diaphragms, including tapered foamed acrylic cores and high tensile graphite fibre and even graphene reinforced skins. A combination of piston operation with better control of out of band resonances is sought. 7.4.2  Phase Plug It has been noted that higher in the working frequency range neither the acoustical behavior, nor mechanical matching at the apex of a cone diaphragm, is well defined. Various schemes have been devised by designers, including a hard centre cap, various sizes of semi‐soft dust caps, in PVC or a coated cloth. These are varied to try to improve the smoothness of the upper range frequency response. Also depending on price, these are variously successful (see Figure  7.12). Where an open pole is appropriate to the design, the cylindrical space to the motor‐coil former leading to the pole constitutes a resonant cavity. Use of an absorbent plug controls the cavity resonance at the expense of upper range output. An open construction is often chosen to avoid the secondary resonant modes present for many dust caps, but which aperture may also give rise to distortion at lower frequencies due to the high air velocity around the pole structure under high excursion conditions. The cavity effect may be controlled by the addition of a short ‘phase’ plug, fabricated or moulded in plastic or metal. This forms a short extension of the pole face, preferably tapered at the tip. The interfering cavity is thus removed, and the output may be noticeably smoother. 7.4.3  Domes (MF) Their use is fashionable at present, due to an illogical belief that a dome radiates sound over a wider angle than a cone of the same diameter. In fact, the converse may be true, since in the degenerate bending condition a dome approximates to an annular radiator, whereas the cone reduces to a point source, that is, that formed by the smaller apex area.

Moving‐Coil Direct‐Radiator Drivers 90

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60

50

40 10

(a) Unsealed dust cap (b) Sealed dust cap

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5k

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Figure 7.12a  1 m on‐axis response: (a) Open fabric dust cap. (b) (sealed dust cap) (after Speaker Builder).

The fact remains that dome units are popular among designers, and are also relatively easy to manufacture. Many models employ press‐formed resin reinforced fabric domes, impregnated with some suitable viscous damping material, usually synthetic rubber‐based. The combined suspension/surround is usually contiguous with the dome ­surface, with a small annular ledge for the direct attachment of the motor coil assembly. A dense felt plug is usually fitted just beneath the dome to absorb some of the rear radiated energy. Domes range in size from a nominal 37 mm up to 85 mm diameter, with a v­ ariety of surround and profile shapes. However, most approximate to a shallow, near‐spherical section. Dome structural rigidity is poor and most of the so‐called ‘soft’ domes are in fact in some form of break up from an octave or so above the fundamental resonance, which itself may range from 250 Hz to 500 Hz. The large applied damping component gives these drivers an almost resistance‐controlled acoustic characteristic with frequency, but due to the unavoidable hysteretic behaviour of the usually rubber‐based damping compounds, they may not sound as transparent as their smooth frequency characteristics might suggest. The better examples utilize a tougher diaphragm with less damping maintaining piston operation and clearer sound to higher frequencies. On occasion, dome mid‐unit designs may sound unexpectedly coloured. Two factors can be held responsible. The fundamental resonance frequency is both relatively high and often inadequately damped as the larger units require large and costly magnet ­systems for optimum motional resonance control. Poor crossover design may result in a further weakening of the available electrical damping control of the main resonance, this heard as colouration. Further, adequate acoustic absorption behind the dome is difficult to achieve in the small space and the reflections and resonances from behind the dome are often audible. For more costly units the centre pole may be bored out, ideally, tapered, to reduce self‐ resonance, then leading to a larger damped rear chamber or even a strongly damped

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Figure 7.12b  VIVID 50 mm mid‐ range dome assembly, line terminated covering 800Hz to 20 kHz. Crossover set at 5 kHz, for this computer modelled catenary dome profile powered by a radial Neodymium alloy magnet.

line. This rear bore may include an acoustic resistance to control pipe modes and/or the simple Helmholtz resonance which may be formed with the cavity under the dome. A complete contrast is presented by ‘rigid’ domes employing diaphragms of high strength‐to‐weight ratio, such as stiff card, titanium, beryllium, certain plastics and, more recently, boron‐coated metal. With these diaphragms the structure is designed to be so light and rigid that break up does not occur at all within the required band‐pass. The most spectacular of these designs are undoubtedly those formed in beryllium, which though difficult to manufacture, offer startling gains in rigidity versus mass.[10] The classic Yamaha 88 mm beryllium dome unit is an outstanding example of the art, and provides virtually pure piston operation from 400 Hz to nearly 12 kHz. This potentially results in great clarity, though when the diaphragm does enter break up it does so rather more aggressively than soft domes, owing to the intrinsically low internal damping of the diaphragm material. Laurence Dickie has enjoyed success with his designs for Vivid using an aluminium alloy dome with a long tapered line for rear ­termination (Figure 7.12(b)). Other promising constructions include fabric impregnated with cured phenolic resin, also Mylartm, the latter improved by lamination with another plastic such as PVC, which has a higher internal loss. Hard pulp/paper domes are also employed and have favourable properties suitable for wider use than found at present. As has been explained in Section 3.1 on dome diaphragms, the profile and size is largely dependent on the chosen material. The more rigid domes (metal or strong ­plastic) are often quite shallow in profile, whereas the softer examples need to use a steeper, more conical shape to maintain sufficient structural rigidity and hence extend the working frequency range. However, even with a ‘soft’ dome, the break‐up mode may be sufficiently severe to produce a response peak up to 6 dB high if the chosen profile is too steep. Heavy, well‐damped mid‐range domes may have a surprisingly restricted response, and one well‐known example which was widely employed in European designs ­possesses a gently falling characteristic above 3.5 kHz. Others, by fortuitous choice of profile and material, may extend to approximately10 kHz.

Moving‐Coil Direct‐Radiator Drivers

There is nevertheless one appealing characteristic possessed by good mid‐range dome units. Their sound may be free of the particular subjective ‘hardness’ or ‘shout’ shown to some degree by most cone based units and in this respect, domes bear comparison with the film‐type transducers such as the electrostatic. This characteristic largely accounts for the determined efforts on the part of many designers to incorporate such units into their system designs. 7.4.4  Cones (MF) A coned driver, if of moderate size, may be designed to cover the entire LF/MF range to a good standard. Such a unit may also prove a good choice for mid‐range use only. A  number of recent three‐way high‐performance systems have utilized mid‐range ­drivers which are also capable of bass reproduction in suitable enclosures. By definition, these units have a wide bandwidth, this being advantageous when selecting the optimum crossover point. Coned LF/MF drivers ranging in chassis size from 100 mm to 200 mm have been used, with a separate sub‐enclosure to isolate the driver from the in‐cabinet air pressure variation generated by the LF unit. Specialized mid units tend to be on the small side (typically 80 mm piston radius) since this provides sufficient output down to 250 Hz or so, and yet presents a small enough source for wide directivity over the higher frequency part of the range. They may be fitted with an integral enclosure or, more simply, supplied with a sealed chassis, the space behind the diaphragm fitted with suitable acoustic absorbent. A typical response curve can be quite uniform from 250 Hz to 6 kHz and with care the sound quality can be surprisingly high. The theory concerning controlled smooth transitions from one vibration mode to another is especially relevant in the case of mid‐range diaphragms, since they generally operate in piston mode in the lower range and then in controlled break up in the upper range. The broad region dividing the two generally appears between 1.5 kHz and 2.5 kHz. It is thus essential that the diaphragm be well terminated at its boundaries, that the shape and choice of material be conducive to good transient behaviour, so that the result is free of significant decay resonances. Shallow flared profiles have given quite good results especially with thermoplastic cones and absorptive suspensions. A structure popularized* by the British company of Bowers and Wilkins for the build of a mid‐range unit incorporates many of the above design principles. The cone is fairly rigid, formed from an open weave Kevlartm fibre impregnated with cured resins, which also serve to stiffen the structure. Controlled flexure over the weave area absorbs mode energy while the effect of the weave alignment promotes an optimised resonance distribution as the resulting mode shapes tend to become elliptical. The surround is carefully matched to provide terminating mechanical impedance. The residual ‘bell’ modes tend not to radiate. A more recent development with a new fibre and new weave geometry, silver coloured to aid differentiation, has been modeled for a more uniformly axi‐symmetric breakup where the source size coherently reduces with frequency to maintain better directivity and it exploits a composite construction (see Figure 7.13(a) and (b)). There is a final point worthy of consideration when choosing a cone material. For a practical driver there is often some maximum sound pressure level above which some audible deterioration in quality occurs. This effect cannot be ascribed to the magnet, suspension or crossover non‐linearity and is believed to result from a gross

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Figure 7.13a  B&W 800 series Rohacell core, woven composite midrange cone assembly.

Figure 7.13b  B&W mid driver overview, also note large number of fixing points to improve the coupling to the enclosure.

compression at the neck of the cone due to the applied force exceeding the elastic limit of the material. Operation in such regions means that the material fails to return on its original dimensions for some time (ranging from milliseconds to hours), and the ­resulting distortion, being of the hysteresis type, is unpleasant, sometimes called cone ‘shout’. It appears that some polymers suffer from this effect more than others, and it may well be an important consideration if high sound pressure levels are required. Experimentation is continuing with the design of metal cones. Good results have been achieved with a 110 mm LF‐MF unit with an anodized, spun aluminium alloy cone. The first break up may be deferred to 12 kHz; the diaphragm mass is quite low at 4 g. In another example a 170 mm cone has been pressed out of ductile sheet between two formers. This larger form shows a lower first ‘break’ at 6 kHz. For one exotic and costly example a partially ribbed (on the rear surface) aluminum cone is painstakingly milled from a solid billet. The main reason for continued perseverance with metal lies in the particular clarity of the reproduced sound. Subjectively, this does complement the fine quality of piston operation HF units rather better that the usual pulp or soft polymer cones. However, advanced composites are displacing metal in many more costly applications. As discussed, non‐piston diaphragms generally possess controlled break‐up modes in their

Moving‐Coil Direct‐Radiator Drivers

30

20

10 10° Cone angle Flat cone

dB 0

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Figure 7.13c  FEA modelling of an aluminium diaphragm, 0.2 mm thick as a flat disc (dashed line), formed up into a shallow cone 160 degrees included angle (solid line).

working range and may add non‐musical sounds which are often recognizably ­characteristic of the particular material employed. Working with the FineCone, loudspeaker directed FEA software; Larsen illustrates some pertinent points of cone design. For example, starting with a flat disc of aluminium of normal ‘cone’ thickness, for example, 0.2 mm, the computation shows the first concentric ring resonance at just 100 Hz. The axial frequency and power response then falls with increasing frequency from a reference 88 dB to just 65 dB by 10 kHz. For this 150 mm disc, dishing it to a comparatively shallow angle of 10 degrees has the well known but still dramatic effect of radically increasing the geometric bending stiffness. First resonance is now deferred until 1.8 kHz, four octaves higher, and the response is flat to beyond 1 kHz. Increasing the cone angle to normal values typically moves the first peak to 4 or 5 kHz, with a desirably smooth response now obtained through the usual 2.5 to 3.5 kHz crossover range. Many cone shapes and materials may now be ­modeled, including the complex mechanical impedance of the connected surround (Figure 7.13(c)). 7.4.5  Suspensions (MF) The suspension is usually integral with the diaphragm for dome mid units, effectively a doped, half‐roll surround is formed at the perimeter. Rocking is one unwanted mode of vibration which may be troublesome with single suspension designs where axial balancing may be difficult to achieve. Soft‐dome assemblies are noted for this defect which may promote sub‐harmonics and an increase in intermodulation distortion. The balancing of the assembly in respect of its axis, plus the shape and related physical constraints offered by the surround are critical factors here. In the case of cone diaphragms, suspensions are usually manufactured from corrugated fabric, but due regard must be paid to their geometry and possibility of self‐resonance, which may be measurable and audible through the mid‐range. One obvious solution to rocking is the adoption of a spaced double suspension. However, two even moderately spaced suspensions take up  considerable depth and necessitate a longer motor‐coil former, which may be

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Figure 7.14  50 mm diameter double‐suspension, fabric dome mid‐range unit (ATC).

disadvantageous in a dome radiator, the higher mass reducing sensitivity. The resulting assembly is also more difficult to produce and is generally restricted to the more ­expensive designs such as the unit illustrated in Figure 7.14. Ferrofluid may be added to the  magnet gap, providing an additional centering contribution and also helping to ­suppress the rocking mode. 7.4.6  Surround (MF) The choice of a surround material presents a considerable problem for the designer of a driver covering both mid and higher frequencies. The commonly used materials— Neoprene, PVC, and so on—have complex mechanical properties that vary greatly with frequency. Ideally, their energy absorption, damping property should be resistive and constant with frequency, but invariably elastic, rubber‐type materials are hysteretic to some degree, and show a memory effect, that is, a time lag exists between deformation and subsequent recovery. Consequently, these materials stiffen greatly and become less absorptive with increasing frequency. To date a lightly impregnated grade of foamed plastic has proved successful for the higher frequencies. Since relatively little excursion is required of a mid‐range unit the surround profile may also be a simple flat strip, no half‐roll or similar device being strictly necessary, provided that self‐resonance is inhibited though the choice of material and geometry. 7.4.7  Motor Systems (MF) The magnet structures of cone and dome mid units present a great contrast in terms of their size; whereas a scaled‐down assembly of typically down to 19 mm diameter is ­sufficient for the cone, the dome requires a massive structure energizing a 50 mm or even larger pole. Ideally, the magnet diameter for a mid‐range cone should be small, so that the minimum of reflecting surface is present immediately behind the cone. This suggests the use of a cylindrical Alnico or neodymium magnet rather than the much larger ceramic ‘­pancake’ type. Too many mid‐units have inadequate acoustic clearance behind the

Moving‐Coil Direct‐Radiator Drivers

­ iaphragm, and the resulting reflections and cavity effects from frame and magnet may d be found in the decay responses and are often audible. There is scope for improvement with larger voice coils, where shallow highly reinforced composite diaphragms, carbon fibre of ceramic or even pure diamond made by plasma deposition are ideally driven at or near the first nodal locus. Thereby the next active mode is placed well beyond the working band‐pass. Compact neodymium motors are most useful helping to keep the assembly acoustically open at the back. The use of Ferrofluid may prove advantageous where the short‐term power input is high and the cone excursion small. Large increases in power handling are possible with its use, up to two or three times in the short term. Where very low distortion levels are required, secondary harmonic sources such as eddy currents in the poles must be controlled. Suitable remedies include copper plating, lamination of the pole structures or the use of a high‐resistivity magnetic material for the poles themselves. Again, the use of Ferrofluid may offer some reduction in distortion. The choice of a Neodymium magnet may lower distortion, thanks to its electrical conductivity suppressing eddy currents induced by coil current and coil motion. The need for predictable and controlled break‐up modes from mid‐range diaphragm assemblies means that the location and method of attaching the lead out wires to the motor coil must be carefully considered. Ideally the connection exits should be symmetrical, and preferably at the motor‐coil former rather than haphazardly stuck to the cone, perhaps to one side, as is frequently the case. The local mass offset resulting from the latter practice can promote asymmetrical break up and other odd modes, especially at higher frequencies, though these are not always as audible or significant as they appear on a response graph.

7.5 ­High‐Frequency Units The general classification for HF units embraces a 1.5 to 50 kHz bandwidth, thus ideally overlapping the upper mid‐band by an octave or so. Overall it spans six octaves, which is almost impossible for a single unit to achieve satisfactorily, and hence this is loosely split into three: low range (1 to 10 kHz), full range (3 to 25 kHz) and high range or ‘super tweeter’ running up to 50 kHz, typically from 7 kHz. Conventional cone diaphragms are rarely used in high‐performance systems for this frequency band as operation would very likely be in the break‐up region, where the output is falling and is generally both irregular and unpredictable. Nevertheless, some smaller 15 mm cone/dome hybrid forms have enjoyed success in the lower‐cost sector and have satisfactory frequency responses. In addition, some experienced designers have built commercially successful cone drivers for HF application, if with acknowledged limitations. Two issues arise concerning extending the upper response, one the relatively small subjective improvement obtained, often at considerable cost, which may be provided by well‐behaved response extension beyond say 16 kHz. Note that many highly regarded BBC speaker designs stopped at 14 kHz for example, with little negative comment. However recent research has shown that while few listeners hear discrete information beyond 15 kHz or 20 kHz concerning continuous tones, the perception of transient

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waveforms included the equivalent of a 50 kHz bandwidth, even in the face of environmental and age related losses. A designer needs to continue to make rational decisions on bandwidth based on a system performance, matched to application, size and price. That extra 10 kHz of extension beyond 15 kHz, usually of increasingly narrow directivity, and subject to production variability, needs careful consideration, especially for cost/benefit. 7.5.1  Dome Diaphragms (HF) Domes are undoubtedly the most common HF diaphragm form and are available in a wide variety of shapes, sizes and materials. Additionally, the chassis and mounting plate structure may be contoured, acoustically tailored, to provide some equalization for both polar and/or axial response characteristics and may include integral waveguides. The 25 mm doped, soft fabric dome first became popular in Europe (Philips) after that first technology introduction in the USA, and its use has since spread throughout the world, with more than 30 types frequently available from various manufacturers (Figure 7.15(a) and (c)). Soft dome HF units are also produced in the 34 mm and 19 mm sizes. (See also the related ring radiator Figure 7.15(b).) Plastics are also widely used for the production of dome diaphragms, notably polyester, often in a laminated form bonded with a PVC or similar damping layer. Sizes 19 mm, Figure 7.15a  A chamber loaded, wide range, fabric dome HF unit, nominally 28 mm diaphragm (Morel).

Figure 7.15b  An advanced 28 mm ‘ring radiator, a doped silk dome with a central clamp; behaviour is more bending/rolling than pistonic and may extend to 70 kHz on axis. (DST‐Scan).

Moving‐Coil Direct‐Radiator Drivers

Figure 7.15c  An exploded view of a modern soft dome HF unit (Wharfedale) showing self‐centering construction components and the eddy current suppressing copper ring to the rear of the assembly.

Figure 7.16  25 mm rigid‐dome treble unit; f = 20 kHz, showing the surround in anti‐phase (after Bank and Hathaway).

25 mm and 38 mm are all available with lower fundamental resonant frequencies, ­ranging from 600 Hz to 2 kHz, and upper cut‐off frequencies from 15 kHz up to 35 kHz. Yamaha designed at an early stage, mid‐1970s, a very costly deposited beryllium foil HF unit of 30 mm nominal diameter, whose first break‐up mode is beyond 40 kHz, ensuring piston operation over the entire 2 to 18 kHz usable range. The diaphragm thickness was 30 µm with a mass of 30 mg which compared with a soft dome counterpart at 100 mg and of similar thickness. The rigidity of beryllium is generally too high to employ an integral suspension and instead a separate, tangentially pleated cloth surround is used, with a damping coating composed of two resin types to help dissipate energy at the rim. However, for this design as for many others, the surround necessarily forms a significant part of the radiating area, perturbing the upper range output (see Figure 7.16, surround moving in anti‐phase at 20 kHz). In the case of a 37 mm dome driver (Celestion), particular care was taken to minimize the surround contribution. In this unit, the diaphragm was electroformed in pure copper and the structure continued to a cylindrical section to provide an integral coil former. This one‐piece construction has the advantage of allowing the whole dome to act as a heat dissipator, and a short‐term rating of 50 W was quoted. This design also

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exhibited a very low sensitivity of typically 82 dB/W due to circulating eddy currents in the construction and to high mass. Even with a material as unfavourable as copper (­chosen mainly for its good electroforming properties) the final break‐up mode is held to just above 20 kHz. However, the breakup frequency was rather close to the 19 kHz low‐level pilot tone for FM stereo multiplex. The dome Q is rather high, between 20 and 40 and could amplify the pilot, and in the commercial system, a costly notch filter, with a resulting punishing impedance dip, had to be fitted to the crossover network. From the available materials (Table 7.2), it can be seen that amongst the more common metals of useful thermal conductivity, aluminium is technically a rather better contender than copper, and so it has proved. A one‐piece diaphragm can be economically produced by precision deep drawing once the tool has been made. Hard anodizing provides a final improvement, a good finish and an electrically insulating surface. Still deeper anodizing provides further reinforcement. In recent years, metal dome high‐frequency units have become increasingly popular, with the 25 mm size as the norm. The 32 mm and 19 mm types are also in production, but the larger sizes are quite expensive. Sensitivities of 88 to 90 dB/W are typical for an ‘4 to 8Ω’ unit. The dome is generally of hard anodized aluminium alloy foil, often with 5% magnesium content, while pure titanium is also a popular choice. For the 25 mm size a first resonance in the 22 to 27 kHz range is typical, peaking by some 10 to 25 dB. This first mode frequency is partly dependant on the stiffness seen at the rim, and the quality of bonding to the suspension and coil former in this area, rather than the expected ‘oil can’ ‘reflex mode’ for the dome centre. With such a high resonant Q, the main peak is frequently preceded by a dip of 4 to 6 dB in the 18 to 22 kHz range making it difficult to deliver a flat response to a specified nominal 20 kHz. In any case the natural high frequency response of a dome unit is decrementing in the piston range (Figure 7.17(a) and Figure 3.2). The high Q factor for a plain alloy dome resonance, where some examples peak by 25 dB, implies high amplitude vibration, susceptible to excitation from 20 kHz bandwidth material. Distortion and ultrasonic tones may be present with harmonics in this dB 10 0 –10

–20 20

Hz

100

1k

10 k 20 k

Figure 7.17a  Natural response of a metal dome (25 mm); note the inherent acoustical downwards drift, and the in‐band dip preceding the normally ultrasonic, high Q resonance. The dotted response shown may be obtained by including the contribution from the surround–suspension annulus and/or by the use of a correcting ‘phase plate’ or a small reflector placed in proximity to the dome apex. These devices may become audible from further irregularities in the off axis response.

Moving‐Coil Direct‐Radiator Drivers

high range, and particularly from the wider bandwidth programme now becoming available. At high input powers with complex program excitation the cap resonance may give rise to intermodulation distortion, where the difference products may then lie in the readily audible range below 20 kHz. In this connection this author had noted a mild ‘tizzy’ sounding artefacts from a given HF unit in series production which at the time were considered to be inherent in the programme but which were than found absent subjectively when a speaker was installed of flat response but with a first ­resonance an octave higher. During the 1980s the pursuit of linear phase saw greater interest, and systems with time alignment for the drivers became popular, such as the KEF R105, also pure planar, aligned piston examples from Pioneer, Sony and Technics (the latter Reference Monitor pictured on the cover of the third edition). Sony’s series was called APM and included a pure piston HF unit, essentially flat to 25 kHz, and employed a rectangular aluminium 30

Simulated acoustic frequency response

20 10 0 –10 –20 –30

30

Frequency (Hz)

10 000

20 000

100 000

Simulated acoustic frequency response

20 10 0 –10 –20 –30

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20 000

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Figure 7.17b  FEA for axial output from a 25 mm aluminium dome, upper graph, and for an equivalent of ion deposited crystal diamond, 50 μM thick (Source: Courtesy B&W).

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Figure 7.17c  Assembly components for a wide bandwidth diamond coated beryllium 25 mm driver, nominally 2 kHz to 45 kHz (Magico).

honeycomb diaphragm but with a 25 mm voice coil. Technics, 28 mm planar, circular HF unit (1985) had a distinctive B&K microphone grid pattern grille, also a honeycomb core diaphragm but here used carefully selected low loss reinforcing skins of mica. This driver was quite uniform in output to 40 kHz, with high frequency losses in the motor controlled by high magnetic pole saturation, driven by powerful samarium cobalt ­magnets. Extended high frequency bandwidth was attained here but at a price. This driver also appeared in a 200 mm coaxial design with a planar bass-mid, an alloy composite, the  latter driven on the nodal circle via a conical voice coil coupler located behind the HF unit. 7.5.2  Drive Units: Beryllium and Diamond (HF) The ultra‐light and stiff metal beryllium had been used by Yamaha in their 1970s generation of mid‐ and high‐frequency domes. The process, using vapour deposition in a vacuum, is an expensive one. There remain toxicity issues for manufacture. More recently, Brush Wellman of the United States have developed a method of forming the hitherto intractably rigid foil in alloy form, though the unit diaphragm cost is still 20 to 30 times that of an ordinary alloy aluminium dome. Effective Be–Al composite foils are also produced for audiophile grade bass and mid‐driver cones. For many years Focal have also produced a pure beryllium inverted diaphragm made from thin 25 micron industrial foil, here by high temperature thermo‐forming, and with positive air pressure protection for the operator. This application operates with the dome inverted and uses a drive coil close the nodal circle. As a matter of record, Be puts the first break up for a high‐frequency dome up to nearly 50 kHz, from typically 25 kHz

Moving‐Coil Direct‐Radiator Drivers

for aluminium this comparable with pure oxidized alumina ‘ceramic’. A 20 mm concave dome produced in vapour deposited diamond shows the highest first mode yet at about 70 kHz (Thiele‐Accuton, DE). B&W also run a long‐lived speaker series with a 25 mm profiled dome made in electro vapour‐deposited diamond, also with first bending at 70 kHz (Figure 5.17(b)). A piston dome of 25 mm will show an inherent fall in output by 20 kHz due to the size and geometry, but which has been considered inconsequential. Historically, when reports of the audible benefits of >20 kHz super‐tweeters have been checked by this author, leakage into the audible sub 20 kHz range has invariably been present under the test conditions. However recent investigations have suggested that fast transients, with effective bandwidth to 60 kHz, remain relevant to perception, and that it is the impulse rise time that matters, rather than the presence of steady state tones beyond 20 kHz. Thus, a greater than 20 kHz bandwidth may be worthwhile to preserve wave fronts, if the source material is available and the application warrants it. For domes in general, some degree of equalization is often required from the matching crossover network while the transducer designer might also resort to some acoustic tricks to level the axial response. Often, a central disc of 5 mm diameter can be used just in front of the dome to block/suppress the main peak and help fill in the preceding notch via this additional cavity resonance. Meanwhile the usual half‐roll surround, commonly of polyamide, may also be allowed, even encouraged, to act as a weak annular radiator at higher frequencies also helping to fill in the inherent dip. The latter artifice is fairly harmless, since pure piston operation is still available from this part over the fundamental 2 to 15 kHz range though now of a greater effective diameter. The use of ‘phase correcting’ discs or plates in front of the dome may induce cavity ringing effects which can be audible as a mild roughness, particularly off axis. The main virtue of a purely pistonic transducer is its clarity and harmonic purity, with an absence of the mild ‘tizz’ or ‘grain’ which is audible in the upper range of several types of soft dome driver. While a fabric dome often possesses a quite well‐damped fundamental resonance fo, thanks to applied tacky compounds, simple plastic domes may show quite a high Q, as much as 10 at the natural mass‐suspension frequency. Various means may be used to control the Q, ranging from applied damping layers and dope to acoustic anti‐resonant circuits formed by venting the rear cavity behind the dome into various resistively damped chambers formed in the magnet structure. In the upper range above 8 kHz or so, polymer domes may suffer from break‐up problems, either due to lack of rigidity, or from resonances in the surround. One example showed a surround resonance near 10 kHz, which resulted in a marked rise in second harmonic distortion. This was cured by appropriate damping added to the inside of this outer suspension. Where the dome itself is in resonance, a doping layer can be applied nearer to the centre, or alternatively a small plug of polyurethane or similar foam may be placed in contact with the offending area. This kind of partially intermittent contact may give rise to subharmonics. Other techniques include the juxtaposition of a more complex acoustic ‘phase correction’ plate which may block, direct, resonate or delay the output. These operate over limited frequency bands, controlling the radiation from specific areas of the dome to try to smooth the integrated far‐field response. An unusual and highly successful, though now ancient example of a rigid dome HF unit was undoubtedly the HF1300, manufactured by Celestion (UK) (Figure  7.18). Variations of this design had been in production since the mid‐1950s, and have been

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Figure 7.18  Rigid phenolic doped fabric dome HF unit, with sophisticated acoustic loading, front cavity resonator, rear resistively coupled resonator.

used in a number of systems, including many BBC monitors. Almost all of the details of its construction have proved to be critical, these range from the particular grade of cured, phenolic impregnated fabric used for the diaphragm, to the spacing of the phase correction plate at the front. The centre dome is conical, about 19 mm in diameter, and has a shallow, rather broad ‘surround’ actually larger in area than the dome itself. The diaphragm as a whole has an overall diameter of 38 mm. The surround is in fact the main radiating element; piston operation holds to beyond 30 kHz and the diaphragm is particularly free of hysteresis effects. This, in conjunction with its ­relatively uniform axial frequency response, contributed to its unusually favourable subjective qualities. The diaphragm’s intrinsic pressure response shows a peak at fundamental resonance (1.7 kHz) which is damped by resistively controlled air vents to the cavity, these within the enclosed pot magnet. The centre pole has a conical profile to closely follow the contour of the underside of the dome, this placing the first cavity mode at a very high frequency. The output of the naked diaphragm falls naturally above 7 kHz or so, and to compensate a perforated front plate is fitted, formed to follow a similar contour to that of the diaphragm. This results in a damped cavity loading the diaphragm, and provides a correcting delay path between the dome and surround radiation. The output is then uniformly maintained on axis to 14 kHz. Good examples correctly mounted in a panel may demonstrate a ±2 dB characteristic from 2 kHz to 14 kHz, with the range 4 to 12 kHz held within very tight ±1 dB limits. Clarity and transparency were particularly good as hysteretic materials were avoided. The secondary resonance, to be found above 15 kHz, was judged inaudible with the programme used at the time. 7.5.3  Motor Systems (HF) With suitable coil winding techniques, the larger treble units with 30 mm centre poles and over will have power ratings of 8 to 15 W corresponding to a system rating of the order of 100 W on continuous programme. The smaller 19 mm motor coils may have ratings under 8 W, and these may be provided with fuse protection in the accompanying

Moving‐Coil Direct‐Radiator Drivers

speaker system to guard against high‐level, high‐frequency drive, which used to occur during tape spooling, less common now, but also from amplifier instability and/or amplifier clipping. As has been mentioned in connection with other drivers, the application of magnetic fluid to the magnet gap will offer considerable protection against thermal overload. A viscosity grade may be chosen which will also provide damping of the fundamental resonance and some control of rocking, the latter potentially a problem with HF as well as MF dome units. The significant variation in fluid viscosity with gap temperature, which may run up to 40°C, must not be forgotten at the design stage if such damping is considered part of a crossover alignment. When high acoustic levels are required of dome mid and HF units their relatively low efficiency necessitates very large magnets and these can prove costly. Where higher efficiency and directivity control is useful, horn or waveguide loading employed. This offers useful control of coverage and a better acoustic match between the air load and the diaphragm. Using phenolic or aluminium domes with fully coupled horn loading, efficiencies of 20% are possible, contrasting with the 1% to 2% typical of simple direct‐ radiator dome units. With the increasing use of shallow horns or waveguides, the latter are often blended into the enclosure to help tailor the directivity. This better matches the mid output directivity and not least provides a useful efficiency boost. The latter will only occur at lower frequencies as this type of shallow ‘horn’ does not acoustically couple to the dome at higher frequencies. Note that the strongly modified frequency response will need some equalisation. Taking into account coil inductance, imparting a rising impedance load at higher frequencies, it is now customary for some treble unit voice coils to be wound to a significantly lower resistance, for example reduced from 6.4 ohms down to 3 ohms, to improve output. When used with a well‐designed crossover, a 5 to 8 ohm system rating will still typically be possible for the combination unless a flat out efficiency is required. SEAS has devised a novel magnet arrangement to circumvent the need for a centre pole, noting that the latter, even when bored out, may promote some unwanted reflection behind the diaphragm. In the new development, inward‐directed neodymium bar magnets are set in a radial array outside the voice coil, leaving the inner diaphragm region entirely clear, this then leading to an acoustically damped rear chamber. Concerning flux density, using Permendur gap components, 1.9 T has been reported in a commercial HF unit having a 19 mm pole, and more recently 2.5 Tesla for a neodymium energised radial magnet, here for a 25 mm pistonic alloy dome tweeter by Dickie. While at B&W, Laurence Dickie researched tapered, terminating lines for back‐ loading all the drivers in the seminal Nautilus project, and the idea now is seen adapted to more‐compact forms for a variety of high‐frequency units, even for moderately priced systems. A more extended lower range, aiding improved crossover behaviour, is said to result. 7.5.4  Ultrasonic Driver, Dual Coil To extend the frequency response of a dome tweeter, Sony have patented an improvement [US 6,587,571] where a second, single turn coil, thus of very low inductance, is added to the usual higher inductance one, these wired in series. At high frequencies,

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the larger coil is shunted by a capacitor, thus directing more current through the low inductance coil and helping to maintain a more constant overall impedance, and thus maintain a more constant input current up to 100 kHz. The suggested gain at 100 kHz is some 25 dB over a conventional single coil construction. There are also a few piezo and ribbon units which have useful output into the ultrasonic region though the piezos generally have a very ragged, multi‐resonant frequency response.

7.6 ­Full‐Range Units A few examples of full‐range moving‐coil drivers are in manufacture, and though they generally do not completely satisfy a generalised ‘high‐performance’ criteria, certain of the design techniques involved are worthy of note. In addition, there is a particular subjective quality of directness and superior articulation together with evidently highly expressive musical dynamics, which continues to appeal to some markets despite the known technical limitations. Thus some full range driver systems remain available. Direct coupling of driver to the amplifier does show a gain in aspects of sound quality, dynamic expression, micro detail and musical timing (leaving aside active systems for now). Here accepted standards for tonal balance, coloration and bandwidth are necessarily relaxed in return for those other benefits. 7.6.1  Full‐Range Drive Unit E.J. Jordan designed an interesting example of an aluminium cone unit in the mid‐1960s that was produced by Jordan‐Watts. The diaphragm has a hyperbolic flare with a centre dome alloy stiffener, and also, a carefully matched, viscous treated, low Q sealed plastic foam surround. The cone diameter is 100 mm, which was considered to be an optimum compromise between LF radiating area (the unit was intended for use in lower power domestic applications) and adequate dispersion at the higher frequencies. It certainly achieved most of the designer’s aims and was undoubtedly a commercial success with a long production life. At a fairly early stage it demonstrated the value of a flared cone profile and good termination, plus the effectiveness of a high linearity magnet and ­suspension, together with a non‐resonant die‐cast box chassis (see Figure 7.19(a)). Another development for the design of a full‐range planar driver, here by Manger, employs a flexible diaphragm engineered so that the mechanical load presented to the motor coil is almost wholly resistive and is thus independent of frequency. The moving structure consists of a pre‐loaded flat web of synthetic fibre (polyamide/nylon group) impregnated with an air drying visco‐elastic coating, probably of the PVA type (Figure 7.19(b) and (c)). A split motor coil, using differential drive, was employed, with the optional injection of an offset current to allow centering of the coil in the magnet gap height in the absence of a spider. A star‐shaped plastic foam section on the diaphragm acts as a supporting and stiffening component. With a fundamental resonance frequency partly dependent on the drive amplitude (20 to 40 Hz), the unit is nominally flat to 15 kHz on axis. The maximum displacement was quoted at 3 mm so an LF unit is usually required to work with it for higher quality applications and the sensitivity is quoted as 3.2 W for 96 dB SPL. at 1 m. At low frequencies the full diaphragm area is active, but with increasing

Moving‐Coil Direct‐Radiator Drivers

Figure 7.19a  An early, full range, modular, aluminium alloy diaphragm drive unit of advanced design by Jordan. The cast frame has porous openings.

Figure 7.19b  Manger planar driver, bending mode pattern at 3 kHz.

Figure 7.19c  Manger planar driver: modal pattern at 7 kHz, showing desirably reducing radiating area.

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Low

Mid-range

Wide-band diaphragm

Aluminium basket

Frequencies high

Low

Air channels

Pole piece

Two voice-coils

Mid-range

High-end damping

Low-end damping

Figure 7.20  Sectional view of Manger driver (see Figure 7.19).

frequency the radiating area contracts smoothly toward the centre, resulting in the smaller source required for better high‐range performance, including directivity.[11] The unit is intrinsically minimum phase with an impressive impulse response, but at realistic sound levels has higher than average distortion, typically approaching one ­percent, probably due to mild bending non linearity. This audible level of distortion is offset subjectively by the fine phase response (Figure 7.20). For another full range driver example, the multiple driver Bose 900 series loudspeaker employed an array of small, fibrous‐cone, full‐range ‘modular’ drive units. Here a special electronic equalizer is employed ahead of the power amplifier to provide a uniform frequency characteristic. In the 1960s, while at Goodmans, Jordan had also developed a notable 200 mm full‐ range Axiom 8 driver using a deeply flared paper pulp cone and covering 50 Hz to 15 kHz with reasonable uniformity. Forty years later, recognizable derivatives are made today, and despite the known problems, do have a small following. Direct amplifier connection, a coherent single source, and very good resulting subjective dynamics contribute to an unexpectedly rewarding sound when judged on purely musical grounds. 7.6.2  A Full‐Range Moving‐Coil Tensioned Film Panel Transducer The isodynamic principle as used by Magneplanar, Apogee and others is focused on the use of a tensioned planar film diaphragm driven over its surface by a distributed motor. It comprises an open array of fixed magnets and a zigzag or similar current path adhered to the diaphragm. The latter may be realized as a deposited or laminated metallic ­pattern or even by bonded round wire conductors (Magneplanar). The idea is to drive the lightly tensioned film relatively uniformly over its surface to reduce the majority of resonance effects. In the case of the Aria speaker by Sumo, inventor Paul Burton,[12] chose to drive a large rectangular Mylar polyester film panel, quite tightly stretched like a drum skin, from a single, near central point, the latter delineated by a low‐mass moving‐coil motor. Intentionally, the system operates as a controlled drum at low frequencies, constrained by diaphragm tension. With rising frequency the outer areas become progressively

Moving‐Coil Direct‐Radiator Drivers

decoupled relative to the central region. Thus, with careful design the axial output can be made fairly linear with frequency and also show a desirable progressive reduction in radiating area with increasing frequency. Thus, quite good directivity is maintained over a wide frequency range. In the final octave the residual acoustic source comprises the motor coil and its piston‐like centre cap. Low‐frequency modes are partly controlled by porous acoustic resistance panels fitted to the semi‐open back of this floor standing, dipole design, while the impulse to avoid a corrugated type of rear suspension or spider has generated a design solution in the form of a copper shielded magnet gap, medium coil length, with a selected Ferrofluid; the latter performs three functions: that of a fluid bearing for coil centration, also mechanical damping and finally cooling. The magnet system is very powerful, mounted on strong rear crossbeams to help maintain good alignment. A sensitivity of around 85 dB/W is achieved. The motor details are interesting; to achieve a wide electrical bandwidth and a good electromechanical response to the higher frequencies the motor‐coil inductance is held to a low 0.1 mH (out of the gap) with just 45 turns on a 33 mm former; coil height 15 mm. The excursion limit is ±10 mm. A copper capped pole and aluminium eddy current damping ring are used. A 200 W peak programme capacity is claimed while the complete coil assembly, including centre cap, weighs only 2.2 g. Whatever residual problems such a design may have, for example centration under power, and mild rocking modes at some frequencies, the design has the fundamental qualities of simplicity, where a nine octave bandwidth is achieved without the need for multiple sources and without crossovers or equalizers. The single motor coil is connected directly to the amplifier and the system demonstrated good clarity and dynamic quality: long term reliability remained an issue. 7.6.3  ICT—The Inductively Coupled Transducer During the design of a one‐piece metal dome tweeter with integral coil former, transducer engineer Elei Boaz investigated the properties of the shorted turn represented by this continuous conductive element. Some electrical power is lost in this shorted turn, while some of the benefits conferred include damping at fundamental resonance and a small reduction in magnetically induced distortion. He conceived the idea of a full‐range concentric driver where the HF element was simply this one‐piece metal dome with integral former, placed over the centre pole and sharing the magnetic gap of an LF‐MF unit (see Figure  7.21(a) and (b)). The theory relies on the inductive coupling between the motor coil of the main driver and the single or shorted turn represented by the inner HF element, with the potential for designing a full‐range, transducer operating with direct coupling to the amplifier and avoiding a crossover or filter network.[13] As with other concentrics, problems arise at higher frequencies due to the acoustic mismatch between the dome radiator and the immediate acoustic load, resulting in variations in output in the upper frequency range. A simple phase ring was helpful, but a more complete solution was found found in the form of a phase correcting plug placed over the dome radiator, similar to that used in high‐frequency horns, this providing the appropriate delay paths. Simple elastic sleeve suspensions are effective for the dome which is built as a close fit over the centre pole. The properties of the suspension, its damping and stiffness define

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(a)

(b)

ZL Shorted turn dome suspension

ZL = ZM(st)

N:1

ZM Shorted turn dome

Electrical equivalent circuit

Figure 7.21  (a) The ICT or inductively coupled transducer as a two‐way coaxial unit. (b) The construction and simplified equivalent circuit (after Boaz[13]).

dB SPL (1W;1m)

without shorted turn dome with shorted turn dome

80

Impedance

70

fo 10dB

20

50

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Figure 7.22  The practical performance of an ICT unit comparing the results with and without the dome in place (after Boaz[13]).

the mechanical crossover point for this radiating element. Established techniques, that is, cone flare, mass, and attachment to the motor coil are exploited for the lower range diaphragm to design an inherent low‐pass behavior for the bass–mid‐unit. Among the known advantages of the ICT design are the absence of any power handling limit for the HF section, and in reduced system complexity. High‐quality drivers for automobile and sound distribution were produced, and in some numbers: additional development would be required for higher fidelity applications (see Figure 7.22).

Moving‐Coil Direct‐Radiator Drivers

7.6.4  Dual Concentric Drivers Variations of dual concentric drivers have been produced for a very long time and for many reasons, not least the convenience of a single frame, integral full‐range device. A high‐frequency driver mounted concentrically with a larger low‐frequency section confers many benefits, especially symmetrical off‐axis directivity (Figure 7.24). Those awkward off‐axis lobes present in the crossover region, which are common with spaced multi‐driver systems, are avoided. Also, easing crossover design and enhancing ­performance, steps can be taken to align the effective radiating planes for virtual time coincidence. In the case of a centre horn type such as used by Tannoy, this correction may be achieved by electronic delay to the high‐frequency section (see Figure 7.23). Thanks to the development of a high‐performance magnet material using neodymium alloy it has proved possible to miniaturize the magnet assembly for a fairly standard 25 or 32 mm diameter dome HF unit to the point where it may be placed on the centre pole of the conventional larger cone driver (Figure 7.25). Provided care is taken over the gap tolerances and the adjacency to the start of the cone flare, fine results can be achieved despite some axi‐symmetric response ripple above 10 kHz (significantly ­ameliorated from 10° off axis, this the preferred direction). With careful design, the time alignment is very good, significantly aiding in the design of the crossover while the off‐axis frequency characteristics are predictably well behaved in consequence.

50 dB 40

30

20

Axial 15° Vertical 30° Lateral 45° Lateral

10

0

10 Hz 20

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Figure 7.23  Example of the uniform forward responses of a horn‐loaded concentric system (the rear‐mounted piston HF unit employs the main diaphragm as a horn, driven via fine apertures in the centre pole). The responses are for 2 m measuring distance with a crossover at 1 kHz (Tannoy DC 1000).

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20

Figure 7.24  A example of the beneficially uniform off‐axis responses achieved by a concentric system where a miniaturized HF unit is located on the open pole face of the LF–MF unit (UNI‐Q, model C95) (also see Figure 7.25). Figure 7.25  A UNI‐Q driver KEF, a full‐range coaxial with a miniature dome HF unit mounted on the centre pole. The sound sources are effectively coincident.

To date, the finest exposition of the principle has been in a four‐way speaker design where this type of concentric driver is operated above 800 Hz and is not called upon to provide significant cone displacement. Some doubt exists concerning the viability smaller concentric types for full‐range duty since significant intermodulation products can be produced between the LF and HF ranges. Substantial LF power input generates a displacement of the main diaphragm in a dual concentric which in turn modulates the acoustic load presented to the HF dome. Frequency and amplitude modulated components can be generated at audibly higher levels than with a conventional, equivalent, separated‐driver system. One benefit of the coincident driver approach is the high degree of control and uniformity for on‐ and off‐axis frequency responses, achieved by virtue of good crossover conformity with the acoustic target function. A floor mounted system using the UNI‐Q(KEF™) principle was measured in one‐third octave bands at 2 m in an anechoic

Moving‐Coil Direct‐Radiator Drivers

B: 1/3 OCT

KEF*095*

RANGE: –39 dBV *ROOM

STATUS: PAUSED RMS:64

158.5 uVrms

5 dB /DIV

1.585 START: 25 Hz X: 400 Hz

BANDS 14–46 Y: 66.30 uVrms

STOP: 40 000 Hz

Figure 7.26  In‐room averaged response for a floor mounted system employing the concentric driver. Note the good correlation shown between the fine off‐axis performance and the uniform in‐room characteristic here particularly above 400Hz, noting the floor dip at 80 Hz.

chamber for the axial, 15 degrees vertical, 30 degrees lateral and 45 degrees lateral axes. The resulting graphs (Figure 7.23) illustrate the remarkable correspondence between the on and off‐axis responses. Such good directivity improves stereo focus by markedly reducing the incidence of amplitude and phase differences normally present for a stereo pair of speakers. Examining the spatially averaged room response, the typical mid‐bass anomaly is due to interference from the prime, floor reflected mode, while at higher frequencies the smooth frequency characteristic confirms the uniform nature of the output in the axial direction for a well‐designed concentric system (Figure 7.26).

7.7 ­Dynamics and Engineering The term ‘dynamics’ is used in a general sense to characterize certain aspects of sound quality and relates to a feeling of liveliness and power in the reproduced sound. The sense of ‘attack’ and ‘speed’ of natural acoustic instruments, percussive transients, the feeling that the loudest parts of a programme section are reproduced without ­audible limiting, distortion or compression, are pertinent. The term ‘micro dynamics’ is also used, where quieter transient and percussive sounds still retain that innate sense of attack and presence, but on a smaller scale. All sound reproducers and reproducing systems show a significant loss in dynamic power and expression compared with the original sound, and frequently renewed acquaintance with live sound will always a salutatory experience for a loudspeaker and audio engineer, clearly illustrating the large gap that remains between live and reproduced music.

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A number of aspects of loudspeaker engineering, both obvious and subtle, affect subjective dynamics. There are also more logical associations with other aspects of sound quality such as frequency response and energy balance. For example, a false emphasis in the lower treble may well improve the subjective rating for dynamics but this is likely to be achieved at the expense of a false timbre on broader range sounds, and increased listener fatigue is also likely. Amplifier design practice indicates that dynamics may be compromised when one quantity controls or modulates another. For example, heavy bass transients may cause compression and or loss of detail in the mid and treble registers for an amplifier. Loudspeakers also suffer from similar effects and these are now examined in more detail. 7.7.1  Modulation of Motor‐Coil Inductance with Position in the Magnetic Gap In addition to the inherent and complex non‐linearities present in the inductance characteristic of the motor coil, its numerical value is also subject to variation according to the length of the coil immersed, and thus flux linked, to the magnetically permeable pole system. With large cone excursions there is also a substantial variation in inductance where bass signals may modulate mid‐range information, and in addition modulate the electrical impedance that the driver presents to the crossover network. Solutions include the use of an overlong, high inductance coil where the impedance variation with low frequency excursion is controlled. A favoured response is a short coil operating in a long magnetic gap, but this is often disproportionately expensive. And even at small excursions a component of non‐linearity for coil inductance results from the audio related eddy currents induced in the iron parts of the magnetic circuit. Remembering that the moving‐coil motor principle includes the equivalent circuit of an audio frequency transformer, for best sound quality the latter would normally be built with a finely laminated core to minimize eddy currents—quite a contrast to the block conductive poles of a magnet system. It is possible to minimize the eddy currents by placing elements of high conductivity, made from aluminium or copper, in or near to the gap, or shrouding the poles. These preferentially draw in the eddy current fields imparting a linear back e.m.f. and thus shielding the poles. In addition, the inductance of the coil is beneficially reduced. The reduction in distortion is audible both as improved timbre and superior dynamics while the greatest benefit lies in the reduction of the third harmonic, which can be improved by a factor of two or three times. The crossover network also benefits from a reduced and more constant motor‐coil inductance, stabilizing the dynamic performance of the filter and thus minimizing the modulation of the mid‐band alignment by such variations due to low‐frequency cone excursions. 7.7.2  Modulation Effects Due to Common Baffle Another source of intermodulation between two frequency ranges is a consequence of the local acoustic load for one driver being modified by the proximity of another driver. For example, a tweeter placed in proximity to a woofer ‘sees’ the woofer surface as part

Moving‐Coil Direct‐Radiator Drivers

of its acoustic load. When the woofer is under heavy excursion, part of the acoustic boundary from which the treble energy is launched is now moving, thus modulating the output of the tweeter. This is more serious in the case of concentric drivers where the lower frequency diaphragm defines a very high proportion of the baffle or local acoustic load for the treble unit. Specifically, the acoustic impedance of the radiation load on the treble unit is modulated in both amplitude and frequency. With moderate size, full‐ range concentrics, this is considered an audible factor in reducing dynamic accuracy, and we can also include a secondary problem at the highest frequencies where the acoustical blend from the edge of the tweeter to the cone flare may result in a step of variable height under heavy bass excursion, resulting in local response irregularities of typically 10 dB peak‐to‐peak. Thus, the more successful examples of the smaller coincident concentric drivers (e.g., Uni‐Q™) are used in three‐way or more systems where local cone excursion is minimized in respect of the concentric HF unit. 7.7.3  Effect of Flux Density on Modulation and Dynamics As a general rule, higher strength magnet systems and higher efficiency tend to provide better subjective dynamic expression. For moderate excursion signals the voice coil non‐linearities are reduced with higher efficiency in proportion to the ratio of fixed to varying flux. The first is defined by the magnet, the second by the audio current in the coil. Viewed from an alternative viewpoint, it can be shown that taken overall distortion is largely dependent on current. This explains why low sensitivity speaker systems, which draw relatively high currents, generally suffer from greater distortion than high sensitivity systems. The latter simply require less current to produce an equivalent sound level. Associating linearity with subjective dynamics, it is obvious that great care is required in the design of small, full‐range lower impedance systems if they are to offer satisfactory dynamics. And in general, the larger higher efficiency systems do have better perceived dynamics, even at more moderate sound levels. 7.7.4  Effect of Bass Alignment on Dynamics Low‐frequency alignments which tend to reduce cone excursion provide a payback in improved dynamics, provided that they are executed without significant loss in transient response control, or with an increase in colouration. For example, bass reflex ­loading can be tailored to minimize cone movement in the region of maximum bass energy for a typical programme, considering level, frequency, and the typical time history of the programme. If the cone generally moves less, and allowing for an occasional lapse due to unusual momentary peaks, perhaps at ultra low frequencies, then from a statistical viewpoint modulation effects for a bass‐mid driver are reduced and the dynamic quality of the mid‐range may be optimised. 7.7.5  Doppler Modulation Even if a driver had a perfectly linear motor system, large excursions eg for a bass‐mid driver may produce Doppler (frequency‐modulation distortion) at significant levels. Historic analyses on the subject have been restricted to fairly modest sound levels[14]

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or have relied on pure tone analysis under single‐channel or monaural conditions. A more critical view is required when stereo sources are taken into account, for e­ xample, at more typical higher sound levels. The aural sensitivity to several of the more subtle distortions is certainly substantially higher when using high‐quality stereo programme with experienced listeners. While this distortion is not present on axis, FM distortion components do figure for off‐axis and thus reflected signals. 7.7.6  Low‐Frequency Alignment Variation with Dynamics The consequences of position‐dependent inductance for the motor coil have been noted above. Of similar importance is the variation of fundamental driver parameters with power, for example, Thiele–Small. These are generally not constant with increasing power. T‐S frequency parameters are generally measured and specified at low power levels of 0.5 W and frequently rather less. And yet typically the classic high pass low‐­ frequency design of a system is focused on these parameters. Unfortunately, T‐S values may vary substantially with power, frequency and time. In consequence, under heavy drive, and depending on the thermal history of the proceeding programme section, the effective low‐frequency alignment of the system may be altered significantly. Direct consequences are an uneven and ill‐controlled low‐­ frequency range and a change in tonal balance between bass and mid‐range. For a given driver, increasing excursion also results in non‐linear stretching of the suspension and surround thereby increasing the driver dynamic resonance frequency. At the same time, the Bl factors reduces as less of the coil is fully coupled to the available flux and this increases the alignment Q factor slowing the time response. For the box tune itself, the smaller domestic enclosures, if reflex loaded, have comparatively small ports which are only linear up to relatively low power levels, for example, 90 dB. Increasing power beyond this point causes increasing turbulence which reduces the active area and increases damping; in extremis, the port output is reduced near to zero. Considering low‐frequency output, these mechanisms result in dynamic modulation of damping, of response uniformity, and of bandwidth with level. It could be argued that a designer may have to consider a trade‐off between the sealed box, and its greater tolerance of low‐frequency misalignment, and the reflex option which has a greater sensitivity to misalignment, but has the potential for superior mid‐range dynamic expression in its safe working range. This consideration will also logically lead to a preference for larger speakers of three‐way design, probably with a sealed‐box low‐frequency section and thus a mid‐range free of low frequency modulation effects. 7.7.7  Temperature Effects After prolonged use at high powers, motor coils will reach high enough temperatures to materially increase their electrical resistance. In a multi‐way system in particular, the result will be an imbalance between the frequency ranges of each driver due to the ­differential sensitivity changes. There will also be some attendant mis‐termination of the crossover filters further altering the tonal balance of the system. Note also that motor‐coil resistance is a major factor in the value of driver Q and the low‐frequency alignment of a speaker will change significantly when the bass driver has

Moving‐Coil Direct‐Radiator Drivers

reached a higher coil temperature. These changes bring medium term dynamic errors. Aiming for consistency of sound quality over a range of operating powers is an ­important system design consideration. 7.7.8  Mechanical Vibration Through magnet reaction, moving‐coil drivers generate substantial accelerations at their mounting points, the recoil from driving the mass of the diaphragms. The resulting vibration energy will be coupled to the enclosure and may also cause the driver frames to resonate at natural structural modes. Where several drivers share a baffle vibration energy may be coupled from one to another, this constituting a modulation of position of one frequency source by another at another frequency. Subjectively there is a loss of clarity and definition; transients are blurred and there is also a loss in dynamic quality. Where a tweeter is perturbed by the mid‐range unit the treble sound may be roughened subjectively, the description invoking the word ‘grain’ and with an effect similar to excess jitter in a digital audio interface. Remedies include local reinforcement of the driver baffle, while rigid non‐resonant driver chassis or frames are helpful, particularly when designed with more generous provision for mounting points, for example, from three or four, now increased to six or eight points. Some designers have successfully exploited separated baffle or enclosure designs to combat this problem (see SBL design in Figure 5.21).

References 1 Nakazono, J. et al., Coaxial flat plane loudspeaker with polymer graphite honeycomb

sandwich plate diaphragm, J. Audio Engng Soc., 29, 11 (1981).

2 Tsukagosh, T. et al., Polymer graphite composite loudspeaker diaphragms, J. Audio

Engng Soc., 29, 10 (1981).

3 Harwood, H. D., New BBC monitoring loudspeaker, Wireless World, March, April and

May (1968).

4 Bolanos, F., Frequency domain experiences in loudspeaker suspensions, Proceeding of

the Audio Engineering Society, 116th Convention, Berlin (2004).

5 Harwood, H. D., Loudspeak distortion associated with LF signals, J. Audio Engng Soc.,

20, 9 (1972).

6 Keele, D. B., Comparison of direct‐radiator loudspeaker system nominal power

7 8 9 10 11

efficiency vs. True efficiency with High‐Bl drivers, Proceeding of the Audio Engineering Society, 115th Convention, paper 5887, New York (2003). King, J., Loudspeaker voice coils, J Audio Engng Soc., 18, 1, 34–43 (1970). Mellilo, L. and Raj, K., Ferro‐fluid as a means of controlling woofer design parameters, J. Audio Engng Soc., 29, 3 (1981). Button, D., Magnetic circuit design methodologies for dual‐coil transducer, J. Audio Eng. Soc., 50, 6, 7 (2002). Yuasa, Y. and Greenberg, S., The beryllium dome diaphragm, Proc. Audio Engrs. Soc. 52nd Convention, October–November (1975). Pfau, E., Ein Neuer Dynamischer Lautsprecher mit extrem nachgeibiger Membran, Funkshau, March (1974) (Also Manger—inventor).

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12 Butler, T., Tailored by Burton, Hi Fi News, 34, 6 (1989). 13 Boaz, E., The application of an inductively coupled shorted turn and the dual coil

loudspeaker system, AES Reprint, 2548 (G‐2), 83rd AES Convention (1987).

14 Allison, R. and Villchur, E. On the magnitude and credibility of FM distortion in

loudspeakers JAES, 30, 10 (1982).

Bibliography Beranek, L., Acoustics, McGraw‐Hill, London (1954). Briggs, G. A., More About Loudspeakers, Wharfedale Wireless Works, Idle, Yorkshire (1963). Cohen, A. B., Hi Fi Loudspeakers and Enclosures, Newnes‐Butterworth, London (1975). Ferrofluidics Corporation, Massachusetts, USA, Leaflet, Ferrofluidics. Gilliom, J. R., Boliver, P. and Boliver, L., Design problems of high level cone loudspeakers, J. Audio Engng Soc., 25, 5 (1977). Ishiwatari, K., Sakamoto, N., Kawabata, H., Takeuchi, H. and Shimuzu, T., Use of boron for HF dome loudspeakers, J. Audio Engng Soc., 26, 4 (1978). Jordan, E. J., Loudspeakers, London (1963). KEF Electronics Ltd., You and Your Loudspeaker, KEF Electronics Ltd. (c. 1970). National Panasonic, The Technics SB1000 High Linearity Loudspeaker, Technics Promotional Leaflet. Rice, C. W. and Kellog, E. W., Notes on the development of a new type of hornless loudspeaker (1924). Reprinted in J. Audio Engng Soc., 30, 7/8 (1982). Yamamoto, T. et al., High fidelity loudspeakers with boronised titanium diaphragms, Audio Engng Soc. 63rd Convention (1979). Also Loudspeaker, Vol. 2, Audio Engineering Society.

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8 Systems and Crossovers Previous chapters have shown that a single diaphragm driver cannot fully meet the standard implied by the term ‘high performance’. The need for a large radiating area for effective low‐frequency reproduction conflicts with the very small diaphragm necessary for satisfactory HF performance. In consequence, an uncompromised high‐performance loudspeaker is almost invariably a ‘system’ which, in its simplest form, consists of an enclosure of defined acoustic properties plus two or more specialized drivers working with an electrical filter. The latter directs the correct sections of the frequency range to the appropriate drivers and is termed the crossover network (Figure 8.1). For advanced systems, the crossover will also be responsible for other engineering functions such as attenuation and equalization. Benefits may result from this division of the working frequency range. All modulation distortions are considerably reduced, particularly frequency modulation, the latter resulting from the physical movement of a low‐frequency diaphragm whilst simultaneously reproducing a higher frequency (FM, Doppler|). Some residual FM will occur in all systems except for those special cases where bass horns or substantially spaced drivers are employed, as a low‐frequency unit will still occupy a proportion of the enclosure radiation surface. While there is an absence of agreement concerning the audibility thresholds for FM perception, for a given loudspeaker it may well depend on the presence of other potentially masking harmonic and intermodulation distortions. Some sound power from the higher frequency units will be incident on the lower frequency diaphragms and as a result will undergo a modulating excursion, or viewed differently, a proportion of the acoustic load for the higher frequency drivers will be modulated by the excursions of the larger driver. For multi‐way passive systems, it must be said that crossover network circuits may introduce additional loss and distortion, and frequently result in a challenging electrical loading for the matching power amplifier. With appropriate choice of matching loudspeaker drivers and their working frequency ranges, acceptably close control of directivity over frequency may be achieved. The accompanying superior uniformity of off‐axis responses over frequency as compared with a single driver, benefits stereo imaging, and also contributes to a more neutral reverberant sound field in the listening room. The presence of discontinuities in the off‐axis responses for poorer directivity loudspeakers can often be heard as a colouration in the reverberant sound field, particularly deriving from the side wall reflections. Concentric drive units do provide High Performance Loudspeakers: Optimising High Fidelity Loudspeaker Systems, Seventh Edition. Martin Colloms and Paul Darlington. © 2018 John Wiley & Sons Ltd. Published 2018 by John Wiley & Sons Ltd.

High Performance Loudspeakers 0 –3 –6 Level (dB)

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–9 12 dB octave

–12 –15 12 dB octave

–18

10

20

50 100 200 Low pass frequency band

1k fc Crossover point (500 Hz)

2k

5k 10 k High pass frequency band

20 k

Frequency (Hz)

Figure 8.1  Two‐way crossover filter responses (second‐order 12 dB/octave) (high‐frequency power fed to HF unit, low‐frequency power fed to LF unit).

improvement for off‐axis outputs and the power response, thanks to their essentially coincident source alignment. Skillful crossover design can result in good acoustic integration between the outputs of adjacent drivers to ensure a uniform forward directed output through the crossover frequencies, despite driver displacement and phase integration difficulties. Further, in design, the optimum listening axis may be adjusted to that pertaining under actual conditions of use, as this may differ significantly from the usual 1 m or 2 m distant ‘axial’ test microphone position (Figure  8.2). Some speakers have been designed with the driver baffle tilted back over height with respect to the listener; in conjunction with the crossover alignment this tilt may be chosen to partly compensate for the overall driver delay due to physical displacement of the sources and accounting for their intrinsic transfer function. With a loudspeaker designed for stereo use, the directivity in the vertical plane may be narrower, as the relative heights of speaker and subject fall within reasonable limits. A suggested standard for vertical directivity might be ‘the deviation from the axial response shall be less than 2 dB over a ± 10‐degree vertical angle, up to 12 kHz. In the horizontal plane, a radiation angle of two to three times this criterion is desirable. While some designers aim for maximum uniform spread of sound pressure at all frequencies, there is no solid evidence that the stereo image quality improves as a result. Harwood suggests on the evidence of BBC tests, that there may be an optimum directivity for stereo imaging. A very small, wide directivity BBC speaker gave poorer imaging results in situ than a much larger model whose radiation was consistently closer to an intrinsically limited ±30 degrees.[1] With wide directivity designs the reverberant sound intensity will be greater relative to the direct sound than with narrower radiation types, also side wall reflections will be stronger and perhaps this may partially account for that perception of degraded imaging. Conversely, a narrowed horizontal directivity

Systems and Crossovers

(a) Listener directed axis HF

Optimum axis

θ

Normal test axis

LF

(b)

W

Figure 8.2  (a) Optimum radiation axes. (Crossover phase difference results in a listener directed axis at angle θ to normal axis.) (b) Combined in‐phase wave‐front W directed off‐axis by mounting method. Advancement of LF driver radiation centre to plane of HF driver will allow some correction of inter‐unit time delay/phase shift on axis. For (b), some designers simply invert the enclosure, combined with a low stand.

may colour the reverberant sound as less of the more uniform character of the forward radiation will be heard. To address this aspect some designs have additional rear directed higher frequency units to improve the power response by indirectly illuminating the room acoustic. With psycho‐acoustic research confirming the greater subjective importance and dominance of the ‘early’ direct sounds that is, those within a 10 to 20 ms transient period from sources, sources which are placed near to local reflective boundaries will excite reflections which are subjectively judged as a component of the source. In the case of a loudspeaker placed in its room environment, for the mid‐treble range the strength of such local reflections will obviously depend on the directivity. A designed, controlled forward directivity will help to improve the ratio of ‘focused’ direct sound to the reflected sound and thus may sharpen the perceived stereo image focus. Conversely, when they do occur the reflected sound images are more obtrusive when they have a different signature, so a uniform off‐axis response remains desirable for neutral sounding reflected energy. Within a desired or specified ‘solid angle’ of forward radiation, good uniformity over angle is highly desirable to minimize the smaller differential phase and amplitude variations which will still occur with respect to a listener, especially for a stereo pair. Small differences resulting from the relative angle, or from head height or indeed the loudspeaker azimuth, should not result in phase and amplitude differences which

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Figure 8.3  A classic BBC derived three‐way vertical‐in‐line monitor system. This design may be tri‐wired. Model S100, 300 mm Bextrene bass, 160 mm polypropylene mid, 19 mm doped fabric high‐frequency (Source: Courtesy Spendor Ltd).

are audible. When present, such artefacts may begin to confuse and fatigue the perception of the sound field, and will be subjectively judged as weakened stereo image focus. This focus requirement, for a uniform and symmetrical directivity in the horizontal plane, suggests that the main drivers should be mounted in a vertical in‐line formation. There is no doubt that this particular configuration is important for stereo image stability and, if further evidence were needed, data collected during a consumer test of thirty pairs of loudspeakers provided strong indications that vertical in‐line systems (Figure 8.3) gave superior stereo focus.[2]

8.1 ­Passive Loudspeaker System Design There are no hard and fast rules for the design of a successful loudspeaker system. The designer will benefit from a variety of skills, mechanical, acoustical, electronic, together with knowledge of the relevant markets, of pertinent standards, of the theory of sound and music, and not least, perception and evaluation of sound quality. Two distinct loudspeaker system design routes exist: systems designed in every detail by a loudspeaker manufacturer including manufacture of the drive units, and secondly, systems assembled from OEM (original equipment manufacturer) drivers possibly from multiple sources. In the case of the former, the acoustic engineer has complete control of the process and can design more or less precisely a system to meet a given standard of performance. From the target specification, you may establish the optimum driver and enclosure characteristics, design the units to meet these requirements and complete the system with the addition of a matching enclosure and crossover. More often than not, even the manufacturers who make a range of their own drivers will not have the resources to design individual units for each system type.

Systems and Crossovers

For  economic reasons, they will be forced to rationalize and are likely to produce a fairly well‐ordered but limited range of drivers each capable (with possibly some small detail variation) of meeting the needs of several system designs. High frequency units are rather specialised and are often bought in. The perfect driver has yet to be developed, and each presents its own unique engineering and performance compromises. While the designer has a vast number of permutations and combinations to choose from, there is less control here over OEM driver uniformity and the very existence of such a wide selection brings its own problems including supply continuity. A high‐performance system is by definition a consistent product, and it is vital that the driver characteristics remain constant during the production cycle. The possibility of significant variation must be investigated at the design stage with numerous sample tests, a design centre’s specification should be established with allowable agreed deviation limits, and provision made to correct for the inevitable remaining tolerances, for example, in the system crossover network or electronics, and by careful matching and perhaps left‐right channel pairing of components and/or systems. The performance variations may concern any aspect, but once a drive unit is chosen for the design with its manufacturing details kept under close control, test criteria of frequency response sensitivity and rub and buzz alone are usually sufficient to satisfactorily qualify the unit for use in production. With more critical system build, it may prove necessary to carry out the QC test with the crossover in circuit in order to account for possible interaction between the two before final assembly. 8.1.1 8Ω Versus 4Ω Rated Speaker Impedance Competition between speaker manufacturers is extremely keen. So far as sales are concerned it has long been known that as for the automobile market, where ‘faster is better’, the corresponding law for loudspeakers is ‘louder is better’. Good wideband loudspeakers may not be very efficient due to the mutual conflict of the physical laws governing frequency range, colouration, reduced distortion, finite size, and efficiency. Historically most UK, U.S., French and Japanese speakers have been 8Ω impedance, based on a +/−20% definition where the impedance modulus is 6.4Ω or higher, while countries following the DIN specification have selected 4Ω, this largely based on the need to extract maximum power from the less expensive and lower voltage solid state amplifiers of the time. When first introduced, such electronics provided sufficient current but a more restricted voltage headroom. Given that that possible description of a modern solid‐state power amplifier is a ‘voltage source of relatively unlimited current’, loudspeaker manufacturers have increasingly drifted towards a 4Ω specification for greater perceived loudness at a given volume control setting, taking the view that a customary amplifier will deliver the excess current when required. With voltage drive, normally if incorrectly referenced to a 1 W, 2.83 V, 8Ω level, the quoted ‘sensitivity’ for a 4 ohm loudspeaker is 3 dB greater than for the equivalent 8Ω speaker for a given loudness. However, the 4Ω example, is in my view compromised, as it must draw double the current from the amplifier. With complex multi‐way speaker systems, the instantaneous load impedance may fall well below that minimum found when using a steady‐state measurement of the impedance modulus. For example, a well‐known three‐way 4Ω speaker with a rated

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nominal 3.2Ω minimum modulus was found to fall to the equivalent of 1.82Ω for complex music related transients related to the internal amplifier currents. An equivalent 1.8Ω worse case loading is highly unwelcome, both for the amplifier, but also considering of the resistance of the several in‐series connectors and contacts concerned, and not least the inevitable speaker cable impedance. Some manufacturers of 4Ω speakers have produced models with a nearly constant resistive load impedance, this achieved via internal conjugate compensation networks, here contending that the 3 dB extra voltage sensitivity has been achieved without imposing undue frequency related stress on the cable, contacts or the power amplifier. With certain exceptions, notably for some low current amplifier models and those few valve or tube designs, this is often a fair assumption (see also Figures  8.27 and 8.34b,c). Note that such conjugate compensation will be imperfect since there will be changes in low frequency alignment at high power near to overload which will not have been modelled. Thus, the system cannot be wholly compensated. And in overload the effective impedance compensation will quickly drift away from its design centre, perhaps with more harm than good for sound quality. Considering the resistive load line for an amplifier, this pertinent to the maximum loading, the worse‐case loading from a loudspeaker system may not be at the lowest impedance modulus indicated. Here, at the point of inflection the load will be resistive. For the amplifier, it is the more adverse combinations of phase and impedance which are more relevant, where the loading is most severe. To a good approximation this is where the phase angle reaches 45 degrees, with consequent doubling of load line current in the output transistors. By calculating combinations of impedance and phase angle values, the effective minimum load may be estimated. Solid‐state amplifiers suffer dynamically and thermally under such high current demand, while thermionic designs with their higher output impedance will sound altered and coloured as the impedance variation is heard reflected in their finite output resistance, typically 1 to 2 ohms, and for low feedback models as high as 4 ohms (Figure 8.4(a)). 10.00

90.0

Ohm

deg

8.00

54.0

6.00

18.0

4.00

–18.0

2.00

–54.0

0.00 10

20

50

100 200

500

1k

2k

5k

–90.0 10 k Hz 30 k

Figure 8.4a  Impedance of a large three‐way ‘audiophile’ loudspeaker with an awkward input impedance, dipping to almost 2.2 ohms and with troublesome phase angle/load combinations, for example, 36 deg/3 ohms at 70 Hz.

Systems and Crossovers

With very high‐quality speaker designs, doubt remains concerning the possible quality losses from the additional passive components required to effect the conjugate compensation. Listeners have noted some loss of subjective dynamics and transparency associated with this technique. This partly because the load impedance to be compensated is partly dependent on low‐frequency programme history and level and the passive compensation fails to fully track these changes. Also, each crossover component has minor losses and errors when considered over a wider frequency range and it is a rule of thumb that crossovers should be no more complicated than is absolutely necessary. Consequently, many newer designs are seen to be reverting to uncompensated crossover networks. 8.1.2  Factors Affecting the Choice of Drive Units Many system engineers rely on intuition when selecting a driver line up from independent suppliers. Familiarity with a large number and variety of units is a prerequisite, and the choice is generally made on the basis of the limitations of performance discussed in Chapter 5, but occasionally there are exceptions. For example, the better class of 160 to 200 mm chassis cone driver currently manufactured in the U.K. produce a good performance that extends to 5 kHz, well beyond that which was attainable using older cones. This allows the crossover point to be placed comfortably between 3 kHz and 4 kHz, high enough to consider transfer to a small 25 mm or 19 mm high‐frequency dome unit for the upper range. Some fine classic systems of necessarily limited maximum acoustic output have been produced along these lines from KEF Electronics (R103, R104, etc.), Spendor Audio Systems (BC1, SP1, SP2) and Rogers (LS7, Studio One). (As we will find later, the market has since moved on to more compact enclosures with 150 to 110 mm bass‐mid drivers). Cone behavior indicates that a 200 mm driver will be operating in break up above 600 Hz or so, and this is indeed often the case. However, the particularly consistent properties of the synthetic cone material employed allow the designer to adequately control the break‐up modes such that the range may be smoothly extended by a further three octaves. A normal paper/pulp cone cannot often achieve this level of performance and in consequence the crossover point for a high‐performance application may need to be placed at around 1 kHz. This would entail the use of an additional mid‐range driver to meet the bass unit at 1 kHz, and a further HF unit would probably be required to complete the frequency range. Pulp cone designers are now meeting the challenge of synthetic materials and are producing new generations of well controlled, better‐sounding paper cones of usefully higher sensitivity than the moulded polymers. A number of these pulp cone bass–mid‐range units are now tolerably well behaved to 4 kHz or so though the superior models are quite costly. Woven diaphragms of resin bonded Kevlartm, glass fibre and carbon fibre have also joined this group. The need for adequate low‐frequency acoustic output from a credible high‐performance system suggests that the minimum size of bass unit should be 250 or 300 mm in diameter or an equivalent pair of smaller drivers (the single 200 mm based systems are generally insufficiently loud for professional monitoring unless optimized and high order band limited through active drive). Three way design also helps by spreading the power load.

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8.1.3  Low‐Frequency Drivers The choice of LF driver will depend on the level of colouration which may be acceptable, together with considerations of bandwidth (LF excursion), efficiency, power handling and enclosure size. Depending on the volume of the enclosure, the LF unit may be loaded in several ways and the electro‐acoustic properties of the individual driver are an important factor in this choice. In domestic locations, compact systems are strongly favoured for aesthetic reasons and, in general, most purchasers consider that a loudspeaker system should be no larger than is strictly necessary. Recent developments in compact dock and wireless connected loudspeakers have further increased the market pressure on larger higher quality passive designs. Few LF drivers will function adequately beyond 1 kHz and the maximum safe crossover frequency is generally 500 to 700 Hz for the better 250 mm units and 350 to 500 Hz for the 300 mm sizes. With these larger drivers, a further reduction in frequency to 250 Hz may help to further reduce subjective colouration, particularly for critical vocal reproduction. 8.1.4  Mid‐Frequency Drivers Taking 350 Hz as the basic lower limit, it is desirable that the mid‐range unit provides an adequate performance from at least two octaves lower, that is, 100 Hz. It goes almost without saying that its range should possess a reasonably uniform pressure response free of significant resonances or colourations. Such a driver is usually a cone unit 80 to 200 mm in chassis diameter, often capable of bass/mid‐range coverage in its own right. The better examples of mid‐frequency driver will have a clean output up to 5 kHz or 6 kHz allowing the transition to an HF unit to occur smoothly between 2 and 3 kHz (ideally the upper range of the mid unit should extend further but this is rarely achieved). To date, the dome mid‐range units which have been produced range in diameter from 35 mm to 85 mm and considerable problems have been experienced in the attempt to provide a sufficiently wide response. To cover the basic 350 Hz to 5 kHz range well, an overall 100 Hz to 15 kHz response is desirable, amounting to seven octaves. The best examples so far cope reasonably well from 350 Hz to 5 kHz, but indicate crossover points around 600 Hz and 4 kHz with accompanying high slopes of perhaps third‐order, 18 dB/octave roll‐off. A worthwhile target is 90 dB/W for sensitivity at 8 ohm rated, but this is rarely achieved. One 75 mm dome has attained this sensitivity but at huge magnet expense and cone units are generally more cost effective, though they do need a back box. 8.1.5  High‐Frequency Drivers Sensitivity will also be an important factor in the selection of an HF driver since only a few of the high‐quality designs are truly efficient. Some recent examples of 25 mm dome units have managed to combine qualities of smoothness, high linearity and adequate sensitivity and these are now widely employed since at this quality level, cone units are virtually ruled out. If higher levels of acoustic output are required, then this may be obtained only via horn loading. Focal have succeeded in reaching 96 dB/W for a 25 mm inverted beryllium dome using very large magnets.

Systems and Crossovers

95 HF

Sound pressure (dB)

85 75 65

MF

55 45

LF

35 50

100

200

500

1k

2k

5k

10 k

20 k

Frequency (Hz)

Figure 8.4b  Ideal driver responses for three‐way system, with generous overlap (suggested crossovers at 350 Hz and 3 kHz).

With a crossover point probably in the range 3 to 6 kHz, the HF unit should ideally have a response extension below 1 kHz for optimum crossover performance. Most 25 mm dome units fulfill this condition, although the amplitude of Q at fundamental resonance must be taken into consideration for crossover matching. The ideally broad overlap of driver response is best shown in terms of a system (Figure 8.4(b)) illustrating the responses of an ideal ‘three‐way’ set of drivers. 8.1.6  Sensitivity Matching Ideally, the in‐band working sensitivities of the drivers making up a system should be equal when measured on the system axis after equalization, compensation and crossover losses have been taken into account. The latter can be difficult to predict and it is often useful to first establish the low‐frequency sensitivity. The mid and treble drivers should then be selected so that sufficient sensitivity remains in hand for fine tuning. Since even high‐quality drivers can vary in sensitivity by up to ±1.5 dB in production frequently some selection or final balance adjustment may be required for the completed system. Moderate values of series resistive attenuation does not unduly affect the driver or crossover performance for the mid and high frequencies, but such practice is likely to significantly disturb an LF unit especially near the bass resonance, and sensitivity control must be ruled out for the bass unless a large tapped winding auto‐transformer is employed (or the system is active with gain controls at line level). It is therefore usual to drive the low frequency section directly via the crossover, and to reserve any attenuation requirements for the remaining drivers. 8.1.7  Auto‐Transformer Level Matching for Drivers When designing reference grade loudspeakers, obtaining the most natural and lifelike tonal balance, and overall loudspeaker accuracy for monitoring, will be dependent on close matching of the mean level of mid and treble bands to within +/− 0.5 dB typically,

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High Performance Loudspeakers

R(z)

C(x)

Ly, tapped inductor/transformer

HF Driver

Figure 8.5  Tapped ratio transformer inductor for level matching. R(z) may provide damping, C(x) is a component of the filter function and Ly is the matching tapped primary inductance.

and +/− 0.25 dB ideally. While the BBC designs department had supported the costly use of tapped, air‐gapped mu‐metal or radiometal cored auto‐transformers for such driver level alignment, Thiele has examined the particularly useful case of an economic air‐cored matching auto‐transformer for a high‐frequency unit. His exposition provides for nearly equal 1 dB steps when used as the first shunt inductor in a crossover network, while its modification to finer level tappings is straightforward. The detrimental effect of leakage inductance is examined even for such a simple winding, leading to a recommendation for multi‐filar windings to reduce flux leakage.[3] A trade‐off may be found between the suggested complexity of air‐core windings and the better coupling and lower leakage inherent using a ferromagnetic cored inductor. For moderate cost applications, here a bi‐filar winding will be effective on an open magnetic core, for example, a stack of ‘I’ laminations or a simple ferrite bar, this winding being also used as the defining inductor value for the high‐pass network (Figure 8.5). If the crossover is an active, electronic design, separate power amplifiers feed each driver and sensitivity matching is easily accomplished via preset gain controls. Nevertheless, the driver sensitivities and power handling must still be chosen with due regard to the maximum acoustic output of the system as a whole and with regard to the power spectrum of the programme likely to be used. Active crossovers are increasingly popular for professional monitors as the overall system performance gains are widely recognized in this field.

8.2 ­‘Two‐and‐a‐Half‐Way’ System Design When designers expand a given range of speakers, it has become popular to take the basic design of a stand‐mount two‐way loudspeaker, and make a floor‐standing model by adding a further bass driver. Traditionally, a three‐way speaker would be the result, that is, bass, mid and treble—but these days with the use of smaller bass units, typically 5 in (110 mm) or 6.5 in (170 mm) bass units, there is a need for still greater bass output and power handling. This can be achieved by having both these drivers share the work. With the tweeter mounted in its often‐preferred, topmost position in the enclosure, the drive to the lowest bass unit must be rolled off to prevent its output from interfering at the crossover between the upper bass driver and the tweeter. Because a full crossover is not present, this class of system has been classed as 2½ way. There are some interesting design aspects. For example, the crossover equalization to the bass–mid‐driver of the original two‐ way may be realigned to a higher sensitivity, typically by 2 to 3 dB, with adjustment of the crossover, here substantially reducing the series inductor, assuming that the treble unit

Systems and Crossovers

can follow suit at the new higher sensitivity level. The additional, bass only driver employs a crossover that shapes its output to sum constructively and largely in phase with the upper driver to restore the low frequency output to uniformity. Often, a single inductor is sufficient for this crossover section, of considerable value, that is, in the range 5 to 12 mH. As regards enclosure design, there are benefits in separating these two drivers into two separate enclosure sections thus allowing them to be individually loaded and tuned. This often provides better bass response, control and extension. Note that the two bass driver sections are wired in parallel, essentially imparting a halving of system impedance at low frequencies, unless corresponding adjustments have been made to the driver impedances. Where an existing two‐way system has reasonably high impedance, say 8Ω, certain alignments for 2.5 way may allow the bass‐only driver to operate with a higher impedance coil of 12 to 16Ω. This, when added to the main system, provides for a satisfactory overall load impedance. Given that in a sense that low frequency driver is only supplementing the main response the principle of sound power addition means that the auxiliary bass unit needs only to operate a lower level than the main driver, and extra moving mass of up to 50% may be added to the lower bass driver, which then usefully extends the intentionally tapered low frequency response to still lower frequencies. With such systems and related paralleled bass systems, when defined as a part of the original design, it is also possible to adjust the individual driver characteristics and their enclosure tuning such that the dips and peaks in the impedance characteristics interleave the low‐frequency range. The result is a smoother impedance curve for the system, with the objective of better matching to amplifiers, particularly single ended and low feedback tubed designs with their typically high output impedances (these have measured from 1.5Ω to as high as 4Ω).

8.3 ­The Crossover Network and Target Function While the following section reflects the classical approach to loudspeaker system design using established filter practice to define the crossover network, sharing power between the drivers by appropriately dividing, and apportioning the frequency ranges, the concept of a target function for the system has become very useful. Here, the entire transfer function is considered from electrical input to radiated acoustic output over angle and distance, and including modeling of the power response. Even when consideration of all the relevant parameters and behaviours are beyond available resources the target function concept remains valuable. It helps keep the whole picture in mind and should prevent undue concentration of time and bill of materials resource to one aspect of technology, or structure, or system design. The aim is well balanced engineering where the defined available resources provide a well‐balanced contribution to the overall performance and sound quality. Established teaching describes a crossover network as a passive, high‐power filter circuit, made up from various capacitors inductors and resistors, designed using standard theory, commonly to a Butterworth response characteristic, and which provides maximum amplitude response flatness with a well‐defined and specified roll‐off. This is of course assuming uniform driver impedance and flat driver responses when fitted to the enclosure, and also with no inter‐driver time delay present.

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High Performance Loudspeakers

8.3.1  First‐Order Crossovers The simplest form of parallel crossover is a two‐way network of first order, that is, single pole, which consists of an inductor to direct bass power to the low‐frequency unit and a capacitor, to pass treble power to the high‐frequency unit (the two sections are connected in parallel to the voltage source or amplifier). Such networks are simple and inexpensive and are often, but not invariably, found in low‐priced systems (Figure 8.6). While this basic low‐order form is quite common, and even preferred in some cases, it may provide inadequate control of both power sharing and frequency response for high‐performance applications, except in those exceptional cases where extremely wide‐range drivers of defined spacing (including a common radiation plane) and dispersion are employed, for example, concentrics. (Where for now, it is now enjoying increasing favour.) In the latter case, it provides the best method for achieving a moderate‐ phase shift between the drivers and hence helps in designing for ‘minimum phase’. However, such low order systems, usually built with physically displaced and delay‐compensated drivers, will suffer from poorer vertical directivity with resulting interference patterns due to the broad driver overlap. Certainly first‐order networks are more effective for coincident and concentric drive units as there is no lateral displacement. Classical crossover theory teaches power matching filters of maximum transfer efficiency, these complex variants concerning ‘m’ filter derived networks where the concept of iterative impedance is employed running along the cascade of filter sections. Here, the ideal termination impedance, that of the driver, is notionally reflected via the filter stages back to the input terminals. In practice, simple crossover filters cannot reflect complex impedances very well and as such practical networks in common usage are based instead on the constant resistance platform. This means that for the complete network, the load resistance presented to the amplifier should be more or less constant. Such constant resistance filter networks are also less critical of driver impedance variations over their working range and are well suited to modern low output resistance amplifiers (see Figure 8.7). 8.3.2  Second‐Order Networks While single‐order networks are sometimes used, often with specially designed drive units, higher‐order networks are ubiquitous. Second‐order 12 dB/octave roll‐off designs are an effective compromise on cost and performance grounds. At the crossover frequency the driver outputs are in theory 180 degrees electrically out of phase. Assuming + Input impedance R ohms

+ R

–

C

L

+ HF

R –

–

Figure 8.6  First‐order circuit and equations, L = R/(2πfc), C = 1/(2πfcR); for example, R = 8 Ω, fc = 3 kHz, L = 0.42 mH and C = 6.6μF (in theory with a 6 dB/octave roll‐off ).

Systems and Crossovers LF

HF

0 –3

Level (dB)

6 dB –12 6 dB

octave

–24 18 dB

12 dB octave

–36 10

20

50

octave

18 dB

100

200

12 dB octave

octave

octave

500

1k

2k

5k

10 k

20 k

Frequency (Hz)

Figure 8.7  Two‐way crossover responses, comparing 6, 12 and 18 dB/octave roll‐offs, first, second and third order.

L1 R

C2 +

C1

LF L2

–

HF

– +

Figure 8.8  A standard second‐order crossover circuit showing the HF driver polarity inverted, the usual connection.

the units to be in the same time datum or launch plane, a well‐integrated sound output will only be obtained if one of the drivers, usually the HF unit, is phase‐inverted, that is, by 180 degrees since at the crossover frequency the low pass lags 90 degrees and the high pass leads by 90 degrees, summing to 180 degrees. The remainder of the high‐ frequency range is thus phase‐inverted relative to the bass a possible cause of contention concerning overall phase linearity. As usually implemented the second‐order network sees a parallel inductor wired across the HF unit, which may helpfully be used to beneficially damp its motional impedance towards its fundamental resonance, this usually located at frequencies below the crossover point. Figure 8.8 illustrates the second‐order filter configuration. The following classical ‘m’ derived equations: L1

C1

R 22 f 1 2 fR

L2 C2

R 2 f 1 2 2 fR

L2

2 L1 C1

2C2



351

352

High Performance Loudspeakers

contrast with the constant resistance version that is now more usual for a maximally flat voltage response target for each section, where



C1 C 2

1 L1 2 2 fR

L2

2R 2 f



The situation is complicated by the inevitable phase shifts at crossover frequencies and this raises the question posed by the more distant observer, namely what actually sounds like flat response, particularly for the summed acoustic power which is radiated. Here the standard crossover alignment actually gives rise to a small lift in summed power at crossover which may be trimmed back by reducing the Q value for the two networks, or by moving their calculated frequencies slightly apart, de‐tuning the pair. The calculated frequencies for the low pass and high pass sections may be allowed to drift apart, say by 5%. For a lower ‘Qf’, for the Linkwitz‐Riley form, the voltage outputs are now −6 dB (rather than −3 dB) at crossover, and this version is designed using the following formulae:

C1 C 2

0.08 and L1 Rf

L2

0.32 R f

This form has become increasingly popular. In practice, there is often some degree of sound power infill at the crossover point. A relatively minor adjustment of component values will generally provide a satisfactorily uniform axial response with only mild changes to the decay slope. Because of the variations inherent for driver acoustic outputs, and also the usual differential time delays present between drivers from their geometry and their mounting displacement, rarely can strict rules be applied concerning crossover order. Those crossover ‘rules’ should be interpreted with flexibility, with the aim of producing a smooth, well‐integrated, combined acoustic output from the drivers concerned, at the proposed listening distance, this termed the acoustic target function. Some attention is also required to the resulting input impedance to make sure the chosen implementation when it has been optimised for frequency response does not unduly compromise amplifier loading. One successful system using a ‘low‐order’ filter employs a transitional first‐order low‐ pass with a second‐order high‐pass. In theory the phase shift at crossover should be between 90 degrees and 180 degrees, but at the crossover frequency chosen, the drivers showed good integration with the HF unit connected phase reversed, this taking account of the final acoustic delays involved (here a 25 mm dome and a 200 mm cone LF‐MF). 8.3.3  Higher‐Order Networks Higher‐order networks are also common, with third order providing a nominal 90‐degree phase shift between driver outputs and offers steeper slopes, improving driver separation over the stop bands. However, that final series capacitor seen in the high pass circuit can cause difficulties with the HF driver’s resonant impedance (see Figure 8.24). At first pass the crossover is designed in theory to see a pure resistive loading at the specified value. Third‐order Butterworth networks naturally impart up to 3 dB of amplitude peaking on the primary axis at the crossover point, but not for the summed power response as

Systems and Crossovers

phase plays a part. In practice, the engineer can adopt a slightly different fc for the complementary high‐ and low‐pass sections, sliding fc1 and fc2 apart from the original fc and thus aiming to smooth both the amplitude and power response through the transition. To calculate the third‐order network in Figure 8.9,

3R 4 f

L1

3 L2

2 L3 , C1

2 3 fR

2 C3 3

2C2



where R is the nominal, ideally resistive impedance, of the drivers. Example circuit values are shown in Figure 8.10. There is a simple method for deriving general numerical component values for a third‐ order crossover network. The Butterworth crossover in Figure 8.11 may be scaled to any required frequency by simple multiplication as the component values are inversely proportional to frequency. The values given are for 1 kHz with nominally 8Ω drivers. Thus, to readjust for 4Ω systems, the capacitance values are doubled and the inductors halved. Likewise, for 16Ω systems the inductance values are doubled and the capacitors halved. For 2 kHz all the values are halved, for 200 Hz all values are multiplied by 5, and so on. The agreement of the final system response with the theoretical function will also rely on the driver input impedance being nominally constant, that is, resistive, and it also requires that the amplitude/frequency response for the chosen drivers is uniform. Popular interactive software based speaker system ‘solvers’ will accept ‘in situ’ measured frequency and phase information for the drivers, and also their impedance variation with frequency, and account for these when calculating the actual component values necessary for the desired target functions, both acoustic, and for the load impedance. Fourth order is probably as high as is economically practicable or necessary, and is still sensitive to component tolerances, but has several virtues. A shunt inductor returns, C2

L1

C3

L2 R

+ C1

+ or –

LF

HF L3

–

Figure 8.9  Third‐order crossover model.

4.4 μF

0.64 mH

13.2 μF

0.21 mH Zin , 8 Ω

+ 8.8 μF

LF , 8 Ω

+

0.32 mH

HF , 8 Ω

Figure 8.10  Theoretical 8Ω, 3 kHz, third‐order crossover with nominal values.

353

354

High Performance Loudspeakers 1.9 mH

0.64 mH

L1

L2 LF

C1

Input

26.5 μF

13.3 μF

39.8 μF

C3

C3 L3

Input

0.95 mH

MF

Ro = 8 Ω nominal

fc = 1 kHz

Figure 8.11  A scalable third‐order Butterworth, constant resistance network for 8 ohms and 1 kHz.

3.54

0.8 0.4

7 +

10.6

+

2.34

0.267 LF

1.2 HF

Figure 8.12  24 dB/octave, fourth‐order passive crossover; 8Ω, 3 kHz; scale to any frequency. Assumes no inter‐drive‐unit delay: a cascaded Butterworth filter (after Linkwitz[4]).

connected across the HF driver terminals (and which may help to terminate the motional impedance), while the roll‐off slopes are so steep at 24 dB/octave that potential out‐of‐band driver problems are quite well attenuated. In theory with textbook drivers, fourth‐order indicates an in‐phase connection for the drivers. A 6 dB deep notch is potentially present at the crossover point but in practice, this region is now so narrow that any such dip in the measured axial response of a system is hard to find, and may easily be filled in by a fractional frequency overlap for the sections. Due to its in‐phase symmetry, this fourth‐order alignment, when combined with delay spaced drivers, allows for a well‐defined and essentially minimum phase system to be designed. As proposed by Siegfried Linkwitz, the cascaded Butterworth filter to fourth order will also provide the best axial polar response symmetry. Interestingly, this filter assumes the general properties of an even‐order all‐pass network, though is not linear phase (see Figure 8.12). Theoretically such an all-pass filter does provide a flat frequency response but shifts the transfer function further from the linear phase condition.

Systems and Crossovers

8.3.4  Energy Contour Plots Energy contour plots of an in‐phase connected fourth‐order system (Figure 8.13(e) and (f )) show a desirably broad control, obtained with symmetric minor side lobes. By comparison, the second‐order type (Figure 8.13(a) and (b)) has broader side lobes and a narrower central focus. The plot for third order with the customary anti‐phase driver connection illustrates the significant asymmetry predicted by Linkwitz, with an upwards directed main lobe, which may be inconvenient. However, this feature may be exploited to partially direct the desired listening axis, or conversely, the implied network delay may be used to balance out the greater delay from a low‐frequency driver (Figure 8.13(c) and (d)). For the numerical theory, and resulting computed spatial energy plots, we assume that the drivers are perfectly uniform in output, have no differential time delay and present resistive loads. Real components and systems do not conform to these criteria and the loudspeaker designer needs to make many judgments with compromises. Our design goal could be defined as an acoustic target function, presented to the defined listener location whereby the final crossover implementation generates the required crossover frequencies and slopes in the acoustic output from the drivers, both on and off axis. The latter is important so that the character of the power response sent into the room environment is usefully consonant with the first arrival output. 8.3.5  High‐Frequency Units Operating to Lower Frequencies Neville Thiele has considered that high‐frequency units could be advantageously driven much nearer their fundamental frequency, especially for a closed back type, even though this could result in a distortion increase for some drivers. Instead of working as usual an octave or more above resonance, in order to avoid the expected difficulties due to motional impedance, Thiele’s approach is to correct the motional impedance in combination with a third‐order network, to achieve a target fifth‐order high pass response. Then, by employing a third‐order low‐pass filter for the matching low‐frequency driver, the resulting output can enjoy a Linkwitz–Riley all‐pass behaviour for the completed system. This potentially useful on several grounds, though when installed in a practical enclosure this theoretical alignment will also require provision for considerable tailoring of the in-situ responses and also for the differential driver delay. A powerful interactive network design solver can cope with this problem when given the right build data, the target responses and slopes. 8.3.6 Mis‐Termination As has been noted, the design of crossover networks may be complicated by matching to impedance loading issues. The constant input resistance promised by Butterworth crossover theory assumes that the input impedance of the drivers is also a constant resistance, for example, nominally 8Ω for the network illustrated in Figure 8.10. Certainly there is a part of the frequency range where the input impedance of a moving‐coil driver is a fairly constant resistance, here an octave or two above the

355

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High Performance Loudspeakers

(a) dB

+32°

0

–32°

Hz fc (b)

+32°

dB

0

–32°

Hz fc (c)

+32°

dB

0

Hz

–32° fc

Figure 8.13  Computed three‐dimensional energy plots in the frequency domain: (a) and (b) are for second‐order filters measured a little below axis, where (a) is in‐phase (b) connected in anti‐phase. (c) and (d) are for the third‐order filter (from below) (c) in‐phase driver connection, (d) out of phase, (e) and (f ) are fourth‐order, from below, (e) in phase, (f ) for anti‐phase driver connections (after Bank and Hathaway).

Systems and Crossovers

(d) +32°

dB

0

–32°

Hz fc

(e) +32° dB

0

–32° Hz fc

(f) +32° dB

0

–32° Hz

Figure 8.13 (Cont’d)

fc

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High Performance Loudspeakers

mass‐compliance resonance. Figure 8.14 shows that at lower frequencies a more or less well‐damped motional resonance occurs, then the motional impedance passes through inductive, resistive and capacitive regions.[5] At higher frequencies, beyond resonance the inductance of the motor coil becomes significant, imparting rising impedance. When this complex load is connected to a calculated standard filter a degree of mis‐ termination occurs, with resulting irregularities for both the amplitude and phase response of the filter and thus the sound output. An active crossover is essentially immune to these problems, since optimal network termination is easily provided in the low‐level circuitry, and the power amplifiers voltage‐drive the driver voice coils in a near ideal fashion. The advantages of this approach are discussed more fully in Section 8.3 on active crossovers. Interestingly, there is a different crossover termination in the case of horn loading, here the reactive load element of the effective mass of the diaphragm now becomes resistive due to the acoustically coupled horn. Figure  8.10 shows a theory‐based calculation for a two‐way 8Ω network operating nominally at 3.0 kHz. By contrast the network from a successful commercial system is reproduced in Figure  8.15. It is hard to see much resemblance between these two 80 70 Impedance (Ω)

358

60 50 40 30 20 10 10

20

50

100

Inductive (Suspension and enclosure air stiffness)

200

Capacitive

500

1k

2k 5 k 10 k Frequency (Hz)

Resistive

20 k

Inductive

(Moving (Mainly d.c. coil mass) resistance)

(Due to coil inductance)

Fundamental resonance

Figure 8.14  Moving‐coil driver input impedance. 2.7 mH

4.2 μF 5 μF

0.6 mH Zin (Not constant)

+

–

LF 5 μF

HF –

0.25 mH

+

Figure 8.15  Successful commercial 3 kHz, third‐order crossover (KEF R104 system).

Impedance (Ω)

Systems and Crossovers

128 64 32 16 8 10

50 100

500 1000

5000

20000

Frequency (Hz)

Figure 8.16  KEF Model 104, impedance frequency (note historic use of a logarithmic amplitude scale).

solutions. So how may useful crossovers be designed if the basic theory appears to have so little relevance? The answer lies in the extension of filter network theory to include the other relevant parameters represented in the overall loudspeaker system. In particular, this involves computing the crossover response in terms of the combined acoustic output of the drivers instead of using the academic theory for simplistic voltages to be applied to the driver terminals. By moving outside the system, and in front of the enclosure, it becomes obvious that the crossover requirement is for the overall response or transfer function, and to additionally include the in situ acoustic output of the mounted drivers. The driver parameters—motor‐coil inductance and resistance, frequency and phase response and the loaded motional impedance must also be accounted for in the overall network theory model, while also ensuring that the system as a whole still offers a sensible impedance load for the matching amplifier. The characteristic loading generated in Figure 8.15 is shown in the system impedance curve (Figure 8.16), and is clearly not a constant 8Ω. In this example this does not cause any great difficulty for the driving amplifier as there are no harmful dips. However, for this successfully manufactured example there remained some lack of correspondence between the measured acoustic output and the Figure 8.15 target crossover network response, and this is shown in Figure  8.17. The discrepancy gave  rise to some errors for the completed system response, and also some mild colouration. For the second generation of the design, the network of Figure 8.15 was further developed to incorporate electrical compensation, both for the motional impedance of the fundamental resonance, and also for the overall intrinsic impedance characteristic of the HF unit. The equivalent circuit for these electromechanical components was entered in a computer program, together with data for the intrinsic amplitude response. A new network was synthesized which was designed to more closely approach the intended 18 dB/octave Butterworth response for acoustic output. The success of the new network is now seen in the close agreement between the measured and calculated responses and is shown in Figure 8.18. Figure  8.19 illustrates the initial theoretical form of this compensated high‐pass network with Figure 8.20 illustrating a practical realization, while Figure 8.21 reveals the numerical values used in a commercial system. For calculation, the following relationship holds

CA

C1C2 CB C1 C 2 C 3

C1C3 CC C1 C 2 C 3

C2C3 C1 C 2 C 3

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High Performance Loudspeakers

Figure 8.17  20 mm T27 HF unit output; measured (bold) and target responses amplitude and phase (see Figure 8.15; Source: KEF, with permission).

100

90

80

70 Theoretical

60

Measured

50

+180

+90

Sound pressure (dB)

360

0

–90

500

1000

2000

–180 5000 10000 20000 40000 Hz

Figure  8.20 was derived by applying the Star‐Delta transform to Figure  8.19. For a simple analysis it was sufficient to view the circuit as a lumped approximation and it can be readily seen that the damped Q of the shunt inductor provides a first slope of 6 dB/ octave, summing with the driver’s natural 12 dB/octave slope to provide the required 18 dB/ct. The second capacitor C4 is equivalent to the moving mass of the diaphragm and forms part of the complete synthesis. C4 causes the derivative of the current waveform in the driver to follow the Butterworth curve, so resulting in constant motor‐coil acceleration. Interestingly the practical values of the basic ‘T’ section network are now quite close to those established theoretically for a driver with a perfectly resistive load. 8.3.7  Non‐Time Coincident Drivers and the Effect of Distance Ideally, the time origins for the output of drivers in multi‐way loudspeaker systems should be coincident. If this can be accomplished crossover design follows the theoretical principles much more closely, provided that allowances have also been made for enclosure diffraction and the natural frequency and delay characteristics of the drivers.

Figure 8.18  New high‐pass network; measured (bold) and theoretical responses (Source: Courtesy KEF Audio).

100

90

80

70

60

Theoretical Measured

50

+180

Sound pressure (dB)

+90

0

–90

500

1000

2000

–180 5000 10000 20000 40000 Hz

Figure 8.19  Theoretical circuit of new third‐order compensated high‐pass section (Source: Courtesy KEF Audio).

CB

CA

R2

Cc

C4

– HF

L + R1 +

Figure 8.20  Practical realization of new network.

R2 C1

C2

C3

C4

–

L R1

HF +

362

High Performance Loudspeakers 0.6 μF

3.3 μF

10 μF 0.3 mH +(0.55Ω)

Figure 8.21  Finally, the values used in the commercial system (R104AB) (Source: Courtesy KEF Audio), and with 0.55 ohm damping incorporated in the 0.3 mH inductor.

3Ω

10 μF

– HF +

In practice, most drivers are mounted on a common baffle plane for convenience, and to control cost, and are consequently non‐coincident. For a typical 3 kHz MF–HF crossover frequency, the resulting time difference may require an additional 90 or even 180‐degree phase shift between the drivers so that the combined acoustic outputs to integrate satisfactorily in the far field. Certainly, it is possible to tweak the textbook crossover component values to try and shape amplitude and phase in the respective crossover bands in order to achieve the best axial and off‐axis compromise, and this is done frequently, but a further problem remains. Suppose such a compensating optimization is undertaken at the typical 1 m measuring distance. Now, move out to 2 or even 3 meters, and we may see such efforts prejudiced by the relative phases of the drivers continuing to alter with distance, this due to a fundamental lack of time coincidence. Conversely fully active systems, may, to their advantage, have electronically corrected these time delay errors at source. Designers of passive systems should seek to exploit geometrical possibilities for the enclosure, with respect to listener head height, to adjust and minimize radiation and arrival errors, for example, in some examples by inverting the high‐frequency driver location, now to sit below the mid unit. In the case of some more costly systems, the front panel may be slanted and progressively narrowed to tilt the radiation plane of the respective driver away from the listener so improving the relative driver delay and the effective power response. 8.3.8  Compensation for Driver Impedance, Motional and Electrical A moving‐coil driver may be represented by an electrical equivalent circuit consisting of the coil components Rc and Lc, and the transformed, mechanical components LCES, CMEC and REC (see Figure 8.22). For a low‐frequency unit, usually, but not invariably, the fundamental resonance component is driven directly by the amplifier and does not require compensation in this crossover termination context. However, with mid and HF drivers, their fundamental resonances can be sufficiently near the crossover region to cause mis‐termination and are often worth neutralizing as a first stage in network design. Figure 8.22 can be simplified if specific frequency ranges are considered separately (Figure 8.23). A consequence of the mis‐termination of a crossover filter is clearly shown in Figure 8.24. Here a proposed first order crossover at 7 kHz consisted of a single capacitor and was to be used with an HF unit having a response curve ‘A’. While the roll‐off down to 1.5 kHz approximates to the intended 6 dB/octave slope in the resulting curve ‘B’, the increase in motional impedance at driver resonance (850 Hz) then causes the output to rise sharply,

Re Lc

Rc

Moving system element

Motor coil Zin CMEC R nominal

LCES

REC

Figure 8.22  Moving‐coil driver equivalent circuit. Figure 8.23  Simplified driver impedance equivalents over specific frequency bands (see Figure 8.22). (a) At mid frequencies, (b) at high frequencies and (c) at near resonance; low frequencies.

(a) Rc

(b) Rc

Lc

(c) Rc CMEC

Sound pressure (dB)

–9

Natural rolloff 12 dB octave

Basic driver response 6 dB

–15 –21

100

octave

A

–27 –33

REC

Upper resonance

+3 –3

LCES

18 dB B 200

Theoretical 6 dB octave response

octave

500

1k

2k

5k

10 k

20 k

fc Frequency (Hz)

Figure 8.24  Moving‐coil driver response, high pass; A, alone; B, with first‐order series capacitor, fc = 7 kHz.

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High Performance Loudspeakers

Rc

Req

Lc

Ceq Compensation

Driver

Figure 8.25  Circuit and equations for motor‐coil inductance compensation; Req = RC, C eq

LC /Rc2 .

almost peaking to reference output level. Then, below resonance, the slope now follows an 18 dB/octave roll‐off due to the capacitor summing with the intrinsic second order driver roll‐off of 12 dB/oct, below resonance. Finally, at the highest frequencies that seemingly simple series capacitor filter now begins to weakly resonate with the tweeter coil inductance, imparting some rise in output beyond 10 kHz. The overall response result bears little resemblance to the required 6 dB/octave high‐pass characteristic. To fix this massive error due to the mis‐termination of the series capacitor, firstly the voice coil inductance may be compensated by a series R and C combination connected in parallel with the driver terminals (Figure 8.25). If the motor coil values are Rc and Lc, to a first approximation the equalization components are calculated as follows: Req

frequency.

Rc and Ceq

Lc ……… where Rc is the a.c. resistance at the required Rc2

A typical 25 mm diameter voice coil HF unit might have a 6.4Ω resistance and a 0.15 mH inductance, suggesting respective values for Req and Ceq of 7.5Ω and 0.366μF. The fact that this compensation is available also gives the designer some freedom for adjusting the response at more extended frequencies. The driver motional impedance also peaks at resonance, and a simple compensation may comprise a series resonant circuit, this connected in parallel with the voice coil, largely accounting for the electrical equivalent components of the motional resonance, and thus imparting a uniform input impedance curve for the combination; the latter is shown before and after correction in Figure 8.26. The correction circuit used is shown in Figure 8.27. The mechanical resonant frequency and its Q may be determined from the impedance curve and an equalization circuit synthesized to match these results. The inductance compensation values may be found by experiment, which in practice proves relatively simple to achieve. If added to the driver, an appropriate viscosity of a magnetic fluid may also serve to fully damp the motional resonance, then allowing use of a simple first order crossover using a series capacitor, this a well‐practiced technique. 8.3.9  Low‐Order Crossover Considerations Designers argue at length about preferred crossover orders, and not least, crossover complexity. High‐order crossovers provide opportunities for fine‐tuning both the

Systems and Crossovers

Resistance (Ω)

20 A

15 10 5 100

B

f0 200

500

1k

2k

5k

10 k

6.4 Ω

20 k

Frequency (Hz)

Figure 8.26  Curve A, impedance curve of 10 mm plastic dome HF unit. Curve B, as for curve A but with compensation circuit of Figure 8.27. Figure 8.27  Full compensation circuit for non‐uniform impedance of HF driver shown in Figure 8.26 (values here were determined by experiment).

9.2 Ω

8.6 Ω

1.6 mH

1.47 μF

8.7 μF (for f0)

(for f1)

amplitude and phase of the driver target function while the steep roll‐out slopes which can be realized help minimize the acoustic overlap between the drive units. This behavior looks good on measurement, particularly in respect of a well‐defined and consistent axial response. But some designers may still argue that the poorer transient response, that is, with the potential for more extended ringing on music impulses from higher order filters, may be audible in the overall sound quality. High‐order filters have greater phase shift and may ‘ring’, perhaps with audible timbre. Consequently, a number of designers are returning to low‐order crossover filters, taking care to control relevant matching aspects of driver parameters so that good results may still be achieved, despite the much reduced number of variables that now remain to the loudspeaker system designer. It could be argued that higher‐order crossovers are more the province of the independent designer working with available drive units, while the designer blessed with the resources to define customised units will take the opportunity to use simpler crossovers to achieve a well‐integrated design. When optimally executed, loudspeaker systems with low‐order crossovers, in particular first order, often sound as if the several drive units are blended more smoothly. The transition to a tweeter, often audibly voiced with a degree of ‘nasality’ heard in many loudspeakers, may now be rendered undetectable, while the power response of the speaker will also be more uniform thanks to the broader region of blend and overlap between the drivers. Benefits also include a greatly reduced number of crossover components which may result in lower cost. Greater perceived

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transparency may be heard, together with improved subjective dynamics. Those latter qualities do seem to suffer a progressive dilution with increasing crossover complexity. Control of inter‐driver phase is vital, otherwise broad suck‐outs will occur in parts of the frequency response. Good phase control must be achieved via the inherent, designed characteristics of the driver diaphragms and their well‐behaved motional impedances, also noting the calculated phase shifts from the chosen crossover type, then the relative phase of the drivers (and their polarity), and finally any helpful compensation for inter driver delay afforded by enclosure design and suitably displaced driver mountings. Ideally, the low‐frequency driver, mounted in the required cabinet and with the latter located as directed with respect to local boundaries, will be designed for a naturally uniform frequency response, and ideally terminating in a well‐controlled roll‐off at the intended crossover frequency. Such a characteristic may be achieved by design of the voice coil winding, its mass and inductance, for example, by using a heavier four‐layer winding with higher inductance. The variables of cone design also may be iterated to generate the target response shape through control of material thickness, flare curvature, surface coatings and surround termination. Via the adjustment of magnet flux, the system Qtc may be adjusted to give an optimum bass balance to the mid‐range timbre for a given enclosure design, working in that defined acoustic space. If necessary a remaining degree of response excess may be easily controlled by a small series inductor, perhaps augmented by a vestigial, low Q and compensating termination. For the high‐frequency unit it is necessary to account for that essential series capacitor which keeps the low frequencies out of this delicate driver. We noted that a series capacitor reacts unfavorably with the moving‐coil driver’s motional impedance (see Figure 8.24) and where the resulting response curve was strongly modified by the complex impedance loading presented by the driver. For a first‐order crossover design the treble driver should be designed so that its motional impedance characteristic is largely resistive, for example, derived from mechanical damping (the viscosity of the Ferrofluid, the diaphragm suspension characteristics, and if used the role of extended acoustic chambers and associated resistive damping). In effect the mechanical properties and frequency response of the tweeter, defined and designed in situ for the enclosure, are then tuned with the crossover capacitor for the desired response. In such designs the tweeter may well have to accept more power in its low‐frequency band and its power handling and linearity may need to be superior to those drivers customarily used with higher order crossovers. An interesting behavior for such designs concerns the effect of adjusting the series capacitor (of usual value between 2.2μF and 4.4μF) for the first‐order filter type. In addition to moving the crossover point, it may simultaneously act as an effective attenuator over the treble range. Because of the broader overlap for the driver pass bands, quite small changes in capacitor value, or for that matter for the series inductor to the bass unit, will substantially alter the sound of the system as the changes will be audible over several octaves. It is clearly a great advantage to use drivers with smoothly extended frequency ranges and which also have low colouration outside of their intended working range. Perhaps fortuitously with first order, the broad transitions present between the drivers will help to smooth out dips in the frequency response of one driver thanks to the infilling overlap provided by the other. If well executed in the system design, a desirably uniform power response results, and consequently there is a more natural reverberant sound in typical listening

Systems and Crossovers

rooms. Also small errors in relative driver sensitivity will alter the sound quality rather less than with high‐slope crossover designs, avoiding that frequently audible ‘response step’ artifact that may occur with adjacent high‐order driver pass‐bands when they are significantly mismatched in level. 8.3.10  External Crossover Location Where the price point permits, there are good arguments for placing the crossover outside the enclosure. Noting the increase in cost for an extra cable and connections, and depending on whether a captive harness or alternatively a detachable set of cables is chosen, an external but nearby location for the crossover assembly will improve overall sound quality through its removal from the acoustical, vibration, electromagnetic, and static magnetic fields present within the enclosure. Design for an external crossover requires an additional pair of small boxes to enclose, and to provide sturdy cable terminations. The method allows for easy changeover, upgrade, to active operation, where the passive external crossover is simply omitted from the cable run and matching active filters are then connected ahead of the required number of power amplifier channels. Where a few manufactures offer this option the performance gain is substantial, though at considerable additional expenditure. 8.3.11  D’Appolito Configuration For the vertically orientated, ‘M–T–M’ mid‐treble‐mid, three‐driver configuration popularised by D’Appolito (but which was also used in much earlier loudspeaker designs, including the 1980 Bob Stuart designed M2 active), matched moderate‐sized bass–mid or mid‐range drivers are located above and below an HF unit or tweeter. The larger drivers carry identical signals which aspect beneficially confers radiation symmetry in the vertical axis. This contrasts with the common M‐T array which is certainly not symmetric in the vertical plane. One could view the M‐T‐M arrangement as a laterally truncated section of a concentric driver, and some of the directivity advantages of a concentric are attributable to the array. Laurie Fincham also used this array for the mid‐treble section of the ground breaking KEF R104II system back in 1984. The crossover design aims to integrate the phase of the MTM drivers as accurately as possible in order to attain a sufficiently wide lobe in the vertical plane. The greater than usual source height narrows the azimunth radiation pattern. It is thus a good idea to choose a lower crossover frequency in order to widen this lobe, but the result still be significantly narrower than for a conventional two driver mid‐treble arrangement. At the frequencies concerned the directivity in the horizontal plane is generally dominated by cabinet width. Also note that over the crossover region the phase control required to get a uniform axial response may result in an unexpected variation for off‐axis power. For a particular example, an enclosure 22 cm wide allowed for the installation of a three‐driver MTM array using two 17 cm frame mid units and a 25 mm dome tweeter (typically on a 10 cm chassis). The overall source height is nominally 45 cm. Note that at the usual 3 kHz crossover point the wavelength is around 10 cm and thus the directivity in the vertical plane will be significantly narrowed (Figure  8.28) due to array height. Also, some irregularities may be added to the tweeter output as compared with the more usual flat baffle location due to the proximity of the pair of acoustic cavities

367

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High Performance Loudspeakers

50° 40°

20° 10°

–30

–20

–10

–3

dB +3

+10

–10° –20°

B3 L–R 12/ + 18dB/OCT

–40° –50°

Figure 8.28  Vertical polar response, three‐driver, central tweeter MTM/arrangement, 2 kHz crossover point. 2 × 110 mm bass mid, 28 mm dome. Key: – – –, even‐order Linkwitz type (in phase); ____odd‐order Butterworth (third); – · – · – even and odd mix (12/18 dB. D’Appolito seeks 90‐degree shift held constant through crossover region to maintain vertical lobe symmetry and uniformity) (after D’Appolito).

presented by the mid‐range cones. If the system is of sufficient quality, the designer might consider flat or very shallow diaphragms for this configuration to improve this aspect. Comparing with the sound quality of a conventional two‐driver array with the tweeter uppermost near the top of the cabinet, you have to consider the trade‐off between the symmetric but narrowed lobe at crossover for the M–T–M, compared with a potentially asymmetric but wider angle of vertical axis response for the standard crossover arrangement. Making the assumption that for both types the designer has obtained a usefully uniform and balanced axial reference response, with good driver integration, there will still remain a significant difference in ‘character’ for the sound quality, due to the different way in which the room acoustic is driven. For the conventional type, with the tweeter in the uppermost position the tweeter is radiating into a wide angle acoustic load, located near the enclosure perimeter; it is effectively placed at the edge of a prism with significant energy is also directed into the space above the loudspeaker. As regards the room driven sound, it will carry a sample of that energy reflected from the ceiling; this brighter sounding ‘acoustic’ helps give such upper mounted tweeter systems their characteristic sense of life and air.

Systems and Crossovers

Conversely for the triple driver array, two factors conspire to reduce the amount of energy directed off axis over the vertical axis or plane. First, there is the defined narrower directivity due to the increased height of the array in the crossover region, and secondly, the placement of the tweeter farther from the top edge of the cabinet, which acoustically ‘shadows’ the region above the cabinet. (This latter consideration also applies for the equivalent orientation for a two‐driver arrangement where the tweeter is placed below the mid or bass–mid‐unit, usually for reasons of phase and/or delay control.) Consequently, the sound of these systems may be duller and less ‘airy’ in the room acoustic. Octave by octave, tweeter level matching may need sensitive balancing to give a satisfactory result. In addition the high frequency output may not be as uniform, since the adjacent and driven, moving ‘depressions’, effectively these a local baffle represented by the bass –mid, or mid units, do not really constitute an ideal acoustic load. 8.3.12  Open or Top Location for an HF Unit This is a convenient point to consider another extreme for tweeter placement, namely that of a baffle less or ‘bullet’ style of tweeter mounting where the complete high‐frequency unit is barely larger than the dome itself and is presented on the top surface of the cabinet, either alone or on an equivalent small baffle, or perhaps on a locally narrowed, tapered cabinet section. The effect of a vestigial or complete absence of baffle or mounting surface for the tweeter confers an unusually wide directivity in its lower operating range. This must be taken into account during the system alignment since it may cause problems when attempting to design for a smooth energy transition with frequency; e.g. the transition from the mid‐range (with its narrowing directivity) to the tweeter (here a sudden transition to a much wider directivity). Without skilful control of energy balance, these systems have a tendency to leave the tweeter sounding ‘exposed’, perhaps lacking the best subjective integration achievable with the full baffle types. The exposed tweeter mounting may also be rendered audible from the step in power response as it integrates into the room acoustic. Comparing this latter wider directivity case with the D’Appolito, centrally mounted tweeter, or similarly for the two‐driver, ‘low mounted’ tweeter case, their effectively narrower directivity will require consideration concerning the target energy response. Frequently a balance between the energy response and the axial response is the designer’s goal. This balance may appear subtle but is significantly different for each of these mounting configurations, and the difference may not be clearly revealed in computer‐ aided syntheses. Measurement and listening is essential to confirm the validity and usefulness of computed analyses, and further adjustment may be required. 8.3.13  High‐Order Crossover Considerations High‐order crossovers have their advocates. If executed with top‐quality components, with low losses and close tolerances, they can provide reassuringly consistent transfer functions for the whole speaker; variations in driver performance which may be present out of band are essentially blocked from affecting the final result. Additionally, the narrow region of crossover overlap delivered minimizes the audible effect of this troublesome region on the desired output.

369

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High Performance Loudspeakers

In practice losses of both power and fidelity accrue with increasing order and complexity. An ‘acoustic’ effective fourth order is as high as most designers are prepared to venture. Note that the ‘order’ represents the acoustic target function and reaching it is not necessarily the sole responsibility of the crossover network as the inherent driver characteristics also need to be accounted for. Borrowing from the more complex theory of mutual inductance coupling, long used for high‐slope band‐pass filters in radio engineering, one designer (Richard Modafferi: inventor of the ‘Infinite Slope’ US patent 4771466) has patented its application to loudspeakers, and shows how usefully high slopes may be obtained with minimal overlap while using a basic network, but one which has been augmented by deceptively simple mutual coupling elements, essentially defined by the critical placement of existing inductors on the circuit board. In practice slopes of 100 dB/octave are possible over short sections of frequency, while circuit analysis using the pole‐zero technique, allows the completed system to have a smooth phase response thanks to the clean join achieved at the crossover points where the summation technique is most precise. If near brick wall shapes can be attained for the high‐ and low‐pass functions at the crossover point, then the negligible overlap of driver energy ensures tight control. Figure 8.29 shows a two‐way design, essentially fourth order, where the very steep initial slope is generated by additional impedances derived from the small ‘stray’ mutual coupling arranged between the inductors. Briefly, poles and zeros are respectively the roots of the denominator and numerator polynomials for the transfer‐function equation which characterizes the amplitude and phase response of the filter network; for example, on the complex plane, poles indicate the level at or near their frequencies, while at or near zeros, the level is zero. For an example given by Modafferi (Figure 8.30) a conventional fourth‐order low‐pass crossover is compared with the mutually coupled alternative Figure 8.29. Here greatly simplifying the electrical theory which governs the operation, the circuit is altered such (a)

(b)

C2

Input C1

Output

× ×

× ×

O

jw

Two zeros at infinity S

(c) 100 dB/octave

Frequency

Figure 8.29  (a) Infinite slope woofer filter circuit. (b) Upper LHP pole‐zero plot. (c) Amplitude response.

Systems and Crossovers

(a)

(b) L1

Input

jw

L2

C2

C1

Output

× ×

× ×

Four zeros at infinity S

(c) 24 dB/octave

Frequency

Figure 8.30  (a) 24 dB/octave low‐pass filter circuit. (b) Upper LHP pole‐zero plot. (c) Amplitude response.

that an allowed pair of the four zeros, which in the standard form would lie at infinity, are now brought near to the poles (the diagram in Figure 8.29 shows one pole, the other is in the ‐jω quadrant and is not shown). The magnetic mutual coupling has an implied, multiplying, ratio transformer which features in the underlying equations and results in the high roll‐off slope shown in the final response. Higher‐order crossovers may executed in the digital filter domain where a fascinating variety of choices become available and may be readily prototyped, aided by sutable electronic delay where required. 8.3.14  Notched Crossover Networks Thiele gives a practical analysis and design guidance for ‘notched’ crossover filters where a really steep augmented roll‐off is desirable, for example to suppress a nearby, if just out of band, response peak. Some aspects of the work presented are the subject of a patent application.[7] 8.3.15  Amplitude Response Equalization Equalization of the driver impedance has been discussed, but this step may be academic unless the driver frequency response is already uniform, which is rarely the case. Thus in most high‐performance systems some form of response equalization is almost invariably included. For a passive design the crossover takes on this task, for the active, the signal is appropriately equalized at low level in the electronics Equalization is possible where the response irregularities are in the form of gentle trends rather than severe narrow‐band discontinuities with associated non‐minimum‐phase characteristics. Clearly, passive equalization will alter the input impedance of the entire system. A rise in impedance due to response correction is of little consequence, but a

371

High Performance Loudspeakers

significant fall in load impedance, as a result of compensation for response droop, may be undesirable due to amplifier matching problems. In practice, sound pressure dips of around 2 dB maximum may be equalized successfully, and no limit appears necessary for the correction of excess level, provided that the errors to be corrected are moderate in slope. A typical 170 mm plastic‐cone bass/mid‐range driver, when mounted in a 15‐litre enclosure designed for stand mounting, may exhibit a well‐behaved axial response continuing to rise from approximately 400 Hz to 2 kHz and possibly beyond. This will be due to intrinsic cone behavior plus a degree of enclosure diffraction lift, that 3 dB step. If the objective is a balanced and uniform axial sound pressure response in the far field then equalization must be applied. With active crossovers, an equalization stage may simply be added to the electronic filter, while in the case of the passive crossover filter the equalization is usually integrated with the crossover design. In the case of the 200 mm driver (Figure 8.31), the upwards response slope may be seen to approximate to 4 dB/octave, which characteristic could be compensated by a suitable series inductance fitted with a parallel resistance. When setting the values, the motor‐coil inductance must be also taken into account, the latter typically of the order of 0.35 mH for a long‐throw design. Approximately 2.2 mH of additional series inductance is required for the equalization, and the inductor may be split into 1.6 and 0.6 mH sections, the latter with a parallel 22Ω resistor (Figure 8.32). The latter value is selected to equalise the slope to match the rate of rise from the driver and system at upper frequencies. A third‐order low‐pass ‘T’ configuration crossover may be successfully aligned with such equalization by adding the necessary capacitor at the inductor junction, and dimensioning it for the desired crossover frequency (Figure 8.33(a)). The Butterworth relation no longer holds for the crossover due to the non‐standard values and due note should be taken of the altered overall frequency and phase response of this filter/ equalizer. With this third order configuration noted, a peak may readily develop at crossover, which is usually adequately damped by an additional resistance; fortunately this is already present in the example given previously (R in Figure 8.32(a)). A resistor in

80 Sound pressure (dB)

372

70

Driver alone

60 Equalization Equalized driver

50 20

50

100

200

500

1k

2k

5k

10 k

Frequency (Hz)

Figure 8.31  Electrical equalization of 200 mm frame size plastic‐cone driver.

Systems and Crossovers

Figure 8.32  (a) Passive equalizations; (b) damped shunt resonant circuit to provide equalizing dip in crossover characteristic (L is often combined with R by suitable choice of wire gauge); (c) series resonant circuit to provide equalizing dip in response to correct for a peak in an HF unit response (typically 12 to15 kHz for a dome unit—example values are for 13 kHz).

(a)

R L1 L2 Equalization

R

L2

L1

Rc Equivalent circuit Lc

(b)

L1

Damped shunt resonant circuit

L C

C1

R

(c)

1 μF 6.2 Ω

0.15 mH

series with the shunt capacitor also provides useful scope for adjustment of the network Q factor. Where large series inductance is required for such primary equalization, the ability to readily shape and, if necessary, peak the response in the range close to crossover can be very helpful in fine‐tuning the amplitude and phase response of the system, particularly on the required listening axis. A wide range of equalisation and phase angles may be readily obtained.

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High Performance Loudspeakers

(a) 22 Ω 1.6 mH 0.6 mH 4 μF

Bass/mid driver

(b)

4.7 μF 0.35 mH

L

Figure 8.33  (a) Equalized third‐order low‐pass filter incorporating Figure 8.32. fc ≃ 3 kHz, 18 dB/ octave; (b) terminated series/shunt notch filter for high Q dome resonance.

For Figure 8.32(b) an alternative shunt form of equalization is shown. This is useful for controlling a rise in output present over a limited frequency range, perhaps half to one octave. Finally, a useful circuit is shown which is often employed to equalize the mild peaks often found in the upper range response of dome HF units (in Figure 8.32(c)). This is a fairly low Q circuit. Where narrower band compensation is required more elaborate circuits may be required. For a particular example using a dome HF unit the high‐pass network was nominally 12 dB/octave second‐order but the acoustic output was marred by a significant 5 to 6 dB rise at its fundamental resonance. In compensation the shunt inductor was set rather lower than usual (by 30%) to improve the response. This driver also exhibited a first resonant mode of rather high Q at 21 kHz, considered undesirable, and it was subjected to equalization. A series notch filter proved insufficient and could not be designed to provide sufficient depth. This required termination with a second shunt network placed across the driver terminals. Above 21 kHz the system then presents a rather low and capacitative input impedance (Figure 8.33(b)). When several filter sections are cascaded, as for the band‐pass section of a mid‐range driver, further unwanted interaction may occur and hence some trial and error modification of the theoretical values is to be expected, this quite easily expedited with speaker system design software. Some commercial crossovers are shown in Figure 8.34(a) and (b). 8.3.16  Computer‐Aided Crossover Design Many programs[8–10] and software packages have been devised to synthesize crossover networks according to a target function. The latter corresponds to the desired combined acoustic output from the driver and enclosure set. The drive‐unit parameters are entered e.g. Rdc, Lc, f0, etc. plus data corresponding to the intrinsic axial, and ideally also the off axis frequency responses. Trial networks may be formulated, and according to

Systems and Crossovers +

16.8 μF

1.75 mH

8 mH 9 mH 12.2 μF 22 Ω

56 Ω

6.8 μF

20 μF

1.93 mH

LF

15.5 mH

1.75 mH

33 Ω

4.4 μF MF

10 Ω

– 1.5 μF (S.O.T)

HF

3Ω

0.047 mH VHF

2.2 μF

4.4 μF

(S.O.T)

2.2 μF

Figure 8.34a  Commercial high‐performance four‐way third‐order crossover (Spendor BC3). Crossover points at 500 Hz, 3 kHz, 13 kHz. ‘S O T’ = adjusted on test to match HF sensitivity. HF unit (HF1300) rolls off naturally above 14 kHz. LF is a 305 mm Bextrene cone, MF a 200 mm Bextrene cone, HF a 38 mm dome and VHF a 19 mm dome (see Figure 8.3; Source: Courtesy Spendor Ltd). 100 μF

480 μF 5.7 mH

2.2 Ω

100 μF

8.4 μF

0.27 mH

0.34 mH 8.4 mH LF

240 μF

3.4 mH 7.5 mH

+

600 μF

– 68 Ω

12 μF LF

0.56 mH

–

16 μF

50 μF

30 μF

10 Ω

240 μF

+

11.2 μF

11.2 μF

0.56 mH

+

+

+ 0.17 mH

8.1 mH

–

6.8 Ω

1Ω

–

10 μF

–

450 μF

Figure 8.34b  A computer‐aided design of crossover for a three‐way moving‐coil design incorporating full input impedance compensation, to realize a near 4Ω resistive load. The vertical directivity is adjusted by the delayed input to one of the mid‐drivers, R104II (Source: Courtesy KEF Audio).

the program options, choosing second, third or fourth order. In effect, the computer, via an iterative successive approximation process generates an equalizer/crossover network for an overall acoustic output approaching the target function. The result should correspond to the required response, in this case the fourth‐order Butterworth (Figure 8.35(a) and (b)) or one that the designer may enter. For the example, the driver response is far from ideal in the intended crossover region and has been corrected by an equalizer which also includes the required crossover characteristic. Other refinements include the trial substitution of nearest standard value components with a second analysis to establish how close this constrained solution comes to the ideal. The effect of all tolerances may also be examined, while system input

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High Performance Loudspeakers

(Ω) 8.0

Impedance

376

6.0

4.0

2.0

0 0.01

0.1

1

10

20

Frequency (kHz)

Figure 8.34c  The resulting load impedance for the compensated system of (b). Between 20 Hz and 12 kHz, it lies within ±0.5Ω of 4Ω. Rg

~

Equalizer

Load

Zq(w) ZL(w)

Figure 8.35a  Equalizer/crossover principle.

impedance and off‐axis response simulations are also useful features (see Figure 8.35(b)). (See Appendix A for software.) 8.3.17  Acoustic Centre and Delay Advanced computation of crossover networks, including prediction of phase control, is founded on knowledge of the acoustic driving point relative to the mounting plane. It is useful to consider the relative delay between a mid and a high‐frequency unit. For dome tweeters, the driving point is considered to be very close to the rim of the dome. For a cone driver, the apex, at, or just below the dust cap, is a good starting point. For a typical 170 mm driver 2 inches or 51 mm delay is allowed from the baffle plane; perhaps 1.5 inches (38 mm) for a shallow, larger voice coil type. Relative to the mounting plane the tweeter delay will be in the range of 2 to 4 mm, which is almost negligible in phase terms.

Systems and Crossovers Measure RL(w), XL(w) Specify VL(w) Calculate T(w2) Fit approximate network to VL(w)

Calculate approximate Xq(w) Find Rq(w) from 3 Find new Xq(w) by H.T.

Substitute Xq(w), Rq(w) into 2

Is error in T(w2) less than ?dB

Calculate new Rq(w) from 3 using new Xq(w)

No

Yes Stop iteration, print Rq(w), Xq(w)

Figure 8.35b  Early flow chart for crossover synthesis (after Jones[9]).

The 170 mm chassis example cited would show a delay of about 180μs. When a crossover frequency is specified, note that additional factors will affect the phase shift present, for example, the electrical inductance of the driver voice coil, together with a delay contribution from the natural, low‐pass, characteristic frequency response of the filtered driver. For example, if a 3 kHz crossover point is selected and the driver has a 12 dB/octave second‐order filter, together with a natural roll‐off at 6 kHz, then this intrinsic low‐pass characteristic will result in an additional phase shift at 3 kHz. For a given frequency fc, the phase shift (in degrees) = delay × 360 × fc.



delay

s

acoustic distance mm 343 000



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High Performance Loudspeakers Active filter crossovers +8 +4 0 –4 Response (dB)

378

–8 –12 –16 –20 –24

500

1k

2k Frequency (Hz)

5k

10k

Figure 8.35c  Computer synthesis for motor‐coil response to equalize axial response irregularity at crossover: ‐ · ‐ · ‐ required speaker response (second order); __ actual speaker response; – – – motor‐coil response;  –— ‐ –— ‐, sensitivity corrected motor‐coil response (after Jones[9]).

The driver delay is somewhat dependent on frequency. For example, the value for 25 mm tweeter delay does not settle down until above 4 kHz, well above of the ­f undamental resonance. At 1.6 kHz the delay may be halved by the additional effect of the fundamental resonance and may also depend on its Q factor. These changes are precisely in the region where phase control is important to help predict crossover design and control performance. Such complications help to explain why it is sometimes worth trying out total phase inversion to the tweeter during the development of a speaker system. That 180 degrees of phase shift, even if at first sight theoretically incorrect may well provide sufficient freedom to then realign the networks in this alternate phase connection to see if the  design will achieve effective phase integration through the crossover region (see Figure 8.36).

8.3.18  Passive Delay Several designers have employed passive delay networks to bring dissimilarly spaced drivers into the same time envelope. Multiple half‐section networks have been used but have proved costly in components and the inevitable cumulative loss introduced must be held

Systems and Crossovers 600 500 400 300 200 100 0 –100 –200 –300 –400 –500 –600

0

0.503

1.006

1.509

Figure 8.36  Impulse response for a system with woofer 35 mm in front of tweeter (· · · · ·) and with the tweeter 35 mm in front of the woofer (‐‐‐).[6] Figure 8.37  (a) High‐pass ladder delay network, and (b) all‐pass symmetric delay network (for 25 mm dome, 200 mm bass, fc = 3 kHz, delay = 152 us ≡ 5.2 cm). This network is for 8Ω but is in practice is mis‐ terminated (Source: Courtesy Tannoy).

(a)

(b) L2 = 0.59 mH

C = 4.7 μF

L1 = 0.53 mH

C

8Ω C

C

L1

8Ω

L2

to sensible levels. Recently an all‐pass delay network has been tried which looked to be an attractive solution. In practice, the results from this basic network may be confounded by frequency response ripple, both in and out of band, plus accompanying additional phase shift, in part resulting from unavoidable mistermination of the all pass network. Thus, they are suspected of introducing as many problems as they solve (Figure 8.37).

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8.3.19  Series Connected Crossovers Rather than the popular shunt types discussed so far there is an equivalent set of crossover alignments based on the series connection of the drivers. These are little used since the transfer function of one arm of the network is rather dependent on the mix of impedances presented at the other arm. Advantageously, the overall input impedance tends to be better controlled than the parallel or shunt type, but the complex interaction of the required combination of components, passive and acoustical, makes for something of a design headache. However, the wider use of moderate cost crossover network simulators may increase its popularity. Nicolao and Maffioli[11] have neatly summarized their idealised proposition for loudspeaker system design in their published papers, which explore this often‐neglected group of series networks. They state that in general suitable drivers should have, and I quote: ‘equal sensitivities, wide frequency ranges, conveniently wide directivities constant with frequency, equal phase response in the broad crossover region, time origin coincidence and finally purely resistive input impedance: and experience reveals this hardly ever happens.’ The authors continue by concisely itemizing the vital responsibilities of the crossover network; 1) Balancing driver sensitivities; 2) Filtering the signal appropriately to the drivers in respect of their best, low diffraction bandwidth region; 3) Equalizing the pass‐band of each driver and adjusting their responses to meet the target function; 4) Taking account of, and as necessary compensating for, reactive driver impedance. However, their chosen subject is series crossovers of higher order. These rely on a level of computation which is orders of magnitude more difficult compared with the usual parallel filter due to the cross coupled interaction of every variable, this multiplied by the number of ways.

8.4 ­Crossover Component Considerations The larger high‐performance loudspeakers may need to handle considerable power, up to 1000 W of peak programme, this derived and scaled from the rated continuous output of an amplifier when driven to clipping point, for programme of average and application specific energy distribution over frequency. For PA applications some degree of overdrive, signal clipping or limiting, might well occur while for domestic conditions one has to assume that a costly audio system will be used with some discretion and largely kept out of overload. Nevertheless, the crossover network components for high‐fidelity application should exhibit low losses and possess an adequately high voltage and current capacity. Note that passive crossover parts are not as benign as they might at first appear from their

Systems and Crossovers

nominal values and specifications. Certainly, they are generally more accurate and more linear than the speaker drive units but it would be a mistake to imagine that some non‐linearity for the crossover components would never be audible in the overall reproduction, even if these errors are certainly not as damaging to fidelity as gross mechanical driver limiting. The choice of crossover component technology, and the particular quality of materials, design and manufacture, can have audible implications for high quality systems. 8.4.1 Inductors In the case of an inductance in series with a large LF unit, peak currents greater than 30 A are possible. With the sizeable inductance values required for third‐order networks, e.g. 8Ω rated, for crossover frequencies in the 250 to 500 Hz range, it is certainly costly to produce air‐cored components of sufficiently low loss, but it is certainly done at the high end. In a few cases the increased winding resistance may be exploited ‐ to provide control of crossover filter Q or to reduce excessive electromagnetic damping for a given low Q driver choice. Air core would be chosen preferentially for an absence of magnetic distortion and possible core overload, but will be costly and bulky due to the large copper content. The best of these are foil wound. The negative peak current reflected by a loudspeaker driver near resonance may be rather higher than anticipated due to the reactance generated by the substantial diaphragm moving mass. This can arrive sufficiently delayed, according to the bass driver transient response, to begin to sum with a following programme transient at the amplifier. Thus the main series inductor to a bass driver may need to handle a short‐term peak current greater than the rated power input to the driver might suggest.[12] Tests using simulated programme signals indicate that for a number of 8Ω rated, two‐ and three‐way systems of ‘steady state’ sinewave measured impedance, can reflect to the amplifier an equivalent transient or dynamic impedance just 25% of their nominal rated value. This may well lead to premature amplifier clipping and audible distortion bursts. The main lead inductor, if cored, needs a generous rating in this light. 8.4.2  Cored Inductors While adding a ferromagnetic core to the inductor allows the winding length to be considerably reduced, the core itself must never be allowed to enter saturation approaching peak level. For a given magnetic saturation point the ampere‐turns rating for ferrite cores is proportional to the core diameter, the latter limit usually taken to be for a 1% third harmonic distortion level. If low distortion figures for the system are important (this is particularly relevant in view of the more subjectively intrusive odd rather than even harmonic nature of magnetic core distortion), then the specified peak core flux for the design should be de‐rated by as much as 30%. As an inductor core is driven to saturation, the incremental inductance decreases sharply. This is due to the failure of the magnetic flux in the core to continue to rise linearly with the increasing current. Such a loss of ‘dynamic’ inductance may produce a sudden reduction in the system impedance during peak levels, particularly so for low‐ pass filter sections. This is likely to induce premature current overload in the driving

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amplifier and consequently increased distortion. The result may be a characteristic ‘cracking’ sound from the speaker as the inductor clips, this sound often blamed on the amplifier. High‐power tone burst signals may be used to explore this aspect of filter behavior. For 100 W peak programme rated 8 ohm systems, high‐quality ferrite cores of 19 mm diameter are adequate for inductor values up to 5 mH. At lower power levels, for example, up to 50 W, 12 mm cores are satisfactory while the ubiquitous lower power, two‐way 25 W systems commonly utilize cores in the 9.5 mm diameter range. For higher‐quality and/or lower impedances the core grade and size can be proportionally stepped up, noting that it is ‘ampere turns’ driving the flux density and usually fewer inductor coil turns are required for a lower impedance system. Well‐designed conventional air‐gapped transformer type cores are advisable when large inductance values are required and which have low loss and high current capacity. Ferrite cores need some consideration for critical applications as there is a significant variation in core quality between manufacturers and suppliers. Some grades exhibit notable hysteresis (i.e., the ‘S’ curve for magnetization is too ‘open’) and the resulting complex distortion products can mask fine musical detail. Magnetostriction is another side effect whereby the inductor core vibrates mechanically with the applied current, introducing vibration which can mask low level detail; also, its recovery to the quiescent state over the hysteresis cycle is accompanied by the delayed distortion signal induced in the current and magnetisation loop. Long BBC experience has suggested that plain, ordinary grade silicon iron laminated, gapped cores are subjectively quite favourable, while particularly good results for low distortion and high subjective transparency have been obtained using the costlier high nickel content Permalloy and similar specialized magnetic alloys for the laminations, here with a suitably toleranced air gap for the closed transformer types to define the required saturation margin and inductance. 8.4.3 Capacitors Electrolytic capacitors commonly used in crossover networks have acquired a poor reputation historically due to wide tolerances, poor stability and an increased loss factor at the upper audio frequencies. These criticisms are now less justified, since fine quality, moderately priced, reversible back to back electrolytic capacitors specifically designed for crossover use are available. High‐performance versions have also been developed, which offer lower loss and greatly improved tolerance and stability for general commercial applications. Life tests on normal grade (±20% tolerance) components have shown long‐term stability of better than ±2% (two years’ service), while at a premium they can be obtained to the 5% of value tolerance which is advised for the more critical applications. In the case of high‐performance designs such capacitors may be selected to a 2.5% tolerance by the speaker manufacturer. The usual rating of 50 V AC. allows a reasonable safety margin with 8Ω‐based systems, for up to100 W programme level, and 100 V versions are available for high‐power applications. Where the much‐increased cost can be justified, selected film capacitors are preferred for stability and lower loss. For networks where heavy equalization is involved note that voltages may rise considerably above the input value at certain nodes due to local voltage peaking and the

Systems and Crossovers

proposed network should be fully analysed with voltage and current ‘probes’ during synthesis, and in practice, to assess the ratings which may be required for the components; in some cases, up to 150 V AC may be necessary. Again, in the highest quality applications, loss factors such as variations for dielectric charge memory, together with the finite absorption factor of reversible electrolytics, may not be low enough for critical work. Tests have shown that under higher power music‐related impulse conditions (rather than steady‐state sine‐wave excitation) a bi‐polar electrolytic (reversible) cannot determine how to self‐polarize, and with a transient, may show a small degree of asymmetric rectifier‐like behaviour. Several designers now bypass electrolytics with smaller 5% to 10% of value, plastic film types to address this. Many prefer not to use electrolytics at all, especially now that large value film capacitors have become more widely available, many designed specifically for high power crossover duty. Electrolytic capacitors exhibit have some aging behavior over decades of use. Where lower losses, long life and closer tolerances are required, plastic or polymer film capacitors provide the answer. Some deposited film varieties have the additional advantage of self‐healing from transient voltage overload in the event of a minor film puncture. Values of 60μF and above are costly, and are usually built from combinations of smaller components. Where a high‐quality high‐power 50μF or 80μF capacitor is required, the designer should employ one of those special types designed for the purpose. Film capacitors might appear perfect from their electrical specifications but can exhibit susceptibility to physical vibration, and may also show mechanical self‐ resonance; indeed one proposal for an HF drive unit employed a flat‐case film capacitor as the motor element deriving from the intrinsic piezoelectric properties of the film dielectric. Imperfect capacitor charge recovery after transients, due to dielectric absorption and/or piezoelectric self‐resonance, is a potential source of audible ‘delayed’ resonances, though at present these are considered rather less serious than those found in drive units and enclosures. But that does not mean that they are not audible. Some designers have undertaken careful listening tests on a range of capacitor types. A typical 4.7 uF polypropylene film component may exhibit mechanical self‐resonance in the range 12 kHz to 18 kHz and this behavior may become audible as a very mild ‘fizz’ in the audio output of the system. A dampening jacket may help, while selecting for a higher rated voltage is advantageous; alternative constructions may be found with reduced self‐resonance and/or where the mechanical resonance frequency has been shifted to above the audible range While plastic film capacitors are widely used in critical applications for mid and high‐ frequency crossover sections, the larger values in used for the low pass section are frequently of the electrolytic type. At these lower frequencies the loss factor is usually sufficiently low, and the fairly small residual internal losses may be accounted for in the design. Only in the most critical designs are film capacitors used throughout. There are a few examples using mixed technology materials, even copper foil with oil‐filled paper insulation. 8.4.4  Crossover Circuit Geometry and Printed Circuit Board Design Due to the presence of potentially high currents in inductors, particularly when part of electrically resonant circuit filter loops, also noting the possible mutual inductive

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coupling of thoughtlessly orientated adjacent inductors, the construction and layout of crossover network components is highly important. If inductors need to be closely spaced (separation less than 20 mm), then they should always be positioned symmetrically, and with their axes at right angles to minimize mutual coupling. If this aspect is not addressed the residual breakthrough coupling signal can be as high as −20 dB or 10%. Where a printed circuit board is employed, then the conductor foils should be of adequate breadth and foil thickness to ensure low resistance, and in addition the track layout should be designed with a star layout so that common return paths for the various filter sections are avoided. The designer should also note the potential for an inductor to induce stray currents in a conductor track beneath it causing electrical crosstalk into another filter section. This consideration also concerns possible induced eddy currents in the conductor track below the inductor which may also increase the loss and reduce the designed Q value. When employed, the enclosure for the crossover also matters and in several manufactured networks have been placed in metal, or part metal enclosures with highly detrimental results due to significant electromagnetic coupling. A trial measurement may fail to clearly show much effect but a careful audition will reveal the error. Some manufacturers pot the crossover in a rigid setting resin to add substantial mechanical stability and damping to the assembly, though this makes service repair impossible. A faulty crossover must then be swapped out in its entirety. 8.4.5  Subtle Aspects of Crossover Component Behavior For critical applications, screening has been proposed for inductors (note that transformer‐type and ferrite pot cores are self‐screened) and this, taken together with a physical separation of high and low pass sections to address possible leakage, has proved worthwhile. With potentially high peak currents circulating in a complex crossover, generous current capacity track foil widths and thickness are also necessary. Likewise, for electrical connection to the system, strong, high conductivity, high torque binding posts are to be preferred to spring clip connectors and the like. Some critics note that copper based connections sound better than the usual, lower cost plated brass examples. The potential impairment has been noted for the popular provision of bi‐wireable connection arrays with hard brass terminal links which are often found to become loose in service. There are some general observations covering design aspects for crossovers which can improve sound quality. While several designers favour air‐core inductors on the basis that magnetic ‘core’ distortion is entirely avoided, they may fail to fully consider disadvantages of bulk, cost, stray flux radiation and lower Q of the air core. When used for low impedance designs low resistance, high inductance air‐core coils can be massive affairs with 50 m or more of copper winding. Subjective clarity is considered by some to be impaired in some instances by such long windings, which incidentally also include some stray self‐capacitance, which increases with size and length, and appears in shunt. At some higher frequency, electrical self‐resonance is possible. The appropriate use of good linearity ferromagnetic cored or even full transformer‐type inductors, (with appropriate anti‐saturation air gapping) can greatly reduce winding length and reduce such losses. Bonded iron dust cores are more expensive than ferrite. At low signal levels these types may show moderately raised distortion figures of 0.1% to 0.15% as compared with

Systems and Crossovers

0.02% to 0.05% possible for high grade ferrite. Conversely, ferrite distortion rises more rapidly when approaching the saturation region. To its advantage, the more gentle saturation of the iron dust type is considered to be less audibly annoying towards overload, this in view of the usual and significant non‐linearity from a moving‐coil bass unit at these typical power levels (15 to 100 W). With these softer cores, end caps may be added forming a ‘dumbbell’, and then these larger iron dust types offer a similar permeability (inductance gain) to simple rod type ferrite cores but with better copper economy. Transformer type cores (E and I, or equivalent patterns, air gapped) especially those manufactured using thin 50% Mu‐metal (B‐grade Radiometal) laminations, perform very well, where the high permeability very short copper (even of silver) winding lengths to be used. Such inductors also have the advantage of a very low stray field but are certainly very costly for materials and labour. Audiophiles have approved of the neutral sound and greater subjective transparency. Ferromagnetic cores do have mild audio signatures and need to be selected carefully for critical applications such as audio transformers, both at signal level and for power amplifier output coupling to the loudspeaker load. Where resistors are required in a crossover, for example, for damping purposes, in some instances the wire gauge of an associated inductor may be chosen to provide all or most of the required resistive attenuation. Simple ‘padding’ resistors or ‘attenuators’ used to match driver sensitivities may be found detrimental to subjective clarity. Whenever possible, the respective driver’s sensitivities and/or impedance should be adjusted by original design and by unit QC selection to provide the required sensitivity matching for the system build. Driver distortion has some dependency on source impedance. With top‐quality systems, any unnecessary elements added to a crossover may be found to reduce subjective quality, in particular protection elements and fuses, which may well exhibit non‐linear behaviors. The benign subjective sound properties assumed or claimed for many electrical devices and components cannot be taken for granted. These include fuses and overload protectors, push‐on connectors, variable attenuators and screw terminals. The choice of crossover capacitors can be important and specially made polypropylene capacitors, with copper substituted for the usual tinned steel lead out wires, are becoming available in a wide range of values up to 120μF. Their use generally results in a touch more detail in the mid‐range and a greater treble purity. Note that there is a clear correlation between higher rated voltages and increased sound quality, though this naturally comes at increased cost. Likewise, at some additional cost, film and foil constructions provide lower loss and may offer better transparency than those ubiquitous, lower cost, metallised film examples. Nevertheless the standard components used for mass‐produced loudspeaker crossover networks perform well enough for normal applications and millions of reliable products have been made using electrolytic capacitors and modest quality, ferromagnetic cored inductors. Where very high standards are demanded, better performance is possible, at a price. Often design decisions are based on careful subjective assessment, and where measurement does not provide the full picture. For a given system the unqualified replacement of ‘standard’ components with costly low‐loss types may not be a good idea since the precise system alignment may well have been adjusted to account for losses, for example the Q values of a given resonant network

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used for compensation, or the relative levels of two frequency bands, or even the intrinsic sound quality of the parts themselves. Upgrade of an existing crossover network may well alter the sound but may actually degrade overall performance. The high‐quality amplifiers used to drive a costly loudspeaker will have been subject to extensive research with regard to the effect of the sound quality of their component parts. In addition to utilizing the fundamentals of good circuit design and overall build quality, it is logical that the audio components used in a matching loudspeaker system should be of comparable quality, subject to the same carefully auditioned scrutiny. 8.4.6  Capacitor Sound Quality In controlled subjective tests, usually employing high‐quality stereo programme, different makes and grades of bi‐polar capacitor may be differentiated. Further, when assessed using a familiar reference audio system, with well selected speaker drivers, preferences may well emerge for certain types. In such tests inherent component losses such as stray resistance will need to be accounted for. Some designers have also reported minor audible differences with regard to electrical connection directionality for crossover components and, where possible, directionality, for example, the start of windings for both capacitors and inductors, should be identified and once decided, maintained at same connected orientation for production. There is no mystery about most of these differences. For example, electrolytic capacitors suffer from small but identifiable errors which, according to type, vary to a small degree with frequency and include distortion, dielectric losses and series resistance. Subjectively there may be mild colouration, a loss in sensitivity, certain frequency emphases and a perhaps a mild impairment in subjective dynamics and clarity. Film capacitors have rather lower losses, for their dielectric and for the equivalent series resistance (ESR), while different makes and constructions also show differences in subjective sound quality. Each of the common film materials has its own sonic character which might either aid a given system, or have a negative effect. For example, polypropylene is generally favoured on the grounds of measured losses, which are very low (df at 0.003 or better) and with reliably good sound. Yet when these are used in crossover networks there are still minor audible variations according to make and type, and more particularly the working voltage. The higher the rated voltage the better, but cost is also proportional to rated voltage. Build quality matters, as in all things—the tightness of the wind, the termination method, and whether the conductive layer is metal foil or deposited metallization. The metal used for the foil also subtly affects the sound, with the now banned tin‐lead foil with polystyrene film much favoured in the past. More complex geometries have been introduced to reduce self‐inductance, for example, by distributed foil winds, and also back to back, symmetrical winding geometry. Listening tests are essential to check whether such costly refinements actually deliver better sound in the application. While polystyrene is considered to be the best sounding film, and is used preferentially in active analog crossover filters, it is impossibly costly in sizes suitable for speaker level networks. And yet, in some systems, relatively economical polyester film capacitors (df 0.05 typically), regarded by some critics as mildly ‘forward’ and hard sounding, may in some cases provide the right tonal balance and quality for a particular design and a particular set of drive units.

Systems and Crossovers

What is known about film capacitors is their mildly microphonic tendencies. When transmitting audio power they vibrate due to the piezo properties of the film, while conversely, vibration from the loudspeaker drivers can induce mild colourations in the electrical output of these components. An anti‐resonant wrap or jacket can be helpful. Low vibration mounting methods, full resin potting of the crossover, or complete removal of the crossover assemblies from the loudspeaker enclosure can all be helpful in minimizing such vibration‐related anomalies. 8.4.7 Resistors Resistors also exhibit rather moderate non‐linearities, for example due to a residual temperature coefficient, the variation of resistance with temperature. Higher power rated components tend to sound better than low power types, while those with very low ‘tempcos’, for example, the bulk metal foil designs, are significantly better sounding but are hugely expensive. Resistors do have subjective sound quality losses, typified as a shortfall in clarity and ‘immediacy’, weakened micro dynamics, sometimes the intrusion of subjective ‘grain’. Where a system can be designed by adjusting coil impedances and/or magnet flux to avoid the use of series resistive attenuators, the sound is invariably better. This is one of the notable advantages of active system design by offering direct coupling of the amplifier to the driver terminals. Speaker drivers do sound better driven from a low source impedance while distortion generally increases with the use of series resistance since distortion is often expressed in the non‐linear input current to the voice coil. High power resistors may sound a little better when bolted to a heatsink. 8.4.8 Inductors Inductors have their own problems. If air core, this type considered the most neutral sounding owing to the absence of a magnetic core, note that the longer winding length required to achieve larger values, say for over 5 m of wire, will have a mild negative influence: the longer the path, the greater is the effect. At the amplifier output, audio enthusiasts strive to employ high quality low impedance speaker cables for greater clarity. Thirty metres of ordinary wire in a crossover coil inside the speaker, for the main inductor to the bass unit, might appear to defeat this objective. Of course, the external cable is driving the whole system broad‐band and not just the series LF inductor. Part of the long wire problem lies in the indifferent dielectric properties of the polyurethane enamel used to insulate ‘magnet’ wire for inductors. It does not make very good speaker cable and experimental trials with superior dielectrics, PTFE‐, cotton‐ or silk‐wrapped wire tend to confirm this though, with a very likely much higher cost to implement. Other factors concerning air‐core inductors include the very large stray magnetic field. This requires careful location and orientation with respect to other components. The typically higher winding resistance may partially reduce sensitivity, and there may also be significant skin effect and self‐capacitance; the latter negligible when using magnetically permeable cores with the typically shorter windings. Audiophile grade inductors are also available, for example, made with flat ribbon or tape windings that minimize self‐capacitance and skin losses. Litz wire (individually insulated multi‐strand) conductors are also used for the windings on some types, maintaining the nominal designed value to higher frequencies.

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8.4.9  Inductor Cores: Distortion Inductor cores have had a bad press, mainly because of their aggressive sounding distortion which occurs when they are overloaded. With competent system design, this should never happen and with a sensible choice of core, type and size, operating distortion can be very low, while the winding gain arising from the high permeability allows typically one‐ third of the copper length to be used for a given value thus reducing wire losses. Magnetic cores can be of ferrite, and the selected audio grades may perform very well either as self‐screened pot constructions or as open rods. Alternatively, bonded powdered iron dust, or a low‐profile stack of iron transformer laminations are common. The laminations may be an E or I section, or used as a transformer assembly, here linearised with a saturation controlling air gap of typically 2 to 4 mm. Powdered iron (see above critical aspects) has proved popular in recent years owing to its ‘softer’ overload characteristic, but there are disadvantages too. Permeability is lower, requiring more turns while the distortion at normal levels may be higher than good ferrite, mainly third harmonic. Note that these cores are partially conductive, a few ohms per square, indicating the need for special care with the winding to avoid shorts to the core. Silicon iron transformer cores are acceptable at low frequencies; but also show frequency‐dependent loss and inductance, the latter with as much as a 15% decrease in the decade 100 Hz to 1 kHz due to eddy currents. Finer laminations are superior in this respect. Mu‐metal stacks are costly but effective (used historically for BBC designs) and are wire efficient. Note that audio grade iron toroidal cored inductors can perform very well at high inductance values for lower frequencies with a usefully low stray field and very high power handling. Figures 8.38 to 8.42 show measurements of harmonic distortion for various comparable sized and powered cores. Taking the large iron dust type first, 45 mm dia. by 45 mm long, with end caps, value 8 mH, with 100 Hz drive at 20 W, the distortion measured

5 dBV

A: MAG

RANGE: 21 dBV WICON DB DS

STATUS: PAUSED RMS: 40

10 dB/ DIV

–75 START: 0 Hz X: 100 Hz

BW: 7.5 Hz Y: 22.07 dBV

STOP: 2 000 Hz THD: –49.14 dB

Figure 8.38  Large iron dust core with end caps (45 mm dia. overall, 45 mm long). THD 0.36%, with a long harmonic spread. Saturation is soft and progressive with level, but distortion remains at the 0.2% to 0.3% level throughout.

Systems and Crossovers

0.36% with a wide spread of harmonics. Saturation is progressive with no sudden step in linearity while the distortion, mainly third, does not improve much at reduced power, and is typically remains at 0.25% over a wide range of frequencies and powers and might well be considered unsuitable for more costly systems (Figure 8.38). These figures are comparable to a normal drive unit. Examining Figure  8.39 and Figure  8.40, here assessing crossover grade ferrite rod from a good maker, 20 mm dia. by 75 mm, the distortion is of the type expected from a

5 dBV

A: MAG

RANGE: 21 dBV FERRITE DS

STATUS: PAUSED RMS: 40

10 dB/ DIV

–75 START: 0 Hz X: 100 Hz

BW: 7.5 Hz Y: 22.03 dBV

STOP: 2 000 Hz THD: –68.05 dB

Figure 8.39  Crossover grade ferrite core, 20 mm dia., 75 mm long, THD 0.04%, typically 0.03% over the frequency range. Second and third are similar, note a mild fifth harmonic at a low −82 dB.

5 dBV

A: MAG

RANGE: 21 dBV E SECTION DS

STATUS: PAUSED RMS: 20

10 dB/ DIV

–75 START: 0 Hz X: 100 Hz

BW: 7.5 Hz Y: 22.09 dBV

STOP: 2 000 Hz THD: –62.01 dB

Figure 8.40  22 mm thick silicon–iron E section laminations 40 × 66 mm: Less than 0.1% THD, mild upper harmonics, typical levels of 0.08%.

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5 dBV

A: MAG

RANGE: 21 dBV TRANSFORMER DS

STATUS: PAUSED RMS: 30

10 dB/ DIV

–75 START: 0 Hz X: 100 Hz

BW: 7.5 Hz Y: 22.29 dBV

STOP: 2 000 Hz THD: –35.00 dB

Figure 8.41  8 mH, 20 W delivered to 8Ω at 100 Hz. Distortion typically −35 dB overall, steadily increasing with level. Laminations 24 mm deep, 5 cm × 6 cm frame, silicon–iron with 1.5 mm air gap, E and I core. 1.5% THD at 20 W, predominantly odd order with extended harmonics (Audio grade Permalloy or Mu–metal is far superior, typically 50 W. Typical distortion is 0.035% wide band.

increasing dielectric losses, and with potential mechanical self‐resonance. Whether high frequency interference suppression also plays a part in this is uncertain but the fitting of 10 nF high quality, for example, polystyrene ‘correctors’ for to shunt, for example, 3 uf of series capacitor does have a small audible effect, usually to the good. Some designers fit a series network, such as 100 ohm with a series 1 nf capacitor, across the input to the crossover, intended to partially terminate RFI induced in the assembly wiring and the loudspeaker cable. Certainly a loudspeaker represents a significant radio aerial while even inexpensive twin pair loudspeaker cable, never mind ordinary house wiring, exhibits quite low overall losses up to 1 GHz, even if such long transmission paths exhibit multiple resonances. RFI induced in the loudspeaker and cable will also be fed back the amplifier output port. This port is designed for the audio band and frequently has poor RFI rejection; as such, signals which may enter the circuit are demodulated in some sections and may subtly alter sound quality. Thermionic amplifiers are rather less susceptible to such interferences, lacking those multiple semiconductor junctions and operating at higher signal voltages. A small series resistor for a suppression capacitor is always helpful; to dissipate, rather than resonate, stray RFI. All metal loudspeaker enclosures could be grounded to audio system ground, effective at lower frequencies but ineffective from VHF and upwards. The increasing proliferation of radio sources in the home and the environment does make the attainment of high subjective transparency for an audio system that much more difficult. WiFi and similar sources should be as remote as practicable from the audio system. Where possible the behavior of a crossover network should be modeled to high frequencies, with the actual imprecisions of the inductors and capacitors included. A simple looking configuration might be one set of filters and designed termination at audio frequencies, and something else at radio frequencies say beyond 40 kHz.

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Note that at much higher frequencies an inductor begins to look like a capacitor, and an inductor a capacitor, the former due to capacitance in the windings and the latter due to lead out inductance. 8.4.11 Wiring The internal wiring in a speaker should not be taken for granted. A twisted pair cable to each driver is optimum, helping to reducing the influence of stray field coupling, and it is also mechanically more stable than plain wire. The wiring grade may prove audible in critical applications and should be selected on similar grounds to that used for high‐ quality external speaker cable. Cables should not be allowed to rattle around inside the box, should be routed away from the driver magnets, and be set in a consistent production layout which has been specified by the designer. Note that in operation the random movement of internal cables may well affect subjectively heard music dynamics.

8.5 ­General Design Considerations, Voicing and Balancing Loudspeaker designers will employ a set of personal values for perceived sound quality, relying on a combination of theory, experience and good taste. By valuing and assessing the comments of others, a designer can seek to identify his or her preferences, and then can take these into account during the design process, here constantly aiming for a more neutral and universally acceptable result. For the designer, it may simply be personal knowledge of some assessed acuity difference, for example in the upper treble. If unaccounted for, this could lead such a designer to set higher levels for the tweeter high range and/or to fail to properly assess response irregularities in the last half octave up to 25 kHz. Cross checking using alternative and younger ears is worthwhile, while such a designer may also use his experience to take particular care designing for the treble range knowing that aural judgment may be less acute in this region. The well‐known curves for hearing sensitivity and for perceived loudness with frequency are widely accepted, but what is less well appreciated is that they represent an average of a wide sample of the population. Variation amongst individuals of good health is large: as much as +5 dB to −10 dB, and each of us has an inherent natural ‘frequency response’ to which we are well adjusted. Despite internal adjustment or compensation for what is notionally perceived as a ‘flat response,’ that intrinsic variation between listeners will still moderate individual assessments of sound quality. For example, persons may differ widely on their judgment of loudness. What is realistic and comfortable for one person may be unpleasantly loud, even painful for another. Accordingly, the perceived frequency response of any audio system, but especially for the loudspeaker, will vary with loudness. It is also the loudspeaker which intrinsically is subject to rather greater sound quality variation than any audio component in the listening chain. We understand that the uniformity of an axial frequency response for a loudspeaker is one representation of its behaviour, though it can be a fair indicator of sound quality. But this is still only an indication. Response variations off axis, the trend of energy or power

Systems and Crossovers

response and how they with the room, the inherent acoustics of rooms; and also the effect of immediate boundaries and their reflections, all affect the sound quality perceived at the listening position. This is why a skilled designer must take care to use aural experience and good judgment to evaluate and validate the perceived tonal balance of a speaker system as it will be used, and not at a single arbitrary test or designer location. And all this is before we have accounted for errors of colouration and distortion. Even if fairly tight commercial tolerances of ±3 dB are adopted for the sound output over a defined frequency range, for the purposes of voicing there remains ample scope for finely balancing the octave‐by‐octave response to achieve the optimum subjective result, that is, what is judged to be the best sound quality available from the design. For example, a nominal ±3 dB tolerance for the specification of the anechoic free‐ space sound output is even sufficient to accommodate the adjustment required to compensate a speaker for wall mounting. Depending on the application, and the technologies employed, response variations greater than +/− 3 dB may well be found satisfactory in some applications (see also Chapter 10). 8.5.1  Test Sound Levels: Checking Quality Over a Range of Sound Levels Owing to the varying perception of frequency response for different sound levels the appreciation of tonal balance and timbre for a speaker system is also strongly dependent on loudness or level. Consequently, the sound levels chosen for testing and for subjective evaluations with music programme are very important. When comparing speakers in development, it is also important in a comparison not to listen too long to one example, otherwise our powerful ear/brain processor will unconsciously adapt to and largely compensate for the errors of that example. This adaptation may be so powerful that the otherwise known superiority of a reliable reference speaker may be rendered unrecognisable when switching back to it. In addition, a speaker with moderate flaws of spectral balance may begin to sound quite reasonable, even plausible, when played loudly enough for the adaptive processing in the brain to ‘flatten out’ the high spots, given that the raised sound level now is sufficient to bring those depressed regions back to into the perception region. Also, when testing subjectively, it is often found very useful to play a speaker at quite low sound levels. It is here that the common flaw of an emphasized upper mid‐range is exposed, now revealed as an unnaturally thin sound, like a small transistor radio. While deep bass will not be heard due to the natural hearing curve loss, well recorded, far‐field speech excerpts should still sound natural, articulate and lifelike. Such listening at reduced loudness may also show whether a speaker is lacking in clarity in some areas, or is weak in reproducing fine detail. A well‐balanced, well‐integrated system will retain good clarity at low levels, for example, at 50 to 60 dB at 1 m (quiet conversation level). However, systems with an uneven join or step between drive‐unit ranges, and/or which are poorly balanced overall, may be revealed as surprisingly defective at moderate loudness settings. Programme quality matters greatly and designers should be aware of the potential design errors resulting from using modern highly compressed popular material especially for radio. The substantially processed, more constant loudness with time and frequency

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obscures the dynamic qualities in the test speaker, preventing them from being fully appreciated. Also, as found with excessive loudness where the ear response tends to mask differences, errors in frequency response appear filled in, corrected, when using dynamically compressed programme sources. 8.5.2  Test Location Ideally the intrinsic tonal balance, and lowest colouration, will be expressed when the example loudspeaker system is positioned well away from room boundaries, even in free space. In fact, a few designers swear by free‐field testing, listening to domestic speakers in an anechoic chamber or rather impractically in a field, up on an open platform. In practice this practice is of limited value, since a room has a profound effect on the sound quality of a given speaker, and in a real sense, is a component of the design. Whenever possible evaluation should be undertaken in the well‐controlled room conditions, with a reliable, representative acoustic, and with the test system sensibly located with respect to boundaries, correctly orientated, to direct a representative sample of the sound output to a complementary, chosen, observer location. 8.5.3  Loudspeaker System Design: Some Practical Aspects for Crossover Tuning and Voicing Speaker system design for exceptional sound quality can be a long and tortuous process. Here are a few tips which may help speed up the process. However these should not be adopted as a short cut to understanding the design process a whole. A) It is very important, on a frequent basis, to try to associate design changes with sound quality differences. Freely mix measurement and listening, using familiar music programme of known quality. B) Beware of voicing a single loudspeaker prototype using only one channel of a familiar stereo signal source. The two signal channels should be summed up via a simple resistor network at the source, the latter to avoid one channel output driving or loading the other. A remote controlled preamp/amp with a mono function is also convenient, greatly helping in the comparison of two examples. C) While single speaker testing is often the starting point in the design process, a design will sound substantially different when a stereo pair are up and running, properly located with respect to the local room boundaries. Also remember that mutual coupling for a pair enhances the lower frequencies thus significantly altering the timbre or frequency balance. D) It is almost impossible to compare two stereo sets of loudspeakers at a time due to their inevitable placement differences and the unavoidable acoustic interaction, reflection and mutual coupling between the systems. One professional devised a listening room with a stereo pair of large turntables on which four loudspeaker designs could be placed, and successively rotated into position for audition. Loss in quality due to platform structural weakness, and not least from the proximity of the other speakers would likely rule out such a device for critical listening evaluation. Nevertheless, it has proved very important for workable double‐blind testing to assess the importance of fundamental issues such as response uniformity, both axial

Systems and Crossovers

and off axis. A primary result showed that a uniform on‐axis response as measured in free field, ideally at about 2 m anechoic, was judged the most natural sounding, especially when accompanied by well‐behaved off axis output, indicative of low diffraction and good driver output integration. Historically the infamous multiple loudspeaker connected switch box comparator, used for rapid and convenient for A/B sound quality comparisons, was a showroom evil which misled many customers, never mind the disastrous practice of stacking the loudspeakers under assessment as a wall of sound reproducers, here suffering from chronic interactive coupling and unrepresentative local acoustic loading. E) A digital music player equipped with a custom set of familiar and representative speech and music tracks recorded on a file, USB stick or CDR, is most useful. This can also provide quick access to a number of personally selected music excerpts, also conveniently including one‐third octave and full band pink‐noise test signals. The established popularity of music streamer replay, employing convenient control surfaces, namely pads, phones and pods of the ‘i’ variety and otherwise, provides almost unlimited access to near CD quality programme. Preferred test playlists maybe organized. Hi fi quality playback streamers are common, while separates audio combinations can then take the medium almost to the highest audiophile level if required, for example using a local hard drive streamer store with HD audio material loaded. The smaller market sector using LP records must not be ignored as the particular sound quality, including altered timbre and bandwidth, with the potential for infrasonic noise, may interact unduly with particular loudspeaker designs. Prerecorded LP material is useful but operation with live replay remains valuable for assessing feedback and microphony for the room coupled reproducing system. F) When designing and trying out crossovers ‘on line’ with active music replay, it may be found helpful at this stage to remotely wire the crossover(s) to a small workpiece local to the listening location, making sure the extended cables are suitably neutral sounding and low impedance. Take care that potentially heavy cables do not drag the crossovers off their support, and work with a medium size power amplifier with fail safe output protection (ideally a modern example with relay shut‐down and auto‐reset). This will save a lot of possible hassle with blown amplifiers and/or fuses in case of experimental errors of wiring and crossover components. G) Have a small test jig handy for the rapid and frequent checking of the evolving load impedance for the system. It can be all too easy to follow a promising experimental path to rewarding subjective and measured response uniformity and then find that the input impedance of the system has fallen well below acceptable levels. H) Have a nearby laptop with a synthesis program running, also allows for rapid checking of crossover design progress, comparing the calculated frequency responses and predicting impedance loading variations. I) Many designers use double‐ended hermaphroditic 4 mm plugs for crossover development working with a handy 4 mm socket equipped patch bay. Trial components are soldered to the plugs and may be reasonably reliably stacked and connected in almost any combination to aid early development trials. However, note that the sound quality will not be the same as a fully worked, laid out, soldered and installed crossover network. J) While primary crossover development may be convenient employing a remotely located, cable‐connected board, the final balancing and tuning for the system has to be done with the crossover built and placed exactly as it would be for the system

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manufacture. This is because of those factors including the local acoustic and vibration environment inside the speaker, but also cables, connectors, specific choice of components, and the crossover layout used in manufacture will significantly affect results. These can all subtly affect the sound quality, even if very little change may be observed on the precisely measured axial response for these two build situations. K) Do not imagine that speaker system design is not a highly critical process just because the measuring microphone reveals much larger errors or variations in response for a loudspeaker than are routinely observed for audio electronics. When voicing a speaker an 0.5 dB or 5% variation over frequency band matters, particularly if it is present over a wider range, e.g. an octave or more. Some quite small changes in an attenuating resistor may barely show on a typical measurement, but may be readily heard using critically judged subjective comparisons. L) When assessing, and also when adjusting the frequency response, continue to check the prototype speaker’s sound output from many angles. If odd variations are found, investigate whether they are restricted to a local frequency region and whether the variations still ‘balance’ around the ‘zero’ or reference sensitivity level, namely the averaged output level for the frequency response range concerned. If not, such irregularities may need further attention. Variations in level, such as those may be weighted over narrower sixth octave bands, are subjectively less important than those of one‐third octave and wider. This is because the energy difference for a given amplitude variation is naturally greater over a wider frequency weighting or band. It is helpful to use both instrument and/or visual weighting to average the fine detail of measured responses, say in stages form one‐third octave to full octave bands, and these are then displayed with successively greater amplitude resolution to reveal the broader frequency balance errors. For example, a 50 dB vertical scale might suffice for swept sine or equivalent, narrow‐band measurement of one‐ twelfth octave or better: third octave weighting benefits from a scale amplification to 25 dB. For whole octave, here very useful for overall frequency balance assessment a highly resolving 10 dB full scale may be selected. The purpose of this successively adjusted, proportional amplitude scaling is to show those more audible errors in broad‐band output more clearly. Given that 0.5 dB of variation in overall tweeter sensitivity is clearly audible as a change in loudspeaker ‘character’, a 10 dB vertical range scaling will reveal this, even when using octave bandwidth averaged analysis. M) While a visually smooth response is not essential for a good sound from a loudspeaker, it is a great bonus for a designer since it allows the intrinsic, subjectively associated amplitude/frequency response to be seen more clearly. Well‐behaved drive‐units working in low diffraction enclosures have more consistent responses, on and off axis, facilitating greater design precision. And this author considers that as such, frequently they do sound better. N) In design, when assessing overall frequency response, it is also valuable to keep a constant track of the individual responses of each driver section and the behaviour of the related crossover. Roll‐off slopes which look right will sum correctly in the acoustic output, but only if the crossover phase/delay is correct in the crossover region. If there a significant response dip is found, a simple inversion of phase for one driver (usually the tweeter) should show improvement while the alternative of fudging the crossover by increasing the overlap between the drivers will not help

Systems and Crossovers

matters. With too much overlap, especially with non‐optimum phasing, additional out of phase errors are likely to occur on other axes despite the possibility of a smooth output on axis. An unsuspected power lobe may well be increasing the output somewhere off axis, to the detriment of the overall sound quality. O) On the rare occasions where a crossover design solution for an aesthetically uniform response seems intractable, it is usually better to allow some intrinsic driver response errors to remain in place than excessively elaborate the crossover in an attempt at a more attractive measured response. P) For a given configuration, control/adjustment of phase/delay in the frequency region of the crossover may be available via several electrical methods. For example polarity inversion of one driver results in a 180‐degree shift, while steps of approximately 90 degrees in the region of the crossover frequency can be achieved by modifying the ‘order’ of the crossover, for example, from second to third. Smaller, corrective phase shifts can be obtained by subtly shifting and recalculating the actual crossover frequency individually for either or both filter sections. For example, inherently broad acoustic responses for a given pair of drivers might permit a flexible choice of crossover anywhere in the range from 2.3 kHz to 4 kHz. At 3 kHz, the acoustic wavelength is 11.3 cm. The acoustic origin of an average tweeter in a typical system when mounted a simple flat baffle is delayed by 3 cm. This amounts to 90 degrees at 3 kHz. Adjusting the crossover frequency can now provide a sensitive control of relative driver phase to help find that sweet spot, where they integrate well, and where the overall output is also well behaved off axis. Aiming for reasonably symmetrical output over the vertical axis for a driver pairing is well worthwhile, providing a more predictable sound quality. Q) Beware of damaging errors which may result from poor measurement technique, particularly in the case of the taller ‘tower’ systems, which are currently fashionable. While for the case of compact speakers the usual and convenient 1 m mic location is reasonably ‘far field’ for the measured response, it poses a problem for a tall speaker. This is due to the much more widely separated drive units which can be a metre apart. Consider a microphone on axis (and what axis should you choose?) with widely differing measurement distances and relative angles to the sound sources. These impart consequent amplitude differences and relative delays. For such tower designs a 3 m measurement distance would be more like the desired free field location but is almost impossible to achieve. It is worth noting that at 1 m mic spacing a vertical driver displacement of 0.5 m may account for a differential angle to the microphone of 25 degrees plus a path difference of 11 cm, more than 10% of the reference mic spacing. From inverse square law, that extra distance will also account for a 20% loss of sound pressure alone, some 2 dB at the mic position. In addition a possible 25 degrees, worse‐case radiation angle to the mic will account for a further frequency dependent loss for some drivers, never mind the directivity behavior of the enclosure/system. Such measurement will not be representative of the acoustic output, either for the speaker designer or the for relatively untutored technical reviewer. It may be more realistic to measure the complex nearfield pressure response (e.g., with gating, and for real and imaginary data points) individually for each driver, on their respective axes, and then mathematically sum and scale the data to a final response for an imaginary listening position several metres away.

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R) If a 2 m measuring distance can be employed, the measurement accuracy for such multi‐driver systems is significantly improved. However, where gated measurements are involved in finite spaces, the greater microphone spacing makes for a shorter path to the first boundary reflection, unfortunately reducing the length of the ‘anechoic’ measurement segment. In any case in‐room gated measurement is largely inaccurate below 500 Hz. Note that the range up to 500 Hz contains most of the notes in speech and music; middle C is 261.62 Hz. Thus the customary in‐room measurements are seriously blinkered. Acoustic averages taken over the listening space are often more informative. High‐roofed warehouse space is appropriate for measurement, but only if ambient temperatures are going to be representative of use. Many warehouses are unheated and thus the local climate will also be an issue. S) In some cases when measuring a tall loudspeaker in a finite room it can be placed horizontally on a suitable open stand (taking care first to ensure safety and stability). This would bring all the drivers to a uniform height, and at a greater spacing from the first reflecting boundary, to be more easily gated. Also check that the proximity of the support components does not unduly perturb the measurement. Even thin frame sections are easily ‘seen’ by the microphone. Acoustic foam wraps are helpful on stand sections. Vertical off‐axis measurements are now possible with this orientation. T) Acquiring the horizontal directivity data will require creative placement of speaker and mic according to the frequency range covered. If you can get it, a large anechoic chamber will reveal much about intrinsic performance, this the actual free‐field acoustic output. As compared with in‐room gated methods previously hidden information about enclosure behavior and sound radiation will be revealed, especially below 500 Hz. U) When developing a speaker crossover network using that convenient ‘remote work station’ technique use high‐grade, low‐resistance speaker cable, and not bell wire. Over that substantial path length, from the crossover design position to the speaker drivers themselves, cable losses may well be sufficient to modify the results, both measured and heard. V) Where it is found essential to A/B test the axial sound quality of single examples of a loudspeaker design, use free‐space placement, well away from boundaries and take care to repeat the comparisons with the speaker positions swapped. This is to reduce errors imposed by the local acoustics. Also take care to monitor the observer/ assessor’s head angle relative to the test speaker, to control HRTF variations. W) In design, also check for possible proximity effects of installed crossover inductors with each other, and with local metal work, magnets, and so on, especially when building up the final prototype. In one example, the designer had placed the crossover in close proximity to the magnetic shielding steelwork on the back of a driver. The nearby inductors suffered values altered more than 15% while further unwanted mutual coupling was occurring between several other inductors via fields induced in the common steelwork. While the measured frequency responses remained almost within the defined production tolerance, the sound quality had shifted unacceptably from the designer’s intention. X) Reversing the phase of one of the drivers is a good test for crossover behavior, while also measuring on and around the designed/listener axis. Where the phase integration is fine, and when optimally designed and connected, phase inversion for one driver only should result in a clean, symmetrical notch at the relevant crossover

Systems and Crossovers

frequency. Also, a well‐balanced and moderate loss will appear just above and just below the target frequency. Odd notches and bumps which appear at unexpected places in the crossover region indicate poor phase control and perhaps undesirable overlaps in the operating ranges of the drivers. If the presence of such overlaps are considered necessary to fine tune the overall energy response of the system, in order to voice it to the design aim, then the designer should at least be aware of the consequences in terms of impaired uniformity for the frequency responses off axis, and thus a poorer consistency of sound quality when installed. Y) Where a system is designed to be active from the outset, direct coupled from amplifiers to drivers, something of a design short cut can be made by modelling the system and executing the crossovers using programmable digital filters driving multiple power amps. Filter slopes, equalisation and level matching are easily accomplished and test music can by fed in, for in‐progress listening tests. For economy prototyping a multiple channel home theatre receiver can be pressed into service for the amplification. Z) Even when active operation is not the objective the above method can be instructive for prototyping but will still present a problem when the project is moved to the passive domain. Here the noted interaction of the motional impedances of the drivers with the passive crossover network will need solutions, and even when well executed, the passive version will never sound quite the same, or as good as the active. AA) An audiophile two‐way stand mount, a vented system of exceptional transparency for the time, was prototyped for active working. The gain in sound quality was memorable, with near doubling of power handing in the bass and a very substantial lift for focus, macro and micro dynamics, and not least clarity. This sort of gain easily transcended the costly expense of better cables and amplification, these frequently considered when improving passive loudspeaker installations. 8.5.4  The Difficulties Associated with CAD, Computer‐Aided Design Frequently, CAD‐based loudspeaker designs may look impressive on paper, or should I say on‐screen, but do not always work out so well in practice when you get to listen to them. Hours of interactive effort can be modelled with CAD, but when the proposed system is built as a working model it may have a disappointing sound quality, and show poorer than expected correlation with the theoretical model, that aimed for acoustic target function. First of all, the model must be based on good data, representative of the sensitivity, complex impedance, production tolerances, the intended sound character and not least the directivity of the drivers. For the enclosure, baffle size and consequent considerations of diffraction effects on frequency response and directivity, also the driver spacing and relative driver delays, all complicate the issue. It is of benefit that most well‐behaved drivers are, of themselves, minimum‐phase devices, and consequently their phase characteristic may largely be computed out of the frequency response. Tonal balance, or subjective timbre, is one of the most difficult aspects to quantify in loudspeaker design; it is so easily heard and yet its characterization through measurement is troublesome and often remains hidden in the overall complexity of responses. Likewise, the theoretical target responses suggested in the CAD design process are hard to predict for sound quality.

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For example, the innate tonal quality, the timbre, the subjective perceived frequency response, for a bass–mid driver, will depend not only on the axial response but also on its directivity over frequency, also how well it integrates with the high‐frequency driver. Also its inherent colourations, and a particular identifiable ‘sound character’ pertains when coupled with and on the chosen enclosure. Not least, we have the effect of each particular bass alignment, including damping, response shape and extension, and of course any stray non‐musical contributions from the port, including non‐linearity, turbulence, resonances, and dynamically varying group delay. It is worth noting that carefully measured driver responses, especially the axial trend to be used as a CAD target response, should be an average of several traces taken over the forward 10‐degree solid angle to obtain a more representative reference for computation. Blips and minor discontinuities are inevitable for the computed target function given the complex interaction of phase, resonances, diffraction and directivity for the installed active components. Multiphysics software has somewhat narrowed the gap between objective and subjective design, but it must still remain the servant of the system designer. 8.5.5  Practical Example of a Two‐Way Crossover at 2.2 kHz; Subjective Effect of a Given High‐Pass Crossover Alignment Designed using CAD, the system response for a particular loudspeaker porotype measured quite uniformly and was well balanced, here using the usual shunt or parallel type of two‐element, second‐order high‐pass network a 7μF lead capacitor with 0.33 mH shunt inductor to a nominally 5Ω‐rated HF unit. However the sound quality showed some mid‐ range ‘glare’ or ‘shout’, this judged to be an energy excess in the 800 Hz to 1.2 kHz region. Examining the relevant graph, the acoustic tweeter roll‐off curve was fine with a tidy 12 dB/octave slope. Trying alternative solutions, an equally valid ‘flat’ alignment for the overall, combined system response was also found where the 0.33 mH treble shunt inductor was reduced 30% to 0.23 mH. The change in the overall axial response trace was almost undetectable, but the subjective effect was one of greater ease and aural comfort in the upper mid‐range, while the ‘glare’ which had hitherto been incorrectly blamed on the mid‐range driver diaphragm had now been addressed. Technically, the crossover points for each ‘way’ were now moved slightly apart; however, the axial responses continue to sum on the response curve as desired, while the audible excess energy in the crossover region was now satisfactorily controlled. This example illustrates that calculated component values for crossover networks are not set in stone. The designer needs to interpret them flexibly in the light of particular, local response features, phase shifts and directivity. The increased use of crossover and system modelling helps to combine the driver responses to reasonable accuracy, almost automatically adjusting the component values, but these many possible solutions still need to be checked subjectively. 8.5.6  Multiple Driver Combinations: Series and Parallel, Voltage Sensitivity and Impedance For a driver of 8Ω impedance and a reference range 90 dB sensitivity, consider the results for some interesting combinations of drivers and parameters which are readily available to the designer: 1) Rewind the voice coil to 4Ω, holding the force factor Bl constant. A 2.83 V reference input level now provides a doubled 2 W of power and there is a corresponding output

Systems and Crossovers

increase to 93 dB s.p.l. for the same amplifier voltage level. This sensitivity gain is paid for at the amplifier with a doubling of output current. (Note that as a rule amplifier sound quality is inversely proportional to output current, if to a moderate degree.) 2) Take two of the original 8Ω drivers, and operate them in parallel for 4Ω loading; a 2.83 V input is now 2 W, but you now get 3 dB more, 96 dB s.p.l. (because two radiating areas of equal power, close coupled at lower frequencies, add an additional 3 dB). 3) Now wind the reference driver impedance to 16Ω, but maintain the Bl or ‘shove’, and with the 2.83 V input it will now draw a reduced 0.5 W. The result is 87 dB s.p.l. 4) Parallel two of the above 16Ω drivers and the loading is 8Ω. 2.83 V input, that is, 1 W, now gets you a very useful 93 dB s.p.l. over the reference range. Two diaphragms more efficiently couple to the air load. 5) Series connect two 4Ω drivers to 8Ω you still get 93 dB s.p.l. for 2.83 V input. In practice, of the two double driver options, the paralleled 16Ω option is preferred since in practice it is typically 1 to 1.5 dB louder than the 4Ω alternative owing to the potentially better magnet gap utilization efficiency of the finer spaced, lower gap loss 16Ω winding. 6) For four 8Ω drivers, here connected in series–parallel, for an 8Ω load, a 1 W input will generate a 96 dB output, since we now have four drivers worth of coupled area efficiency boost (10 log 4 = 6 dB). 7) Or, series connect two 8Ω drivers of 90 dB each and input 2.83 V, these drawing 0.5 W total, and still get 90 dB because the 3 dB coupling efficiency gain compensates for the 3 dB drop in input power to each. And here the load is an easy 16Ω. As Richard Pierce has explained (diyspeakers.net), series connection of matched drivers does result in the expected doubling of impedance but also note that for this combination, no other TS parameter is altered, for example, Fs, Qm Qe or Qt. 8.5.7  A Practical Crossover Example Crossover design is a multi‐parameter problem providing an unusual degree of freedom for creative design. Here is an example of what can be done with a pair of rather imperfect real‐world drivers for which a crossover is required in the 3 kHz region. The bass unit is a 90 mm (120 mm chassis) pulp cone unit of 87 dB nominal reference sensitivity, that is, in a 2 pi plain baffle, the tweeter a 25 mm soft dome, at 88 dB. Plotted from 200 Hz, the ‘17 dB’ level shown in the graph is equivalent to 87 dB s.p.l., while for the bass unit the practical in‐cabinet reference sensitivity at 200 Hz is now seen to be 3 dB less at 84 dB, as it is no longer mounted on an infinite baffle. Note that these drivers are mounted in the required enclosure, a 7‐litre miniature intended to be used in free space mounted on 60 cm high stands. While the driver reference sensitivity is 87 dB from the manufacturer, based on the usual Thiele–Small calculation, this is only valid for 2π half space and not for a box system, intended for use some distance from room boundaries. Thus the practical sensitivity, equivalent to 4π full space, is actually some 3 dB less, at 84 dBW. (Note that pressure and power are broadly equivalent in the low frequency nearfield.) For Figure 8.43 that reference level is seen at 200 Hz. The averaged inherent response trend of the bass–mid unit rises some 5 dB from 200 Hz to 1.5 kHz, this quite typical in‐cabinet behaviour (dotted trace) and is unacceptable. Above 1.5 kHz the response is rather uneven, while ideally it should be well maintained to well beyond the crossover point, for example, 6 kHz and then decay smoothly. In this real‐world example, it also remains peaky up to 14 kHz, this at first sight an unpromising candidate.

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High Performance Loudspeakers Transfer function magnitude - dB volts/volts 22.0 17.0 12.0 7.0 2.0 –3.0 –8.0 –13.0 –18.0

5 inch direct and with crossover

–23.0 –28.0 overplot 1000.0

10000.0

Log frequency (Hz) CURSOR: y = –11.7243 5 inch direct, and with crossover

x = 20080.5652 (658)

Figure 8.43  5‐inch driver direct (dotted), and with crossover (bold). Lower frequencies are truncated by measurement gate setting).

Noting the output of the high‐frequency unit (Figure 8.44, dotted), the sensitivity is 4 dB too high relative to the 84 dB reference level system target. It does have a respectably smooth primary range, 4 to 15 kHz on the reference baffle. Unfortunately, when mounted in this small enclosure, the response peaks by 3 to 4 dB at 1.5 kHz partly due to diffraction gain from the enclosure edges, while a cross check against the impedance curve confirms that this is also partly due to an under‐damped fundamental resonance. If the option is available, the system designer could specify the addition of Ferrofluid or other damping medium, or a back‐loading termination to help control the resonance. Nevertheless, it is still possible to design a fairly straightforward crossover network for this apparently unpromising driver pair. To begin, the mid‐range rise needs to be equalized to an approximately level response, this largely achieved oversizing the first inductor value for the low‐pass crossover filter. In this case a larger than usual value, here upped to 2.1 mH, delivers an appropriate corrective slope. Our next target is a fall to −6 dB at the 3 kHz crossover point. A maximally flat response can be achieved by damping the now undersized shunt capacitor with a small series resistor. The capacitor addition results in a second‐order network. If this series resistance is set too low, the network resonates too strongly, peaks at 1.5 kHz, and so we have something of a variable equalizer at this point. The values of C and R are now balanced to provide the smoothest objective and subjective response, the aimed for −6 dB point, together with a satisfactory out‐of‐band roll‐off. For the high‐frequency unit, in view of the in situ output, the electrical drive may well need adjustment of network values to provide some reinforcement in the 2 kHz range. In the absence of a driver redesign, the overall excess sensitivity also requires a reduction of 4 dB. Insertion of a series resistor is the most common, in this case 7Ω. The final

Systems and Crossovers M L S S A

27.0 22.0 17.0 12.0 7.0 2.0 –3.0 5 inch direct and with crossover

–8.0 –13.0 –18.0 –23.0 overplot 1000.0

10000.0

Log frequency (Hz)

Figure 8.44  25 mm direct (dotted line), and with crossover (note, lower frequencies are truncated by measurement gate setting).

value will arrived at after the crossover design is itself nearly complete since further iteration of the crossover values can also act as a level control, this dependent on the degree of response equalization considered necessary. Initially, a second‐order high‐pass network was tried but was rejected on two counts. Firstly, the phase agreement between the drivers was unsatisfactory at the nominal crossover frequency, leading to poor output integration plus an inconsistent response above and below axis, this true for either connection polarity. A good check for good crossover behavior is to invert the phase to one unit and see how deep a cancellation notch for the driver pair can be achieved at the intended crossover point on the listener axis, perhaps in the range 20 to 40 dB. The cancellation was poor in this case and accordingly, third order was selected for the high‐pass network which gave an additional phase rotation, a further shift of 90 degrees, which offered more freedom to smoothly integrate the summed phase through the crossover region. The steeper roll‐off slope of the third‐order network also helped to tame the inherent 1.5 kHz driver motional resonance peak although it cannot wholly suppress it. The acoustic output is set to be nominally −6 dB at 3 kHz for the crossover, while the intrinsic third‐order 18 dB/oct roll‐off slope is not achieved until below 1.5 kHz due to the filter summation with the natural response of the high‐frequency unit. For this design the enclosure is bass reflex loaded, which for this size of box tends to add some extra output in the low mid‐range (this partly due to port output contribution above system resonance) in addition to the desired, tuned increase in the bass. Consequently, the system may be run a little brighter in the treble than theory suggests and the subjectively approved response for this system is seen in Figure 8.45. Respectable amplitude limits of ±2.5 dB are met by the system over an 80 Hz to 18 kHz frequency range at 1 m, this without the need for any graph smoothing, although it is certainly true that the output is a little ‘strong’ from 1.3 kHz to 2.5 kHz; this is a mildly audible feature of this design, lending a hint of ‘bite’ and ‘crispness’ to the sound of this low‐cost example which might otherwise sound

403

404

High Performance Loudspeakers M L S S A

17.0 12.0 7.0 2.0 –3.0 –8.0 –13.0 –18.0

5 inch direct and with crossover

–23.0 –28.0 –33.0 overplot 100.0

1000.0

10000.0

Log frequency (Hz)

Figure 8.45  Complete inexpensive system (bold) and crossover responses including drivers (dotted) +,− 2 dB 100 Hz to 20 kHz (note LF measurement shows measurement gate truncation).

a touch ‘boxy’. Good uniformity is seen for the off‐axis measurement, confirming that a satisfactory phase characteristic has been attained through the crossover range. This example illustrates how at first sight unpromising drivers can in fact be guided into satisfactory crossover alignment without great complication. Ferrofluid damping for the tweeter would add that final touch and help to mildly settle the output in the 1.5 kHz region. 8.5.8  Some Commercial System Examples A) An example of a complex full range floor‐standing design, the Wilson Audio Alexandria XLF (Figure 8.46). This is an example of high‐performance loudspeaker system design. While designed mainly for domestic use it stands nearly 2 metres high, is transported as a set of modules in crates of total weight 866 kg. Much of the construction uses heavily cross‐braced, very high‐density mineral filled industrial resin panels finished in an automotive quality lacquer finish. Unusually, low frequencies are handled by 380 and 330 mm drivers, sharing a common 140‐litre volume, tuned to 20 Hz by a high‐capacity rectangular duct, with option for exhausting to the rear or the front to suit local acoustics. Arranged in an MTM vertical array, two 177 mm treated pulp coned bass–mid drivers flank a high‐efficiency 25 mm treated silk dome driver fitted with a diffraction reducing felt ring. Working beyond 7 kHz, an additional high‐frequency unit is located on the rear facet of the enclosure supplying diffused, upper range energy to the ambient field. All three upper drivers assemblies are separately spike interfaced to control vibration and these also facilitate adjustment for driver axis and arrival time to allow precision calibration of wavefront arrival and system integration at the listener seat. Further adjustments are available on the back panel for pass band level matching and for low frequency electrical damping.

Systems and Crossovers

Figure 8.46a  Alexandria XLF.

Figure 8.46b  XLF, showing adjustment facilities.

405

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High Performance Loudspeakers

Such calibration potential at the time of installation adds significantly to sound quality. Extremely heavy and inert in construction and intended for larger listening rooms, this design specifies a 20 Hz to 30 kHz ±2 dB response with a 500 W power handling, 4Ω nominal impedance and a usefully high 94 dB/W sensitivity. It stands on massive floor locking steel spikes. Despite obvious logistical difficulties and a very high price, production for this loudspeaker series, which commenced with the X‐1 version in 1994, has been steady at about 10 pairs per month (Figure 8.46(a) and (b)). B) Beolab 90 by B&O (Figure 8.47a, b) There are seven 30 mm high frequency units (three front firing and four aimed to fire at different angles, to give 360‐degree coverage), plus a similar array of seven 86 mm‐coned

Figure 8.47a  B&O Beolab 90 loudspeaker (Source: Courtesy B&O).

Systems and Crossovers

Figure 8.47b  B&O Beolab 90 loudspeaker showing the DSP controlled directivity, consistent over frequency (Source: Courtesy B&O).

64 125 250 500 1000 2000 4000 150 8000

90

5

120

60 0 –5 30 –10 –15

180

0

210

330

240

300 270

midrange each of these 14 units individually driven by 300 W amplifiers. The bass is supplied by a front‐firing 26 cm driver, with three more of 21.2 cm firing to the sides and rear with each bass driver fed from 1000 W amplifiers. The DSP can drive them in a complex phase relationship to fine‐tune the response and directivity over angle. Thus one unit could be tuned for a corner and one for free space with the listener located still further away, off axis from the pair. We will see more of the designs which are adaptive to their environments. Here the system (via a remote control app), is adjusted for controlled DSP computed axial directivity showing the near constant directivity from 64 Hz upwards, in octave steps. (Key: from the left: increasing frequency, slightly narrowing to the right.) Even at 64 Hz there is a near perfect null to the rear axis. C) An Advanced Low Diffraction Enclosure Shape for a High‐Resolution Three‐ Way System Enclosure edge diffraction is avoided by acoustically absorbent 12 mm‐thick felt panels surrounding the drivers and incorporated in the grilles, which are designed to be left on. The sound quality is much reduced if the grilles are detached. The effective enclosure width reduces with frequency and the source origins are in step at the listening position. Each driver is pistonic over its working range, namely a pair of lower Q vent tuned low distortion Kevlar composite 275 mm units, from 25 Hz to 350 Hz, a 90 mm pure alumina concave ceramic to 4 kHz and a 19 mm concave diamond radiator operating to 70 kHz (Figure 8.48). Figure 8.49 is for another low diffraction design from Magico.

8.6 ­The Amplifier–Loudspeaker Interface It is accepted practice to assume that an amplifier is a voltage source, effectively zero source impedance[13] and that loudspeakers or loudspeaker systems are linked to the amplifier by an appropriate two‐wire cable of negligible loop resistance (4, the damping is dominated by QES and in the simple case is given by

QE

2 f s Md Bl

2

,

here ignoring QM and QTS With the driver RE at a typical 6 Ω (and for more recent examples probably closer to 3.6 ohms) and QT at 0.707, that is, set for a maximally flat response, consider a combination of amplifier and cable which together provides a damping factor of 16 for an 8Ω speaker rating, for example, from a total source resistance of 0.5Ω. The system QT will rise by around 11% to 0.77 and results in little change in resonance region frequency response. For example, the tiny peak due to under‐damping is only 0.12 dB high, with a slightly larger variation at lower frequencies of perhaps 0.6 dB.

Systems and Crossovers

Conversely, the series resistance will attenuate the rest of the frequency range, with a 1 dB audible difference between the low and upper ranges heard on an A/B test for an average 5 ohm impedance load. Here some small variation in frequency response will also be present with that slight loss of loudness, reflecting the usual variation of a speaker’s load impedance with frequency. The frequency balance shift will be proportionally greater with lower impedance loudspeakers. In tests with high‐quality audio systems, using a range of matched cables, and where the significant variable was limited to loop resistance, where the test amplifier had a low source impedance and the speaker had a even, well‐damped and extended bass response, experiments with simulated cable resistance showed a greater subjective change than anticipated. Unexpectedly, it proved possible to readily characterize sound‐quality differences by ear even in the range 0.2Ω right down to 0.05Ω of added resistance, with the most percussive persuasive and articulate low‐frequency character consistently associated with the lowest resistance. Contact effects were also present for these comparisons. 8.6.7  Cable Design Factors The physical weight and rigidity of a cable is largely proportional to a greater metal content required for the lowered resistance, so it is possible that some electromechanical factor is also at work here. Accelerometer analysis has shown that at high currents the conductors may mutually vibrate if they are not sufficiently restrained by the speaker cable build. The AC current in the loop results in attraction and repulsion between the conductors. Also note that most thermoplastic insulators have a mild piezo‐electric property which may add a touch of dielectric microphony noise. In critical sound quality applications loudspeaker cable performance does matter and many varied formulations have become available, most unfortunately designed on an empirical basis and, in consequence, marketed with a disappointing degree of conflicting pseudo‐technological claims. These do their designers little credit. However, careful subjective analysis indicates that significant and valued sound‐quality differences do exist between cable formulations and for which some factors are also independent of the well‐known known issues of loop resistance and impedance. From a review of an evaluation database for 150 cable types, factors affecting sound quality include conductor metallurgy and purity, its state of annealing and any surface treatment plating or coatings are also relevant. In addition, single or multiple stranding, including the use of differential strand diameters or separately insulated strands and/or more complex strand winding methods, are all influential. Geometry also plays a part, for example whether flat twin, twisted pair, or coaxial, planar ribbon and cross weave tube‐like transmission line formulations. Finally, the dielectric quality of the insulating medium may be influential, together with more general mechanical properties such as molecular weight, stiffness and damping. For one cable design, a weighty filling of lead particles was added to increase the mass and damping for a high‐power speaker cable, with a clearly audible and positive result. Cost‐effective results can be obtained using 0.8 to 1 mm high‐purity, single‐strand copper conductor, with polyethylene insulation arranged as a tightly twisted pair. Such a cable offers low dielectric loss, a mechanically rigid construction, low inductance and moderate resistance, together with a well‐defined geometry and conductive path.

413

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High Performance Loudspeakers

Another tried and tested example is the so called flat twin, the extant Naim NAC ‐A5 example comprising two low resistance, 0.45 × 10−3 ohm per metre single conductor bundle of stranded copper in an extruded separating jacket of selected high rigidity polyethylene (DF better than 0.0004 at 10 kHz for 5 m). The mild self‐inductance, 1 uH/m loop offers some attenuation of induced RFI. 8.6.8  Electromagnetic Screening Loudspeaker and Cable, EMC Effects The upper limit of reproduced sound quality for a system will frequently rely on an accumulation or summation of many small setup and installation improvements, derived from attention to detail. One of these is awareness of EMC, electromagnetic compatibility, here practicing electromagnetic screening. As our environment becomes increasingly radio‐emission rich, its impact on the performance of a replay system has become increasingly apparent. This unwelcome radio frequency smog includes the contributions from numerous transmitters present both locally and in the home from DECT, portable and mobile telephones, radio‐linked remote control and data transmission systems including streaming Bluetooth numerous nearby and local WiFi stations, Bluetooth TV, and computers, radio, and video devices. EM radiation does not mysteriously affect the sound of a passive loudspeaker. Rather, the loudspeaker’s internal circuit, crossover, wiring loom and the cable connecting to the amplifier constitute a form of receiving aerial feeding EM interference back to the amplifier. Amplifiers vary considerably in their susceptibility and a simple reporting of measured, and possibly audible low‐level interference levels will only go part of the way in determining whether sound quality will be affected. A potentially worthwhile design step is to provide for common grounding of the main metal components of the loudspeaker, also possible shielding of the crossover network (taking care to avoid electromagnetic coupling to the internal components), options for shielding of the speaker cable via a third wire/braid, and provision to take this radio signal shield connection either to the amplifier chassis, or to the main signal ground, whichever is preferable. (Some power amplifiers have a balanced output requiring a chassis ground for this connection.) In double‐blind A/B testing I have observed that this grounding technique is moderately beneficial with several types of high‐quality power amplifiers significantly, if modestly, improving the sound‐quality score for loudspeaker/cable combinations that are equipped with this grounding facility (e.g. Figure 8.52(a)). Here the loudspeaker is screened using a partially conductive enclosure. The conventional schematic, L‐type high pass, band pass and low‐pass audio band crossover network is supplemented with additional low loss, low‐value radio frequency filter components, which importantly include resistive damping, for example, 37, 53, 62, these in the range 68 to 200 ohms, these RFI sections operative well beyond the audio range, that is, above 0.5 MHz. Inductors 65 and 66, together with C36, form a balanced filter to RF energy travelling back to the amplifier. Additionally, the cable to the loudspeaker is balanced and shielded, also fitted with resistive damping 37 between the shields. The driver connections themselves have low value suppression capacitors across them. The drivers have metal frames and are also grounded to the shield. For a high‐quality audio system a 0.0005 uF capacitor, with or without resistive damping, shunt or series, of say 68 to 680 ohms, may be subtly beneficial, and some instances

Systems and Crossovers 9 43

2

3

4

65 36 66

7

7b

5

50 37

6 8

46

45

7a 1

48

40 44 52

49

54 51 53

41

58 7c

56 63

59 57

55

60

62

42

61 64

Figure 8.52a  Robert Grodinsky’s approach to RF interference suppression for an amplifier driving a cable‐fed loudspeaker system, using high‐frequency shielding, RF dissipating networks and a balanced, RFI‐filtered cable connection (1986).

the make, the type of dielectric and the voltage rating are further variables. In one case, 1000 V‐rated paper and film dielectric capacitors were preferred. If these are due to RFI effects then some good modelling is required to explain what was heard. The mechanism suggested is that non‐linear dielectrics, noting that a very wide RF range is involved in our modern environments, may subtly modulate lower audio frequencies, which can flow back to the amplifier. The Q value of radio grade capacitors varies greatly with value, type and frequency, noting that signals to beyond 5 GHz may be involved. When tested for transmission loss in a 50 ohm terminated system ordinary ‘speaker twin’ cable, with a polypropylene dielectric, was understandably multi‐resonant at 1 GHz at 5‐meter length but still constituted an effective aerial, readily feeding RFI to an amplifier port. Generally the latter is not equipped to deal with such a signal and there is an entry path via the customary if suitably small negative feedback capacitor. By this route RFI may be dumped at the differential audio input junction where it gets demodulated, and even if inaudible as a signal, it can modulate the operating point so affecting the clarity of sound reproduction. Many amplifiers are more susceptible to RFI that was anticipated, the power and audio frequency, paths and circuits behave very differently at much higher frequencies. RFI may enter an amplifier via slots in the casework, via the mains power input, and via the designed input and output ports. 8.6.9  The Sound of Metal Conductors Contentiously perhaps, claims have been made about the sound quality of different metal conductors. A proof of the audibility of sound‐quality differences between silver and copper conductors was devised by this author. A small high‐performance two‐way speaker, which in manufacture was built to high precision and close tolerance using high‐quality copper conductors, was replicated with all the electrically conducting

415

416

High Performance Loudspeakers

parts made in silver (99.99% purity or better). During its development individual silver content components were built and auditioned, revealing interesting differences, but from this work it still proved impossible to anticipate the effect of executing the whole local replay signal path in silver, this including the crossover network and all the cables back to the power amplifier. For the completed pure silver example, several aspects of sound quality were altered significantly for this test loudspeaker, with general agreement that these were not merely differences, but were agreed to be qualitative improvements resulting from the silver substitution. Most interesting was the noticeable reduction in mid‐range colouration. A degree of emphasis and upper mid ‘hardness’, previously suspected to be cone‐ related, showed improvement, indicating that it was in fact related to the conductor metallurgy. With this gain came an improvement in mid‐range clarity and transparency. Transients were also judged more articulate, while the bass sounded more precise with clearer note differentiation. For the high frequencies, the silver wired tweeter appeared to have a purer, sweeter sound, with reduced ‘grain’ and related subjective distortions. While this author was solely responsible for the experimental work, design teams from two major loudspeaker companies attended listening tests and confirmed the findings. Based on the research one of these chose to manufacture a costly limited edition series, whose commercial success and production volume far exceeded expectation. It was nonetheless a very costly exercise and roughly similar improvements can be obtained through attention to detail in all aspects of design and construction, without that massive expense in silver metallurgy. We have yet to identify a conduction mechanism in physics which can explain these differences in sound quality. Some cable designers have experimented successfully with various metal alloys. The practice of annealing cables and/or wires in liquid nitrogen also has its supporters, this altering the structure and ductility of the wire.

8.7 ­Active Loudspeakers At present the consumer market shows a great reluctance to accept loudspeakers that employ active crossovers with their accompanying outboard, or inboard multiple power amplifiers. The hi fi market has remained firmly wedded to the concept of a chain of audio components such as pre‐amplifiers, power amplifiers, special cables and selected loudspeaker systems. For such a chain, the consumer has freedom of choice to pick and choose, and replace or upgrade constituent components more or less at will. This contrasts with the pro‐audio market where active monitors, and stage and event public address, are now dominated by active designs However, the active technique offers the greatest scope for the advancement of the loudspeaker art. Important benefits, and in no particular order, include: 1) A reduction in intermodulation distortion in the accompanying amplifiers due to their operation over narrower bandwidths. 2) The sound quality of well‐designed active systems exceeds expectation when comparison is made with the single amplifier/passive crossover alternative. Characterizations of ‘louder’ and ‘clearer’, more dynamic, clearer bass, are frequently made, and are believed due to the reduction in ‘stressful’ loading on the individual

Systems and Crossovers

amplifiers. For example, when a main amplifier clips or enters distortion, as may occur during a momentary powerful bass transient, the distortion harmonics will be clearly reproduced by the treble driver in a passive system. In contrast, the active configuration keeps the bass amplifier distortion to the bass driver and the treble range remains clear and undistorted. (This is in fact a special case of the intermodulation improvement noted above.) This quality advantage still holds true for two‐way systems with a typical crossover at 3 kHz, provided that the bass/mid‐unit has a reasonable intrinsic roll‐off above the crossover point. If not, a simple passive low‐pass filter could be fitted between it and the output terminal of the respective drive amplifier. 3) Bass equalization may be readily incorporated in the active crossover. This is valuable if the low‐frequency alignment requires it, or is designed for equalization but also helpful for fine adjustment for varied locations including listening spaces (e.g., 4, 2, 1, and 0.5 Pi drive). 4) The association between driver and amplifier may be beneficially extended to include the LF driver in the feedback loop of the matching amplifier (these are the so‐called ‘motional feedback’ or ‘servo bass’ designs). 5) Production variations in driver sensitivity may be easily trimmed out via low‐level gain control potentiometers and /or settings for filter path gain. 6) Because each power amplifier feeds a single driver, the overload protection thresholds may be set more precisely than is possible for a passive crossover and the single power amplifier alternative. 7) Beneficially, the power amplifiers are connected directly across the terminals of each driver. The units are thus driven from a voltage source which will tend to control the fundamental resonance via electromagnetic damping: the degree depends on the driver Q. Particularly with treble units the absence of the usual series capacitor component in a matching passive crossover avoids the motional impedance problem previously discussed in Section 8.2, although that final upper frequency roll off due to the motor‐coil inductance will still remain. 8) The amplifier output impedance can be made negative if required, providing further control at the fundamental driver resonance. In addition, distortion from the inherent non‐linear current in the driver voice coils is also suppressed by direct, lower impedance coupling 9) Electronic filters, particularly digital, may provide a considerable variety of equalization, response shape and phase characteristics which may prove unwieldy if not impossible to realize with passive networks. In addition, electronic filters may be easily adjusted during production via S.O.T. (‘select on test’) components or settings. Where the control/filter section is more versatile, particularly when in the digital domain, individual driver characteristics may be included in the advanced filter modeling to increasing the overall response accuracy. 10) For the signal paths to specific drivers delay stages may be provided electronically allowing compensation of relative delays which may exist between units in the system when mounted for an optimum directivity. Such compensation is also useful for the maintenance of symmetrical directivity in the lateral plane over the several important octaves around the crossover frequencies. Extended time‐delay correction can also facilitate minimum‐phase design.[4] 11) Active filters have lower distortion than passive, due to the elimination of cored

417

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High Performance Loudspeakers

inductors, electrolytic capacitors and the suppression on non‐linear input current arising from motional impedances. 12) Where drivers have excess sensitivity, either overall or in parts of the frequency range this may often be translated into greater headroom or greater loudness for the subsystem. Typically, an active version of a given design driven on music programme will play 3 to 5 dB louder than the passive equivalent before audible distortion sets in. 13) Digital active design builds on this foundation potentially adding time alignment, control of group delay, modeling of the drivers’ electrical and dynamic headroom with frequency, the inbuilt micro equalisation of drivers calibrated in manufacture, and linear phase equalization at the listener location. Additionally, the effect of rooms and of speaker locations may be compensated in fine detail, in some cases automatically. 8.7.1  Electronic Filter Crossovers A full treatment of active filters is beyond the scope of this book. Details of the subject are well covered.[14] Some basic circuits will be examined here together with examples. Of course, modern loudspeaker modelling software packages offer much greater opportunity for active‐filter design. If implemented in digital, software packages are common, also allowing those developed digital filter implementations to be designed, programmed and then loaded to the chosen DSP chips. A conceptual analogue active crossover system (Figure 8.52(b)) consists of signal level filter sections, gain control and equalization stages. These feed power amplifiers allocated to each filter/driver. Theoretically, an active filter is a more versatile device than its passive counterpart and complex response functions may be synthesized, which would not only be difficult, but might actually be impossible to realize with passive networks. Its great advantage lies in the elimination of the inductor which is probably the least satisfactory electrical Low-pass active filter

Power amplifier

Zin (high, eg 10 kΩ)

Bass/mid driv fc

Input level 0 dB (0.77 V) High-pass active filter

High frequency driver fc Optional equalization and/or delay units Gain/sensitivity control matching

Figure 8.52b  Basic two‐way active crossover system.

Systems and Crossovers

(a) From low impedance low-level source

– C1 +

R1

12 dB octave

R2 C2 f1

(b) From power amplifier

Power inductor L C

Driver

Figure 8.53  (a) Low‐pass second‐order active filter. (b) Passive power filter, second‐order low‐pass.

component for a loudspeaker. With the use of integrated operational amplifier chips and sensible value precision capacitors, for example, 10 nF to 1 mF, rather than the 1 to 100 mF required for the passive case, almost any filter characteristic may be readily and economically synthesized. These lower value capacitors are also lower loss and better sounding. 8.7.2  Second‐Order Low‐Pass Filters Looking at the active and passive forms of low‐pass 12 dB/octave filter, here with a 500 Hz cut‐off frequency fc, a suitable network comprises an integrated circuit ‘op amp’ (operational amplifier) together with two small value capacitors and two resistors (Figure 8.53). Though the cost of the power supplies cannot be ignored in the active case, power might be taken off from the power amplifiers or other sections of the system and need not cost very much. Conversely the passive filter counterpart (Figure 6.53(b)) while avoiding complications of power supplies requires a large inductor, 2 mH for example, with a correspondingly large matching capacitor. If the latter is built to match the stability and accuracy of the active‐filter component, then the total cost may be several times greater than that of the active form. 8.7.3  High‐Pass Filters Figure 8.54 is for a second‐order form of Figure 8.53(a). Here

fc

1 2 RC 2

419

420

High Performance Loudspeakers Operational amplifier – Low-level input

To power amplifier and driver

R + C

C

2R f1

Figure 8.54  High‐pass active filter, second‐order.

8.7.4  First‐Order Low‐Pass Filters Simpler first‐order filters are conveniently obtained with RC networks using an op‐amp serving as a high input impedance, low output impedance buffer to preserve the target filter responses. In less critical applications a simple unity‐gain transistor stage, the emitter follower, may be used (Figure 8.55(a)). Amplifier and signal quality standards have improved a level where a simple emitter follower will likely impose significant fidelity impairment. High‐quality op‐amps for audio use are generally preferred, which may be IC chips or built as discrete component amplifier units or modules. At the highest quality level, the designer will need to devote as much care to filter and power‐amp design for an active speaker as would be expected for a fine pre and power amplifier combination. Design by rote may well produce results that measure accurately and sound plausible but may not fully reach accepted high fidelity levels. This author speaks from experience, where a carefully designed and built active crossover for a costly loudspeaker system measured perfectly but did not fully deliver in high fidelity terms. Further prototyping was required with careful attention to grounding topology before the target sound quality, especially realistic dynamics, and also good transparency, was also obtained. However, with a system, electronic filter network, and amplification to match, a well‐designed active may offer a sound quality which may well appear to transcend choices of driver technology, system size and price. 8.7.5  Higher Orders Filter stages may be cascaded to provide almost any roll‐off rate, but the cumulative effect of the error in roll‐off frequency must be noted; each stage is additive. Conversely, this provides a means of readily controlling the initial slope and shape of the response via the location of the individual −3 dB roll‐off frequencies (Figure 8.56). 8.7.6  Driving Impedance and Noise All the filters sections should be driven from low source impedance. In a multiple‐way system, an additional input buffer amplifier (Figure  8.57) will deliver this, as well as helping to provide high input impedance to the entire active‐filter system. There is a finite limit to dynamic range and compromises need to be found between the maximum

(a) 6 dB octave – R

f1

+ Buffer amplifier

C

+Vs

Emitter follower buffer R

RC filter

out C –Vs

(b)

– (From low Z source)

Vout

A + C R

6 dB octave f1

Figure 8.55  First‐order RC filter; (a) low‐pass form, (b) high‐pass form (with buffer amplifier A). Unity gain buffer R

–

R1

+

C

– +

C1

R2

–

Out

+

18 dB octave

C2 f1

Figure 8.56  Third‐order low‐pass filter, via cascaded first‐order sections.

Zin high

– +

To active filter sections Low source impedance

Figure 8.57  An input buffer (may usefully be combined with audio band‐pass input filter).

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High Performance Loudspeakers

level through the filters, and the additive noise arising down the chain of stages, this including the buffers. Hiss (or hum) should not be audible from the drivers even under quiet 25 dBA studio conditions ideally tested by putting an ear to the drivers. In addition, the filters, notwithstanding the possible peaking for equalisation, must not be allowed to clip on peak program inputs. 8.7.7  Equalization for Driver Sensitivity and/or Network Losses Combinations of passive and active RC networks may provide almost any required broad acting equalization. Where considerable frequency lift is necessary, the clipping headroom of the following power amplifier driving the loudspeaker must be considered in the context of the spectral content of typical programme. For an active crossover, transmission loss in the equalizer networks may be recovered by adding an amplification stage or by adjusting the amplification of the corresponding op‐amps in the filter to some suitable low positive value (Figure 8.58). 8.7.8  Correction for Rising Driver Axial Response Examining the circuit in Figure 8.59, at low frequencies, that is, below f1, C constitutes a high impedance compared with R3 and the network is essentially a resistive ‘L’ 2C

Vin

V0

+ R

R

Figure 8.58a  Active filter with gain. The pass‐band gain A = V0/ Vin = (Rf + Ri)/Ri (if Ri is set, then Rf = (A −1)Ri.

– C Rf

Ri

27 K 1 nF

1 nF + + 56 K

– 33 K 33 K

R1

Rf

Figure 8.58b  A 2.4 kHz high‐pass second‐order network with 6 dB of gain, set by Rf = R1.

Figure 8.59  (a) Equalization of rising driver response, (b) alternative implementation with shunt feedback.

Sound pressure

Systems and Crossovers

Driver response

Equalization f1

f2

Frequency

(a) R1

Buffer R3

C

R2 Equalization

(b)

R2

R3

– +

C

+

attenuator composed of R1, R2 and R3. At high frequencies, above f2, C is low in impedance compared with R3 and R2 and the attenuation is established by the ‘L’ attenuator R1 and R2. Between f1 and f2 the slope of the response may approach 6 dB/octave, when R2 is low and R3 is very high, and the slope rate may be reduced by any degree through adjustment of R2 and R3. The approximate 4 dB/octave slope required by the above example is not difficult to achieve over a limited frequency span. If the second roll‐off at f2 is not required, then R2 is simply reduced to zero. A perhaps more elegant solution (Figure 8.59(b)) employs shunt feedback around a gain stage; with appropriate values, the input impedance can be kept at a higher level. Where it proves necessary to mute the crossover to prevent transient noises at switch‐on, a simple FET muting circuit can be incorporated, with a short delay to un‐mute. 8.7.9  Correction for Premature Driver Roll‐Off Premature driver roll‐off can be compensated by using a boost network such as that shown in Figure 8.60.

423

High Performance Loudspeakers

Figure 8.60  Equalization of falling driver response. Equalization

Sound pressure

424

Driver response

Frequency C

Buffer

R1

R2

In this example the network is simply a resistive attenuator composed of R1 and R2 at low frequencies where the impedance of C is high. At some frequency where the reactance of C (ZC = 1/2πf ) equals R, the response will have risen by 3 dB and will continue to rise by 6 dB/octave thereafter. The slope may be reduced if necessary by adding a further resistor in series with C. 8.7.10  Other Irregularities With good quality drivers it should rarely be necessary to apply a correction slope steeper than 6 dB/octave, and in practice the above equalization usually is provided for final tuning and balancing rather than drastic compensation. However, rather quicker acting equalization may be used, for example in conjunction with a calculated bass roll‐off characteristic. A driver may be chosen on the basis of its high mid‐band efficiency which often implies a high Bl product, with consequent over‐damping at the bass resonance. Such a driver used in a sealed box might provide a system resonance at 40 Hz. Optimally aligned, under standard conditions the output would be −3 dB at that frequency. Now consider a large magnet, high efficiency model, over‐damped, such that −6 dB occurs at 40 Hz, with the response beginning to fall gently from as high as 100 Hz. The normal sealed‐box roll‐off of 12 dB/octave from 40 Hz has become a two‐stage slope, 6 dB/octave from 100 Hz to 50 Hz, and approaches 12 dB/octave only below 40 Hz. If amplifier headroom and programme considerations permit, simple bass lift at a 6 dB/octave rate may be applied to restore the low‐frequency output to uniformity.

Systems and Crossovers

A  suitable network is shown in Figure  8.61(a). Cs is chosen to reduce the gain at infrasonic frequencies (e.g., below 30 Hz) and hence to prevent the bass boost from continuing below that frequency. More complex equalization may be incorporated along these lines, and one commercial example, working in conjunction with the loaded bass driver, constitutes a tenth‐order high pass network overall. This might be an interesting example academically, but the resulting high order high pass filter plays havoc with group delay, potentially corrupting the perceived bass loudness and musical timing. Even fourth order, maximally flat, may damage perceived timing, becoming progressively worse as the corner frequency moves up the frequency range. Linkwitz described a universal low frequency equalizer form (Figure  8.61(b)) that may be used for all driver and/or box combinations, namely LF, mid and HF, to take designed control of operating resonance, Q factor and subsequent, roll‐off rate below resonance. Thus, by this means an HF unit may be used at frequencies lower than normally considered practicable (assuming that power handing and distortion difficulties do not Figure 8.61a  LF equalization. The attenuation from the ‘step compensation filter’ is compensated by the gain network Rf, Ri, in which Cs is also incorporated to provide an infrasonic roll‐off to avoid excessive boost.

R1

+ –

R2

Rf

Ri

C

Cs

C1

(38K3) R1 R1

C1

(3n3)

(3n3)

R2

R3 4K22

R2 (55 nF)

R2 C3

34 K

–

–

– +

+

+ C3 (0.2 µF)

2n2

2n2

68 K

Figure 8.61b  Fundamental resonance equalizer/compensator (after Linkwitz). (Variables in parentheses correspond to f0 = 800 Hz, Q = 0.9, crossover provides 24 dB/octave final roll‐off at 1.5 kHz).

425

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High Performance Loudspeakers

arise). In an example, the circuit provides for a well‐tuned 24 dB/octave fourth‐order acoustic output at a 1.5 kHz crossover frequency, despite the example 25 mm HF driver having a nearby fundamental resonance at 800 Hz, at an unpromisingly high Q of 0.8. The first stage of the filter comprises a damped twin ‘T’ notch filter, providing close control of phase and amplitude for the unit’s natural resonance. In addition, a feedback‐generated phase and amplitude characteristic tailors the input signal to generate a 12 dB/octave roll‐off in the acoustic response summation. This first slope is augmented with the second stage, a 12 dB/octave filter, providing the overall 24 dB/octave target function. Similarly, the first stage of this active filter also may be is used to calculate any in situ loudspeaker system bass resonance correction, and also extend the lower frequency response as required. For the Linkwitz high pass tweeter example above, the driver in question was to be paired with a 110 mm mid‐range unit, whose natural radiation plane is delayed 42 mm, that is, behind the HF unit. To adjust for this delay and bring the driver outputs into phase correspondence a three‐stage delay network can be used to help fully synchronize the driver outputs. This also allowed for a required, in‐phase connection to their terminals. Each stage shown delays the treble output by 22μs or about 14 mm (see Figure 8.62(a)). time delay



2 R2 c 1

2 fR2 c

2

, where RC ≤ 1/20fc, and

fc = crossover frequency.

Douglas Self contributes considerable detail to the art of active crossover design, explaining that active crossovers are susceptible to elegant and well specified design solutions (The Design of Active Crossovers). Analogue‐based active filters may use up to six cascaded op amp stages in the signal path. Care needs to be taken to qualify the noise contributions for these chains, also respecting the effect of the filter behavior on the effective noise bandwidth. Good design is essential if the −120 dBu (0.77 V reference

R1 R1 – (34 K) + (10 K) R2

C (2n2)

Figure 8.62a  Active delay network (after Linkwitz) fc = 7.2 kHz, Delay 22 microseconds ≡ 14 mm.

Systems and Crossovers

level) noise performance of a good power amplifier which will be placed next in the chain is not to be compromised by the active filter preceding it (Figure 8.62(b)). The potential inaccuracy of lower tolerance passive crossover implementations, and the technical imperfections of passive filter components are well known, not least the interaction of a network with the complex termination impedance of drive units. Nonetheless, with care these can be largely controlled to the point where high‐performance conventional passive systems may be realized nonetheless. While the active filter may look simple on paper, using helpfully predictable op‐amp building blocks, unless these systems are constructed, interfaced and powered to equivalent high standards, that is, that of a high‐quality preamplifier, the potential sound quality gain from an active implementation may be lost in the translation. In practice an active filter is a much more complex difficult design task than a line level preamplifier, requires many more capacitors, many of which need very good tolerancing. Also careful selection for sound quality may be required. Provision and protection for power brownouts and dc faults is also important to safeguard the power amplifiers and speakers in case of fault and/or power failure. Good sounding, largely point‐to‐point and unboxed ‘breadboard’ active filters may be translated carefully to fully worked, intelligently laid printed circuit board construction, which nevertheless may then disappoint on sound quality grounds due to vibration/microphony susceptibility, or to enclosure coupling and related problems, or simply the hierarchy of the internal circuit grounding. A central ground layout is vital for the design of a fine if simple active line preamplifier, conferring a sound quality that can make the difference between the merely competent, and the musically interesting. This quality can be more difficult to achieve with a complex active filter network but is just as important. Those potential gains which may be provided by power amplifier drive direct to the loudspeaker drivers, must be complemented by a true high‐fidelity performance from the matching active filters. 8.7.11  Crossover Calculations The powerful, commercial MATLAB software is familiar to many mathematically adept electro acoustical engineers, and, as Hawksford has shown, can provide a versatile environment for loudspeaker system design.[6] LSPCAD is also a valuable and modestly priced visual system design resource especially for modelling circuitry. LinearX also offer sophisticated menu driven crossover design for both analogue (see below) and digital filter domains. Here optimizers have been used for the most uniform target frequency response and the result may be visually elegant but may also be unnecessarily complex, to the point of potentially reducing overall sound quality. Not only is the HF driver impedance corrected, it is equalised and essentially fourth order filtered using no less than 10 elements. There are 14 elements for the low pass to the bass driver including full motional impedance correction, and 34 in total. However, this example, taken from many, illustrates the great power of the synthesis tool provided (Figure 8.62(c,d)).

427

–101.0 dBu

–101.2 dBu

C50 220 nF Polyprop

–101.1 dBu C52

C51 220 nF Polyester

C53

220 nF Polyprop

A20

–

220 nF Polyester

+ NE5532N

R50 1 K3 P

R53 4 K7 P

R54

R55

1 K3 P

R56 5 K6 82 K P P

12 dB/oct Highpass 400 Hz

R59

R61

1 K6 P

1 K6 P

C55

C54

R57 4 K7 P

–

R60 1 K6 P

R58 1 K6 P

NE5532N

R51 R52 82 K 5 K6 P P

A21

–

+ +11.6 dBu 2.94 Vrms

–108.6 dBu

47 nF

47 nF Polyester Polyester

12 dB/oct Highpass 400 Hz

A22

+ C56 NE5532N 47 nF Polyprop

–109.4 dBu

R63

R66

1 K6 P

1 K6 P

R62 1K6 P C57 47 nF Polyester

12 dB/oct Lowpass 3 kHz

Linkwitz-Riley 4th-order Highpass 400 Hz

R65 1 K6 P C58 47 nF Polyester

–

A23

+ NE5532N C59 47 nF Polyprop

12 dB/oct Lowpass 3 kHz

Linkwitz-Riley 4th-order Lowpass 3 Hz

C61 47 nF

R70

C62

47 pF

–102.9 dBu

–103.6 dBu

R77

20 K P R69 R67

C60

1 K6 P R68 4 K7 P

47 nF

+

1K

R73 2 K

2 K7 P

R74

R72

–

–

– 1K

A24 R71

+

1K A25

C63

2K

Second-order allpass filter

+

R75 3 K3 P

First-order allpass filter

Third-order allpass delay compensation: 400 usec

A26

47 nF R76 4 K3 P

–110.4 dBu

+11.8 dBu C40 3 Vrms 220 uF 35 V NP Electrolytic

R78 330R

MID OUT

+3.5 dB RV2 LEVEL TRIM 220R –6 dB

CN3 +2.2 dBu 1.0 V

1 2 3

R70 110R

Figure 8.62b  A bandpass active filter for midrange duty nominally, 400 Hz and 3 kHz by D. Self (this does not include the input buffer circuitry) with permission (Source: The Design of Active Crossovers by Douglas Self, Focal Press).

Systems and Crossovers

Figure 8.62c  The LEAP crossover schematic discussed.

8.7.12  Leap Crossover Synthesis (see Figure 8.62d) 8.7.13 AST AST has been coined by Yamaha for their amplifier‐speaker matching concept. Standing for ‘Active Servo Technology’, it is hard to argue for the use of either term, ‘active’ or ‘servo’. The kernel of the idea is the adjustment of the accompanying amplifier’s output impedance to some suitable low negative value in order to remove from the low‐­ frequency design equation the dc resistance component of the system, which is otherwise dominated by the loudspeaker motor coil. With a suitable design of bass driver, efficient small‐box systems with reflex loading may be produced where the vent or port contribution is unusually effective due to the higher electromagnetic coupling achieved between the amplifier and the bass diaphragm. Strongly working a small vent requires sophisticated duct design. The several techniques employed to reduce windage noise and secondary resonances include the use of a felt‐lined, semi‐rigid duct made of rubber which is beneficial with respect to damping higher frequency pipe modes. Air‐flow shaping is also used to smooth the port exit (Figure 8.63(a), (b) and (c)).

429

100

SPL vs Freq

dBSPL

90 80 70 60 50 40 30 20 10 0 –10 –20

10 Hz

20

50

100

200

500

Figure 8.62d  Leap crossover synthesis: note 120 dB vertical window.

1K

2K

5K

10 K

20 K

40 K

Systems and Crossovers The helmholtz resonator

Rv v

–Ro

E

s I

B: Magnetic flus density (T) L: Voice coil effective length (m) I: Driving current (A) E: Driving voltage (V) Rv: Voice coil electric resistance (Ω) –Ro: Driving impedance (Ω) Driving force F = B • L • I = B • L • Speaker Q factor

Q=

Rv—Ro (B • L)2

m0: Equivalent mass (kg) S0: Stiffness of unit and cabinet (Nm) C: Acoustic velocity (340m/s) s: Port area (m2) I: Port length (m) v: Chamber capacity (m3)

E Rv —Ro

mo*So S ℓ*v

Resonance C fP = 2*π frequency

Figure 8.63a  The realizations and equations for the AST idea (Courtesy Yamaha, see also Figure 8.63(b) and (c)).

(b)

(c) A

B –Ro

Crossover Network

Crossover Network

A

B

C

SPL

C

SPL B 12 dB/oct

C

A

B 6 dB/oct

C

A fp 40

fo 100

fch f(Hz) 2.5 kHz

Conventional speaker system

fp 40

fcl 100

f(Hz) fch 2.5 kHz

Active servo technology

Figure 8.63b and c  Use of amplifier negative output resistance to reduce Qr to allow for equalized overdrive of the LF range achieving extended bass response from a small enclosure (Source: Courtesy Yamaha AST).

The matching amplifier, separate or integrated, is fitted with a socket to accept plug‐ in modules specific to a given speaker model, which programs the appropriate negative output impedance and also the necessary and heavy bass boost equalization. Preliminary results indicate a superior power and clarity in the bass for the size of enclosure using this AST technique. Ultimately, the alignment accuracy will be partly dependent on factors such as the length and resistance of the speaker connecting cable and on motor‐ coil resistance changes with temperature. This may well be significant due to the greater

431

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High Performance Loudspeakers

than usual power input at low frequencies which is required to drive the port to the higher output level. Thermal changes in the driver can be modelled in the amplifier synthesis and compensated for. 8.7.14  Higher‐Order Filters by Direct Synthesis Active‐filter theory is a versatile and powerful tool, and can provide numerous desirable filter characteristics. Ashley and Henne described a two‐way third‐order active Butterworth filter operating at 318 Hz which employed a single integrated circuit incorporating two operational amplifier blocks[15] (Figure 8.64(a)). With a total count of 14 small components plus an integrated circuit, and assuming that the power supply is derived from an accompanying power amplifier, here for lower‐cost active speakers, this realization seems highly effective from both a cost and performance point of view. V0 Vi



s3

LF

0.5 V0 2 2 s 2 s 1 Vi

0.553 2 s2 2 s 1

s3

HF

With fc at 318 Hz, R 8.25 k



C



R1

0.022 F C1

90 k



0.15 F



This basic circuit may be scaled to fit almost any application or frequency. However, a buffer amplifier stage is a worthwhile addition to reduce loading on the source, since the summed input impedance of the two filters is well below 10 kΩ. The exposition may be compared with the equivalent passive filter realization in Figure 8.64(b). Another example of a discrete three‐way active crossover circuit is given in Figure 8.65 and the organization of a complete system is shown in Figure 8.66. R R

R

C

R A

C1

Input

Low-pass CA 3015 A integrated circuit amplifier

C1

Vi C R1 C

C

R

C

A

High-pass

R

Figure 8.64a  Third‐order Butterworth crossover (after Ashley and Henne[5]).

Systems and Crossovers 6.0 mH

2.0 mH

83.4 μF

Input

125 μF

41.7 μF

Input

LF

3.0 mH

MF

R0 = 8 Ω nominal

fc = 318 Hz

Figure 8.64b  Passive constant resistance Butterworth equivalent of Figure 8.64(a). + Vcc (25–30 V)

150 K

0.1 μF

820 pF 51 K 0.001 μF

0.002 μF

75 K

10 K

HF amplifer 25 K

150 K 15 K

39 K

0.01 μF

0.01 μF 0.47 μF

0.002 μF

4.7 μF

68 K

15 K

150 K

0.001 μF

800 pF

In

15 K

10 K

10 K

82 K 0.001 μF

0.039 μF 5600

MF amplifer

15 K 4.7 μF

15 K

470 K

15 K

10 K 0.012 μF

0.018 μF 0.001 μF

0.001 10 K

15 K

LF amplifer

Figure 8.65  An historic three‐way active crossover (f1 = 500 Hz, f2 = 5.3 kHz) (after C.G. McProud). (Unity‐gain op‐amps would now be advantageously substituted for the emitter followers, see Figure 8.48).

8.7.15  Gain Limitation in Active‐Filter Amplifiers The roll‐off rate for an active filter is only maintained as long as there is sufficient gain present in the loop. Up to now the active‐filter treatment here has assumed perfect op‐amp performance, at least over the audio band. This implies that the characteristically

433

434

High Performance Loudspeakers High-pass active filter

High input impedance High sensitivity e.g. 1 Volt

Buffer amplifier

f2

Eq

Power amplifer

HF driver

Buffer Band pass active filter

Bandpass filter 10 Hz to 35 kHz – 3dB

HF balance

Protection

Eq

f1, f2

Optional HF termination

Equalization

Buffer stages

Mid balance f1

Eq

Protection

Protection

MF driver

Low-pass active filter System gain

LF Feed back

Optional LF active feedback Sensor Optiona low-pass filter (–3dB at 2f1)

LF driver

Figure 8.66  Comprehensive three‐way electronic crossover system (equalization may include delay).

high input impedance, low output impedance and high gain expected of such blocks remain decently uniform over the working frequency range including the upper frequency limits. The now ancient 741 integrated circuit is adequate for low‐frequency work, but a wider bandwidth type is recommended for mid and high‐frequency use, for example, an OPA606 or modern equivalents. Also when working near gain/frequency limits, operational amplifiers will understandably produce higher distortion. Some also suffer from mild crossover distortion, since class A/B output stages are often incorporated. The existence of these distortions should be borne in mind, and for highly critical applications a designer may prefer to use special quality op amp modules or even discrete custom circuitry for the active filters. Several commercial high‐performance active crossovers employ specially designed class ‘A’ output, high‐gain operational amplifier modules of wide bandwidth and low noise and distortion. 8.7.16  A Low‐Cost Example An easy entry into active system design is afforded by inexpensive high‐power monolithic operational amplifiers, with output ratings up to 50 W into 4Ω, delivered from a single TO220, five‐lead package. The best examples have decently low distortion, class A/B complementary output stages and include protection against short circuit and excess temperature. It is possible to simply include an active crossover, which may also include some measure of driver equalization, here placed in the external feedback loop. On the assumption that the high‐frequency unit is the more sensitive, alignment of the treble to the mid‐frequency balance may easily be attained via a small resistive attenuator placed at the input to the treble section. For this example a low driving point impedance is assumed, for example, 2 kΩ or less, and many modern sources such as CD players may be connected directly to such a

Systems and Crossovers Vs+ R2 ≤ 2 kΩ 27 k Input

0.1

12 k R1 R2 36 k

1η5 1η5 4k7 68 k

0.1

22 η C1 22 k R4

VS + 16V

Vs+

3η3 18 k 22 k

+

0.1

18 k + 0.1

680 47μF

HF

0.1

270 Ω Vs– 1μF

R3 18 k

–

10 Ω

2 η2

10 Ω

LF – MF

Vs–

– 1μF

(Power IC, eg TDA2030)

Figure 8.67  A simple arrangement for one channel of an active loudspeaker system using a low‐cost two channel power amplifier IC (TDA 2030 or similar where the equalizer and second‐order filters are integrated with the power amplifier circuit.

system, either via their variable output, often present, or alternatively via a simple 10 k logarithmic volume control. This provides a maximum source impedance of 2.5 kΩ (this maximum occurs at −6 dB, the half‐position, constituting two 5 kΩ resistors in parallel). An input sensitivity of 0.3 V is appropriate for full output and a suggested circuit for a two‐way system consisting of a 170 mm flared cone bass–mid and a 25 mm dome is given in Figure 8.67. R1, R2 is the input attenuator for the treble section. R3, R4, C1 forms a simple ‘step’ equalizer for the mid‐range; the remaining components set the amplifier gains and constitute a second‐order or two‐pole crossover, both high pass and low pass. As regards power supplies, a 40 VA transformer will suffice for each channel, providing unregulated DC supplies of ±16 V on load (e.g., for a TDA 2030 and similar examples) and may be incorporated in the enclosure. While the nominal power per channel is quite low, it goes a long way when connected directly to naturally efficient drivers and such a simple design can offer surprisingly good dynamic range, focus, fine clarity and superior bass definition. For anything more complex, separate, buffered active‐filter crossover stages are recommended. 8.7.17  Loudspeaker System Alignment and Service The ability to readily adjust the gain of the various sections of an active‐filter crossover to account for sensitivity variations in the drive units has already been mentioned.

435

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High Performance Loudspeakers

A further facility concerns individual tailoring of the response characteristics. A given equalization may be correct for a typical driver but the performance spread in a batch of units may necessitate individual alignment. By judicious use of pre‐set variable resistors in place of fixed equalization components, provision for such adjustment may be incorporated. Alternatively, with digital systems the individual responses of each production driver, linked to their identities may be loaded up. When a service replacement is required its particular ID coding also may be uploaded to match to the system 8.7.18  Maintenance and Repair When designing for the most critical applications, such as studio monitoring speaker systems must be consistent in manufacture. And if a fault occurs, either due to a blown driver or electrical failure in the crossover, then it must be possible to restore that system to the same standard of performance after repair with recalibrated parts. The BBC had set standards for sample consistency for studio monitors, demanding that a single faulty system from a stereo pair could be replaced by another of the same type and still maintain quality and stereo image precision for the ‘new’ pairing. The obvious penalty of an electronic crossover system is the potentially impaired reliability when compared with its passive counterpart. The very presence of pre‐set gain and equalization controls for some designs will add some difficulty, and also allows an inexperienced operator to misalign the system, putting it out of calibration. Active loudspeaker examples from Linn and Boothroyd‐Stuart (Meridian) serve to illustrate some of the precautions considered necessary to ensure a consistent performance in production. For a three‐way system the drivers are pre‐tested for sensitivity and amplitude/ frequency response. Divided into groups for each system, each group is coded and the amplifier crossover matched to it. In the event of a driver failure, a matching coded unit may be used for replacement, and if a fault develops in the crossover, a complete new panel is supplied, also pre‐programmed to match the serial number codes of the defective system. An alternative approach may involve a careful alignment and calibration procedure for the electronics section, with the relevant product, sample code and level settings available. In the event of a repair the system could then be re‐calibrated via an electrical rather than by an acoustic measurement. For digital filter enabled loudspeakers driver identities may be readily loaded into the DSP filter section as and when required. Design improvements may also be uploaded to the customer for remote installation.

8.8 ­Current Drive It is usual to drive moving coil loudspeakers from amplifiers constituting a voltage source, this by definition providing a near zero source impedance. Standard practice low‐frequency system theory, crossover design, sensitivity matching practice and so on are founded on this constant voltage premise. From the equivalent circuit for a speaker system (Figure 3.14) it is evident that various series elements of resistance and impedance limit the flow of current from the amplifier, and in the case of a moving‐coil system, the motor‐coil resistive component Rac is predominant. However, the accuracy of movement of the drive‐unit diaphragm, and consequently the acoustic output generated depends on the linearity of both the physical and the implied electroacoustic elements of that equivalent circuit.

Systems and Crossovers

Note that a fundamental, if longer term ‘non‐linearity’, is also present due to the thermal coefficient of resistance for an electrical conductor (except for compensated resistive alloys such as ‘constantan’). For copper, the thermal coefficient of resistance is a significant +0.35% per °C. Due the rise in resistance a 6Ω coil operating at 200°C will suffer output level compression of some 4.2 dB as a result of coil temperature, this occurring over quite a long time constant, ranging up to minutes, the latter duration dependent upon the thermal mass of the coil and, to a lesser degree, also that of the magnet structure and how well it dissipates heat in the longer term. While this thermally related non‐linear behavior occurs towards maximum and largely sustained power levels, other non‐linearities are also present, for example, voice‐coil inductance, which under heavy excursion varies dynamically with coil position and excursion. Coil inductance is also in part a complex function of frequency, further complicated by non‐linear eddy currents induced by the electrically active and moving coil located in the pole and magnet structure. In particular, voice coil temperature rise has several significant implications, 1) in respect of driver sensitivity matching in a multi‐way system, 2) for crossover network termination and alignment, 3) for low‐frequency system alignment. For the last of these, the important parameter QT is strongly dependent on voice coil resistance Rc. The degree of non‐linearity for larger excursions may in theory be greatly reduced by designing for a higher voltage power source presenting a high source resistance, that is, providing current rather than voltage and whose ‘pure’ resistance is then dominant in the equation of motion. In its simplest form, a realization may consist of a high voltage amplifier with an intrinsic output resistance much higher than the speaker system, 100 times or greater. More practically an amplifier connection may be configured using a feedback signal from the voice coil to create a current drive output. The behavior of a standard drive unit has been compared for the conditions of voltage and current drive and gave the results shown in Figure  8.68. Note that in the upper

5 dB 0

–5

– 10 20

Hz

100

1k

10 k

20 k

Figure 8.68  Upper trace–simple current drive; dashed–with velocity feedback added. Lower trace–same driver under voltage source condition.

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High Performance Loudspeakers

Table 8.1  Comparison of distortion for current and voltage drive (after Mills and Hawksford[10]). (a) Harmonic distortion Conditions

Harmonic distortion (dB) 2nd

3rd

4th ..> > 5th

100 Hz Voltage drive

−34.5

−42

−52

−65

100 Hz Current drive

−44

−46.5

−58

−58

3 kHz Voltage drive

−29

−60

> − 80

> − 80

3 kHz Current drive

−56

−73

> − 80

> − 80

f2, 3f1

f2, 4f1

(b) Intermodulation distortion Conditions

Intermodulation distortion (dB)

50 Hz: 1 kHz, 1:1

f2, f1

f, 2f1

Voltage drive

−40

−43

−63

−55

Current drive

−46

−45

> − 70

−65

(Note: Test conditions, 1 A peak drive)

graph the high source impedance current drive has allowed full expression of the motional impedance. Note also that the usual loss in output at higher frequencies resulting from motor‐coil inductance is now much reduced. Employing an accurate simulation for this driver,[10] harmonic and intermodulation data for the two conditions of voltage and current drive have also been compared (Table 8.1). Certainly the distortion improvements obtained for current drive look promising. However the effective use of current drive either requires drivers with very low mechanical Q, and/or such a combination with more advanced electronic techniques to take control of the motional impedance. With the use of a second sensing coil, or some other error‐sensing transducer, velocity feedback may be applied to achieve any desired low‐frequency alignment (dotted graph). Velocity feedback also provides some additional distortion linearization which is quite effective at low frequencies. For this test driver the current driven distortion components, for example, third and fourth, were reduced by an average of 10 dB; note that both second and fifth harmonics were unaffected. This latter behavior will also depend on details of the overall motor design which could be optimised for the application. Note that velocity feedback can be used to linearise conventional, voltage‐driven low‐ frequency systems and that in any case, the use of an active crossover, in association with power amplifiers which are then closely coupled electrically to the loudspeaker drivers, also helps reduce distortion deriving from the combination of resistive and complex, reactive components of series resistance/impedance otherwise introduced by a passive crossover network.

Systems and Crossovers

In practice active speaker systems using current drive will likely use a conventional voltage output, feedback type power amplifier where the loudspeaker current return path passes via a sensing resistor, for example, 0.5Ω. This provides the required source of negative current feedback for implementing this current drive source. Current drive design is not trivial and requires a very high open loop gain if good bandwidth and linearity are to be achieved. Stability problems are commonly found for the coupled system. Another sophisticated, if complex solution, employs an open loop power buffer to isolate the separate transconductance or current amplifier from the load.[10] If distortion reduction is the primary objective of current drive, alternatively the careful design of magnet/motor systems may also provide worthwhile improvements, while a combination of higher sensitivity and larger, higher power capacity motor coils will help mitigate the effects of coil thermal compression. Likewise, low‐frequency alignments and crossover networks which are designed for reduced sensitivity to driver Rdc changes are also helpful. 8.8.1  Hybrid System Design: Mixing Cones with Panels Time and again the attractions of open type transducers such as ribbons, electrostatics and open baffle configurations make themselves felt. Often the sound quality subjectively reported is attractively ‘open’ and ‘non‐boxy’ sounding, as the physical implementation would tend to imply. Endemic box enclosure colourations are absent. While understanding that open panel speakers have serious limitations at low frequencies, and taking account of price and size constraints, a designer may choose a conventional direct‐radiator enclosed box system for the bass, to be combined with panel technology for the mid and treble range. Considering the system design, care is required for the voicing and blending of the outputs, mainly because of the disparity between the omni‐directional radiation present at low frequencies and the typically di‐polar radiation of the upper range. Consequently the frequency changeover between the two technologies is often difficult to disguise. The lower frequency, ‘enclosure section’ may also have greater audible colouration and poorer decay responses than the technically superior (faster impulse response) upper section. In addition, within their limits, ribbon and electrostatics are extremely linear with almost zero compression contrasting with the mildly progressive compressive nature of a moving‐ coil box system. If that were not enough, a box type lower frequency section will follow an inverse square law reduction of loudness with observer distance while the panel section will tend to a linear rate of fall off. This means that the perceived relative loudness of the sections, and thus the overall timbre, will partly be a function of listener distance. The more successful of these hybrid examples employ active bass systems of high, or even feedback compensated linearity, this performance gain helping to match the overall performance profile. Another approach to more successful blending, matching a moving coil section to the panel transducer, is to devise dipole or part dipole acoustic loading at lower frequencies by adding an additional phase shaping driver section. A well‐designed ribbon transducer can possess a beguiling transparency and purity, but making it operate sufficiently loud over a wide‐enough frequency range is a problem, and usually results in elongated vertical structures which then show a more complex directivity and amplitude response behavior with distance (see Section 6.2).

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8.9 ­Digital Loudspeakers The idea of a truly digital loudspeaker has been proposed. Here, digitally coded audio is employed, at a sufficient power level, to directly actuate an electromechanical array capable of direct conversion of multiple bits into sound pressure, an acoustic digital to analogue convertor. Given that huge problems exist in creating such a device with sufficiently low quantization and related spurious noises, combined with good directivity, much still needs to be done in the field of digital loudspeaker engineering. However, recent years has seen great progress in MEMS, micro‐electro mechanical systems, where microphones, millimeters and less across, are fabricated on silicon chips to be readily combined with integral low noise integrated circuit amplification and in many cases digitization of the signal. Such data feeds the digital filters and circuit blocks which may include processing for directional and noise cancelling properties. Other functional circuit blocks may be included, for example, low‐power ‘silicon chip’ transducers for in‐ear phones, and especially for hearing aids. Discrete electromagnetic transducers are still required for higher sound intensities and ‘silicon chip’ transducers capable of loudspeaker sound levels are still years away, if they are at all possible. 8.9.1  Hybrid Digital Loudspeaker Driver Philips filed a patent for hybrid loudspeaker for digital and analogue drive signals back in 1983 (US 4,555,797). It notes that available technology of the time limited the maximum resolution to 8 bits for direct digital drive working, here with a single loudspeaker voice coil assembly, multi‐section coil, with the intrinsic, mass integrating, low pass filtering of the digital codes. If efficiency is the primary goal, then this suggestion nevertheless remains a practical proposition for high fidelity applications provided that  the remainder of the dynamic range is filled in by an alternative technique. In Figure 8.69, eight of the windings are fed bit weights up to the eighth (not all are shown). Assuming 16‐bit audio coding the lowest 8 bits are fed to a power level digital‐to‐ analogue convertor scaled to the upper part of its dynamic range, this followed by a relatively small amplifier. This need only be sufficient to cover the output ranging from −60 dB to below. Thus, 0.1 W is sufficient to drive this ninth ‘analogue’ coil section. At first sight, this scheme looks practicable, until the requirements of high‐quality, wide‐ response systems are considered, here limited by a single finite sized radiator. Thus it can be seen that the extension of this hybrid digital method to high fidelity is difficult to execute, for example, where multi‐way designs with good directivity characteristics are desired. 8.9.2  Smart Digital Loudspeaker As Malcolm Hawksford notes,[16] a conventional loudspeaker fed directly with a 1‐bit SDM (Sigma Delta Modulation) signal is in essence a ‘digital loudspeaker’. However, it must also, intrinsically or by design, filter high‐frequency noise components and additionally remain linear in the face of possible high‐frequency intermodulation distortion, this consideration implying that this type may be considered ‘analogue’ after all. A true digital transducer is a multi‐level device, as Hawksford suggests, perhaps a vertically layered piezo‐digital device, an integrated circuit form of micro radiator to be

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Figure 8.69  Amongst numerous proposals for a higher efficiency digital loudspeakers this one is more practical than most. Low levels are dealt with using a small linear amplifier and a digital‐to‐ analogue convertor. High levels are efficiently handled by direct conversion with summing achieved at the motor‐coil assembly (Philips patent, filed Netherlands 1983). Signal processing in back plate

Planar array element

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Figure 8.70 and 8.71  Planar elemental array of multi‐level DETn.

assembled in dense arrays to provide useful sound intensity. In this reference, methods for addressing such arrays are proposed, providing a range of radiation and directional characteristics, the whole termed an SLDA (smart digital loudspeaker array). It is still very early days for purely digital transducers, though patents on the subject are filing thick and fast. Note how quickly the equivalent DLP ‘silicon chip’ video imaging device (Texas Instruments) has developed in performance and popularity in recent years, particularly for video projectors (Figures 8.70 to 8.72).

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+ –

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Figure 8.72  Multi‐level sigma‐delta modulator noise shaper.

8.9.3  Digital Loudspeaker Arrays A DLA is a digitally processed loudspeaker array and comprises DSP, digital amplification, radiation modelling and processing. The power of modern simulation methods allows many complex acoustic devices such as these to be modelled without the difficulty or inconvenience of prototyping. An analysis by Tatlas[17] concerns small radiators and suggested potential viability, at least for mid‐ and high‐frequency use (see B&O Beolab 90 loudspeaker Figure 8.47a and description). Since then the technique has become increasingly common especially in pro audio, and large audience stage music amplification. 8.9.4  Active Transducers (AT) High‐speed, efficient switching amplifiers can be made sufficiently compact to be included in the structure of a moving‐coil driver. Such integration may avoid the need for output filtering as the problem of a long connecting lead from amplifier to loudspeaker is avoided and thus the high‐frequency radiation is held to a low value. Typically, a DC supply would also be provided to the transducer while for a more recent proposal called ACAT, raw AC, even at line voltage potential, is directly converted into audio power via suitable switching type power DACs (Figure 8.73). 8.9.5  Crossover Systems in Digital Loudspeakers An alternative form of a digital loudspeaker uses largely conventional drive units but with multiple ‘bit’ voice coils. Experimental systems have been built with six‐bit data.[18] Such a speaker is termed an MVCDL (multiple voice coil digital loudspeaker), using N binary‐weighted voice coils to achieve a quantized force impulse on the diaphragm; this method was first proposed by Philips in 1982. For a two‐way speaker, the crossover function is a linear operation and may be performed at any position in the processing chain, conveniently upstream. Early results verify the theory and are not unpromising, even if it is still some years from commercial realization. DSP (digital signal processing) has delivered tremendous advances for complex sound system design. With the wide dissemination of digital audio systems throughout professional and consumer applications, for music recording, compact disc, music streaming, satellite broadcast and the like, sophisticated signal‐processing systems are widely available in the digital domain. A digital audio communications interface, called

Systems and Crossovers

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Figure 8.73  Active transducers (a) switching type amplifier on the driver with DC power; (b) a variation where the power source may be DC or AC, direct conversion from the local full voltage source (after Tatlas[17]).

AES‐EBU, has been widely adopted for professional applications. It incorporates the SPDIF (Sony–Philips digital interface) consumer version, the latter used in CD player systems. Digitally coded audio can be conveyed by wire or by an optical fibre. Thus, an integrated, active loudspeaker design fitted with a digital decoder can use such an optical link as the only connection to the audio control equipment and signal sources, working exclusively in the digital format. Such use can avoid ground loop problems and can also reduce interference. More advanced signal formats have also emerged these suited to the now ubiquitous Ethernet data transmission technologies. Dedicated protocols such as for expediting the latest AES standard, AES67 and interfaces allow the transmission of low latency ( 1MΩ 80 pF

Figure 10.11  (a) Power testing noise weighting curve according to DIN45573 (IEC proposal); (b) a possible passive filter to derive this response from a white noise spectrum signal (after Hermans).

ability, now easily judged in the absence of other potentially masking musical content, and finally audible colouration per se at low frequencies. With broad band stimuli, some of the latter distortions and colorations may be masked. All things considered, a quoted power rating remains largely a matter of experience and good judgment and will be an approximation defined by the designer. It may enumerate the recommended maximum per channel amplifier power for ‘unclipped speech and music drive’, and deny warranty cover if the damage found suggests that this advice has not been followed. Most manufacturers will not repair loudspeakers under warranty which show signs of significant power overload, such as the kind of abuse which results from inappropriate use for parties. ‘High‐end’, limited edition, replacement driver units may be charged out at $1,000 each plus installation, and even then, may never be as well matched as the originals manufactured for a given system.

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10.2.8  Compression and Dynamics Both thermal and motor linearity behaviours confer some degree of compression in moving‐coil speakers. Sustained high‐level peaks heat up the voice coil, increasing resistance and temporarily reducing sensitivity. Many evaluators have long been aware that graphing a loudspeaker response at an input level much higher than 0.5 W may include some measurable compression. The usual sweep rate for a traditional tracking sine generator means that only the HF driver with the shortest time constant has time to heat up. By the time 20 kHz is reached, a temporary loss of 1 dB or more in the upper treble range is not uncommon for many published graphs as the unit coil has had sufficient time to heat up a little. 1 W continuous for an HF unit is enough to do this. Pulsed and related, gated measurement methods may help to identify and control this problem. Furthermore, while in theory the varying flux change in the magnet system due to programme excitation of the voice coil should only be a small proportion of the static polarizing flux, under heavy peak drive this may not be so, the peak levels then suffering a degree of amplitude compression. A high‐level L.F. transient may also result in compression of an accompanying lower level mid‐band signal, and this can also be viewed as an intermodulation component near damage limit. High sensitivity systems designed with light diaphragms generally draw less power, are often more linear, need less current in the voice coil, and suffer less from compression. Ferrofluids can assist in greatly moderating the temperature changes experienced by a motor coil but may suffer from a lesser, longer term temperature dependent viscosity. Crossover saturation may also play a part in compression; cored crossover inductors can saturate rapidly at peak levels dramatically changing their circuit values during the current peaks. The crossover modeling should include inspection of peak currents in the sub loops of the network and not just at the input terminals. Horn‐loaded speakers may suffer rapid onset compression as the air pressure changes in the throat approach the non‐linear threshold with a characteristic, primarily odd order harmonic ‘shout’. Colouration in the form of delayed resonances can interact with our perception of compression. If the objective is a high contrast between ‘light’ and ‘dark’, between loud and soft, then delayed resonance colouration will reduce contrasts, ringing on after the transient, smearing that sought for differentiation between loud and soft. Colouration can also make a loudspeaker appear louder, but it is a false and potentially fatiguing additional sensation of loudness. Here is a clear instance where greater subjective ‘loudness’ does not necessarily mean better sound. Reflex systems with a small exit port will also suffer audible dynamic problems. In one well‐known example, low‐level transients with significant bass content were considered ‘boomy’, and this corresponded to a system Q of about 1.3, that is, significantly under‐ damped. However when driven to higher levels, 10 to 30 W peak programme, port turbulence restricted the effective port area to below the nominal 5 cm2 and the resulting alignment was then better damped with a Q nearer to 1. At still higher power levels increasingly severe port turbulence meant that the vent essentially became inoperative save for some chuffing distortion, the system alignment then shifting almost to sealed‐ box loading. Nevertheless, the overall result is dynamic compression of the louder low frequency signals with significant damage to perceived musical timing. Many current commercial designs exhibit similar behavior but may survive casual audition thanks to masking

Loudspeaker Assessment

effects. However direct comparison with an undistorted, dynamically linear example soon educates the listener’s ear as to the difference. Characteristic of port compression is the near chaotic behavior of the low f­requency range with level and frequency, known to impair the accuracy of the low frequency timing. Tone bursts with a low duty cycle may be used to safely explore these dynamic limits. Gated, windowed measurement on pulsed signals will reveal compression and distortion where present, and without thermal damage to the loudspeaker. Ear attenuators will aid the observer during such testing.

10.3 ­Measurement and Evaluation: Introduction From an engineering viewpoint, loudspeaker assessment might appear straightforward; for example drive units seemingly can be specified to a sufficient degree to meet an expected measured standard. However, objective measurement alone is insufficient to fully describe sound quality, and thus subjective evaluation is also required, ultimately, with the loudspeaker system preferably judged by reference to live sound, even if indirectly. Subjective appraisal must the final arbiter in the judgment of quality. While engineering theory and relevant math will provide the foundation for a design, whose technical accuracy and potential performance may be assessed by objective measurement, until a controlled listening test is undertaken under representative conditions of use the true merit of the design cannot be verified. The complete evaluation of a loudspeaker is thus a complex and wide‐ranging operation whose basic content is outlined in Figure  10.1 under the section ‘loudspeaker appraisal’. There are two sections, namely objective and subjective assessment, which are dealt with separately, in this section and also in Section 10.4. There has been something of an explosion in the PC computer test and analysis field for acoustics and loudspeakers (see appendix). Software based systems with dedicated test units such as Dick Heyser’s historic TDS time delay spectrometry sytem, and MLSSA, LMS and Clio packages, have been expanding in versatility and extending their reach in the form of a variety of Windows‐based measurement packages, some of which will operate well when working directly with inexpensive computer sound cards. Here may be certain requirements such as duplex working and synchronization and the software vendors will need to be consulted on the best practice here. The better designs (such as Klippel ‘Lite’) come with an external, powered conditioning unit or interface, which also takes care of the necessary calibration factors. There is a cost penalty but the price is still very fair in view of the extensive functionality especially when compared with the eye‐wateringly expensive arrangements encountered with past generation analogue systems such as classic B&K. Some test packages are freeware, for example, WINMLS and may still be useful for basic comparative evaluation work. Others are associated with system analysis options and have varied and versatile capability in respect of data handling and processing from different measurement systems. Generally for project path control and in particular for design groups where ­s everal data systems are in use, a powerful data interpretation and handling, processing, imaging and project handling programme is a valuable adjunct. VACS is such a package, which includes visualization tools and curve splicing, with data

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computation and whose utility is enhanced by operating with complex data, including this component for smoothed representations. The quality of low‐frequency splicing is particularly good while it may also uniquely calculate power response from a set of accurately interpolated polar responses. Test material may also be conveniently formatted for publication. Those earlier systems have enjoyed something of a renewal adding more functionality though their late adoption of a Windows platform (LMS, MLSSA, CLIO) and their hard‐wired, dedicated interfaces are well respected by professionals. Such products have brought sophisticated measurement and data analysis to almost every loudspeaker engineer’s bench. For the technical reviewer of loudspeaker systems, there is a daunting range of possible techniques that can be applied to evaluations for publication, both objective and subjective. Atkinson[34] has amassed considerable experience in this field and presented a valuable survey of methods and observations on the results for some 330 loudspeakers, particularly examining correlations for subjective and objective data. Useful 3D representations for directional response data have been proposed, these being particularly useful in the crossover regions of multi‐way loudspeaker systems. For loudspeakers with reasonably accurate frequency responses, ‘B’ weighting is suggested as a good indication of perceived, in‐room loudness. For this extended survey of speakers, the industry mean for sensitivity is then revealed as just 85 dB B, being rather lower than might be expected from the clearly optimistic consumer directed marketing literature which averages 87 dB (lin). 10.3.1  Objective, Instrument‐Based Measurements Figure 10.1 covers the bulk of the useful tests which may concern complete loudspeaker systems, or individual drivers when suitably mounted on a specified panel or a semi‐ infinite baffle, or for a representative enclosure. Here are some of the relevant details. Most loudspeaker measurements utilize a precision microphone to capture the sound pressure output from the test loudspeaker at a suitable distance. The test environment is of considerable importance, because under normal reverberant conditions the readings may be strongly affected by local sound reflections. For measurements where such interference must be eliminated, the speaker should be taken to a theoretically ‘free‐field’ or open‐air location and elevated clear of the ground. Cooke[35] indicated that an 8 m elevation is sufficient for measurement at a 1 m microphone ‐to‐ loudspeaker spacing, provided that the speaker is mounted front uppermost with the microphone positioned above it, in order to minimize the effect of even distant reflections. If atmospheric conditions are favourable, then this true free‐field location gives even more accurate results than the alternative artificial echo less environment, usually anechoic chambers of various finite sizes (Figure 10.12). In such a chamber of moderate size, the optimum working range is limited to 200 Hz to 20 kHz, with a typical absorption of 90% of the sound energy, though with careful calibration the useable low‐frequency range may be extended to 50 Hz for the near field. Note that at closer range proximity effects at lower frequencies will become increasingly apparent, altering the slope of the frequency response. Ron Sauro, of NWAA labs, works with large mic arrays in large but climatically contained spaces, for example, a hangar: the mics are arrayed over a 90 degree arc at

Loudspeaker Assessment

Figure 10.12  Small anechoic chamber showing an arc array (vertical, illumination central)) of low‐cost microphones for directivity assessment, A turntable is provided to rotate the loudspeaker automatically. (Note additional microphones for precision measurement.)

5‐degree intervals and are referenced to a single rotational point to a distance accuracy of one sample interval at 48 KHz. This allows accuracy of phase response to better than 10 degrees at 10 kHz. The array itself rotates around the speaker measurement axis in increments of as little as 1 degree. Approximately 19 simultaneous measurements can be made at each angle iteration resulting in a full directivity balloon in about 20 minutes, here with a 5‐degree by 5‐degree resolution. The mic distance to the rotational center is usefully large at 4.01 m avoiding proximity effects for larger sound sources. A smaller array may also be invoked, here at a 1 m mic to source spacing. Sauro comments that some esoteric ‘hi fi’ loudspeakers which have illustrated all kinds of varied ‘ideas’ on placement of drivers, locations of vents, multiple port positions and sizes, and variations concerning interior baffling and interior absorption, have been evaluated. He notes that some results were seemingly inconsistent with the designer’s aim. For one well‐known brand, a two‐way with port, a phantom HF source was observed right in front of the port at 4 kHz and also 8 KHz, this seen on high resolution polar ‘balloon’. These ‘secondaries’ also partially distorted the main HF directivity balloon into a figure of eight. Here a single dome HF driver was located above the bass unit, but it was also designed to back radiate into the enclosure and the subsequent internal reflections were then output though the port as a secondary sources, interacting with the primary response. A further example comprised a design from another company that had a set of two concentric rings about 3.5 mm‐inch‐high and surrounding a 25 mm dome. They were said to help ‘keep the LF in phase with the HF driver’.

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When the system was measured the observed energy surface balloons were substantially chaotic with strange shapes for the low frequency balloons due to the out of phase energy puffing out of the ring slots, while diffraction ‘rings’ surrounding the main lobe of the HF driver were also present on the surface of the directivity balloon. The behavior was as if the edges of the port or slot were diffracting the upper frequency energy, normal to the axis of the port. These untoward effects lessened when the designed sharp edges were smoothed over. Concerning outdoor measurement the inconvenience of ambient noise (passing ­aircraft and cars, etc.), also noise pollution to others near the site, and also climate ­variations means that anechoic chambers, though very costly, are still widely employed for higher precision measurement particularly below 500 Hz. Provided that their imperfections are understood and noted, they are certainly highly convenient for loudspeaker measurement. Typical anechoic chambers consist of a room of massive brick or concrete construction, acoustically and vibration isolated, lined internally with wedges of polyurethane foam or fibreglass up to a metre in depth. Good absorption will be offered down to wavelengths comparable with twice the wedge depth, typically 200 Hz. Below this, the low‐frequency absorption becomes less effective, and the anechoic chamber gradually reverts to a lossy free‐field pressure chamber much like an ordinary room of similar dimensions. A difficulty encountered with true free‐field measurement is the theoretical necessity for the microphone to be in the far field; that is, several wavelengths distant at the lowest frequency in the range covered. Clearly low frequencies will present the most problems. The microphone should also be positioned at a significantly greater distance from the test system than the largest panel dimension, to avoid near‐field diffraction. At 30 Hz the required separation of microphone and system makes accurate free‐field measurement difficult; few chambers are large enough, and if carried in open air the signal‐to‐ambient‐noise ratio is very likely to be inadequate. Data averaging to improve the signal to noise ratio can only go so far. At the usual 1 m microphone spacing, with the tests conducted in an average chamber of 80 m3, the low‐frequency section of a curve at typically below 150 Hz will begin to approximate to a pressure response with the microphone effectively located in the low‐ frequency near field initially with a premature dip in bass output. It is perhaps fortunate that for domestic speaker applications the dimensions of the listening room are not too dissimilar from those of most anechoic chambers. Hence, both may possess a similar if broadly averaged pressure response and the measurements taken in the chamber are still fairly useful, even at lower frequencies. However this situation is only valid for moderate room sizes. Acoustic conditions will be entirely different if a loudspeaker is used in a larger space, even a small hall, where the free‐field radiation will continue down to a correspondingly lower frequency, while noting that the speaker is still likely to be used near at least one boundary, for example, a floor or wall. Methods for amplitude/frequency response measurements using pulse, chirp and swept‐tone burst signals in smaller rooms, where the test room reflections and some ambient noise may be suppressed by suitable synchronized gating, can offer greater flexibility, but the ideal condition, that of removing the microphone to the far field to correctly assess the intrinsic pressure and power response still pertains. While I subscribe to classical practice, namely evaluation of loudspeaker systems in the best available 4π, anechoic free‐field conditions, or an equivalent, together with suitable allowance made at low frequencies for intended use, proximity and expected

Loudspeaker Assessment

local boundaries, some engineers favour measurement in a 2π or half‐space environment. Here an anechoic chamber is used where one wall is solid and without absorption and is fitted with interchangeable, sealing baffles for flush fitting the test system. Tidy diffraction‐free graphs can be produced, free of edge reflections while the low‐­ frequency response predictably follows the textbook model (which generally assumes 2π working). However the matching complementary 2π replay environment conditions cannot be obtained except by approximation, for example where the customer is prepared to flush mount such systems in room walls. An equivalence may occur with miniature systems, that is, install them in a bookcase, the books well‐packed around them. This flush‐mounted practice can also be found with some custom install home theatre systems. In one sense 2π testing is more predictable than 4π in that here at least one practical radiation boundary is taken into account at low frequencies, while 4π measurement takes account of none. Regarding diffraction, it is worth revisiting the system design process to provide some perspective on the issues to be faced, for example, what target function for the overall, multiple axis assessed frequency response, assuming well behaved directivity, will sound naturally balanced in a room? A pure piston of finite mass, close mounted in a large, plane baffle, driven by an acceleration that is constant with frequency, gives rise to a naturally flat pressure and power response with frequency. This behavior is the basis of our classic concept for a mass‐controlled radiator. Ideally, we would like this behavior to continue to higher frequencies, but with practical‐sized drivers several aspects need to be addressed. If the piston were perfectly rigid, the reducing radiated wavelength with rising frequency will result in a narrowing of radiation angle, this behaviour also associated with the generation of lobes in the polar response. Initially, with rising frequency, the overall power radiated remains the same, but the narrowing directivity results in rising pressure response, both on and near to the main axis. For a normal, semi‐reverberant environment, for example, a listening room, the sound which is perceived by the listener is a result of both the direct pressure response and the overall power response delivered to the room acoustic, and these two will have complex behaviours in time and frequency. Divergences between the pressure and power response over the frequency range will be audible as a change in tonal balance, while for transient sounds the additional factor of a temporal, timing discrepancy between the two also causes further subtle distortions of timbre, never mind distortion of the stereo image illusion. Over its primary operating range, a piston driver exhibits minimum‐phase behaviour and some examples may even exhibit a near perfect impulse response and related decay behavior. However this ideal is only present on‐axis, while for off‐axis locations there are the usual lobes is associated with interference and phase cancellation at higher frequencies due to finite diaphragm size. This complication occurs in the range where the radiated wavelength approaches the diaphragm physical size and this will also be seen in a more complex decay response for off axis angles. Most practical drivers generally have a conical or similar‐shaped diaphragm. This has its own impact on the output owing to the acoustics of the energised cavity. Simple inspection indicates that a 170 mm driver with a 120 mm cone will suffer an inherent response aberration, a dip of a few dB, in the 1 to 2 kHz region and some system designers have incorrectly attributed the effect of this simple acoustic cavity to cone break‐up. In fact

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cone designers may seek to mitigate the effect by adjusting the first break‐up peak, with suitable damping, to lie on the natural ‘cavity dip’, with this general region smoothed over by the radiation contribution of a suitably large central dust cap, sufficiently damped so as not to significantly contribute further resonances. Some mid drivers are almost entirely composed of a huge centre cap. Nevertheless, this is a relatively minor problem compared with the complications pertaining when that more or less perfect theoretical driver is fitted to a moderately sized, free‐standing, rectangular form enclosure. The idealized reference plane baffle is a 2 Pi reflection‐free environment where the fundamental, smooth performance of an example of a well‐behaved 90 mm frame diameter cone driver may be viewed (Figure 10.13). Installing the driver on an enclosure changes everything. Phillips[36] reminded us of the magnitude of the enclosure aberration using such a well‐designed 90 mm unit, comparing its pressure responses on the large baffle and on an enclosure in free space, in this case the JIS test box, which many driver designers are required to specify for. The test driver has a mean sensitivity of 87 dB and intrinsically measures +/−1.5 dB 200 Hz to 8 kHz on a 2 Pi baffle, with distortion averaging a maximum of −15 dB up to 150 Hz. In the JIS box, the axial frequency response now has significant, easily heard aberrations of +/− 3 dB while in the upper band for this small driver diffraction has raised the mean sensitivity by about 2 dB in the range up to 2 kHz. The trend of the distortion trace is similarly affected. Moving from this larger test box to a smaller enclosure, still in free space results in similar disturbing effects, but now scaled to a higher frequency in proportion to the reduced size. In addition, while not so clearly shown in this example, the pressure response at lower frequencies is subject to the change from 2 Pi half‐space to 4 Pi full‐ space radiation, and with reducing frequency the lower frequency band ultimately falls by −6 dB relative to the upper frequency, forward directed range. SPL/dB 110.00 105.00 100.00 95.00 90.00 85.00 80.00 75.00 70.00 65.00 60.00

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Figure 10.13  Plane baffle (solid line) versus JIS test box (dashed) responses for a good 90 mm cone driver. Note diffraction irregularities (dashed line) introduced by the box shape and size (also see the Olsen box shapes/diffraction data, see Figure 9.20).

Loudspeaker Assessment

Thus, a 90 dB/1 m typical driver sensitivity, specified by the manufacturer for the usual 2 pi plane baffle condition, is modified when used in a compact enclosure, say 10 litres where in practice it will be heavily equalized by the crossover network to level the resulting frequency response, at least from 100 Hz. This system will now have a typically lowered sensitivity of 85 to 86 dB free‐field, perhaps confounding the designer’s intentions, even with some allowance made for room gain at lower frequencies. With increasing frequency the combination of narrowing driver directivity and also enclosure diffraction results in a loss of sound power, SWL. These difficulties must be addressed as far as is practical, employing good design practice. Diffraction aberrations in the axial output may be partly compensated in the crossover, or even with digital filter compensation in order to attempt near uniformity for the axial pressure response. However, such compensation may be of limited value since the intrinsic aberrations will still remain audible in the off‐axis contributions and power response which is also driving the overall room acoustic. Clearly, larger and wider enclosures are affected by a greater divergence between power response and axial pressure, this also occurring in the more aurally important frequency range This might help to explain the trend to generally higher subjective quality ratings which are observed for smaller or narrower speaker systems in rooms, provided that these systems are of intrinsically high quality, and are used within their power capacity. For a designer, this conflict between the power and pressure response for a direct radiator may suggest that a uniform axial pressure response is not always the optimum objective for a given enclosure size, and that the pressure response may also be tailored for a defined and more favourable, non‐axial listener axis, for example, 10 degrees lateral, to achieve a better design balance between those two characterisations for sound output, namely pressure and power. Diffraction effects are maximum for the central or axi‐symmetric axis, and a suggestion of a moderately off‐axis criterion for the designer target function, that is, for ‘near‐ axial’ rather than axial frequency response, will provide an improved approximation to the overall radiated output from the system, and in addition will generally sound better in the room. A totally reverberant chamber measurement, the power response summation, can give a useful result, not of course in terms of axial frequency response, since the resulting graph is dominated by the usually falling energy response with frequency, but rather in terms of drive‐unit integration, and overall energy uniformity. Here an idea of the intrinsic quality of the reverberant field obtainable in a listening room can be obtained, such as possible gaps in the crossover junctions which would be heard in the listening room. A listening room may be viewed as a partially reverberant chamber. While a laboratory grade reverberant chamber promotes a well diffused sound field of potentially long decay time, up to several minutes duration, by contrast, the listening room Rt reverberation time extends from 0.2 s to potentially to several seconds at the lowest frequencies. This result is also strongly dependent on frequency, source location and observer position. The spatial patterns of sound energy over the room volume are anything but diffuse. However, well‐proportioned and acoustically balanced listening rooms, that is, with reasonably uniform absorption with frequency, are still useful for speaker assessment.

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It has proved worthwhile for published magazine reviews of product to take some measure of the loudspeaker driven in-room sound field, this in the region of optimum perceived stereo staging and focus, perhaps represented a few non‐reflective and not unduly absorbing chairs at the listening position. This sound field data may be obtained by firstly employing optimised speaker positioning in the room, and by computing an average of the responses at a minimum of eight combinations of position (laterally over 2 metres) and height (ear height +/‐0.6 m) in the listening region. The averaging should also encompass both left and right speakers; these must be excited individually for this summation averaging. Approximately 16 averages of pink noise per measurement will get quite close to an end point, and if there is time, a 64 average gets closer still, to allow good settling of level in the bass and better rejection of extraneous low frequency noises. Before running the measurement, do check that there is sufficient signal to noise ratio, at least 16 dB at the lowest frequencies assessed with the stimulus off, otherwise barely audible infrasonic, aircon and traffic rumble may subtly exaggerate the low frequency readings. It is also worth visually monitoring the averaging to make sure that a particular noisy low frequency event is not included. Such spatial averaging is a powerful method for characterizing the perceived timbre and frequency balance of a loudspeaker in the listening room over the listener region. The individual traces can ideally be one‐sixteenth octave resolution and the averaged set may be merged to broader one sixth or one‐third octave as may be required for presentation and more general observational purposes. Quite good correlation is usually obtained between these graphs and the listener perceived timbre and frequency response, particularly regarding the uniformity and extension in the deeper bass. Undue amplitude steps in the frequency/power response will also become evident, particularly for the mid‐treble driver transition. Audible response features which may be more difficult to see in the reference axial output may appear more clearly on this listening area averaged response. Some fall‐off to the high frequencies is to be expected as the directivity limits of the final relevant driver are approached. Instead of a gradual roll‐off from about 8 to 10 kHz, some designs, such as those with oversize ribbon HF units may show a greater loss of off‐axis output in the last audible octave, and this observation does correlate with the measured ‘room energy’ response. Side‐wall reflections are important, these typically energized by the 30 degree off‐ axis output while reflections from a number of particular angles are also considered significant. These may be defined, and a primary set of axis measurements may be chosen to guide these for the anechoic measurement of a loudspeaker. Averaging of the ‘anechoic’ set provides a useful basis for correlating with the in‐room spatial average. A particular set of off‐axis measurements has been proposed for averaging to a defining response, this in view of the potential for significant first reflections, for example, floor, ceiling, front, side and back walls. Devantier[37] has suggested the following: Floor average from 20, 30 and 40 degrees below axis Ceiling average from 40, 50 and 60 degrees above axis Front or driver axis comprising the following

Loudspeaker Assessment

Axial Side Back

10, 20, 30 degrees to left and right 40, 50, 60, 70, 80 degrees to left and right 180, plus 90 degrees to left and right

He suggests the term ‘total surround power’ as the weighted average of the above seventy measurements. Alternatively those full sphere mic arrays may mirror this proposal. A particular finding from this work indicates that the spatially averaged room gain at low frequencies is about 2 dB at 50 Hz, 7 dB at 30 Hz and 12 dB at 20 Hz (for a room of solid construction) and this is in good agreement with other data. It is also a particular guide for the low‐frequency alignments to be chosen for the usual design of monopole loudspeaker. A program may also be devised where such a set of off‐axis responses may be computed to deliver the complex power response or SWL (see VACS for the section on ‘Objective or Instrument‐Based Measurements’). In the absence of serious loudspeaker colourations third‐octave and similar band weighted pink noise and equivalent analysis, spatially averaged data, can show considerable agreement with the subjective assessments of frequency response, tonal balance and low‐frequency extension as heard in the room. Spectral balance between low bass, low–mid‐bass and mid‐range bands is clearly shown, this often somewhat hidden in the free‐field laboratory condition response (see Figure 10.14). Poorly thought out speaker and subject positioning, particularly in combination with an unfavourable room, will introduce sufficient errors to compromise the value of this kind of assessment. Further, one cannot expect a ‘spatially averaged room response’ to extend to the highest frequencies since it consists of a mix of direct and reverberant sound. With the usual narrowing of system directivity with increasing frequency and the generally increasing absorption of room boundary surfaces, also with frequency, the reverberant contribution will naturally and smoothly fall off at high frequencies, imparting a gentle roll‐off in the last octave or two, the degree partially depending on the HF unit diameter. dB 80

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Figure 10.14  Spatially averaged frequency response in‐room over listening region (the dotted response is anechoic, free field, for that loudspeaker: note the room gain at lower frequencies).

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Output power discontinuities, for example at crossover frequencies, are also revealed in this measurement, more or less as they are heard, despite the fact that in many cases their existence may not be at all obvious from the axial response alone. Finally, where accurate low‐frequency only measurements are necessary in the absence of an anechoic chamber; this can be carried out by simulating a giant ‘chamber’ (Gander[38]). This is done by employing a large area of level ground, such as an open car park or perhaps a warehouse floor, as an acoustic mirror, which reflected sound image doubles the effective half‐space to full space. Provided that the microphone is within a few millimeters of the ground and the speaker system is placed on its side on the ground at a suitable distance, for example, 1 m and better still 2 m, accurate equivalent free‐field measurements are possible up to frequencies where driver(s) path length to the ground is comparable to wave length, typically 500 Hz (note that the (PZM) ground plane microphone music recording method is equivalent). Measured sensitivities are doubled due to the reflection gain, thus 6 dB s.p.l. must be subtracted from the nominal microphone readings for the defined distance. With gating techniques such as MLS[39] room or environmental reflections may be eliminated from the measurement and all that is required for speaker measurement is a large‐enough, temperature‐controlled volume in which to work. The larger size is dictated by the need for the lowest desired frequency to propagate sufficiently away from the speaker for its returning reflection to be ‘gated’ out of the measurement and provide the necessary resolution, this consideration including the need to get far enough away from the source for the lower frequencies to be correctly proportioned this for larger floor standing loudspeaker systems at 2 m or even 3 m for better accuracy (see the section ‘Gated Measurement’). More recently, Klippel has developed a moving test rig which at relatively short distances scans the complex pressure and power response over the whole space around a loudspeaker. By suitable calculation this comprehensive data set can be expressed in the usual far‐field pressure response form over a range of chosen distances and axes. Called the near‐field scanner, NFS is a newly developed apparatus for measuring the 3D acoustic radiation of a sound source in a normal room. By measuring the moderately elevated sound source in the near field, reflections are separated from direct sound. The test results can be viewed as 3D ‘clouds’, that is, sound pressure balloons, or as 2D planes calculated for a user‐chosen radius at a user‐defined frequency. Results can also be analysed with full‐spectrum s.p.l., that is, as true ‘loudness’ measurements at any point in space. There are particular advantages. Near‐field measurements have a very good signal to noise ratio and are also less prone to air propagation effects. Interestingly, the scanning process employs field separation where the outgoing wave (direct sound) is separated from the incoming waves (reflected sound). As a result s.p.l., directivity and other far‐ field characteristics can be readily computed from this near‐field information.

10.4 ­Objective Measurements: Amplitude/Frequency Responses (4π, Full Anechoic) 10.4.1  Sine Excitation If a large anechoic chamber is available, a number of tests may be performed with classic sine‐wave and equivalent excitation energizing a power amplifier, which may fed from a suitable automatic sweep‐oscillator system. The usual power level is a nominal

Loudspeaker Assessment

Figure 10.15  IEC Standard test baffle, an open panel for offset driver measurement with reduced edge cancellation effects. The AES also specifies a similar range of baffle sizes.

135 cm

Flush mount driver 165 cm

22.5 cm 15 cm Thick non-resonant panel

1 W referred to 8Ω (2.83 V R.M.S) with the microphone (generally a 12.5 mm capsule) placed at 1 m or better still 2 m from an axis that is generally half way between mid and treble drivers, or is the manufacturers’ defined listening axis. For single‐driver measurements to IEC requirements an open rectangular test baffle is specified where the driver is offset from the centre to try to reduce axisymmetric baffle interference and ideally the driver chassis should also be flush mounted in the fixture to avoid local edge reflections. Even with an anechoic chamber, modern practice usually involves software controlled measurement, and suitable audio test hardware such as Audio Precision, Prism MLSSA set ups and the like. Depending on the open test baffle size, there will be a substantial low‐frequency roll‐off (see Figure 10.15) due to front to back cancellation. The IEC test baffle is long‐established for basic driver response measurements. Clearly, there will be increasing loss at low frequencies due to cancellation of out of phase energy from the back for this merely finite obstruction to the front output. Figure 10.16 is virtually self‐explanatory and shows the test arrangement. The axial response trace obtained (Figure 10.17) is a widely used specification for loudspeakers, and with certain reservations is probably the most important since significant errors cannot be concealed. Near‐field measurement for low frequencies may be complicated by distances and phase relationships between multiple radiator and vented designs and special precautions are necessary here. Each radiating element may be measured close up, and the sum obtained of all the contributions, with due account, calculation made, of the radiating areas for volume velocity and these should include phase where necessary. Note that the appearance and attractiveness for sales purposes of a sine‐wave response trace may be influenced greatly by both test and display conditions; for example, the pen speed on the chart recorder. An exceptionally slow pen speed (or long integration time) will tend to smooth sharp resonances or dips, thus giving a false impression of the speaker’s output (see Figure 10.18). Where paper recorders are still used (typically for test disc and pickup cartridge measurement) paper speed and scaling are also highly influential for the resolution and appearance of the graphs. With modern software‐based measurement it is even easier to do this by using post processing for scaling and resolution bandwidth.

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Preamp signal conditioning Test environment Power/level monitor Calibration

Computer/processor/software

DSP generator

Inout processor/FFT/ETC

Test signals: MLS/sine/Chirp noise,Impulse/etc.

Storage

Print

Display

Figure 10.16  General loudspeaker test system.

Figure 10.17  Anechoic, historic, slow‐swept sine stimulus response curve of a non–hi fi two‐way loudspeaker system, recorded on a pen chart (Source: Courtesy Bruel and Kjaer[40,41]).

Loudspeaker Assessment

Figure 10.18  The effect of display settings on the visual appearance of a frequency response trace. Some marketing departments have exploited this visual effect to flatter their products.

Note that with multi‐unit loudspeaker systems, interference dips may exist at specific axes, and a lateral or vertical displacement of as little as 10 cm for a microphone position can result in one dip disappearing, or another appearing. For these reasons, great care is required in the interpretation of sine‐wave responses and an initial curve, even one for ‘axial’ reference location may need confirmation by further measurements explored at different microphone positions. 10.4.2  Off‐Axis Responses These are typically ±10 degrees or ±15 degrees in the vertical plane and ±20 degrees, ±30 degrees and ±45 degrees in the lateral (60‐degree off‐axis may also be helpful) plane. A speaker with lateral symmetry need only be plotted in one direction. Both sine and noise excitation are common. In addition to the axial response measurement, the loudspeaker may be angled or rotated to allow polar plots at single frequencies off‐axis. These plots often reveal irregularities not shown on‐axis, for example if a unit’s directivity narrows, or the energy at the crossover point between two drivers is not integrating properly owing to phase differences. The presence of such a dip might not be apparent from a single axial response measurement as a result of fortuitous microphone placement (see Figure 10.19). Recent data processing methods such as VACS allow polar response results to be computed as spatial energy plots and also for SWL, or power response. The ability to compare pressure and power responses is increasingly useful (see http://www.randteam. de/VACS/VACS‐Screenshots‐FrequDirPlot.html).

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Figure 10.19  Family of high‐resolution oblique frequency response curves at 0 degrees, 15 degrees, 30 degrees and 45 degrees, 1 m horizontal plane (Source: Courtesy KEF Audio).

0° 15° 30° 10 dB

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10.5 ­Random Noise Excitation Whilst a slowly swept sine test signal is potentially the most accurate and precise stimulus, random noise is also valuable for loudspeaker measurement. There is strong evidence that the ear tends to average short‐term irregularities and is rather more sensitive to broader trends in energy over third‐octave or octave bandwidths. Simple instruments can present the noise signal data in octave or fractional octave bands. MLS and related gated systems also include octave and one‐third octave weighting. Third‐octave or octave bandwidth analysed noise can provide a convenient method for such averaging. From a philosophical point of view, random transient content noise more closely resembles music programme than sine wave, and hence could be considered more relevant to the listening experience. It also readily permits the measurement of the weighted or subjective based loudness of the system. If broad‐band noise is applied to the loudspeaker, a filtered analysis provides some ambient noise suppression, thanks to the narrower detector bandwidth. Alternatively the drive to the speaker may be pre‐filtered in successive bands and the microphone amplifier left in the wide‐band condition (Figure 10.20). While axial sine‐wave data is a valuable reference, the third octave averaged result may give a better idea of the tonal balance and also reveal colourations. The use of higher resolution amplitude limits for averaged responses is well worthwhile to show more detail. If a family of off‐axis responses, also in one‐third or one sixth octave, is shown with the axial result, a good indication may be gained of the forward radiated energy trend, the driver integration and general uniformity of response (see Figure 10.21). Averaging multiple microphone and loudspeaker position responses in a listening room, which data includes both room loading and the forward energy, results in a spatial average which correlates well with listener opinion (see Figure 10.22). It has been suggested that while one‐third octave is satisfactory for the middle octaves, greater resolution, perhaps one‐sixth octave would be more valuable at the frequency extremes. A reason may be found in the presence of the band edges of most speaker amplitude roll‐offs where these slopes require finer resolution for accurate readings. Many audio spectrum analysers provide one‐third and better octave analysis, as do many of the lower‐cost software and computer card test units.

Loudspeaker Assessment

Figure 10.20  Some operators varied the writing speed on the pen recorder during the band‐ filtered sweep measurement in order to give the analysis record a more uniform appearance, usually from 10 mm/s at 20 Hz to 160 mm/s at 2 kHz and above. This trace shows one‐third octave analysis without such adjustment (Source: Courtesy Bruel and Kjaer) (same speaker as Figure 10.17).

90 dB 80 A B 70 C D E 60

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Figure 10.21  Off‐axis ‘forward response family’ (ESL 63) A = axial, B = 7.5‐degree vertical, C = 15‐degree lateral, D = 30‐degree lateral, E = 45‐degree lateral (in one‐third octave).

The overall impedance may also be measured via broad‐band noise excitation, quantified as the complex V/I ratio delivered to the speaker. Such a reading has been considered nearer to the programme value actually seen by an amplifier than the usual ‘static’ graph for swept‐sine on the equivalently measured impedance.

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(a) B: 1/3 OCT

RANGE: 13 dBV ****ROOM

STATUS: PAUSED RMS: 64

–9 dBV

5 dB/ DIV

–49 START: 25 Hz X: 630 Hz

BANDS 14–46 Y: –17.66 dBV

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STOP: 40 000 Hz

Figure 10.22  Use of ‘spatially averaged response’ for (a) a sealed‐box system with optimal Q T and response roll‐off, stand mounted in free space; and (b) a similarly sized enclosure with reflex bass loading and an inappropriate alignment. Both possessed visually flat axial anechoic responses while their perceived quality related more closely to the room‐averaged characteristic. (b) is seen to be less uniform overall while the low‐frequency peak at 50 Hz is magnified by room gain.

Loudspeaker Assessment

10.5.1  Impulse Excitation and Decay Resonances The use of an early digital computer equipped with a fast Fourier transform (FFT) processor at last allowed full analysis of the pulse response of a loudspeaker. A pulse‐gating technique is employed, providing suppression of room reflections. From the pulse analysis, the steady‐state response may be derived and plotted in the usual way (Figure  10.23). Figures  10.24 and 10.25 show a comparison of responses of the same loudspeaker derived by steady‐state sine‐wave, and by pulse analysis.[42] Other systems for gated analysis also allow for the investigation of delayed resonances and reflections through the analysis of the output of a system after the initial excitation is over. For example, the arrangement in Figure 10.16, if used with an anechoic chamber to suppress the room reflections, may be adjusted so that the gating control unit reads the decaying output after cessation of the burst excitation. For pulse testing, the pulse periodicity is adjusted to exceed the room reverberation RT. Unlimited signal averaging may then be applied to generate good signal‐to‐noise ratios. Recent developments have explored full 20 Hz to 50 kHz measurement in a large 7.5 m3 room. Enhancements include the speaker’s excitation by alternate + and − impulses 1s

5μs

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Loudspeaker 12 mm Mic. under test B&K 4133 Test room (300m3) rev. time 1s To X-Y plotter

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DC power amplifier

Pulse generator

Delayed

Digital Fourier analyser

HP 2100 Computer

10 bit ADC sampling rate 50 k Hz

B&K mic amplifier

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Figure 10.23  Historic layout for loudspeaker impulse measurements (after KEF Electronics[43]).

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Figure 10.24  Axial pressure response via computed Fourier analysis of pulse response (KEF). 50

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Figure 10.25  System response by sine excitation: anechoic conditions showing good agreement with the same model as in Figure 10.24.

Loudspeaker Assessment

whose responses are then subtracted in the computer. DC offset and spurious hum signals are cancelled by this technique, allowing some truncation of the measured impulse response in order to speed‐up measurement. Later microprocessor developments enabled the production of relatively low‐cost FFT analysers such as the HP3561 A which could be set up with a pulse generator to produce an effective impulse test system (Figure 10.26(a)). The required analyser time window may be adjusted to examine the portion of the loudspeaker response of interest via a signal gate, Figure 10.26(b). An indication of the importance of impulse testing in the early years was shown by the costly investment made by many companies in acquiring and devising the necessary measuring equipment. The Wharfedale research team achieved early success in delayed resonance analysis; their ‘in‐house’ system developed using a variation of the gated tone‐burst set‐up described earlier, with burst length set proportional to frequency enabling, consistent excitation power over the frequency range. The output is displayed in conventional log frequency format from 20 Hz to 20 kHz.[44] The essential features of this method were in fact first established by Shorter at the BBC as early as 1945. Researchers have since explored analysis using a host of shaped pulses, from raised cosine to controlled, gated tone bursts, and have employed a variety for mathematical transformations of the results to aid their and analysis visual presentation. If a loudspeaker is minimum phase, as most moving‐coil drivers are, then the amplitude versus frequency, and phase response versus frequency are uniquely related. One may be obtained from the other via the Hilbert transform. A complete loudspeaker system is rarely minimum phase. For assessment as to whether a system is minimum phase, the phase response is measured, and then this is computed via the Hilbert transform to an

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(HP3561A) t2 Data output

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Figure 10.26a  The 5 µs pulse is preconditioned before the power amplifier to allow increased energy input to the system. Noise is predominantly low frequency, thus improved via LF pre‐ and de‐emphasis.

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1 0

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ts

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tw

Figure 10.26b  Impulse response and capture. tr is the first reflection from the surroundings (Applied impulse typically 5 µs wide).

amplitude‐frequency response. This result may then be compared with the direct ­measurement. With modern DSP‐based systems, Fourier and similar based pulse ­synthesizers can produce almost any required stimulus. Cumulative spectral decay plotting using apodized tone bursts[45] can provide clearer results than simple cumulative decay representations (see Figures  10.27 and 10.28). Other useful representations have included the Wigner distribution[46] (see Figure 10.29). This presentation is valuable for multi‐way systems, which may be then examined without the kind of overlapping confusion shown in the more basic decay representation. The analysed energy is properly distributed in the Wigner stimulus, allowing a better appraisal through weighting, averaging and transformation steps. 10.5.2  TDS Time Delay Spectrometry This technique, originally proposed and explored for audio use in 1967 by Heyser, was made accessible with suitable equipment produced by Crown B&K and others. In essence, a sine‐wave sweeps the required frequency range at a specific rate. At any moment, partially defined by the bandwidth and response time of the tracking filter, the measurement of the tracking sine‐wave is not the single centre frequency, but rather a distribution of frequencies determined by the sweep rate. The slower the sweep, the closer are the side‐bands and the purer the tone. Given this basic relationship for system resolution, the technique has the ability to exclude boundary reflections and also to explore delayed resonances. As the frequency sweep arrives from the loudspeaker, it suffers time delay due to the path length to the measuring microphone. When the equipment is synchronized, a start frequency of 20 kHz at the speaker will not arrive at the microphone until the generator reaches a lower frequency, depending on the negative or downwards sweep rate or ‘chirp’, and the microphone spacing. The matching

Loudspeaker Assessment

dB

0.0

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–12.0

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MLSSA 100.0 Cumulative spectral decay

1000.0 Log frequency (Hz)

Figure 10.27  Waterfall display of a small 300 Hz Helmholtz resonator, acoustically adjacent to a small direct radiating loudspeaker showing the characteristically high Q value and deeply extended decay. At to there is the signature peak and dip on the amplitude response of the exciting loudspeaker, rather than resonance peak.

selective analyser is offset in frequency to maintain synchronization to the measured signal and also offers the facility for selecting the desired size of time window for measurement. Set to ‘normal’, it captures the direct response, and by tracking in synchronism with the source, it then ignores the reverberant, ambient reflections. These occur after the analysis frequency window has passed. With all gated measurements, for example, TDS and MLS, the measuring space and the path length will control the maximum gate length, and thus the low‐frequency span and consequently the resolution (see Figure 10.30(b)). (Stewart Tyler, the PROAC founder, has noted that with a high ceiling, a measurement pit covered by a safety grid has proved useful by increasing the first reflection distance from the floor allowing a longer gate window.) Offsetting the analyser timing to read slightly after the main swept stimulus energy peak has past the microphone, allows the system to record the delayed resonance output of the test reproducer, the time scales limited by the system dynamic range and by the encroaching reverberant sound. Fourier analysers are applied with advantage to such a measurement systems. Different forms of impulse shape have different advantages. MLS (maximum length sequence) is convenient and quick, and is effective in the presence of ambient noise. MLS is, however, somewhat susceptible to distortion in the measurement chain which will then modify the frequency response. Care must be taken to avoid amplifier clipping and loudspeaker overload. IRS (inverse repeated sequence) measurement is generally comparable, if less common, with some advantage in terms of reduced spurious distortion components.

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Figure 10.28  (a) The cumulative decay spectra for an improved 110 mm bass/mid‐range loudspeaker; (b) cumulative spectral decay plot with apodization, note improved clarity for the spectral decay detail (after Bunton and Small[45]).

Another method is called time‐stretched pulse, involving expansion and compression of an impulse signal in the time domain. The expansion increases the envelope power to improve signal‐to‐noise ratio while leaving the crest value unchanged. Post‐measurement ‘decompression’ allows the deconvolution filter to re‐construct the impulse. ‘SineSweep’[47] employs an exponential, time‐based, increasing frequency sweep, with time‐delay processing applied to deconvolve the primary or linear response. It also deals with the spectrally and time‐separated distortion harmonics, the latter arriving ‘before’ the linear impulse response (this is because they track at the higher harmonic

Loudspeaker Assessment

Figure 10.29  (a) Cumulative decay spectrum of a dome tweeter; (b) Wigner distribution of the dome tweeter (after Janse and Kaizer[46]).

frequencies). ‘SineSweep’ or chirp, may be preferred on grounds of superior dynamic range, but may not be applicable when the measuring space is occupied, owing to the unpalatable noise. 10.5.3  Gated Measurement Howard[48] has surveyed gated measurements, outlining the range of limitations imposed on the data by the usual finite time window. Measurements in typical rooms put a limit at a maximum of 5 ms for gate length, which must have only 100 Hz resolution. Consequently, what can fairly be considered as the primary frequency response of a loudspeaker, namely that located below 1 kHz, is not characterized with anything like the same level of detail that is customary with traditional anechoic chamber results. Ideally, larger spaces, for example, an area of a temperature‐controlled warehouse, are required for higher resolution, longer gated measurement. Howard points out that while this recommendation will suffice for roughly characterizing frequency response,

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Figure 10.30a  A pioneering result for energy versus time taken at 1 m on axis (after Richard Heyser).

h 2

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Figure 10.30b  Travel distances for the first reflections. When the loudspeaker and microphone are centered along all three axes of the room this allows for maximum gate length (after B&K).

and also is effective for mid‐range and treble‐range driver decay analysis, it is still quite inadequate to resolve lower frequency finer detail resonances such as enclosure panels and those pertaining to the bass alignment itself. Here, a 200 ms reflection‐free window is ideally required, and consequently, for the future, a move to reflection compensating processing is suggested. Even so, a single microphone position cannot adequately assess the enclosure resonance contribution, particularly given the radiation of the six surfaces into different planes. This is where laser scanning to sum the volume velocity over area will help, though at considerable cost in time and equipment. He notes that sampling with a localized accelerometer may

Loudspeaker Assessment

give misleading results by failing to integrating phase and amplitude over the radiating area. The radiation efficiency of mode shapes is relevant here. Via the FFT the energy/time decay can be readily obtained, a useful general graph allowing quick comparison of the stored energy of different speakers We need to remember when examining loudspeaker data that middle C is 262 Hz, where much music is present and also be aware that curve fitting, a blunt averaging, takes place between necessarily wider spaced data points. The old B&K pen chart amplitude/frequency analysis, if run slow, had very high resolution over the whole measuring range. 10.5.4  MLSSA, an MLS Measuring System On the basis of a plug‐in interface and matching software for a personal computer, a successful MLS loudspeaker and acoustics test instrument was developed by Douglas Rife, called MLSSA, named after the type of stimulus, namely, maximum length sequence (System Analyser). MLS is a special kind of correlated pseudo‐random noise that stimulates the speaker under test at a satisfactory power over the full frequency range, and may be programmed over a range of useful time intervals. From a single capture of the received data subsequent or immediate analysis can give the following results; amplitude‐frequency response, decay waterfalls (see Figure 10.31), energy‐time curve, gated semi‐anechoic responses, octave and fraction octave smoothed responses, phase and group delay, Wigner distribution, impedance, Nyquist and Bode plots, both minimum and excess phase, and finally harmonic and intermodulation distortion (the latter in conjunction with an external oscillator). Additional functionality is added regularly, for example, T‐S and acoustics measurements and there is a Windows version.

dB

0.00

0.0

0.77

–5.0

1.65

–10.0

2.53

–15.0

3.41 ms

–20.0

MLSSA 1000.0 Cumulative spectral decay

10000.0

Log frequency (Hz)

3.4 dB, 6.325 kHz (285), 0.000 msec (0)

Figure 10.31  Cumulative spectral decay from simulated anechoic impulse response using MLSSA stimulus (here this presentation exploits a correlated noise function for optimum dynamic range) (Spendor SP2‐2).

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Hardware characteristics include 12‐bit, 72 dB dynamic range (wide‐band) and an operating bandwidth up to 50 kHz. Typically, the hardware board was to be installed in a good quality PC to form a complete menu driven instrument. Subject to the usual precautions concerning gated measurements, this now outdated instrument has proved to be convenient and dependable. Its main features are now also represented in several software/test box packages such as the versatile CLIO series from Audiomatica. 10.5.5  Waterfall Presentation and Excess Phase When visually assessing those attractive looking waterfall decay presentations an evaluator should not be misled. The appearance of these presentations is strongly dependent on several factors, many of these even independent of the device under test. If decay spectra are to be visually compared, it is essential that the test and display settings be identical; otherwise confusion will reign. Factors that change the appearance so much, that false conclusions may be drawn concerning the decay behaviour of the loudspeaker include: a) the number of lines or line density; b) the selected filter rise time for the chosen window function; c) the vertical scaling, that is, dB per division; d) the length of the time window; e) the presence of local reflections within that gate period; these are generally more significant than on the axial response transforms; f ) whether the loudspeaker has a severe peak such as a dome resonance high in the range and which causes the vertical scale to ‘down range’ to accommodate the peak and thus falsely give the appearance of a superior decay in the rest of the range; g) whether there is significant excess phase in the speaker transfer function, which there usually is, which greatly distorts the waterfall presentation of decay due to the varying delays across the spectrum from the individual drivers. A single waterfall graph does not have the power to properly resolve both the decay rate and the frequency detail of a decay. It is worthwhile generating at least two graphs, one directed to assessing the early decay speed over the frequency range, the other to better resolve the frequency and duration of the decay resonances. For the former, a 5 dB per division scaling with around 50 lines is useful; Blackman Harris‐weighting and with a fast 0.1 ms filter rise time. For the latter analysis, a 10 dB per division vertical scale working with a 0.2 ms filter gives sufficient frequency resolution; clearly showing the more extended decay ridges in the waterfall field following the initial t = 0 ‘steady‐state response’, this visible at the back of the graph. The excess phase question is more serious. If the drivers for a speaker system are analysed separately, then the decay waterfalls can be surprisingly presentable and are truthful as each are near minimum phase in their range. However, operate the system as a complete assembly and the differential phase content blurs some of the required information. Only if the speaker is minimum phase, or close to it, can the decay response provide a fair representation of the global intent of this test, i.e. for the system as a whole. A solution for this anomaly is available, if awkward to implement (thanks to M.O. Hawksford for finding a solution to this problem). Using a suitable math programme, the numerical data for the impulse response is imported, with the ‘header’ removed, (e.g., if

Loudspeaker Assessment

from MLSSA). It is viewed and windowed, possibly with some sensible corrections at the time response extremes to avoid the computation of awkward or non‐causal numbers. Transformed to the frequency domain using an appropriate filter window, the response is tidied at the band edges, assuming normal rates of roll‐off for the relevant speaker technology. By computation of the data array, the excess phase is removed from the frequency data, separating real and imaginary data using a weighting function, and summing these to deliver a causal impulse where peak energy begins at t = 0 and the outcome is now a corrected minimum‐phase, windowed response. This computed impulse carries the original steady‐state frequency response content but has the phase information removed; it is then obvious that the analysed result resembles that for a system with low‐phase shift. When this processed impulse response is subject to the ‘waterfall’ presentation, the intrinsic decay behaviour can be seen the clearly. Note that the new computed result is not true linear phase; the latter defining an acausal response which exhibits a symmetric spread of energy on each side of the t = 0 position. There are, however, close parallels. An approximation, to be used with caution, may be more simply achieved (e.g., with the MLSSA package) by calling up a stored impulse in the ‘Operations’ menu and cross‐ correlating the impulse with itself. Although lacking the proper windowing, the result implies a multiplying out of the phase content. Displaying this impulse on the decay spectrum provides a clearer view of the decay rate for a complex speaker system (note that the sequence is: Library—Operations—Time files–xcorrellation–Data(a)–corr‐ Data(a) to data(ax).tim). This pseudo‐acausal impulse must be windowed from x(axis) = 0.0 over the required reflection free‐time span. The transformed frequency response is itself unchanged (see Figure 10.32(a) to (e)).

dB

0.00 0.64

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1.34

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3.33 ms MLSSA 125

250

Cumulative spectral decay

500

1k

2k

4k

8k

16 k

IEC frequency (Hz) –13.37 dB, 6348 Hz (104), 0.000 ms (0)

Figure 10.32a  MLS waterfall display of cumulative resonance decay 10 dB per division per 0.2 ms. Filter B/H. Two‐way speaker: note metal dome resonance at 23 kHz (gated time window 5 ms).

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0.00

dB

0.64

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1.34

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3.33 ms MLSSA 125

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500

Cumulative spectral decay

1k

2k

4k

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16 k

IEC frequency (Hz) –13.54 dB, 6348 Hz (104), 0.000 ms (0)

Figure 10.32b  As for Figure 9.34(a) but with the gate window truncated at 3 ms. Note the apparent improvement in the longer term decay, even by 2.0 ms.

dB

0.00 0.64

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1.34

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2.69

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Cumulative spectral decay

500

1k

2k

4k

8k

16 k

IEC frequency (Hz) –24.62 dB, 6348 Hz (104), 0.000 ms (0)

Figure 10.32c  Shows the effect of deleting just 0.1 ms of impulse response at the front of the 5 ms window. Much of the ‘steady‐state’ response has been stripped off.

Loudspeaker Assessment

dB

0.00 0.64

–10.0 –20.0

1.34 1.98

–30.0 –40.0

2.69

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3.33 ms MLSSA 125

250

500

Cumulative spectral decay

1k

2k

4k

8k

16 k

IEC frequency (Hz) –33.91 dB, 6348 Hz (104), 0.000 ms (0)

Figure 10.32d  For these two‐way speaker graphs the low‐pass response is plotted alone. Compare with (a) and note how some interesting metal cone resonances are now revealed in the 4 to 16 kHz range.

0.00

dB

0.64

–10.0

1.34

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3.33 ms MLSSA 125

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Cumulative spectral decay

500

1k

2k

4k

8k

16 k

IEC frequency (Hz) –13.55 dB, 6348 Hz (104), 0.000 ms (0)

Figure 10.32e  The high‐pass section of the two‐way design. It can now be seen how much this section dominates the range above 8 kHz. Resonance series can now be separated more clearly in the range 2 to 8 kHz.

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10.5.6  Audio Precision Audio Precision are responsible for the design and manufacture of a powerful audio and acoustics test units whose pre‐programmed acoustic and audio related test facilities are extraordinarily comprehensive. Both measurement accuracy and limit thresholds are particularly good. Designed to be controlled from a desktop PC, and now a tablet they lend themselves to a variety of routines, including automatic testing. Versions comprises a digital processing module which allows for both stimulus and analysis in all possible modes, D/A, A/D, both in the analogue and digital domains. The combined analogue/digital instruments are being supplanted by wholly digital versions using advanced DA/AD chips still with very good threshold limits and in some cases greater speed, wider bandwidths despite lower costs. Processing software for loudspeakers is available including FFT, impulse, MLS, ­multitone and related techniques while the digital interfacing versatility is directly applicable to digital filter design and the synthesis of digitally interfaced loudspeaker systems (see Figure 10.33). 10.5.7  Reciprocity Method for Measurement at Low Frequencies As has been noted, measurement below 100 Hz may be rendered variously inaccurate due to boundary reflections, present even in fair‐sized anechoic chambers. Merhaut[49] described an application of reciprocity for accurate low‐frequency measurement. Essentially the action of a loudspeaker as a convertor of electrical power to acoustic energy may be reversed or inverted by using the test loudspeaker as a microphone. For moving‐coil loudspeakers, the test motor coil is loaded by an external resistance rather less than that of the coil, for example, for an 8Ω model an 0.5Ω resistor is suitable. A separate non‐critical loudspeaker provides the acoustic stimulus; the sound pressure kept constant at the surface of the test loudspeaker via a precision microphone

Figure 10.33  AP 525 series dual domain digitally processed audio analyser, computer interfaced for control.

Loudspeaker Assessment dB A

Non-critial source speaker

f

Sensing microphone

Low resistance load RL

d dt

Generator

A Constant sound pressure

Differentiator

Compressor loop ( Non-anechoic environment)

Test loudspeaker

Figure 10.34  A reciprocity method for low‐frequency measurement in non‐anechoic conditions. Driven acoustically by a constant pressure, the electrical output of the test loudspeaker is the first integral of sound pressure when terminated by a low resistance or a virtual earth input and carries the response of the device under test. Simple differentiation results in the desired frequency response.

used as a monitor, coupled back into the familiar compressor loop of the generator (B&K or similar). Under these conditions, and when resistively loaded, the output of the test loudspeaker at low frequencies corresponds simply to the first integration of sound pressure and a simple differentiator (6 dB/octave high‐pass) network will provide a true voltage output describing sound pressure at low frequencies where the driver is still non‐directive, for example, below 150 Hz (see Figure 10.34). Clearly it is less useful for multiple driver and vented systems. Merhaut also showed how a number of other parameters may be obtained such as η or efficiency, ka or Bl factor, and the various Q factors. 10.5.8  Harmonic and Intermodulation Distortion Distortion can vary substantially over quite a small frequency interval, and for this reason continuous distortion versus frequency sweeps are recommended. The basic setup for distortion measurement is similar to the amplitude/frequency response arrangement, with the addition of a suitable selective analyser or tracking filter interposed between recorder and microphone. The filter may be offset or displaced by a suitable harmonic interval so that any order of harmonic may be recorded. The use of a two‐ tone generator with a tracking harmonic multiplier also allows swept intermodulation traces to be recorded. Figures 10.7 and Figure 10.8 show two such curves. The 2f2 − f1 second‐order intermodulation product was traced with f1 − f2 = 300 Hz, and the combined tone level was set at 90 dB at 1 m. These swept intermodulation measurements are often more revealing than the usual single harmonic readings.

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One self‐evident point is the relationship between sound level and distortion, the latter increasing with the former. It is thus sensible to choose a standard level for comparative purposes, for example, 90 dB. The DIN standard specified 96 dB, which is on the high side for most low sensitivity HF units tested on continuous tone. This suggests an input power up to 5 w for many designs with heating and potential failure for smaller drivers, for example, 5 w applied to a tweeter. The lower 90 dB test level applies to domestic and low‐level monitor systems, and would not be adequate for high‐level monitor or large audience broadcast arrays, where 100 to 120 dB s.p.l. might be more relevant maximum test sound pressures. Even 90 dB is quite a high level in subjective terms for a distortion measurement on a domestic loudspeaker, which level is reached only during loud passages, with the remaining 10 to 15 dB above this occupied by programme peaks. With the availability of good amplifiers and low distortion digital sources, it is certainly worth examining linearity at lower levels to see just what is possible. In recent evaluations the author[50] has published distortion graphs taken over a range of levels, 96, 86 and 76 dB at 1 m with a resolution to −70 dB. For some loudspeakers, distortion readings fell below −70 dB (0.03%) at the lowest pressure level noted. Computer card‐based analysers, such as AP, Prism and CLIO can readily measure such distortion. Temme[51] provided a helpful general review on distortion measurements prior to more recent computerized methods. Again, here is a reminder of the positive impact of multi‐way speaker design for greatly minimizing broadband intermodulation distortion; by directing different frequency bands to different drivers (see Figure 10.35). The objective testing of loudspeakers is a considerable subject in its own right and D’Appolito[52] has devoted specific attention to it in his eponymous book on the SPL/dB 0 –10 –20 –30 –40 –50 –60 –70 –80 –90 –100 100

1000

10000 Frequency (Hz)

Figure 10.35  Effect on I/M distortion of two‐way (solid) versus comparable full‐range driver design (dashed) of box loudspeaker.

Loudspeaker Assessment

subject, which also includes some valuable advice on system design, for example, on choosing crossover points and how to integrate acoustic outputs from drivers. 10.5.9  Dynamic or Pulsed Distortion Testing Approximately 90 or perhaps 96 dB s.p.l. is the highest level that may be safely applied to a typical domestic loudspeaker for continuous swept tone distortion measurement (proportionately higher for pro and PA designs) and an alternative approach is required for assessing linearity at higher levels. For example an 88 dB/W (1 m) speaker fed 100 W programme will generate peak levels of 108 dB and behavior in this upper level region and beyond is worth assessing. The resulting distortion may include significant compression and may be analysed over the frequency range using short tone bursts, around 10 cycles long, with a 1:10 mark‐space ratio so as not to overheat the system. Compression may be measured directly by inspection of the reproduced tone bursts, viewing a stable gated group of cycles within the tone burst. This may be captured by an FFT analyser and readings of distortion harmonics can also be made including swept over frequency. Experience has shown that an otherwise well‐behaved system may run into unexpected problems towards peak level; in one example, a crossover inductor saturated above 50 W burst power. At 400 Hz, 100 W burst, and the output actually expanded by 1.5 dB as the series inductor saturated increasing the feed‐through. Third harmonic had exceeded 30% at this point, way above audibility. In another example, a shunt inductor in a high pass crossover reached overload at 4 kHz and compressed the output by 2 dB, with 20% of distortion. This explained why the listeners on a panel reported increasing ‘hardness’ with level and with loud percussive peaks. High‐power, low‐frequency tone bursts are also useful in exploring overall linearity and dynamic power handling, particularly for ported and otherwise ducted systems.[53,54] 10.5.10  Doppler Distortion The measurement of Doppler distortion is not easy as the FM components must be separated from the other accompanying distortions and this tends to restrict the range of measurements (Figure 10.36) (Allison and Villchur[20]). However, a simple technique exists for separating amplitude components from the total distortion group. This consists of directing the microphone at 90 degrees to the driver axis. The FM components are essentially axially directed and at 90 degrees the source is no longer moving with respect to the microphone. It is than a simple operation to subtract one from the other, thus leaving the FM contribution. 10.5.11  Intermodulation Distortion and Multi‐Tone Signals Intermodulation distortion may be measured using a random noise signal. The same traditional arrangement as that employed for third‐octave analysis is followed, but with the addition of another, tracking third‐octave filter. One filter operates on the noise source and the other filters the microphone output signal. With the latter filter shifted a harmonic interval above the input or fundamental third octave, various combined harmonic/intermodulation curves may be obtained over third‐octave or less bandwidths. Modern FFT‐based measurement can also provide related intermodulation

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Amplifier

Signal generator 2

Signal generator 1 Analyser

Selective voltmeter

Microphone amplifier

FM discriminator

% FM Anechoic chamber Recorder

Figure 10.36  Classic doppler distortion measurement setup (after Moir[13]).

data. MLSSA techniques can assess noise stimulated distortion as a failure in correlation, while complex digitally derived multi‐tone signals are also useful (e.g., from Audio Precision) here exploring the distortion as those new signals appearing in the gaps between the multi‐tones. The search for a better basis for measurement of distortion has engaged audio engineers for many decades, seeking better correlation with the auditory experience. With certain caveats of the forms available multi‐tone stimuli are emerging with the greatest promise though it is clear that defined/agreed forms of analysis and representation are required to try and obtain useful and comparative numeric quality measures. Czerwinski et  al. have made a substantial contribution to our understanding with their valuable review of established distortion analysis methods. In Part 2 of their investigation,[55] particularly telling results are given for two high‐ frequency range compression drivers, A and B, both presenting remarkably similar total harmonic distortion results but with differing sound quality (see Figure 10.37). Onerous swept distortion analysis to the sixth order did suggest that for type A, fourth, fifth and sixth were at −50 to −70 dB for 110 dB s.p.l., which is good by any standards. B, however, held fourth and fifth harmonics to about −75 dB and sixth to about −90 dB. Turning to the alternative of a multi‐tone stimulus, here zoomed for the not atypical critical range 2 to 3 kHz, the difference in driver behaviours for complex intermodulation and other products now clearly distinguishes between these two drivers (see Figure 10.38). Surveying extensive references, Voishvillo et al.[56] continued a review of loudspeaker distortions for the usual range of measurements, but with special reference to multi‐ tone stimulus. Reiterating the accepted precept that we do not have an effective model of hearing that allows correlation of typically measured distortion results with quality impairment, it is noted that established single and two‐tone distortion measurements

Loudspeaker Assessment

(a) 10 9 8 Distortion (%)

7 6 5 4 3 2 1 0 500

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2000

5000

10000

20000

10000

20000

Frequency (Hz)

(b) 10 9 8 Distortion (%)

7 6 5 4 3 2 1 0 500

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5000

Frequency (Hz)

Figure 10.37  Total harmonic distortion. (a) Conventional reference compression driver. (b) New prototype compression driver. Note similar results.

are often inadequate for defining quality while conversely it is the intermodulation products that are seen to dominate moving‐coil loudspeaker behaviour. Total harmonic distortion is also a poor indicator owing to practical evidence that different harmonic distributions of the same numeric distortion power sound very different. As such, the I/M route is deemed more useful for subjective correlation, at least for design and for comparative QC testing purposes.We can see that multi‐tone stimulus, with sensibly spaced tone frequencies, is confirmed as a rich source capable of usefully revealing broad‐band intermodulation, providing better correlation with perceived sound quality (see Figure 10.38).

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(a) dB 120

100

80

60

40

20 3

2 Frequency (kHz)

(b) dB 120

100

80

60

40

20 2

3 Frequency (kHz)

Figure 10.38  Multi‐tone responses. (a) Reference driver; (b) New design, both zoomed in for the frequency range of 2 to 3 kHz.

10.5.12  Phase Response A high‐quality delay line traditionally facilitated the steady‐state measurement of the phase response versus frequency of a loudspeaker. The phase characteristic may now be routinely derived with quite good accuracy via FFT analysis of the impulse response, and by related computer software based methods.

Loudspeaker Assessment

10.5.13  Minimum Phase Several manufacturers have introduced the so‐called ‘linear phase’ (phase constant with frequency) loudspeakers. In fact, the correct term to describe such systems is ‘minimum phase’. This implies that a well‐defined linear relationship exists between the amplitude and phase response of the speaker; that is the phase varies linearly with frequency. Note that the phase angle itself does not have to be constant with frequency. For a typical multi‐unit loudspeaker system, the drivers are usually mounted on a flat baffle or on a planar front panel, with their effective radiation planes displaced by varying amounts depending on chassis geometry, diaphragm type and panel depth, etc. There are inherent delays in a driver, plus those introduced by most practical crossover networks. In such a case, when measured at the listening position, a relative time delay will exist between the outputs of the different drive‐units, this producing a non‐minimum phase characteristic. With phase measurement and or arrival times from the respective impulse responses, these time delays may be quantified and the units may then be physically and/or electrically aligned so that when required this differential delay may be substantially minimized leading to a minimum‐phase system design, assuming a suitable crossover is utilized and that the result is worth the effort. 10.5.14  Square Wave and Impulse Response A loudspeaker must have a perfect amplitude and phase response over a extended bandwidth to successfully reproduce a square wave with its complex correlated harmonic structure. However, only minimum‐phase loudspeakers are potentially able to do this with any degree of accuracy. Alternative designs will give practically meaningless results on a square‐wave stimulus but should not be criticized for odd looking wave shapes. The impulse response is another matter, as the aim of this measurement is to evaluate decaying ‘delayed’ resonances which may be present from a number of causes including the crossover, the driver diaphragms and the enclosure, viewed via detailed analysis of the narrow pulse response and the die away after effects. Some idea of these delayed resonances may be obtained by direct inspection of the impulse response without post processing, but the use of a FFT analysis has proved most revealing and has considerably enhanced the evaluation of speaker transient performance. Computer systems also offer refined impulse averaging, which may confer an excellent signal‐to‐noise ratio. For larger spaces, an anechoic chamber is not necessary if the receiving microphone output is suitably gated for analysis, thus suppressing local boundary reflections. 10.5.15  Tone‐Burst Response Tone‐bursts here using gated sections of steady sine frequency have traditionally been used to examine speaker transient response via analysis of the continued decay ringing at the test frequency following cessation of the input. This is a less revealing method of examining the pulse, or more strictly the overall transient response of a speaker. However, by judicious selection of gating period and tone frequency, resonances may be investigated. A key point concerning the tone‐burst is the requirement for the envelope to consist of a whole number of cycles, starting and stopping at the zero‐crossing point, so as to produce minimum of asymmetric disturbance. In addition, the measuring

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e­ nvironment must be highly anechoic, or spurious reflections will interfere with the analysis. The recent introduction of gated pulse techniques has made simple tone‐burst testing largely redundant though some software packages offer the facility. Windowed and specially shaped pulses, including tone‐bursts, fall naturally into the impulse testing category together with computed FFT processing and associated post‐ analysis methods (Tone bursts are useful for examining distortion at high powers). 10.5.16  Sensitivity Voltage and Power, Efficiency and Sound Power Output Strictly speaking, sensitivity aims to quantify subjective loudness for a given input power. One standard, for example, is the acoustic output in dB (may be weighted or unweighted) at 1 m on axis for 1 W electrical input. However, most sensitivity ratings are based on a nominal input of 2.83 V (1 W/8Ω), regardless of the actual value of the usually complex loudspeaker impedance, and are in reality ‘voltage sensitivity’ ratings. Here loudness is typically sound pressure level, s.p.l. and not to be confused with perceived loudness, which is stimulus dependent, both as regards temporal and spectral content. For an assessment of the true efficiency the total acoustic output may be measured by employing an integrating microphone arrangement, either a multiplexed array, or a rotating boom‐mounted microphone, the latter used in conjunction with a reverberant chamber. Post‐processing of polar responses may also be computed to sound power. It nevertheless remains difficult to assess the actual power input for a complex loudspeaker. A workable method involves the integration of the voltage and current for a random noise signal applied to the loudspeaker, the measurement being accomplished by a suitable wide‐range RMS function meter while the s.p.l. is also measured. When establishing a linear, ‘unweighted’ sensitivity figure, a single frequency reading will not suffice owing to the usual amplitude/frequency irregularities of most drivers and systems. Good comparability for systems may be achieved by visually integrating a ‘best fit’ line measured from 200 Hz to 5 kHz for the anechoic response, and then taking this mean level as the rated sensitivity. Comparative sound power outputs can be measured in a listening room using spectrally shaped noise, or perhaps well‐balanced music programme, in conjunction with a slow integrating sound level meter. In an average 80 m3 volume room, a stereo pair of speakers will deliver at the listening position an ‘A’ weighted reading around 5 dB less than the mono, axial test result at 1 m. For example, a 90 dB/W, 100 W rated system will produce maximum room levels of 110 to 115 dB or 105 dBA, close to concert hall realism, and subjectively this is considered very loud in such a room. Modern rock enthusiasts may demand 110 dB in‐room, in practice attainable with 200 W/channel unclipped maximae and a 92 dB/W/1 m or greater loudspeaker sensitivity. 10.5.17  Power Rating With changes in the distribution of spectral power with more recent programme material, the long‐established IEC test method for long‐term power handling, while still valuable, now may not satisfactorily define a matching amplifier rating. The later required test standard IEC 60268‐5[57] has further tests to better match to recordings

Loudspeaker Assessment 10

0

Level

–10

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–30 dB

–40

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100

1k Frequency (Hz)

10 k

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Figure 10.39  EIA‐426‐B power test spectrum (after Keele).

and their new musical instruments, synthesized signals, and commonly used compression and dynamic range optimisations. The older ‘IEC 60268‐IC’ specified a band‐shaped and limited noise signal, and is now supplemented by two ratings, namely, the maximum damage‐free input that is possible for 1 second, that is, the ‘maximum short‐term input voltage’, and then for a 1‐minute duration, which is the ‘maximum long‐term input voltage’. Equivalent powers drawn may be computed using the IEC rated impedance value for the system. There is also the US EIA‐426‐B power test, and conveniently a number of useful test signals are available on a CD, exclusively from ALMA ($50). This is a reworking of the earlier EIA‐426‐A, it includes an accelerated life test and sets new standards for power compression (using a special swept tone) and distortion. It brings us nearer to a loudspeaker power rating, better matching the output of the appropriately rated amplifier. The life test uses a spectrally weighted Gaussian noise signal which is soft clipped to a crest factor of 6 dB, and runs for 30 minutes (see Figure 10.39). (A highly informative introduction by Don Keele is available on the AES website concerning this power test.) 10.5.18  AES Recommended Practice for Professional Audio—Subjective Evaluation of Speakers AES20—1996 Much work has gone into this 20‐page document, with practical and commonsense contributions from major authorities in the field. The coverage is broad and ranges from listening practice to score sheets, evaluation and recommendations for room

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acoustics, the use of an anchor or control speaker, and speaker placement. Some of the more subtle sound‐quality criteria from current published review practice are absent, but the overall coverage is of great importance and value. 10.5.19  Laser Measurements Lasers are finding increasing use in the development of loudspeakers. Using the Doppler interferometric technique the previous need for zero vibration, super rigid test arrangements is markedly reduced. Diaphragm behaviour and indeed the mode patterns of loudspeaker enclosure panels are within reach of a scanned, modulated low power laser beam. Its photo‐detector output provides a signal that, after processing, provides data such as the displacement and velocity of the areas scanned. The data may be presented as 3D graphs in relief form or stored in a digital memory and shown on a monitor. With appropriate image processing, slow‐motion animated displays can be produced, greatly aiding the visual assessment of the dynamics of acoustic structures. Sophisticated laser analysis systems, such as the Ometron have been available and new products are also appearing, for example, from Klippel (see Figures 10.40, 10.41, and 10.42). 10.5.20  Electrical Impedance The DIN standard for impedance is a useful starting point and states that the modulus Z should not deviate more than ±20% from its nominal, specified, rated value from nominal values of either 4, 8 or 16Ω, over the working frequency range. The measurement appears straightforward, involving the use of a current generator, simulated by a normal voltage sweep which is fed to the loudspeaker via a high resistance, which may be for example, 100 ohm minimum and ideally greater than 1 k/ohm

Helium–neon laser

Doppler 1 Doppler 2 FM demodulation and filtering

Measuring beam expansion and scanning

Frequency coded velocity

Analog Sin Doppler 2 Reference beam

Cos

Figure 10.40  A laser holography block diagram.

Analog Doppler 1

Analog velocity

Electronic frequency shifting

Loudspeaker Assessment

Figure 10.41  3D scan of clearly developed concentric mode for an isotropic moulded cone. Plan view top right.

Figure 10.42  Note the differing behaviour for a non‐isotropic woven Kevlar tm fabric cone, resin reinforced (plan view of displacement shown in top right). Here the partly randomized vibration tends to interfere much less with the prime response (B&W).

particularly for an individual drive unit. The variation of voltage with frequency at the loudspeaker terminals reflects the variation of impedance. It is usual to substitute a known value resistor in place of the loudspeaker after the test to confirm the scaling, and a linear amplitude scale should be used for clarity. The addition of a phase computation, for example, via direct measurement, additionally allows the recording of the phase component of impedance; this combination presentation is called a ‘Bode’ analysis (simply phase versus frequency), this an important factor where amplifier matching is concerned. A constant controlled output generator may also be arranged to generate a constant current for accurate impedance measurement (Figures 10.43(a) and (b), 10.44, and 10.45). More MLS and chirp‐based computer controlled test software will also readily deliver such information. Loudspeakers with large reactive components of impedance, used with certain otherwise capable power amplifiers may cause premature limiting and a consequent deterioration in sound quality.

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High Performance Loudspeakers

(a)

Power amplifier Source of known level, sine or equivalent MLS

Resistor; e.g. 600 ohm

NC (to avoid ground loop) Data acquisition: Constant current assumed

(b)

Power amplifier Source of known level, sine or equivalent MLS

Resistor; e.g. 30 ohm

NC (to avoid ground loop) Data acquisition: computed for known low source resistance

Figure 10.43  (a) Loudspeaker impedance measurement using equivalent current source; displacement varies substantially with frequency. (b) As for (a) but using defined moderate value resistor, now with correspondingly computed loudspeaker current, to better approximate to voltage drive at a more representative power level.

Phase

Impedance (Ω)

40 30 20 (inductive) (capacitative)

586

10 Impedance (Z)

45° 0°

Phase (θ)

45°

45° 20

50

Helmholtz resonance

100

200

500

1k

2k

5k

10 k

20 k

Frequency (Hz)

Figure 10.44  Impedance: modulus and phase, for a three‐way vented (40 Hz) system (crossovers at 3 kHz and 13 kHz).

Loudspeaker Assessment

Figure 10.45  Vector representation of complex impedance.

Im |Z| φ

+ –φ Re

|Z|

f

φ

f

At present no straightforward method for analysing dynamic impedance is available. Given recent findings concerning input current requirements of loudspeaker systems[33] also authors Benjamin and also Howard, see below, the conventional impedance curve has to be regarded as only one aspect of the potential loading which may be imposed on an amplifier. In particular, amplifier designers cannot rely on a ‘textbook’ 8Ω specified loudspeaker which is supposed to present a 6.4Ω impedance modulus minimum, especially when under heavy drive with complex programme. The effective loading needs better consideration in respect of amplifier design and safe operating area. Considering the latter aspect for an amplifier, it will have current/ voltage limit load line for pure resistance and another for reactive loads, especially when they are inductive, this where the phase angle greatly increases the loading beyond the steady state indication. Howard describes the use of the term EPDR the equivalent peak dissipation resistance. This is the minimum resistive value which effectively loads the amplifier and the value is associated with its curve for maximum power.

587

588

High Performance Loudspeakers Stereophile B & W N802D Impedance Magnitude (ohms) & Phase (deg) vs Freq (Hz) 20.000

Ap

18.000

90.00 67.50

16.000 45.00 14.000 22.50

12.000

0.0

10.000 8.0000

–22.5

6.0000 –45.0 4.0000 –67.5

2.0000 0.0 10

100

1k

10 k

50 k

–90.0

Figure 10.46a  Nominal load impedance B&W 802, modulus magnitude, and phase (dotted).

Problematic speakers are quite common and frequently result in premature amplifier current clipping, also uncharacteristic losses in sound quality even before current clipping limits are reached. John Atkinson measured the B&W 802 D impedance for phase and magnitude noting the resistive minimae of 3 ohms at 85 Hz and at 590 Hz, (Figure 10.46(a)) while commenting on the still more demanding combination of significant phase lagging, inductive phase angles at 4 ohms/60 Hz which was considered of even more concern. In agreement with this view Howard also measured the 802 D and showed that for equivalent inductive current related impedance, now scaled in terms of the safe operating areas of the amplifier output transistors, the loading was even more severe, dipping to 1.5 ohms for 60 Hz but also at 730 Hz, both located in regions of high spectral music programme power. Further, at high frequencies the HF driver load also becomes inductive, as most do, and its nominal 4 ohm rating thus revised for phase also falls to an equivalent amplifier load of 2.3 ohms. Few power amplifiers will maintain their target performance in the face of such loading, and even before the onset of clipping their sound quality is also perceptibly altered. Howard used FFT methods to simulate the effect of programme on these real world load calculations and showed that these worst case conditions really are invoked if occasionally according to the music content, for those troublesome combinations of level and frequency (Figure 10.46(b)). 10.5.21  Computer‐Controlled Testing Over the past decades this subject has changed out of all recognition. Originally there were some specialist arrangements configured at great cost often requiring a reflection

Loudspeaker Assessment 10

8

6 EPDR (ohms) 4

2

0 20

100

1k

10k

20k

Frequency (Hz)

Figure 10.46b  equivalent amplifier referenced load impedance B&W 802 (after Howard). Its minimum modulus of 3.2 ohms (phase angle zero) occurs at 86 Hz and is the conventional reading but is more than double the stressful EPDR minima calculated.

free environment. However, the availability of small computer and an increasing variety of intelligent computer interfaced audio instrumentation, initially from Hewlett– Packard, B&K, and so on, and now several much simpler and lower cost and compact hardware, means that automated and semi‐automated systems are possible for many development and production situations. The ubiquitous larger screen laptop provides a rich visual environment for a host of multi‐coloured data representations. Set‐up and calibration routines can be easily programmed. Spot and swept frequency measurement of distortion is very straightforward and impulse acquisition and analysis is an obvious part of such systems. A historically arranged block diagram of the components of such a system shown in Figure 10.47. Save for the microphone and power amplifier pretty well of this can be put into a cigar box sized test set costing a mere fraction of that stack of earlier tools. In the past few years there has been extensive development in electronic audio measurement systems based on audio ‘sound’ cards, which may be accessory units or provided as a mainframe plug‐in for a PCs. Their operating systems are held on software and subject to frequent and often worthwhile revisions and improvements. At very moderate cost compared with established specialist acoustic measurement products, these PC‐based systems offer surprising versatility, often include calibrated microphone options, and are relatively easy to use. DRA Labs MLSSA system is one of the earlier and best known types, is used extensively by this author, and is conveniently installed in an old Toshiba portable. However, very few of the latter remain which can take this 16‐bit sound card; the alternative is the desktop machine though these are now obsolete and must be sought out from junk yards.

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High Performance Loudspeakers Program and data storage

Display

Keyboard entry

Graphics plot

Computer controller

Peripherals Printer

GPIB

Pulse generator

Audio generators (one, low distortion)

Audio generator

Frequency meter

Switch box (programmable)

DVM

Distortion analyser

Load bank

Fourier spectrum analyser

Monitor oscitloscope

Drive amplifier

Microphone and preamplifier

Figure 10.47  Comprehensive historic GPIB computer controlled audio test system. Display and user input; electronic device under test; loudspeaker, and so on.

Other examples include CLIO, by Audiomatica SRL, Italy, which among its many facilities includes distortion and MLSplus a third‐octave RTA (optional microphone). A similar U.S. design is the (LAUD) by Liberty Instruments which has some interesting features, including one‐sixth octave analysis plus eye‐catching displays. LMS is another high‐quality computer controlled system designed by Linear X. It is highly accurate and has excellent analysis facilities using wide‐range sine‐wave generation. Linear X also produce very good design simulation and data analysis tools. The specific limitations for finite length gated impulse measurements are well known and these and other methods have been comprehensively reviewed by Muller and Massarani.[58,59] Here their research argues for the choice of an augmented sweep excitation method with pre‐emphasis, with an arbitrary spectral content but a controlled frequency‐time envelope. Superior dynamic range, and the effective measurement of distortion in large room conditions is then said to be within reach (Figure 10.48). Kite, for Audio precision,[60] has also evaluated logarithmic sweeps, these a form of chirp signal, focusing on how to increase accuracy, and supplement the evaluation with the measurement of crosstalk. Chirp signals are increasingly common and the more recent CLIO Audiomatica test set iterations include the facility.

Loudspeaker Assessment Log sweep

DA + amp

Ref. Preamp + AD

Freq.resp.

FFT

IFFT

Imp.resp t=0

Reference

Windowing

FFTs

Freq.resp. 2nd harm. shift

Divide D

2nd harm. %

N

Figure 10.48  Signal‐processing stages for evaluation of transfer function and second‐order harmonic for logarithmic sweep excitation. (after Müller).

10.5.22  Driver Parameters While manufacturers who design their own drive units hopefully retain complete information on their development and the resulting specifications, the independent system designer who works with drivers from several manufacturing sources ideally needs detailed technical information which may not be readily available. A surprisingly valuable source of data is the simple impedance curve, taken both in free air and with the driver loaded by a suitable air‐tight box of known volume. Conveniently the idealized frequency/amplitude characteristic at low frequencies for a driver alone or in a system may also be obtained directly from the voltage output with frequency from a low‐mass accelerometer, temporarily fixed to the cone. A difficulty both with the practical realization of theoretical system design analyses, frequency response and parameter measurement is the non‐linear variation of relevant parameters with level and/or excursion temperature, also past excursion history, distant and recent. Discrepancies of 5% to 10% for results are not uncommon, for example in Bl and suspension compliance. In addition, a given Q and f0 measured at 0.1 W may be rather different from the results taken at 1 W and 10 W. The designer needs to assess this power related driver behavior in the context of use and thus optimise the driver design for the application. Many loudspeaker measurement test cards, test sets and associated software calculate the TS parameters automatically but the particular test drive conditions should be considered carefully. Note that Q measurements will only be accurate for values greater than 4 and derived values using Q will need to take this caution into account. Perhaps those easily obtained T‐S parameters must be considered only a guide, helpful to begin a design and perhaps for production control, but the actual system alignment under higher power dynamic conditions may be substantially different.

591

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High Performance Loudspeakers

Many systems are retuned significantly after first construction as the calculated small signal performance, based on low power derived TS parameters, proves inappropriate under a range of normal music driven higher power and excursion operating conditions. Bearing this in mind and noting the co‐dependence and sensitivity of parameters within the calculated relationships we look at the T‐S (Thiele–Small) parameters. 10.5.23  Suspension Compliance, CMS (N/m) This may be found by direct measurement, by placing a known moderate weight M on the diaphragm (axis set vertical) and noting the resulting displacement d, for example, by using a travelling microscope. Now

C MS

1 s

d Mg

where g = gravitational acceleration and s = stiffness. Some error may occur in terms of the overall peak to peak diaphragm excursion owing to the one‐sided measurement. Also note that if the mass loading is excessive it will result in some non‐linearity of compliance and thus a partially erroneous reading. Approximately 2 mm of displacement is an advised value for this measurement but may be scaled to the driver size and expected excursion. An alternative method for obtaining the compliance consists of firstly noting the free‐ air resonance f0, and then an in‐box resonance fc, this given with the driver mounted in a sealed, unlined box of known volume, VB. The air volume of the box will have a calculated compliance CAB. The driver acoustic compliance CAS is related to CMS by SD2, the effective piston area, that is,



C MS

C AS C AS SD2 C AB

1.15

fc f0

2

1

(note that the factor ‘1.15’ is a general approximation and is somewhat affected by the box volume VB) also,

C AB

V

1.4 105

so that C MS

VB 1.15 SD2

fc f0

2

1

10 5 1.4



These two values of measured compliance may be compared to check for consistency. This second method is useful for largely symmetrical excursions and also for a larger range of input powers.

Loudspeaker Assessment

10.5.24  Moving Mass, MD (kg) This may be calculated from the measured free‐air or fundamental resonant frequency, f0, which in turn may be taken from the frequency peak in the motional impedance graph. Having estimated the working diaphragm area (i.e., the projected moving area) by measurement, the equivalent radius, a, may be obtained. Then using CMS

MD

1 C MS 2 f 0

2

3.15a3

The moving mass MD may also be found by comparing the free air f0 with fm, the result with an additional mass m attached:



Mt m Mt

f 0 /f m

where Mt = overall driver moving mass including air load, Ma.

MD

Ma

mf m2 f 02 f m2

The test mass m may be 20% to 40% of the estimated moving mass. 10.5.25  DC Resistance (Motor/Voice Coil), Rc (Ohms) This may be measured by using a DC ohmmeter or, alternatively from the ­minimum impedance value above fundamental resonance. It falls quite close to the DC resistance in the uniform range before coil inductance has an effect. Measured at a suitable low frequency, clamping the diaphragm will also provide the DC resistance even when using the impedance measurement method, this removing the contribution due to motion. 10.5.26  Coil Inductance, lc (Henrys) An impedance bridge may be used at frequencies above 1 kHz or so, here with the driver diaphragm clamped to prevent coil motion. The coil inductance can also be calculated to good accuracy from the impedance curve without the need for clamping if the unit is a low (