Complete Guide to Active Filter Design, Op Amps, and Passive Components [1 ed.] 0131599712
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COMPLETE GUIDE TO ACTIVE FILTER DESIGN, OP AMPS, AND PASSIVE COMPONENTS
COMPLETE GUIDE TO ACTIVE FILTER DESIGN, OP AMPS, AND PASSIVE COMPONENTS Z. H. MEIKSIN
PRENTICE HALL Englewood Cliffs, New Jersey 07632
Library of Congress Cataloging-in-Publication Data Meiksin , Z . H. Complete guide to active filter des ign , op amps, and pass ive components I Z. H. Meiksin . p. cm. Includes index .
ISBN 0- 13- 159971-'2 1. Elec tric filters, Active- Deisgn and construction . I. Title .
2. Operational amplifiers .
TK7872 .F5M45 1990 621 . 38 l '5324- dc20
89-8646 CIP
Editorial/production supervision and interior design: Lorraine Antine and Kerry Reardon Cover design: 20/20 Services Manufacturing buyer: Robert Anderson
© 1990 by Prentice-Hall, Inc. A Division of Simon & Schuster Englewood Cliffs , New Jersey 07632
The publisher offers discounts on this book when ordered in bulk quantities. For more information, write: Special Sales/College Marketing College Technical and Reference Division Prentice Hall Englewood Cliffs, New Jersey 07632 All rights reserved. No part of this book may be reproduced, in any form or by any means , without permission in writing from the publisher. Printed in the United States of America
10
9
8
ISBN
7
6
5
4
3
2
0-13-159971-2
PRENTICE HALL INTERNATIONAL
(UK) LIMITED , LONDON
PRENTICE HALL OF AUSTRALIA PTY. LIMITED , SYDNEY PRENTICE HALL CANADA INC. , TORONTO PRENTICE HALL HISPANOAMERICANA, S.A., MEXICO PRENTICE HALL OF INDIA PRIVATE LIMITED, NEW DELHI PRENTICE HALL OF JAPAN, INC., TOKYO SIMON
&
SCHUSTER ASIA PTE . LTD. SINGAPORE
EDITORA PRENTICE HALL DO BRASIL , LTDA.,
Rio
DE JANEIRO
DEDICATION
To my granddaughter Rebecca
Contents
xiii
Preface HOW TO DESIGN ACTIVE FILTERS
PART I.
1.
2.
1 1
Understanding Filter Terminology
1.1
Introduction
1
1.2
Low-Pass, High-Pass, and Band-Pass Filters
1.3
Filter Order
1.4
Filter Classes
1.5
Normalized Filters
1.6 .
Fine Tuning
1
1 4 5
5
Designing First-Order Filters
6
6
2.1
Introduction
2.2
Low-Pass Filters
6
2.3
High-Pass Filters
7
2.4
Band-Pass Filters
8
V
Contents
VI
3.
3. I
Introduction
3.2
Low-Gain Amplifier Filters 3.2.1 3 .2.2 3 .2 .3
3. 3
3 .4
5.
6.
7.
I0 10
low-Pass Filters 11 High-Pass Filters 12 Band-Pass Filters 13
High-Gain Amplifier Filters 3.3.1 3 .3.2 3.3.3
4.
10
Designing Second-Order Filters
15
low-Pass Filters 15 High-Pass Filters 15 Band-Pass Filters 18
Choice Between High-Gain and Low-Gain Amplifier Filters 19
20
Designing Third-Order Filters
4. 1
Introduction
20
4.2
Low-Pass Filters
20
4.3
High-Pass Filters
23
4.4
Band-Pass Filters
24
25
Designing Fourth-Order Filters
5. 1
Introduction
25
5.2
Low-Pass Filters
25
5.3
High-Pass Filters
27
5.4
Band-Pass Filters
29
Designing Higher-Order Filters
6.1
Introduction
6.2
Low-Pass Filters
31
6. 3
High-Pass Filters
34
6.4
Band-Pass Filters
38
6.5
High-Q Band-Pase Filters
30
30
38
Effect of Component Characteristics on Filter Performance and How to Avoid Pitfalls
7. 1
Introduction
41
41
Contents
PART II. 8.
VII
7.2
Bias Current
7.3
Amplifier Gain
7.4
Amplifier Compensation
44
7.5
Resistors and Capacitors
45
7.6
More information
41 43
46
OPERATIONAL AMPLIFIERS
47
Understanding Operational Amplifier Characteristics
8. 1
Introduction
8. 2
Symbols and Definitions
8.3
Gain
8 .4
Input Resistance
8. 5
Output Resistance
8.6
Common-Mode Gain (CMG) and CommonMode Rejection Ratio (CMRR) 52 8.6.1 8.6.2
47
47
49 51 51
Common-Mode Effect on the Output 52 Maximum Common-Mode Input
53
8. 7
Voltage Supply Rejection Ratio (VSRR)
8. 8
Input Offset Voltage
8.9
Input Bias Current
8 .10
Input Offset Current
8. 11
Gain-Bandwidth Product
8.12
Slew Rate
8. 13
Crossover Distortion
8. 14
Rated Output
8. 15
Power Dissipation
8. 16
Input Overload Protection
8.17
Supply-Current Drain
8. 18
Transient Response
8.19
Input Capacitance
55 55 57 58
58 60
61 61
62 62
63
62
53
47
Contents
viii
9.
10.
11.
8.20
Amplifier Noise
63
8.21
Temperature, Frequency, Supply-Voltage, Source-Resistance, and Load-Resistance Dependencies of Amplifier Characteristics
63
Dual- and Single-Power-Supply Amplifiers, Low- Voltage Amplifiers, and Transconductance Amplifiers
9. I
Introduction
9.2
Single-Voltage-Power-Supply Amplifiers
9.3
Low-Voltage Amplifiers
9.4
Low-Noise Amplifiers
9.5
Wideband Amplifiers
9.6
Transconductance Operational Amplifiers
64
64 64
66 67
67 70 71
Amp/ifier Stability
71
10.1
Introduction
10.2
Phase Compensation
10.3
Internally Compensated Amplifiers
10.4
Uncompensated Amplifiers
71 72
73
76
Amplifier Contigurations
11.1
Introduction ··16
11.2
The Inverting Amplifier 11.2.1 11.2.2 11.2.3 11.2 .4
11.3
76
Voltage Gain 76 Input Resistance 78 Output Resistance 78 Common-Mode Effect 78
The Noninverting Amplifier 11.3.1 11.3.2 11.3.3 11.3.4
79
Voltage Gain 79 Input Resistance 80 Output Resistance 80 Common-Mode Effect 80
11.4
Choice Between Inverting and Noninverting Configurations 81
11.5
The Differential Amplifier 11.5.1
Common-Mode Effect
82 83
Contents
ix
11.6
Three-Resistor Feedback Network
11.7
AC-Coupled Amplifiers 11. 7.1 11 . 7.2 11. 7.3 11. 7.4
12.
PART Ill. 13.
85
Inverting Amplifier 85 Noninverting Amplifier 86 High-Input-Impedance AC-Coupled Noninverting Amplifier Differential Instrumentation Amplifiers 89
Design Examples and How to Avoid Pitfalls
12. 1
Introduction
12.2
Voltage Operational Amplifier
12. 3
Transconductance Operational Amplifier
12.4
Pitfalls to Avoid
90 90 92
95
97 97
Resistors
13. 1
Introduction
13. 2
Carbon-Composition Resistors
13. 3
Wirewound Resistors
98
13 .4
Metal-Film Resistors
98
13.5
Carbon-Film Resistors
13.6
Thin- and Thick-Film Resistor Arrays
13. 7
Thermistors
13.8
Pitfalls to Avoid
13. 9
How to Choose the Right Type Resistor 102
13. 10
Potentiometers and Rheostats (Variable Resistors) 103
97 97
98 99
99 100
Potentiometers (Variable Resistors) Pitfalls to Avoid 105
103
106
Capacitors
14.1
Introduction
14.2
Capacitor Specifications 14.2. 1 14.2.2
87
90
PASSIVE COMPONENTS
13.10.1 13.10.2
14.
84
106 106
Capacitance 106 Insulation Resistance (DC Leakage)
107
Contents
X
14.2. 3
14.3
Dissipation Factor, DF, Quality Factor, Q, and Equivalent Series Resistance, ESR 108
Types of Capacitors
109
14.3 .1 Ceramic Capacitors 109 14.3. 2 Film-Type Capacitors 113 14.3 .3 Mica Capacitors 113 14 .3.4 Electrolytic Capacitors 116 14 .3.5 Trimmer Capacitors 116 14.3 .6 Feed-Through Capacitors 117 14 .3.7 Air-Variable Capacitors 117
14 .4 15.
16.
17.
Pitfalls to A void
117 118
Inductors
15. 1
Introduction
118
15. 2
Air-Core Inductors
119
15. 3
Iron-Core Inductors
119
120
Transformers
16.1
Introduction
120
16.2
Power-Supply Transformers
16. 3
Audio Transformers
122
16.4
Video Transformers
123
16. 5
IF and RF Transformers
16. 6
Pulse Transformers
120
123
124
Diodes
125
17. 1
Introduction
125
17. 2
Diode Characteristics
17. 3
Diode Parameters 127
17 .4
Diode Types
125
129
17.4. 1 Signal Diodes 129 17.4.2 Rectifiers 129 17.4.3 Switching Diodes/Rectifiers 17.4.4 Reference Diodes 130
18.
Component Value Measurement
18. 1
Introduction
131
129
131
Contents
18.2
XI
18.2.1 18.2.2 18.2.3 18.2.4
18.3
19.
PART IV.
20.
135
137 Curve Tracer 137 Volt-Ampere Method
137
138
Component Identification
19 .1
Introduction
19. 2
Resistors and Potentiometers
19. 3
Capacitors 19.3.1 19.3.2 19.3.3 19.3.4
138 138
139
Electrolytic Capacitors 139 Paper Dielectric Capacitors 140 Ceramic Capacitors 140 Mica Capacitors 141
19.4
Inductors
19. 5
Transformers
19.6
Diodes
141 141
142
143
PUTTING IT ALL TOGETHER
143
Comprehensive Design Examples
143
20.1
Introduction
20.2
Design I-Band-Pass Filter 20.2.1
20.3 20.4
Solution Solution
143
143
Design 2-Low-Pass Filter 20.3.1
134
Bridges 135 Q Meters 136
Diodes 18.5. 1 18.5 .2
133
Insulation -Resistance (DC-Leakage) Measurement 133 Bridges-Capacitance and Dissipation Factor Measurement
Inductors 18.4.1 18.4.2
18 .5
Ohmmeter 131 Bridge 132 Substitution 132 Megohmmeter 133
Capacitors 18.3 .1 18.3.2
18 .4
131
Resistors
151
151
Summary and Comments
155
Contents
xii
Appendix A.
157
Manufacturers' Data Sheets
I.
Internally Compensated Operational Amplifier 158
2.
Uncompensated Operational Amplifier
3.
Very-High-Input-Impedance Operational Amplifier 166
4.
Transconductance Operational Amplifier
5.
Single-Power-Supply Operational Amplifier 176
6.
Low-Voltage-Power-Supply Operational Amplifier 182
7.
Very-Low-Voltage-Power-Supply Operational Amplifier 192
8.
Low-Noise Operational Amplifier
9.
Wideband Operational Amplifier
163
174
199 204
Appendix B. Passive Component Values and Identification 1.
Tolerances and Component Values of CarbonComposition Resistors 218
2.
Resistor Color Code
3.
Resistor Types and Ranges
4.
Capacitor Color Code
5.
Capacitor Ranges on the Basis of Dielectric Material 221
6.
Semiconductor Diode Identification
Index
217
218 219
220
222
223
Preface
Essentially all electronic signal-processing systems incorporate filters of one sort or another to separate a selected group of voltages from the remainder, or to improve signalto-noise ratio. Readily available, high-quality operational amplifiers (also called op amps) of small size and low cost make the use of active filters very attractive. The theory of active filters is complex. But the practical design of such filters, if presented properly, is simple and straightforward. This book provides such a practical approach to filter design. Active filters are built with operational amplifiers, resistors, and capacitors. In the real world these components are not ideal. To achieve performance within specifications, the real properties of the components must be taken into consideration in the design. To provide you with the information needed to design active filters properly, this handbook is organized in four parts and two appendices. Part I of this practical guide shows you how to select and design the right filter. If you are designing an amplifying system for an audio frequency signal above 500 Hz, for example, you can filter out 60-Hz line-frequency noise voltage from the power supply by incorporating in your system a simple first-order high-pass filter. There is no need to spend time and money for a higher-order filter. If, on the other hand, you build a system in which you want to process voltages with frequencies between 50 kHz and 75 kHz and you want to reduce the shot noise present in all electronic components, you need a filter with sharper cutoff characteristics. You can incorporate in the system a third-order bandpass filter and you can even, with the formulas given in this book, compute the exact attenuation for all frequencies. Reading Chapter 1 first will enable you to capitalize more quickly on the useful guidelines and specific data provided in this book. This chapter defines filter order, filter classes, and the normalized filter, as well as the basic concepts of low-pass, high-pass, xiii
xiv
Preface
and band-pass filters. You decide what type of filter you need and you go directly to the chapter and section that directs you step-by-step to the desired circuit configuration and, by means of simple equations or tables, to the determination of the component values. First-order filters, given in Chapter 2, are the easiest to design. The selection of components for the desired cutoff frequencies are obtained by the use 9f simple formulas. To design second-order filters, given in Chapter 3, as well as to design higher-order filters, the normalizedfilter concept is used. This approach employs three distinct, clearly defined steps, which are explained with examples. Third-order filters are- presented in Chapter 4. These are the "work horses" of filter design. They are simple, economical, and effective for a wide range of applications. For sharper cutoff characteristics, fourthorder filters, given in Chapter 5, are used. For still sharper cutoff characteristics, higherorder filters must be used. How to design fifth- through tenth-order filters is explained in Chapter 6. Using a multitude of tables would defocus the essential aspects of this design guide. Therefore, a single table is given for all classes and higher order filters, with special equations for all filter stages. It is explained clearly with the aid of examples how to use these equations to arrive at the filter component values in a most straightforward manner. The chapter concludes with the high-Q state variable filter. Chapter 7 shows how amplifier and passive-component performance affects filter performance and how to avoid pitfalls. Part II deals with operational amplifiers. It shows you how to interpret manufacturers' data sheets, how to evaluate operational amplifier performance, and how to incorporate real operational amplifier characteristics into practical circuit design. The extensive material covered in the five chapters of this part is useful not only for filter design, but for electronic circuit design in general. Dual-power-supply as well as single-power-supply and special low-voltage amplifiers-popular in battery-operated systems-are included. Chapter 12 gives complete design examples, which take into consideration the practical limitations and imperfections .of operational amplifiers. Part III introduces and explains passive components. Although active filters use only resistors and capacitors, this part also presents details of inductors, transformers, and diodes, which makes this chapter extremely important for electronic circuit design in general. These components are made of a large number of different materials using a variety of technologies. Materials are complicated and their properties are influenced by fabrication processes that in tum influence component properties. The properties of all these passive components are explained, guiding you to the correct choice of components in your designs. You are shown how to derate power ratings of resistors with increase in temperature and how the resistance of carbon resistors depends on frequency. Capacitor parameters are defined, and curves show the dependency of capacitance and insulation resistance on variables such as frequency and temperature. Also given is the dependency of the dissipation factor on the applied DC voltage. You will even find how to measure values and characteristics of passive components using techniques ranging from simple ohmmeter measurements to sophisticated methods using more complex, but readily available, instruments. Also included in the seven chapters of this part of the handbook is the subject of component identification. A variety of color, symbol, and letter codes are used
Preface
xv
by manufacturers to identify component values, tolerances, and temperature coefficients. With the help of the information given, you will be able to identify virtually any commercial component. The material in this design guide is carefully pulled together in Part IV. Design examples that lead you from the design specifications through the final product are given. You are shown all the design steps and how to choose particular op amps to ensure that the specifications are being met. You are shown how to select the necessary resistors and capacitors, including values, voltage ratings, power ratings, and the particular material from which the components are made, to meet special requirements of the design. Effects of temperature and component tolerances are illustrated. The utility of this well-planned book is further enhanced by the inclusion of two appendices. Appendix A includes a large variety of manufacturer data sheets for op amps selected carefully to give you representative data of the most important op amp types. Appendix B compiles symbols and codes to make quick passive component identification possible. The detailed explanations of the material, the data sheets, design procedures, formulas, diagrams and tables make this practical handbook an invaluable design aid in your present and future work.
ACKNOWLEDGMENT The contributions and suggestions made by Philip C. Thackray are gratefully acknowledged.
COMPLETE GUIDE TO ACTIVE FILTER DESIGN, OP AMPS, AND -PASSIVE COMPONENTS
•
~
Part I
HOW TO DESIGN ACTIVE FILTERS
1 Understanding Filter Terminology
1.1 INTRODUCTION The successful design of filters requires the designer to clearly formulate in the mind, and then on paper, the intended use of the filter. A prescribed set of steps is then followed to complete the design. This process is enhanced by thinking in terms of concepts that are defined and expounded on in this chapter. After the filter is designed and assembled, finetuning is required for demanding applications. This is also covered in this chapter. 1.2 LOW-PASS, HIGH-PASS, AND BAND-PASS FILTERS The ideal transfer characteristics of low-pass, high-pass, and band-pass filters are shown in Figure 1-1. Ideally, the signal is not attenuated at all in the passband of a filter, and is attenuated completely in the stop band. Also, ideally, the phase shift of the signal is linear with frequency in the passband. The phase shift in the stop band has no significance, since the signal is not transmitted in this band. Under these ideal conditions, the signal is transmitted without any distortion in the passband frequency range, and it is not transmitted at all outside this frequency range. In practice, the ideal filter can only be approached to various degrees, depending upon the complexity of the filter. 1.3 FILTER ORDER The simplest filter contains one capacitor for each cutoff frequency. This type is called a first-order filter. Thus, a first-order low-pass filter contains one capacitor; a first-order high-pass filter contains one capacitor; and a first-order band-pass filter contains two 1
How to Design Active Filters
2
g
l~'.I t
t--------,
Stop band
Pass band
---+ f Frequency
f 11
/
High cut-off frequency (a)
uC: :::l '-
...
Stop band
~ V,
C:
...
Pass band
-
~
r-
f1
/
L
Fre4uency
Low cut-off frequency (b)
C:
0
1 I~: ...
_,
u
C:
:::l
'-
1
u
.,
V,
C:
...
~
t--
Stop band
--
Pass band
--
Stop band
fi
' fc
-
fH \
Low cut-off / frequency
Center frequency
-..f Frequency High cut-off frequency
(c)
Figure 1-1 Transfer functions of ideal filters. (a) Low-pass filter. (b) Highpass filter. (c) Band-pass filter.
Part I
Chap. 1
V: V1
Understanding Filter Terminology
t
I
1.0
3
t
V: V1
1.0
0.7
t
1.0
0. 7
0. 7
f ..
(a)
(c)
( b)
1
n =- 2
n = I
f,
I
f11
fc
\
-
(i;
f
1
n
=J
Ve V1
~
f
n =4
l
::t;ppk I
fc (f)
fH
(e)
(d )
V2 V1
fc
-----
(g)
Figure 1-2 Gain transfer characteristics for maximally flat (Butterworth) and equalripple (Chebyshev) filters. (Not to scale.) (a) Low-pass maximally flat. (b) High-pass maximally flat. (c) Band-pass maximally flat. (d) Band-pass equal-ripple, n = 1. (e) Band-pass equal-ripple, n = 2. (f) Band-pass equal-ripple, n = 3. (g) Band-pass equalripple, n = 4.
How to Design Active Filters
4
Part I
capacitors. The next degree of complexity is obtained in the second-order filter, then the third-order, fourth-order, etc. The higher the order of the filter, the more nearly does the filtenng chara~teristic of the filter approach that of the ideal filter.
1.4 FILTER CLASSES A filter of any given order can be made to approximate the ideal filter in different ways, depending on the values given to the filter components. The type of approximation chosen determines the filter class. Two useful classes are the maximally flat (also known as Butterworth) and the equal-ripple (also known as Chebyshev) classes. The difference between the two classes is illustrated in Figure 1-2. Compare, for example, the gainfrequency characteristic of the second-order maximally flat band-pass filter given in Figure l-2(c), (n = 2), with that of the second-order, equal-ripple , band-pass filter given in Figure 1-2(e). The maximally flat filter approximates the ideal filter better in the passband, but attenuates signals in the stop band less than the equal-ripple filter. In Figure 1-2 only band-pass diagrams for equal-ripple filters are shown. Low-pass and high-pass filter characteristics can be deduced by considering the appropriate portion of the corresponding band-pass filter characteristic. The frequency response curve of a fourth-order, low-pass maximally flat filter is compared with the response curve of a corresponding equal-ripple filter in Figure 1-3. The particular order and class chosen for any given design depends on the particular system specifications. The design is usually carried out in terms of steady-state frequencyresponse specifications. However, the same filter components that determine the frequency response also determine the transient response . The mathematical relationships between the frequency response and the transient response are quite complex, and some experimentation in practical design is necessary. The more ''squared-off'' the frequency response is, the more overshoot is encountered during a transient period.
I~~ I
r "',.
1.0 0.9 0.8 0.7
I \v1\
I/
\
0.6
\ \~
0.5 0.4 0.3 0.2 0. 1 0
Equal__.., ripple
\
\ \
"
.......
0.5
1.0
Maximally Flat
~
I"--~ i--__
I. 5
2.0
2.5
. 3.0 f/ L
Figure 1-3 Response curves of magnitudes of low-pass fourth-order maximally flat (Butterworth) and equal-ripple (Chebyshev) filters.
Chap. 1
Understanding Filter Terminology
5
1.5 NORMALIZED FILTERS Filter design is implified, particularly when designing higher-order filters, if the "normalized filter" concept is u ed. One first uses a simple set of design equations or tables to obtain the normalized filter. This filter has a cutoff frequency of I rad/s (or l/21T = 0.159 Hz) and usually resistors of 1 0, and/or capacitors of 1 F. Two additional de ign steps result in the desired practical filter: first, a change of component values (re istors or capacitor ) i made to obtain the desired cutoff frequency, and finally, a change in value of re i tor and capacitors is made in a prescribed manner to obtain realistic orders of magnitude of component values.
1.6 FINE TUNING The values resulting from the computations are given to accuracies considerably beyond the tolerances of practical components. In practice, one uses the closest commercially available components and checks to see whether the filter characteristics are still acceptable and, if necessary, adds either resistor trimmers or capacitor trimmers to tune the filter to the exact desired cutoff frequencies. Remember also that capacitor tolerances are on the order of +80% -20%, +20%, + 10%, or +5%, and resistor tolerances + 10% or +5%, which would necessitate trimmers anyway. Resistors with +I% tolerance are available at a higher cost. Don ' t overlook thick-film and thin-film resistors and capacitors if your product involves a large number of filters. Film components can be trimmed to order during the fabrication process, which can result in savings.
2 Designing First-Order Filters
2.1 INTRODUCTION
First-order filters are the simplest and least-expensive filters. They are suitable for nondemanding applications. In this chapter we show you how to design low-pass , high-pass , and band-pass first-order fi~ters.
2.2 LOW-PASS FILTERS The circuit diagram of a first-order low-pass filter is shown in Figure 2-1. The 3-dB -cutoff frequency is given by
The DC gain is R 2 / R 1 , and the rolloff in the stop band is -20 dB/dee (-6 dB/oct). Example
For a low-pass amplifier with f H = 1,000 Hz and DC gain = I 0 ,
I
6
1,000
Chap. 2
Designing First-Order Filters
7
~ f ,__,____,_i ~ 3dB IY 1
I
(a)
Figure 2-1
( b)
ir t-order I w- pa
filter. (a) Circuit diagram . (b) Frequency
characteri tic .
We have two equation with three unknowns . We can therefore choose arbitrarily any one of the three components. Let C2 = 0.01 µF. From the equation above we obtain R 2 = 15.9 kD , and R 1 = 1.59 kD.
2 ..3 HIGH-PASS FILTERS
The circuit diagram of a first-order high-pass filter is given in Figure 2-2. The 3-dB cutoff frequency is given by
and the high-frequency gain beyond the cutoff frequency is R 2 / R 1 • The rolloff below the cutoff frequency is 20 dB /dee (6 dB/oct).
v.,
(a )
Figure 2-2 characteri stic.
First-order high-pass filter. (a) Circuit diagram.
(bl
(b)
Frequency
Part I
How to Design Active Filters
8
Example
For a high-pass amplifier with JL
Let C 1 kil.
=
= 20
kHz and high-frequency gain of 10,
10,000 pF. From the equations above, R 1
=
796
n and R
2
=
7.96
2.4 BAND-PASS FILTERS
The circuit diagram of a first-order band-pass filter is shown in Figure 2-3. The low and high cutoff frequencies are, respectively,
and
1 fH = 21rR1C1
The mid-frequency gain is R 2 / R 1. There are two capacitors in this circuit, one associated with the low cutoff frequency, and one with the high cutoff frequency. The slopes of the transfer curve below JL and above JH are 20 dB/dee (6 dB/oct) and -20 dB/dee (6 dB I oct), res pee ti vel y.
_____ _1
r--+-1
I
I I
fc (a)
( b)
Figure 2-3 Simple band-pass filter. (a) Circuit diagram. (b) Frequency characteristic.
fH
........ f
Chap. 2
Designing First-Order Filters
9
Example
It is desired to design a filter with fL = 2 kHz , f H = 5 kHz and midfrequency gain = 5. The design equations are
I 21rR2C2 = 2,000 1 21T RIC I
=
5 '000
R2 = 5 R1
We have three equations with four unknown parameters . We can, therefore, choose any one of the four arbitrarily. Let C 2 = 0.01 µF, then R 2 = 7.958 kil , R 1 = 1.592 kil, and C 1 = 0.02 µF.
3 Designing Second-Order Filters
3.1 INTRODUCTION
Second-order filters require more components than first-order filters, but they possess sharper rolloff characteristics. In the stop band containing the frequency range in which signals are to be attenuated, the amplitudes of signals decrease faster with frequency than for first-order filters. The frequency responses in the passband and in the stop band can be shaped by the choice of the filter class: maximally flat (Butterworth), or equal-ripple (Chebyshev) with a specified degree of ripple. There are low-gain amplifier filters and high-gain amplifier filters. These two filter types are explained and design P-rocedures with examples are given for both. Similarities between the two types and differences between them are highlighted, giving guidelines for their respective applications.
3.2 LOW-GAIN AMPLIFIER FILTERS The term low-gain amplifier refers to an operational amplifier with an external feedback resistor and an external input resistor connected to the noninverting input of the amplifier. The gain of the amplifier is unity plus the ratio of the feedback resistor to the input resistor. The complete unit is now considered as a low-gain amplifier element of the filter which includes additional elements (resistors and capacitors) peripheral to the low-gain amplifier. This filter type allows us to use identical resistors throughout the circuit, which makes matching and temperature tracking better and, in large quantities, results in lower cost. 10
Chap. 3
Designing Second-Order Filters
11
, - - -;:i ,-._I I I .>---4..--1__.._---o ---I
I
I
I
I
I R,
:
I
L _ _ _ _j Figure 3-1
Second-order low-pass filter .
3.2.1 Low-Pass Filters A second-order low-pass filter is shown in Figure 3-1 . The gain of the amplifier is K = 1 + Rh/Ra. The transfer function of the filter is determined by the value of the amplifier gain and by the values of the resistors and capacitors. The same transfer function can be realized with different combinations of these values. Three choices are particularly useful: (a) K = 2, which results in Ra = Rb, which in tum gives good matching and tracking; (b) K = I, which results in a voltage-follower amplifier and eliminates the need for the two resistors Ra and Rb-Ra is replaced with an open circuit and Rb with a short circuit; and (c) R 1 = R 2 and C 1 = C2 , which again results in good matching and tracking. Further, whenever equal components are used, there will be a lower cost when a large number of filters are built. The filter design is first carried out for the cutoff frequency wH = 1 rad/s. The component values are then changed in two steps: the first step gives the correct cutoff frequency, and the second step gives reasonable values of resistors and capacitors. Tabl_e 3-1 lists gain and component values for the three choices of wH = 1 for the maximally flat filter and for two equal ripple filters, one with 0.5-dB ripple, and the other with I-dB ripple. Example
Design a low-pass, zero-ripple filter with a cutoff frequency of 1,500 Hz and a DC gain of 2. · The normalized filter is a maximally flat filter with the circuit configuration of Figure 3-1 and the values R 1 = R 2 = 1.00000 f!, C 1 = 0.87403 F, and C 2 = 1.1442 F, as obtained from Table 3-1. To obtain a cutoff frequency of wH = 27r 1,500, we divide all capacitors by 21r 1,500 giving
c1 =
o.87403121r1,soo = 92.7375 µF C 2 = l.14412/21rl,500 = 121.3949 µF
Part I
How to Design Active Filters
12 TABLE 3-1 C in farads)
Component and Gain Values for the Low-Pass Filter of Figure 3-1 for wH = I (R in ohms;
R,
R2
c,
Maximally flat (Butterworth) 3.01 dB at wH
1.00000 1.00000 1.00000
1.00000 1.00000 1.00000
0 .87403 1.4 142 1 1.00000
1.14412 0 .70711 1.00000
Equal ripple (Chebyshev) 0 .5-dB ripple
1.00000 1.00000 0.81220
1.00000 1.00000 0.81220
0.77088 1.40259 1.00000
0.855557 0.4701 3 1.00000
Equal ripple (Chebyshev) I-dB ripple
1.00000 1.00000 0.95237
1.00000 1.00000 0.95237
0 .93809 1.82192 1.00000
0 .96688 0.49783 1.00000
Filter class '
K
C2
2.00000 1.00000 1.58578
-
2.00000 1.00000 1.84213 2 .00000 1.00000 1.95446
Finally, to obtain a set of reasonable values , we multiply the resistors by a factor of 105 and divide the capacitors by a factor of I 0 5 (provided the factors are the same, the filter characteristics will not change). For good economy, we make R 0 = Rb = R 1 = R 2 • The component values of the filter are R I = R 2 = R a = R b = 100 kfl c 1 = 927.375 pF C2 = 1,213.949 pF '
Note: The designer might prefer to choose resistors of values of IO kfl to reduce bias current-offset effects, depending on the particular amplifier used. In this case the capacitors must be multiplied by a .factor of 10, giving C 1 = 0.00927 µF and C 2 = 0.01214 µF. In practice, the designer must use commercially available capacitors. A choice of a ceramic capacitor of 0.01 µF for C 1 and 0.01 µFor 0.015 µF for C 2 is suitable.- Since these are not exactly equal to the calculated values , the cutoff frequency will be slightly different from the one specified. Rarely is this deviation of any consequence. If, for some reason, the precise cutoff frequency must be obtained, it is necessary to shunt the capacitors with trimming capacitors. In this case, the fixed capacitors must have smaller values than the ones computed (e.g., 0.008 µF for C I and 0.0 I µF for C 2 ) , and the trimmer capacitors will be adjusted to add the required amount of capacitance. If a precise cutoff frequency is required, trimmers (capacitor trimmers or resistance trimmers) must be added anyway, since commercial capacitors have typically +20% tolerance.
3.2.2 High-Pass Filters The circuit diagram of a high-pass filter is given in Figure 3-2. Component values for the normalized filter are listed in Table 3-2. To see how to make use of this information the ' reader must refer to the section on low-pass filters, and follow the same procedure. Select
Chap. 3
Designing Second-Order Filters
,--~
R,
---i
c,
13
I
C2
I I
R, V1
Rb
v,.
I ___ _J R.,
Figure 3-2
Second-order high-pass filter.
components from the table for the desired filter class, for wL = 1; divide all capacitor values by the desired cutoff frequency; multiply all resistance values and divide all capacitance values by a suitable factor to obtain reasonable practical values of components and round the values off to commercially available values; use trimmers if necessary.
3.2.3 Band-Pass Filters The circuit diagram of a band-pass filter is shown in Figure 3-3. A band-pass filter is characterized by the center frequency we and by the Q of the filter. The Q of a filter is defined as the ratio offc (the center frequency) to the bandwidth (the difference/H - fL). Table 3-3 lists values of Kand of components for four different values of Q for the normalized (i.e., we = 1) filter. The following example demonstrates how to design a band-pass filter of the configuration of Figure 3-3 with the aid of Table 3-3. TABLE 3-2 C in farads)
Components and Gain Values for the High-Pass Filter of Figure 3-2 for w 1 = 1 (R in ohms;
Filter class
RI
R2
Cl
C2
K
Maximally flat (Butterworth) 3.01 dB at wH
1.00000 0.70711 1.00000
1.00000 i .41421 1.00000
1.41421 1.00000 1.00000
0.70711 1.00000 1.00000
2.00000 1.00000 1.58579
Equal ripple (Chebyshev) 0.5-dB ripple
1.00000 0.71281 1.23134
1.00000 2.12707 1.23 l 34
1.42563 1.00000 1.00000
1.06356 1.00000 1.00000
2.00000 1.00000 1.84222
Equal ripple (Chebyshev) I-dB ripple
1.00000 0.54586 1.05001
1.00000 2.00872 1.05001
1.09772 1.00000 1.00000
1.00436 1.00000 1.00000
2.00000 1.00000 1.00000
Part I
How to Oesiqn Active Filters
14
R2 R1
Ci
,--
K
I
I
I
I
I I
I
I
R,
V1
I
C1
L Figure 3-3
I
I
Rb
R.
V2
I
___ _J
Second-order band-pass filter.
Example
Design a band-pass filter with a center frequency of 10 kHz and a Q of 5. The circuit diagram is shown in Figure 3-3. From Table 3-3, we select for Q = 5 the values: RI = 1.00000, R2 = 0.63439, R3 = 2.57630 c 1 = c 2 = 1.00000, K = 2.00000
The value of K gives the gain of the amplifier: K
= I + Ra
Rb
We choose Ra = Rb = 1.00000, giving K = l + I = 2. TABLE 3-3 C in farads)
Component Values for the Band-Pass Filter of Figure 3-3 for w e
= 1 rad/s (R in ohms;
R1
R2
R3
Cl
C2
K
2
1.41421 1.00000
1.41421 0.74031
1.41421 2.35078
1.00000 1.00000
1.00000 1.00000
3.29284 2.00000
5
1.41421 1.00000
1.41421 0.63439
1.41421 2.57630
1.00000 1.00000
1.00000 1.00000
3.71716 2.00000
1.41421 1.00000
l.41421 0.60471
1.41421 2.63587
1.00000 1.00000
1.00000 1.00000
3.85858 2.00000
1.41421 1.00000
1.41421 0.59076
1.41421 2.69274
1.00000 1.00000
1.00000 1.00000
3.92428 2.00000
Q
20
Chap. 3
Designing Second-Order Filters
15
The circuit of Figure 3-3 with component values listed above gives a filter with the desired Q = 5, but a center frequency we = I. To obtain a center frequency fc = 10 kHz (or we = 21TI0,000), we divide the capacitor values by 21T 10,000:
C, = C2 = ~ - - - = 15 .9 µF 21T 10,000 Finally, to obtain rea onable values, we multiply all resistors by I 0 4 and divide all capacitors by 104 . The result is:
R 1 = Ra = Rb = 10 k!l; R2 = 6.34 k!l; R 3 = 25.8 k!l CI = C2 = 1,590 pF The nearest standard commercial values are: RI Cl
= Ra = Rh = 10 k!l; R2 = 6.2 k!l; R3 = 27 k!l = C 2 = 1,500 pF
These are slightly different from the computed values, causingfc and Q to be slightly different from the specified values. If exact specifications must be met, trimmer capacitors must be added in shunt (parallel) with C 1 and C 2 .
3.3 HIGH-GAIN AMPLIFIER FILTERS The term high-gain amplifier refers to a conventional high-gain operational amplifier used directly as an element of the filter with the peripheral components, fom1ing the required filter transfer characteristics. Unlike low-gain amplifier filters, this type often requires a spread in values of resistors. On the other hand, this type allows us to specify the gain of the filter through a choice of components, as given in the tables.
3.3. 1 Low-Pass Filters The circuit diagram of a second-order low-pass, high-gain amplifier filter is shown in Figure 3-4. Examples of component values for normalized maximally flat and equalripple filters are given in Table 3-4. To obtain a desired cutoff frequency of wH = 21TfH, we divide the values of all capacitors by wH. Then, to obtain a set of reasonable component values, we multiply the resistor values and divide the capacitance values by a single suitable factor just as we have demonstrated for the low-pass low-gain amplifier filter.
3.3.2 High-Pass Filters The circuit diagram of a second-order high-pass, high-gain amplifier filter is shown in Figure 3-5. Examples of component values for normalized maximally flat and equalripple filters are given in Table 3-5. The use of this table to design filters is demonstrated
Part I
How to Design Active Filters
16
c,
V1
Figure 3-4
Second-order low-pass high-gain amplifier filter.
in the following example, which illustrates the required steps to arrive at a practical design. Example
Design an equal-ripple (0.5-dB ripple) high-pass filter with a cutoff frequency of 5 kHz and a gain (at f = oo) of 3. The circuit configuration of the filter is given in Figure 3-5. The component values for the normalized filter are obtained from Table 3-5 . RI
c.
= 0.61099 = 1.00000
R2
= 7.44475
C 2 = 1.00000
C3 = 0.33333
To obtain the cutoff frequency of f 1 = 5 kHz, we divide all the capacitors by wL = 2,rfL = 2,rS,000. This gives
TABLE 3-4 C in farads)
Component Values for the Low-Pass Filter of Figure 3-4 for
wH
= l (R in ohms;
Filter class
DC gain
RI
R2
R:i
Cl
C2
Maximally flat (Butterworth) 3.01 dB at wH
I 3 5
1.00000 1.00000 1.00000
1.00000 l .00000 1.00000
1.00000 3.00000 5.00000
2.12133 1.64991 1.55563
0.47140 0.20203 0 . 12857
Equal ripple (Chebyshev) 0.5-dB ripple
1 3 5
1.00000 1.00000 l .00000
1.00000 1.00000 1.00000
0.65954 1.97863 3.29771
2.46644 1.75741 1.61560
0.40544 0.18967 0.12379
Equal ripple (Chebyshev) I-dB ripple
I 3 5
I .00000 1.00000 l .00000
1.00000 1.00000 1.00000
0 .90702 2.72106 4 .53508
2.82628 2. 15672 2.02280
0.35382 0.15456 0.09887
Chap. 3
Designing Second-Order Filters
R2
C3 C1
17
C2
)
0
v,
R, V2
Figure 3-5
Second-order high-pass high-gain amplifier filter.
c 1 = c2 =
1.0000012'ITs ,ooo = 31.83099 µF C 3 = 0 .33333 /27r5 ,000 = 10.61022 µF
Finally, to obtain a set of reasonable values, we multiply the resistor values by a factor of 104 and divide the capacitor values by the same factor. The component values of the filter then are R 1 = 6. 1099 kn R 2 = 74 .44 7s kn c 1 = c 2 = 3183.099 µF C 3 = 1061.022 pF In practice we use the closest commercially available components and add trimmer pots if precise values are needed. Usually, such a degree of precision for filters is not required.
TABLE 3-5 C in farads )
Component Values for the High-Pass Filter of Figure 3-5 for wL = I (R in ohms;
Gain at f=
Ri
R2
c,
C2
C:i
Maximum float (Butterworth) 3.01 dB at wL
I 3 5
0.47140 0.60609 0.64282
2.12132 4.94976 7.77817
l .00000 l .00000 1.00000
l .00000 1.00000 1.00000
1.00000 0.33333 0.20000
Equal ripple (Chebyshev) 0 .5-dB ripple
I 3 5
0.4752 l 0.61099 0.64801
3. 19061 7.44475 11 .69889
1.00000 1.00000 1.00000
1.00000 1.00000 1.00000
l .00000 0.33333 0.20000
Equal ripple (Chebyshev) I-dB ripple
I 3 5
0.36591 0.47045 0.49897
3.01308 7.03051 11 .04795
1.00000 1.00000 1.00000
1.00000 1.00000 1.00000
1.00000 0.33333 0.20000
Filter class
'.X)
How to Design Active Filters
18
Figure 3-6
Part I
Second-order band-pass, high-gain amplifier filter.
3.3.3 Band-Pass Filters The circuit diagram of a second-order band-pass, high-gain amplifier filter is shown in Figure 3-6. Several sets of component values for different Q-factors and resonant frequency gains are given in Table 3-6. The Q-factor defines the sharpness of the filter. It specifies the ratio of the resonant frequency to the bandwidth (i.e., the frequency band between the low and high 3-dB points). The higher the Q-factor, the wider the spread of the resistor values, making high Q-factors for this design configuration impractical. The component values in Table 3-6 are for normalized filters. In filter design , these values are changed to obtain the desired resonance frequency and reasonable resistor and capacitor values by going through steps similar to those taken in the example for high-pass filters in the previous paragraph, or in the example for band-pass filters using low-gain amplifiers given earlier in this chapter.
TABLE 3-6
Q
2
5
Component Values' for the Band-Pass Filter of Figure 3-6 for w = l 0
Gain at resonance
R1
R2
1 2 4 6
2.00000 l .00000 0.50000 0.33333
0.2857 l 0.33333 0.50000 1.00000
l
5.00000 2.50000 1.25000 0.83333 8.00000 4 .00000 2.00000 1.33333
2 4 6
l
8
2 4 6
R3
Cl
C2
4.00000 4.00000 4.00000 4.00000
1.00000 l .00000 l .00000 1.00000
l .00000 l .00000 l .00000 l .00000
0 . 10204 0 . 10417 0. 10870 0.11364
10.00000 10.00000 10.00000 10.00000
l .00000
l .00000 l .00000
0.12698 0.12903 0 . 13333 0 . 12766
16.00000 16 .00000 16.00000 16.00000
1.00000 1.00000 1.00000 l .00000
l .00000 1.00000 1.00000
1.00000 1.00000 l .00000
l .00000 1.00000 1.00000
Chap. 3
Designing Second-Order Filters
19
3.4 CHOICE BETWEEN HIGH-GAIN AND LOW-GAIN AMPLIFIER FILTERS Low-gain and high-gain amplifier filters can be designed to give similar frequencyresponse characteristics. The choice is dictated by other considerations. High-gain amplifier filters require fewer components , and the desired gain is obtained by the choice of component values. On the other hand , low-gain amplifier filters allow for a large number of identical component values for a given filter , resulting in less room for error and lower production costs in large quantity runs.
4 Designing Third-Order .F_ilters
4. 1 INTRODUCTION
Third-order filters are perhaps the most widely used filters. Like first- and second-order filters, they require only a single operational amplifier, yet in the stop band they provide a steep slope of -60 dB/dee. The tables in this chapter give filter component values. Equations given make it possible to compute the exact attenuation in the stop band. 4.2 LOW-PASS FILTERS
The circuit diagram of a low-pass third-order filter is shown in Figure 4-1. Component values to achieve particular characteristics are listed in Table 4-1. The maximally flat
v,
Figure 4-1 Third-order low-pass filter. (Reprinted from Electronics, November 11, 1976. Copyright © McGraw-Hill, Inc., 1976.) 20
Chap.4
Designing Third-Order Filters
TABLE 4-1 C in farads)
21
Component Values for the Filter of Figure 4- 1 for wH
=
I rad/s (R in ohms;
Filter class
R,
R2
R:1
c,
C2
C:1
Maximally flat (Butterworth) 3.01 dB at w 2
1.00000
1.00000
1.00000
0 .20245
3.5465
1.3926
1.00000 1.00000 1.00000 1.00000 1.00000
1.00000 1.00000 1.00000 1.00000 1.00000
1.00000 1.00000 1.00000 1.00000 1.00000
0.07130 0.07736 0.09691 0.08582 0 .05872
2.503 1 3.3 128 4.7921 7.4077 14.784
0.8404 1.0325 1.3145 1.6827 2.3444
Equal ripple (Chebyshev) Ripple (dB) 0 .001 0.03 0 . 10 0.30 1.00
Reprinted from Electronics, November 11 , 1976; Copyright © McGraw-Hill, Inc ., 1976
filter frequency response curve has an asymptotic slope in the stop band of -60 dB/dee (-18 dB /oct) . The exact attenuation at any frequency w is given by (4-1)
The exact attenuation for the equal-ripple filters in the stop band is given by (4-2)
where e 2 is the ripple factor. Values of the ripple factor for the ripple values in Table 4-1 are given in Table 4-2.
TABLE 4-2
Ripple Factors for Equal-Ripple Filters
Ripple (dB)
Ripple factor (E. 2 )
0.01 0 .03 0.1 0 .3 1.0
0.00230524 0 .00693167 0.023293 0.0715193 0 .255925
Reprinted from Electronics , November 11, 1976; Copyright © McGraw-Hill, Inc. , 1976
How to Design Active Filters
22
Part I
Example
Design a low-pass equal-ripple .filter with a ripple of 0. l dB and a cutoff frequency of 5 kHz. The filter configuration is shown in Figure 4-1. The component values for the normalized filter are obtained from Table 4-1.
R, = R2 = R3 = 1 n; C 3 = l.3145 F
c 1 = 0.09691
F;
c 2 = 4.7921
F;
To have a cutoff frequency of wH = 271'5 x 103 = 31.416 x 103 rad/s, we divide all the capacitors by 31.416 x 10 3 giving
C,
=
3.085 µF; C 2
=
152.537 µF; C 3
=
41.842 µF
Finally, to obtain practical component values, we multiply all the resistor values by 104 and divide all the capacitor values by the same factor, giving RI C1
= =
R 2 = R 3 = IO kO 308.5 pF; C 2 = 0.0153 µF; C 3
=
0.0048 µF
The frequency response of the filter can be obtained with the aid of Equation 4-2. This equation is for the normalized filter. To use it for the denormalized filter, w must be replaced with f!JH, where JH is the passband cutoff frequency.
r]"
V2 -_ - ; : : : - - - - - - - - - - , - - I- - - - - = - - - - - - - - - - 2
-
v,
[ I + 0_.023293 ( 4
l. 2 S ~ IO" -3 S
!
103
where we replaced E 2 with 0.023293 as given in Table 4-2 for 0.1-dB ripple. For an illustration, we -~ompute the attenuation at 5,000 Hz and at 7 ,000 Hz. At a frequency of 5,000 Hz: V
_
1
-2 - - - - - - - - - - Vi [ 1 + 0.023293 (4 - 3)2] 112
1 (l.023293)112 __:_ 0.98855
In decibels, 20 log 10 0.9886 = -0.1000 dB That is, at 5 kHz the gain is down by O. 1 dB from the DC gain. At a frequency of 7,000 Hz:
V2 _ V, -
l [ 1
+ 0.023293 ( 4
X
3.43 l. 25
X X
10" -3 10 11
X
7 5
In decibels, 20 log 10 0.6951
-3.159 dB
X X
103 )2] 112 = 0.6951 1Q3
Chap. 4
Designing Third-Order Filters
23
Thus, at 7 kHz the gain is down by 3.159 dB from the DC gain . Additional points can be computed to plot the complete frequency-response curve of the filter.
4.3 HIGH-PASS FILTERS
The circuit configuration for a high-pass filter is shown in Figure 4-2. The component values for the normalized filter are given in Table 4-3. If the cutoff frequency must be wL
C.1 ,....._--.--4 ,__......,_-4 ...- .......---4
o--,
Figure 4-2 Third-order high-pass filter. (Reprinted from Electronics, November 11, 1976. Copyright© McGraw-Hill, Inc., 1976.)
= 2TIJL rather than w = 1, all the capacitors must be divided by wv just as was done in the example for the low-pass filter. Finally, to obtain practical component values, all the resistors are multiplied by a given factor and all the capacitors are divided by the same factor. This was also demonstrated for the low-pass filter. TABLE 4-3 C in farads) Filter class Maximally flat (Butterworth) 3.01 dB at w 1 Equal ripple (Chebyshev) Ripple (dB) 0.01 0 .03 0.10 0.30 1.00
Component Values for the Filter of Figure 4-2 for wL
= 1 rad/s
(R in ohms;
R2
R3
Cl
C2
C3
4.93949
0.28194
0.71808
1.00000
1.00000
1.00000
10.9130 10.09736 10.3188 11.65230 17 .0299
0.39450 0.30186 0.20868 0.13499 0.06764
I. 18991 0.96852 0.76075 0.59428 0.42655
1.00000 1.00000 1.00000 1.00000 1.00000
1.00000 1.00000 1.00000 1.00000 1.00000
1.00000 1.00000 1.00000 1.00000 1.00000
RI
Reprinted from Electronics, November I I, I 976; Copyright © McGraw-Hill, Inc. , 1976
24
How to Design Active Filters
Part I
The frequency responses for the normalized low-pass maximally flat and equalripple filters are given respectively by Equations 4-1 and 4-2. For the normalized highpass filters, w in these equations must be replaced with l /w. For the denormalization, high-pass filters w in Equations 4-1 and 4-2 must be replaced with JL!f, where JL is the cutoff frequency.
4.4 BAND-PASS FILTERS
Band-pass filters are realized by cascading low-pass and high-pass filters. To prevent interaction between the filters, one connects a voltage follower between the two stages.
5 Designing Fourth-Order Filters
5.1 INTRODUCTION
Fourth-order filters consist of cascaded second-order filters. Since there is interaction between the two stages , the total filter must be designed as a single entity rather than as a cascade connection of two separate entities. The component values for the two sections are not the same , and the order in which the sections are connected is important. The tables in this chapter provide all the required information; the worked-out numerical examples illustrate the use of the tables.
5.2 LOW-PASS FILTERS The circuit diagram of a fourth-order low-pass filter is shown in Figure 5-1 . The values of the components are determined with the aid of Table 5-1. The table lists component values for a maximally flat response and for an equal 3-dB ripple response. Many different combinations of components yield the right characteristics. In Table 5-1 we list two possible combinations of components for each stage of each class. Either set of components of the first stage can be combined with either set of the second stage of the same class. Components for the first set of each stage are selected so that either both resistors or both capacitors and as many other components as possible are equal to unity . Components for the second set are chosen so that the gain of the amplifier is equal to an integer. This makes it possible to use two resistors of the same value for the amplifier. In particular, a gain of 2 results in resistance values (of Ra 1 and Rb 1 for the first stage and Ra 2 and Rh 2 for the second stage) of unity, since the gain is given by unity plus the ratio of the resistances. 25
LE
Chap. 5
Designing Fourth-Order Filters
27
A filter with these components has an upper cutoff frequency wH = I rad/s. To shift the cutoff frequency to the specified 800-Hz value, we divide all the capacitor values by 21r800 . This yields
I C, = C2 = 21rgoo = 0.000199 F Finally , to obtain reasonable resistor and capacitor values, we multiply all resistor value by I 04 and divide all capacitor values by I 0 4 : RI = R2 = Ral = 10 kn; Rhl = 1.522 kn
C, = C2 = 0.0199 µF Commercially available values are: RI = R2 = Ra, = 10 kn; Rbl = 1.5 kn c 1 = c 2 = 0 .022 µF
The design of the second stage is similar to that of the first stage. From Table 5-1 select R3 = R4
= I n; C 3 = C4 = 1 F; K = 2.2346
choosing Ra2 = 1 n gives Rb2 = 1.2346 n. Divide the capacitor values by 21r800: C3
=
C 4 = 0.000199 F
Multiply all resistors by 104 and divide all capacitors by 104 : R3
=
R4 = Ra 2
C3
=
C4
=
= 10 kn;
Rb 2 = 12.346 kn
0.0199 µF
Commercially available values are: R3 C3
= R4 = Ra 2 = 10 kn; = C 4 = 0.022 µF
Rb 2 = 12 kn
The commercially available components are not all equal in value to the computed value. Furthermore, components have tolerances (e.g., resistors +5%; capacitors +20%). This results in a cutoff frequency different from the specified value. If the specification is critical, the filter must be trimmed using resistor and/ or capacitor trimmers.
5.3 HIGH-PASS FILTERS The circuit diagram of a fourth-order high-pass filter is shown in Figure 5-2. The values of the components are determined with the aid of Table 5-2. The table lists component values for a maximally flat response and for an equal 3-dB ripple response. Many different combinations of components yield the right characteristics. In Table 5-2 two possible
Part I
How to Design Active Filters
28
R1 Ci ~
,---:7 K1
I
C1 R2 V1
+
I I
c4
I
I
I
I
R,
I
C.1
I
I
R~
I
Rh i
,----Kl
I
I I
_ _ _ _J
Figure 5-2
I
+
I I _ _ _ _J
\,' :
Fourth-order high-pass filter.
combinations of components are listed for each stage of each class. Either set of components of the first stage can be combined with either set of the second stage of the same class. Components for the first set of each stage are selected so that either both resistors or both capacitors and as many other components as possible are equal to unity. Components for the second set are chosen so that the gain of the amplifier is equal to an integer. This makes it possible to use two resistors of the same value for the amplifier . In particular, a gain of 2 results in resistance values (of Ra 1 and Rb 1 for the first stage and R a2 and R b2 for the second stage) of unity , since the gain is given by unity plus the ratio of the resistances . TABLE 5-2
Component Value~ for the Filter of Figure 5-2 for
Filter class
wL
= I (R in ohms; C in farads)
R1
R2
Cl
C2
Kl
R3
R4
C3
C4
Ki
1.0000 1.0000
1.0000 0.5412
1.0000 1.0000
1.0000 1.8478
I ._I 522 2.0000
1.0000 1.0000
1.0000 1.3065
1.0000 1.0000
1.0000 0 .7654
2.2346 2.0000
1.0000 1.0000
1.0000 0 . 1613
1.0000 1.0000
0 . 1960 1. 2 152
0 .9808 2.0000
1.0000 1.0000
1.0000 0 .2960
1.0000 1.0000
0.9031 0 .2673
2.6358 2.0000
Stage 2
Maximally flat Stage 2
(Butterworth) Equal ripple (Chebyshev) Stage Ripple: 3 dB
2
Example
Design a fourth-order equal-ripple (3-dB) filter with a cutoff frequency of 2 kHz. The circuit diagram is shown in Figure 5-2. From Table 5-2 we choose for the first stage
Chap. 5
Designing Fourth-Order Filters
n,
29
o.
n
R 1 = 1. 0000 R2 = 1613 C 1 = 1. 0000 F, C2 = 1. 2152 F Kl = 2 .0000 For the second stage we choose
R3 = 1.0000 n, R 4 = 0.2960 n C 3 = 1.0000 F, C4 = 0.2673 F K 2 = 2.0000 ResistorsR 01,Rb1 , R02 , Rb 2 arecomputedfrom I+ Rb 1 /Ra 1 = K 1 = 2and 1 + Rb2!R a2 = K 2 = 2. A good choice is R a l = Rbl = Ra2 = Rb2 = l n. This gives a large number of resistors with an identical value. Divide the capacitors by 211' X 2,000. This gives C 1 = C 3 = 0.0000796 F C 2 = 0.0000967 F C 4 = 0.0000213 F Multiply resistor values by 105 and divide capacitor values by 105 .
R1 = R3 = Ral = Rbl = Ra2 = Rb2 = 100 R2 = 16.13 kn R4 = 29.60 kn
kn
C 1 = C 3 = 796 pF, C 2 = 967 pF, C4 = 213 pF The designer now chooses appropriate commercially available components and trims the circuit if necessary.
5.4 BAND-PASS FILTERS Band-pass filters are realized by cascading low-pass and high-pass filters. Interaction between the filters is prevented by interfacing them with a voltage follower.
6 Designing Higher-Order Filters
6.1 INTRODUCTION Higher-order filters provide very steep rolloff in the stop band. It would be too cumbersome and lengthy to provide tables for all the components of the many possible filters . Instead, we shall provide one table with expressions from which all the component values can be computed. Higher-order filters are designed by cascading lower-order filter configurations with component values obtained from the table in this section. The lower-order filters forming the links of the higher-order filters will not be identical. An even-order filter consists of cascaded second-order filters such as shown in Figure 3-1 for low-pass filters or in Figure 3-2 for high-pass filters. An odd-order filter consists of second-order filters as above and a first-order filter as shown in Figure 2-1 for low-pass filters or in Figure 2-2 for high-pass filters. The first-order filter can be replaced with a simple passive RC network as shown in Figures 6-1 and 6-2. The maximum gain of these filters in the passband is unity, whereas the gain of the active filters of Figures 2-1 and 2-2 is given by the ratio of the R 0
1\/V\,
IC
v,
I
0
WH
Figure 6-1
30
=
0
V2 0
1 RC
Passive first-order low-pass filter.
Chap. 6
Designing Higher-Order Filters
31
C
0--1--------(} R
WL
Figure 6-2
=
1 RC
Pass ive first-order hi gh-pass filter.
feedback resistor to the input resistor (R 2 / R 1). When the passive filters of Figures 6-1 and 6-2 are used , they must constitute the last stage of the filter to avoid loading problems. This assumes that the filter looks·into a high-impedance circuit or device. If this is not the case , the filter 1nust be followed with a voltage follower for buffering. If a buffer is used , then of course the stage can be used anywhere in the chain of the cascaded filter, and it would be just as appropriate to use an active first-order filter in the first place. A property of active filters is their low-output impedance because of the low-output impedance of opamps, which makes loading by the next stage negligible.
6.2 LOW-PASS FILTERS The expressions for the second-order filter links in Table 6-1 have the form
The constants a I and a0 are used to design the several stages of the normalized filter. This is followed by two steps that we have introduced earlier, namely, dividing the capacitor values by the desired cutoff frequency wH and then multiplying the resistor values, and dividing the capacitor values by a chosen constant to obtain a set of reasonable component values. For the normalized filter (see symbols in Figure 3-1)
l R 1C 1
+
1 R2 C 1
+
l - K = a, R2C2
(6-1)
= ao
(6-2)
and
1 R 1R 2 C 1C 2
We have two equations with five unknowns: R 1 , R 2 , C 1 , C 2 , and K. Therefore, we can choose arbitrarily any three values and solve for the remaining two. For example, we can choose R 1 = R 2 = C 1 = 1 (ohms and farads). From the second equation above, we then have C 2 = l/a 0 . We substitute this value for C 2 in the first equation above and solve for the remaining unknown K. Or, we can choose K = 2, R 1 = R 2 = 1. This results in Ra = Rb (Figure 3-1), which will give good temperature tracking. Using the two equations
w
N
TABLE 6-1
Filter class
Expressions for Higher-Order Filters (Normalized filters) 2nd Stage
I st Stage
Filter order
3rd Stage
5
x 2 + l.6180x + I
x 2 + l.6180x + I
x+I
6
x 2 + I. 93 I 8x + I
x 2 + l.4142x+ I
x 2 +0.5176x+ I
7
x2
8
4th Stage
5th Stage
,
Equal ripple (Chebyshev) 3-dB ripple
Maximally flat (Butterworth)
+ I .2470x + I
x 2 + 0.4450.r + I
x+l
x 2 + I .96 I 6x + I
x 2 + l.6630x + I
x 2 + l . 1 l 12x + 1
x 2 + 0 .3902x + l
9
x 2 + l.8794x + I
x 2 + l.5320x + I
x 2 + 1.0000x+ I
x 2 + 0.3474x + 1
x+I
IO
x 2 + l .9740x + 1
x 2 + l.7820x + l
x 2 + l.4142x + I
x 2 + 0.9080x + l
x 2 + 0.3l28x + I
5
x 2 + 0.2872x + 0.3770
x 2 + 0. 1096x + 0 .9360
x+0.17 75
6
x 2 + 0 .2854x + 0.0888
x 2 + 0.2090x + 0.5219
x 2 + 0.0764x + 0.9548
7
x 2 + 0.2288x + 0 .2042
x 2 + 0.1575x + 0.6273
x 2 + 0.0564x + 0. 9685
X
8
x 2 + 0.2 I 70x + 0.6503
x 2 + 0.1340.r + 0.3269
x 2 + 0.1230x + 0. 7035
x 2 + 0.0432x + 0.9742
9
x 2 + 0.1848x + 0. 1267
x 2 + 0 . 1506x + 0.4224
x 2 + 0.0982x + 0 .7547
x 2 + 0 .2342x + 0.4796
X
IO
x 2 + 0.1746x + 0.0323
x 2 + 0. I 576x + 0 .2 140
x 2 + O. I 250x + 0.5079
x 2 + 0.8825x + 0.8018
x2
+ l.8020x + I
x2
+ 0.1265
+ 0.983 + 0 .0276x + 0. 9833
Chap. 6
Designing Higher-Order Filters
33
above, we olve for C 1 and C 2 • Clearly, many combinations of component values are po ible. For the fir t-order fi lter link in Table 6-1 we have the form
For the circuit configuration of Figure 6-1 we have
l
-RC = ao
(6-3)
We then choo e either R or C and compute the value of the remaining component from thi equation. If we u e the fi lter configuration of Figure 2-1, then R and C represent R 2 and C 2 in Figure 2-1, re pectively. The value of R I in Figure 2-1 is chosen arbitrarily. It doe not affect the freque ncy re ponse of the filter and provides a DC gain R 2 ! R I for the tage . Example
Design a ixth-order maximally flat low-pass filter with a high-frequency cutoff f H = 4 kHz . We note in Table 6-1 that for the maximally flat filter the coefficients a0 of all the stages are equal to unity. Choosing for all stages R 1 = R 2 = C 1 = 1, we have from Equation 6-2 , C 2 = 1, and from Equation 6-1,
3-K=a I K=3-a I or, for the first stage,
a1
1.9318
g1vmg K
= 3 - 1.9318 = 1.0682
or
or
Rb/Ra
=
1.0682 - 1
=
0 .0682
Letting Ra = 1, we have Rh = 0.0682. By a similar procedure, for the second stage, K = 3 -1.4142 = 1.5858
Ra
=
1
Rh
=
0.5858
How to Design Active Filters
34
Part I
and for the third stage, 3 - 0.5176 = 2.4824 Ra = l Rh = 1.4824 K
=
Summary for the normalized filter: 1. All Rs = I 0, except R1:, = 0.0682, 0 .5858 , and 1.4824, for the first, second , and third stages, respectively. 2. All Cs = 1 F.
To get the desired cutoff frequency JH = 4 kHz , we divide all Cs by 271'4 ,000, giving
C = 1/271'4000 = 39. 7887 µF Finally, to get reasonable values for the resistors and capacitors, we multiply all the resistors by I 04 and divide all the capacitors by 104 . This gives all R I s, R 2 s, and Ras = 10 k11 Rh = 682, 5,858, 14,824 11 for the first, second, and third stages, respectively. all Cs = 3979 pf The complete filter is shown in Figure 6-3. Again, as in the previous cases, commercially available components must be used and capacitor or resistor trimmers added if necessary.
6.3 HIGH-PASS FILTERS The design of high-pass filters also makes use of Table 6-1. But before the a values (or the several stages can be obtained, certain computations with these expressions must be made. Specifically, the x in the expressions is replaced with 1l y. Thus,
become
I a1 -+-+ao y2 y
I
-y +
ao
We multiply the first expression by y 2 and the second by y: aoy2
+
a1 y
+
1
Next, we divide the expressions by a 0 : y2
+ a_, y + I ao
ao
y
1 ao
+-
3979 pF 1o kn
V1
I
3979 pF
3979 pF
1o kn
3979 pF
3979 pF 682
n
3979 pF 5.858 kn
14.824 kn V2
10 kn
10 kn
Figure 6-3
w u,
Sixth-order low-pass filter.
10 kn
How to Design Active Filters
36
Finally letting
~ = h 1 and ao
Part I
1 - = h0 , we have ao y + ho
For a second-order link, the relation between the component value and h 1 and h 0 is given by (see Figure 5-2) (6-4) and (6-5) For the first-order link (Figure 6-2), the relation is 1 RC= ho
(6-6)
If the active filter of Figure 2-2 is used instead of the passive filter of Figure 6-2 the Rand C are replaced with R I and C 1 , respectively. Resistor R 2 can assume any alue. The gain at f = 00 of this link is given by the ratio R 2 / R 1 • Note that for the maximally flat (Butterworth) frequency re pon e in Table 6-1 a0 = 1. Consequently, h 1 = a 1 and h0 = a0 . For equal-ripple (Chebyshev) response, the relationship is
Example
Design a fifth-order equal-ripple (3-dB ripple) high-pass filter ith a low-frequency cutoff at JL = I kHz. From Table 6-1 we have for the first stage a 1 = 0.2872 and a 0 -:0.3770. Hence, l = 2.6525 ao
h0 = -
Let R 1 = C, = C2 = l. From Equation 6-5 ,
R2
=
l
b
=
0.3770
0
Substituting into Equation 6-4 and solving for K K = (I
But
+
l - 0.7618)0.3770
+
1
1.4668
Chap. 6
Designing Higher-Order Filters
37
Let Ra = l , then Rh = 0.4668. Summary for first stage
R 1 = Ra = l
n; R 2
= 0.3770
n; Rb
= 0.4668
n; C 1 ~
C2 = l F
For the second stage, from Table 6-1 , a 1 = 0. 1096 and a0 = 0. 9360 giving b 1 = 0 . 1171 and b0 = 1.0684. Following the same procedure used for the first stage, we have: Summary for second stage RI
= Ra = I n; R2 = 0.9360 n; Rb = 1.7624 n; c, =
The third stage is a first-order filter. From Table 6-1, a0
C2
= lF
= 0.1775 , from
which b0
1 ao
= - = 5.6338
From equation 6-6 , RC = 5.6338. Let C = 1 F. Then R = 5.6338 n. To provide the cutoff frequency of JL = 1000 Hz, all the capacitor values are divided by 21'1'1000 giving for all Cs the value 159.1549 µF. Finally , to have reasonable component values, we multiply all the resistors by 105 and divide all the capacitors by 105 . The component values are then as follows: First stage: R 1 = Ra = 100 kn; R2 = 37.70 kn; Rb = 46.68 kn c 1 = c 2 = 1,591.55 pF.
Second stage: R 1 = Ra = 100 kn; R 2 = 93.60 kO; Rb = 176.24 kn
C 1 = C 2 = 1,591.55 pF. Third stage: R
= 563.38 kn;
C = 1,591.55 pF
Examining these values, we find that the third stage will have better values if we divide the resistor values by 100 and multiply the capacitor values by the same factor. This gives Third stage: R
= 5.63
kn;
C = 0.1592 µF
How to Design Active Filters
38
Part I
The circuit diagram of the filter is shown in Figure 6-4. As in all previous cases , in practice , commercially available resistor and capacitor values must be used and trimmers added if needed.
93 .6 0 kn
37. 70 kn
~
-----1 -------
1592 pF 1592 pF
1592 pF 1592 pF
100 kn
100 kn
46.68 kn
176.24 kn
100 kn
100 kn
Figure 6-4
5.6 2 kn
Fifth-order high-pass filter.
6.4 BAND-PASS FILTERS Low-Q high-order band-pass filters can be obtained by cascading low-pass filters with high-pass filters. Usually band-pass filters are designed to obtain high selectivity, which requires high-Q filters. Such ·,filters are discussed in the next section.
6.5 HIGH-Q BAND-PASS FILTERS The Q of a band-pass filter is defined as the ratio of the center frequency to the bandwidth (i.e., the frequency range between the 3-dB points). A high-Q represents therefore a "sharp" or highly selective filter. The band-pass filters discussed in previous sections are low-Q, or broadband, filters (Q of the order of 10). The circuit diagram shown in Figure 6-5 is a high-Q filter (Qs up to several hundreds). It is known as a state-variable filter. A design procedure can be formulated by letting , for the normalized filter,
R I =R 2 =R 3 =R 5 =R 6 =ID and C=C=lF I 2
Chap. 6
Designing Higher-Order Filters
39
The remaining resistor, R 4 , is then computed from R4
2
= -1--1- -1 Q
Ai
A2
w~ere. A I and A2 are the open-loop gains of the amplifiers as shown in Figure 6-5. For gains m the hundreds of thousands , and Qs in the hundreds, we have
+ o---+---1
+
-
+
\ ':
\ '1 f'
-1--
1-
Figure 6-5
+ \'11p
-1-
State variable filter.
The open-loop gain A 3 must be high, but does not enter the calculation. The gain at resonance (w 0 = I rad/ s for the normalized filter) is R 4 !R 1 • Since R I is I fl, the gain is numerically equal to R 4 . We shall illustrate the use of these equations and show how to design for a desired resonance filter with practical component values in a design example. Example
Design a high-Q band-pass filter with a center, or resonance, frequency at 5 kHz and a Q of 250. We select amplifiers with gains of 10,000, resistors (except R 4 ) of 1 fl, and capacitors of I F. The normalized filter is obtained by setting
How to Design Active Filters
40
R4
2
= -------- =
I
I
1
250
10,000
10,000
Part I
526.314 D
To shift the center frequency to fo = 5,000 Hz we divide the capacitors by w0
= 2TI5,000: C1 = C2 =
1
7T , = 63.662 µF 2 5 000
Finally, to obtain practical values for all the components, we multiply all the resistors by 10 3 and divide all the capacitors by 10 3 . The resistor and capacitor values become:
R I = R2 = R 3 = R 5 = R6 R4 = 526.316 k!l C 1 = C2 = 0 .06366 µF
=
1 k!l
The designer now specifies commercially available components and incorporates capacitor and/ or resistor trimmers if necessary .
Note: The state-variable amplifier can also be used as a low-pass filter and as a high-pass filter if the proper output terminals are used as shown in Figure 6-5. This is an expensive version compared to other low-pass and high-pass filters, but has the advantage of low Qsensitivity to circuit parameter variations. The DC gain and cutoff frequencies for the lowpass filter are
and
J; H -
1 (
27T
R6 R,R2R5C1C2
) I /2
The high-frequency gain and cutoff frequency for the high-pass filter are
. I G am= 1
+ R6 /R 5 + R 3 /R 4
and
J; _ L -
I (
R4
) 112
27T R 1R2R5 C 1C 2
These expressions simplify for the case R 1 = R 2 = R 3 = R 5 = R 6 and C 1 = C 2 , which we used for the band-pass filter .
7 f
Effect mponent Characteristics on Filter Performance and How to A void Pitfalls
1-1 .f ··RODUCT. 0 ideal operational amplifier dra no bias current into the two input terminals, and it ha infi 'te gain ti all freqllencies. A real operational amplifier does draw bias current, it ha nite gain and the gain decreases ith increasing frequency. In very demanding igns · propert' es of real amplifier · mus be incorporated into the filter design, as eal properties of pa si e components.
72 B
CURRE · o ensm that there is no output o fset oltage r ulting from bias currents, it is neces ary to haY the current into the in erting and n nin erting terminals flow through the same effecti e esi tance al~ so that the an1e oltage drops exist at both terminals . A DC ana i1 nuts be perfonned to trace the JY.rths of the bias currents. k, an example, we ~nine Figu e 3- l. The figure is reproduced ith the addition of the bias compen ation esistor 3 in 1gure 7-1. Remembering that C signal sources offer negligible impedance to DC currents and that the output impedance of operational amplifiers is negligibl small, e can assume , for a DC anal u;? that terminals A and C are grounded. The resi ·tance R , seen from the -~~,...""''e rting tenn· nal of the operational amplifier to ground is the series combination of 1 and~? or ?
R
= R J - R2 41
How to Design Active Filters
42
Part I
Bn------------4~--.________-vD Figure 7-1
Bias current compensation for the filter of Figure 3-1 .
The resistance R _ seen from the inverting terminal of the operational amplifier is equal to R 3 in series with the parallel combination of R 0 and Rb. That is ,
or
In order for the resistances seen from the noninverting and inverting terminals of the operational amplifier to be equal, we set R + = R _ , or
from which we solve for R 3 ,
Now, resistors R 0 and Rh are selected to give the desired amplifier gain K, which together with the selection of R I and R 2 result in the desired filter characteristics as was explained with the help of tables and formulas in Chapter 3, and for similar configurations in other chapters of the book. To minimize the bias current effect on filter performance, a resistor R 3 computed from the equation given above is inserted in the circuit as shown in Figure 7-1.
Chap. 7
Filter Performance and How to Avoid Pitfalls
43
7 ,3 AMPUFJER GAIN Repre entative amplifier gain ver u frequency curve are shown in Figure 7-2. Thi s figure how curve for an internally compen ated amplifier as wel l as for an unco mpenated amplifier and for an externally compen ated amplifier. 120
Internally compensated
-20 dB/dee
x ternall y
compensated 100
-
0
-
60
co
-;:, ....,, ,...
C
-40 dB/dee -20 dB/ dee
B
0
Uncompensated o pen loop
-40 dB/dee - - - ~ -20 dB/ dee
'
40
- 60 dB/dee
A
0
~
-40 dB/ dee
1-+----- ----------------...,,_______________..___..__ IO
100
10 k
I k
100 k
IM
10 M
Frequency F (Hz)
Ftgnre 7-2 Amplifier compensation-uncompensated, externally compensated, and internally compensated gain-frequency response curve.
The flat portion of the gain-frequency response curve should extend at least to the frequency in the passband of the filter. In Chapter 3 we discussed low-gain amplifier filter and high-gain amplifier filters. From Figure 7-2 we conclude that an internally compensated amplifier is not, in general, usable in high-gain amplifier filters, since its break point (i.e .~ the 3-dB point is at less than 10 Hz. But the amplifier is usable in lowgain amplifier filter . When an amplifier is used with negative feedback , as shown in Figure 7-3 , then the closed-loop gain of the amplifier i.e., the gain with the feedback resistors as sho n is given in terms of the ratio of the resistor values as Gain= I
+
Rh
Ra
or in decibels Gain (dB )
= 20
log 10
An amplifier is stable if its closed-loop frequency response (as given by lines A , B, and C for three different gains intersects the open-loop gain response curve at a point here the 1 ~ has a slope of - 20 dB / dee. Accordingly, for a gain of 10 , with Rh= 90
How to Design Active Filters
44
Figure 7-3
Part I
S tting amplifi r am .
kfl and Ra = l 0 kfl, for exan1pl , or in d cibel , for Gain dB = ... l 1 l 0 = _0 dB, the amplifier is stable and the re pon e curv i flat up t appr imat 1 -0 kHz. Th amplifier can be used in this configuration for filt rs up t ab ut 10 kHz .
7.4 AMPLIFIER COMPENSATION
For higher-frequency filter , amplifier that are not int mall mpen at d n1u t b u d . Referring to Figure 7-2, we see that the uncomp n at d amplifi r i t bl , ith ~run corresponding to line C. This line (when extended) inter t th pen-I p frequ n response curve where the latter has a slope of -20 dB. The amplifi r an b u d in th IMHz frequency range. For a gain corresponding to lin B th amplifi r uld b un tabl . since the line intersects the open-loop frequen r pon ur h slope of -40 dB/dee. To use the amplifier with thi gain it mu t adding resistors and / or capacitors external! to modif th frequ n re p n n in the figure. The steps that must be taken to compen at an amplifi rare u uall ,...i , n b the manufacturer. With this external ompen ation line B int t th pen-1 p frequency response curve where the latter has a lope of - 0 dB /d . In filters that use voltage followers (e.g. , Figure -1) a mp n ti rk n be incorporated, as shown in Figure 7-4. A th oltag frequ n in r a . f th current fed back from the output through R 0 flo s through , and I · th an1plifi r, thus decreasing the negative feedback and maintaining higher gain. Th n1p n nt alu are obtained from the relation
I
R()C()
= 2.6 x 2TI/,.,
where fa is the 0-dB frequency of the amplifier. The Q of the high-Q band-pass filter of Chapter 7 i limited b frequency response. To have a filter essentially independent of the b a the amplifiers, the amplifier must be selected so that
Chap. 7
Filter Performance and How to Avoid Pitfalls
45
Q ~ Aofp/4fo
where JP i the 3-d the filter.
break frequency f the amplifier, and.f, i the resonance frequency of
Co
igor 7-4 frequency .
1 kn
1106 pF
requency c mpen ation to
hunt feedback current at high
7 r5 RESISTORS AND CAPACITORS
ominal resistor values have been chosen and tandardized by manufacturers to avoid w te in manufacturing. That i , any resi tor manufactured subject to process control lim·tation fall within the tolerance of a nominal value. Accordingly, resistors with + 20'½ tolerance are available with the followi ng nominal values: 10, 15, 22, 33, 47, 68, and l and in multiple of l O of these values; resistors with + 10% tolerance are available with the nominal value of IO, 12, 15 , 18, 22, 27, 33, 39, 47, 56, 68, 82, and 100 n and multiple of 10 of these values; and + 5% tolerance resistors are available with the nominal value of 10, 11, 12, 13, 15, 16, 18 , 20 , 22 , 24, 27, 30, 33 , 36, 39, 43, 47, 51, 62, 68, 75, 82, 91, and 100 n and multiples of 10 of these values. Tighter tolerance re i tor are often pecified in fractions of ohms, and manufacturers' or suppliers' catalogs hould be con ulted. The computed re · tance and capacitance values are usually not of standard commercial products. When the filter is built with standard available components , trimmers must be incorporated in the design . Remember also that capacitor tolerances are on the order of + 20% and resistor tolerances are commonly + 10% or + 5% which would nec.e itate trimmer anyway. Components are subject to drifts with temperature. The filter mu5t be te -ted over the required temperature range and adjusted or compensated as needed. etal-film resistors are available with long-term stability and with temperature coefficients as low .as 1 ppm/°C. This makes them particularly suitable if resistor values must remain nearly constant over a wide temperature range. Least expensive are carboncomposition resistors. They can be used when cutoff frequencies with changes in temperature need_not be tightly maintained. Wirewound resistors are not , in general, suitable for filter , becau e of their inductance. " oninductive" bifilar-wound resistors are relatively expensive. A large variety of capacitors is available. Ceramic capacitors and film capacitors are
How to Design Active Filters
46
Part I
suitable for low-voltage electronic filters. The .. temperature-stable" medium-K ceramic capacitors are a good compromise between temperature stability and dielectric constant value. Capacitors with zero-temperature coefficient of capacitance are available. These, however, have small dielectric constants and are limited in capacitance value to 5,000 pF. On the other hand, ceramic capacitors with higher dielectric constants are highly temperature- and frequency-dependent. Popular in filter design are film capacitors. Polystyrene is an excellent dielectric for low-voltage applications and operating temperatures below I 00°C. Polypropylene has similar characteristics in a somewhat smaller package. Polycarbonate and polyester (Mylar*) capacitors offer good performance over a wide temperature range . Teflon* can be used at temperatures up to 200°C. The best capacitor for a given application depends on the required stability temperature range, capacitance value, frequency, and other parameters. Detailed tables and curves describing the various commercial capacitor types can be obtained from manufacturers. Thick-film and thin-film resistor arrays and capacitors are available. They should be considered for products involving a large number of filters. Film components can be trimmed to order during the fabrication process and can result in savings.
7.6 MORE INFORMATION
Detailed information about operational amplifiers and passive components is given in Parts II and III of this design guide. How to select the right amplifier and passive components based on their real-world properties is discussed and illustrated by examples in Part IV of this book.
*DuPont registered trademark.
Part II
OPERATIONAL AMPLIFIERS
8 Understanding Operational Amplifier Characteristics
8.1 INTRODUCTION The central element of modem linear electronic circuits is the operational amplifier. We distinguish between voltage operational amplifiers and transconductance operational amplifiers. A voltage operational amplifier is a high-voltage-gain, high-input-impedance, low-output-impedance amplifier. The term operational is used for historical reasons, as this type of amplifier was first developed to perform mathematical operations in analog computers. A transconductance operational amplifier is a high-input-impedance, highoutput-impedance. amplifier characterized by its linear transconductance, that is, by an output current proportional to the input voltage. The voltage operational amplifier is by far the most commonly used amplifier. In this book the term operational amplifier will imply "voltage operational amplifier," unless qualified by the adjective transconductance. The operational amplifier underwent several stages in its development in rapid succession: vacuum tube amplifier, discrete transistor amplifier, and integrated circuit (IC) amplifier. The IC amplifier achieved a high degree of perfection, and a large variety of amplifiers is available.
8.2 SYMBOLS AND DEFINITIONS The symbol of an operational amplifier. is shown in Figure 8-1 . All the voltages are referenced to ground, as shown in Figure 8-2. The voltages v+ and v - are the positive and negative power supplies, also referenced to ground. In most applications the operational amplifier is connected to positive and negative power supplies. The amplifier has no 47
Operational Amplifiers
48
Part II
Inverting input terminal
Output terminaJ
a
b
Noninverting input terminal
Figure 8-1
The operational amplifier symbol.
ground terminal, but the voltages in the amplifier circuit become referenced to ground through the power supplies and through the external input and output circuits. There are also circuits in which the operational amplifier operates from a single polarity power supply. In this case one terminal of the amplifier is connected to ground. The operational amplifier can be utilized with three different configurations of the external circuitry. The signal voltage can be applied to the inverting terminal input (terminal a in Figure 8-2), to the noninverting terminal (terminal b), or as a differential input, between terminals a and b. Each configuration offers unique characteristics and applications. The manufacturer supplies the application engineer with a set of specifica-
a
b Va
Vo
-Figure 8-2 The operational amplifier voltages referenced to ground. va = . . . mvertmg mput voltage. vb = noninverting input voltage. vO = op amp output voltage. V+ = positive voltage of power supply. v- = negative voltage of power supply.
49
" ese pecifica io ~ impo~ C()O~train on he or pa icuJar c haJJ i t atio , Jn la chapter ,f hi~ part f peci 1cati 1 ~ a e i duded in he debign cep and de ini i n~,
Ii
J
ified j te
,~
e diffi rential input
of
ltage
outpu terminal and ground, The negati e Jtage at terminal a is ~iti e ith respect to the vu.a..1. tenninal i~ negati e ith re~pect to ground. oltage fi equency f : the gain is highe~t for DC and ea~ i incre1 ing frequency . or stable operation the , ·c mu meet certain pecifications, depending upon the een
.1UL
#
121)
--
-,
I
I )(
~
:
,,
I
I
-
~ I
··~
-
-
'
I~
~
'
'X
,,'
21)
~
·
I\ - 2fj
'
IO
l fJ
Hz]
~.,.~-- -e S--3 Gain-fi eqceJJCY espom-e cu e of operational amplifier pe L. I ~ an ,nterJJall c o r ~ ~ arnplifier, ~ ote the 1011 f equenc- of about 5 Hz at H3-dB poi, H and the uband idth" of J • Hz (i,e,. freq enc'J at uni g;lin or 0-dB gainJ.
Operational Amplifiers
50
Part II
Curve for externa l compensation with JpF capacitor
Gain I Aj
[ d BJ
120 ~
100
K
80
I ~.
60
~
40
20
~
'\
"
0
....
-20 10
100
IK
IOK
I00K
IM
I0M
Frequency f (Hz]
Figure 8-4 Gain-frequency response curve of operational amplifier type LM 748 with external compensation. Note the higher frequency of about 50 Hz at the "3-dB point" and the higher frequencies for comparable gains of the LM 741. For example, at 40 dB the LM 748 has a frequency response of 100 kHz compared to 10 kHz of the LM 741.
external circuitry in which the amplifier is used. To meet these characteristics, certain operational amplifiers are compensated inte1nally by the manufacturer, while other operational amplifiers must be compensated by the user. Each type has a field of application. Chapter 10 deals in detail with the compensation problem. The gain-frequency response curves of an internally compensated operational amplifier (type LM 741), and of an uncompensated operational amplifier (type LM 748) are shown respectively in Figure 8-3 and Figure 8-4. Note the difference in the magnitudes of · the frequencies at the respective 3-dB points, and the differences in the slopes beyond the 3-dB points. Operational amplifiers are characterized by high DC gain values on the order of hundreds of thousands. The gain is often specified in decibels (dB). The decibel is defined as 20 times the logarithm (to the base I 0) of a number: Gain (dB) = 20 log 10 A For example, a gain of 100,000 corresponds to a gain of 100 dB. 20 log 10 100,000 = 20 X 5 = 100 dB
Chap. 8
Understanding Operational Amplifier Characteristics
51
8.4 INPUT RESISTANCE The input resistance of an amplifier is defi ned as the resistance between the inverting and the noninverting input terminals. It is shown symbolically as Ri in Figure 8-5. Values lie in the range from hundreds of kilohms to hundreds of megohms. The input of the LM 741 amplifier, for example, is specified as "typical" 1 MD and minimum 300 kD. The LM 741 has a junction transistor input stage. Input resistances of tens and hundreds of megohms are available in operational amplifiers with field-effect transistor input stages (e.g., the LH0042) , or "super beta " transistor input stages (e.g., the LMI08) . The input capacitance is very small, on the order of a few picofarads.
v+
vFigure 8-5
Voltage offset balancing circuit. (Also shown symbolically are input and output resistances.)
8.5 OUTPUT RESISTANCE The output resistance of an operational amplifier constitutes circuitry responsible for the difference between the amplifier output voltage under no load and under load, due to current flowing in this part of the circuit under load. It is represented symbolically as R 0 in Figure 8-5. It can be seen from the figure that if no load is connected to the output terminal of the amplifier, no current flows through R 0 and the output voltage is equal to the no-load voltage: vo(NLJ = -A vab' where A is the gain of the amplifier and vab is the voltage between terminals a and b. A load connected to the amplifier draws a current iL from the
Operational Amplifiers
52
Part II
amplifier. The output voltage is reduced by the voltage iLR 0 across R0 , giving an output voltage v0 , under load
Output resistances of operational amplifiers are on the order of a few tens or hundreds of ohms. In an ordinary application of the operational amplifier, when peripheral feedback and input resistors are connected to the operational amplifier, the effective output resistance of the amplifier is only a few ohms or a fraction of an ohm.
8.6 COMMON-MODE GAIN (CMG) AND COMMON-MODE REJECTION RATIO (CMRR) The operational amplifier ideally amplifies only the difference between the two signals applied to the inverting and noninverting input terminals. Ideally, if the two signals are equal in magnitude and in phase, they are not amplified at all, since their difference is zero. Such signals are called common-mode signals. They can be caused , for example, by 60-Hz signals induced from neighboring equipment or circuits, or by the drift of a differential output stage of a transducer feeding the operational amplifier. In practical operational amplifiers, common-mode signals are amplified to some degree, since perfect matching of components inside the amplifier is impossible. This is called common-mode gain (CMG). To minimize the effect of common-mode signals, operational amplifiers are designed to have low common-mode gain. The degree of interference seen at the output due to common-mode input depends on the relative magnitudes of the differential and common-mode input signals and on the relative amplifications of these signals. Accordingly, the common-mode rejec;ion ratio (CMRR) is defined as the absolute value of the ratio of the differential gain divided by the common-mode gam:
CMRR =
A(w)
CMG
. (8-1)
As an example, suppose that ICMGI = 3 and IA(w)I = 100,000 for low frequencies. Then
CMRR = IOO,OOO = 33 333 3 ' and in decibels
CMRR (dB)
=
20 log 10 33,333 = 90.46 dB
8.6.1 Common-Mode Effect on the Output The amplified common-mode input signal appears at the output together with the amplified differential input signal, the former being amplified by the common-mode gain,
Chap. 8
Understanding Operational Amplifier Characteristics
53
CMG, and the latter by the differential gain -A(w). With reference to Figure 8-2, the
output v 0 , is given by the relationship (8-2) where va and vb are respectively the voltages, measured with respect to ground, at terminals a and b , and vcm is the common-mode voltage appearing at terminals a and b, as measured with respect to ground. Solving Equation 8-1 for CMG and substituting the result in Equation 8-2 we obtain Vo
=
-A(w) [ (va - vb) +
ci!RR ]
(8-3)
which expresses the effect of the common-mode signal on the output in terms of the common-mode rejection ratio CMRR which is specified by the manufacturer. Note that in Equation 8-3 the positive value of l'vcm/CMRRI is preceded by a + symbol, as it is impossible to know a priori whether the common-mode signal is amplified by a positive or negative gain. The sign can be different for two ICs of the same type and model. It will be shown in Chapter 12 how common-mode signals affect the output of practical amplifier configurations.
8.6.2 Maximum Common-Mode Input There is an amplitude limit to common-mode input voltages that may be applied to the inverting and noninverting terminals. Beyond this limit, the amplifier does not operate linearly. This limit is often given in the specification sheet for the amplifier. Maximum common-mode input voltage is an important consideration in applications such as comparators, where a reference signal is applied to one terminal and to the output switches when the signal at the other input terminal just exceeds the reference signal, or in applications where only a single voltage supply is used and the quiescent voltages at the input terminals are above ground.
8.7 VOLTAGE SUPPLY REJECTION RATIO (VSRR)
The characteristics of an operational amplifier are given for a certain set of test conditions including the voltage supplies such as + 15 V. If the voltage supply drifts from its nominal value, the output voltage of the amplifier, in general, changes. The change in output voltage is expressed in terms of an equivalent differential input voltage which causes the same change in output voltage. Thus, the effect of power-supply voltage variation, that is, the supply voltage rejection ratios, is given in terms of an equivalent input voltage per 1-V change in the power-supply voltage. The units are microvolts per volt or millivolts per volt. A typical value is 20 µ V /V. The supply voltage rejection ratio is also given in decibels. For example,
Part II
Operational Amplifiers
54
20 log 10 20 µV/V = 20 log 10 20 x 10- 6 = -94 dB Usually the absolute value, that is, 94 dB, is given in the specification. Depending on the degree of output stability required, the designer must choose a suitable operational amplifier and a suitable power supply. Obviously, the poorer the amplifier's voltage supply rejection ratio, the better the regulation and drift characteristics of the power supply must be. Example
Consider an amplifier of the configuration shown in Figure 8-6(a) with R 1 = 10 kD and R 2 = 50 kD. The VSRR of the amplifier is specified as 200 µ V /V. A voltage drop of I 00 m V at the V + terminal is caused by other components of the system. By how much will the output voltage change as a result of the change in power-supply voltage? Solution. The supply voltage drop of 100 mV, or 0.1 V, has the same effect on the output as the effect caused by 20 µ V, or 20 X 1o- 6 V, between the input terminals of the operational amplifier. The effect is calculated by multiplying this voltage by the quantity (I + R 2 /R 1). Vo
__ (
1
50 l0
+
X X
103 l0 3
)
20
X
10
_6 _ -
6 X 20 X I0- 6
=
120
X
10-6 V
or 0.120 mV.
Feed back resistor
R2
Input resistor
\
/
Input resistor
R~
/
Feedback resistor
R1
v,,ut
Signal source
T'
(a)
~igure 8-6
l-
You1
Signal source
1-
(b)
Basic operational amplifier applications. (a) The inverting amplifier. (b) The noninverting amplifier.
Chap. 8
Understanding Operational Amplifier Characteristics
55
8.8 INPUT OFFSET VOLTAGE An ideal amplifier has zero output voltage for zero input voltage. Since real components cannot be perfectly matched, and since components in symmetrical positions may be at slightly different temperatures, the differential amplifier stages of an operational amplifier are, in general, not balanced perfectly. Consequently, there is a finite output voltage with zero input voltage. The offset voltage is defined as the differential voltage that must be applied to the input terminals to reduce the output voltage to zero. This voltage can be a few millivolts in magnitude. The polarity of the offset voltage is not known a priori. The quiescent output voltage resulting from the offset voltage depends on the closed-loop amplifier design and is approximately equal to the offset voltage multiplied by the closedloop gain of the amplifier. To balance the amplifier, a potentiometer is connected to a pair of balancing terminals , as shown in Figure 8-5. The potentiometer is adjusted to obtain zero output voltage. A resistance value for the potentiometer is usually supplied by the manufacturer; it is typically 10 kfi or 50 kfi. Since the offset voltage, like other characteristics of the amplifier, is temperaturesensitive , the offset voltage can be balanced out only at a given temperature. It is therefore necessary to set the balancing potentiometer at the operating temperature and to check the output over the relevant temperature range.
8.9 INPUT BIAS CURRENT DC currents must be applied to both input terminals of an operational amplifier to bias the amplifier transistors properly. The circuitry that allows this bias current to flow is supplied externally to the operational amplifier and is the responsibility of the application engineer. The manufacturer specifies the magnitude of the bias current for the operational amplifier. In practical operational amplifiers , the two input transistors are not matched perfectly, and in general the two bias currents / b 1 and / b 2 are different. The specified value / b is the average of the two:
Improper design of the bias circuit causes an undesirable output voltage which may exceed that caused by the input offset voltage. To understand problems that can arise from improper bias circuitry and to learn how to alleviate such potential problems, we must pause for a moment and look at the two basic applications of the operational amplifier shown in Figure 8-6. The inverting amplifier has an output voltage that is 180 deg. out-of-phase with the input signal voltage, while the noninverting amplifier has an output voltage in phase with the input signal voltage. Each configuration offers certain unique features that are described in Chapter 11, Sections 11.1 and 11.2. To consider the bias problem, we recall that to study DC charac-
Operational Amplifiers
56
Part II
teristics of an electrical circuit, AC voltage sources are replaced with short circuits. Shorting the signal sources in Figure 8-6, both amplifier configurations take the form shown in Figure 8-7(a) . Because of the high gain of operational amplifiers and because of the negative feedback in the amplifier of Figure 8-7(a) , there is a tendency of the potentials at the inverting input te_rminal a and the noninverting terminal b to be the same. If, say, the potential at a were higher than the potential at b, then there would be a negative output voltage. The output voltage is fed back through R 2 , lowering the potential at a . If the open-loop gain of the operational amplifier were infinite , the difference between the potentials at a and b would be zero. Since terminal b is held at ground potential , we say that terminal a is at virtual ground. In first-order analyses, we can assume va - vb = 0, where v0 and vb are respectively the potentials (or voltages with respect to ground) at terminals a and b. We now study the bias problem. Since terminal a is at virtual ground potential , the bias current into terminal a must flow through R 2 . (If bias current were to flow through R 1 , there would be a voltage drop across R I causing the potential at a to be below ground, which contradicts the imposed condition that a is at ground potential.) To allow the bias current lb to flow through R 2 , the output voltage rises to a value of /~ 2 , equal to the voltage drop across R 2 . The noninverting terminal b receives bias current from ground through the base emitter junction, and the current flows to the negative supply terminal. We thus find that the circuit of Figure 8-7(a) has an output voltage/~ 2 with no signal input. This is an undesirable condition, since we want zero output with zero input. This undesirable condition is avoided by the addition of a compensation resistor R 3 , as shown in Figure 8-7(b). The value of R 3 must be equal to the value of the parallel combination of R 1 and R 2 .
With R 3 in the circuit, the bias current into terminal b flows through R 3 producing a voltage at b of magnitude
(a)
Figure 8-7
l-
-
/
Compensation resistor
1-
~
(b)
The amplifier of Figure 8-6 with short-circuited voltage sources. (a) Not compensated for bias imbalance. (b) Compensated for bias imbalance.
Chap. 8
Understanding Operational Amplifier Characteristics vb
Since as noted above va
-
vb
= 0,
57
= I,/?1
the voltage at terminal a is va
= - I,fi3
This value in tum determines the currents through R I and R2\ Let lb' be the current through R 1 , and// the current through R 2 • We have
and, for zero output voltage,
The total bias current into terminal a is
I/ + I/ . Since we chose R3
=
IbR3
=
RR R, ~ ~
, 2
U, - ~J
therefore R3
=
IbR3
Rk~;
2
k
R +R 2 R = 1 and 1 2
lb'
+ I/ = lb
Thus, we get the required bias current while maintaining zero output voltage as required. Thus , the choice of R 3 • Example
Let lb= 200 nA, R 1 = 2 kD, and R2 = 50 kD. Then R3 = R,IIR 2 = l.9 kD , va =vb= -0.38 mV, and v 0 = 0 V. If R 3 were not used, we would have va = vb = 0 and v0 = Itfi 2 = 10 mV. The lowest permissible values of R 1 , R 2 , and R 3 are determined by input impedance and gain requirements as is made clear in Chapter 12 in which design examples are presented; the upper limit is determined by the input offset current discussed in the next section.
8.10 INPUT OFFSET CURRENT In real operational amplifiers the bias currents Iha and Ibb into terminal a and b, respectively, are not equal. The difference II ha - I hhl is the offset current. The offset current causes an output of the amplifier in the· absence of an input. Consider Figure 8-7(b). Let R 2 = 500 kD and R 1 = 100 kD. We compute R3 = R ,IIR 2 giving R3 = 83.3 kD. Letibb = 300 nA and Iba= 400 nA. Then vb= -Ihtfi 3 = -2 mV. But v0 = vb, giving the current
Operational Amplifiers
58
Part II
through R 1 as lb' = -vh!R 1 = 250 nA. The difference I/ between Iba and lb' flows through R 2 . Thus I/ = Ih - lb' = 150 nA and v0 = v0 - Rif/ = 10 mV. We see that the input offset current causes an undesirable output just as does the input offset voltage. Usual1y, the application engineer designs the circuit so that the effect of the offset current on the output is less than the effect of the offset voltage. The offset current puts an upper limit on resistor values that can be used to keep the output voltage within the prescribed specifications.
8.11 GAIN-BANDWIDTH PRODUCT
The gain-bandwidth product of an operational amplifier is given by the product of the DC gain of the amplifier and the 3-dB frequency. The 3-dB frequency is the frequency at which the gain is down by 3 dB from the DC gain. Since the manufacturer does not know the closed-loop gain that will be employed by the user, the open-loop gain-bandwidth product is specified. This is a meaningful figure if it is known that the gain rolloff beyond the 3-dB point is -20 dB/dee (-6 dB/oct), as in Figure 8-3. Knowing this, it is possible to predict the gain-bandwidth product for any closed-loop gain. The intersection of the open-loop transfer curve and a straight line drawn parallel to the abscissa at a height equal to the closed-loop gain gives the 3-dB frequency. Multiplication of the closed-loop gain by this frequency gives the gain-bandwidth product. Note: For a rolloff of -20 dB/dee, the open-loop response curve intersects the 0-dB (unity gain) line at a frequency equal to the gain-bandwidth product of the amplifier (1 MHz in the example of Figure 8-3). When the open-loop response of an amplifier rolls off at a greater slope than 20 dB/dee, the open-loop gain-bandwidth product has no significance for closed-loop operation. In this case, the manufacturer usually specifies the unity gain frequency, which is somewhat more indicative of closed-loop capabilities, but in either case the usefulness of this information is limited and the complete frequency response curve is needed for closed-loop performance prediction. It is also important to keep in mind that the response curve is changed entirely if the amplifier is compensated for stability. Compensation is discussed in Chapter l 0.
8.12 SLEW RATE
The slew rate, SR, is defined as the highest possible rate of change for the amplifier output voltage.
SR _ ( dv 0 dt
)
max
This specification is important for large signal operation. The slew rate of an amplifier is limited by the currents available for charging parasitic capacitances or deliberately intro-
Chap. 8
Understanding Operational Amplifier Characteristics
59
duced capacitors in the amplifier. At certain points in the circuit of an operational amplifier the response to a signal at the input terminals is dependent on a current source. This current charges the various capacitances building up the output voltage in response to the input voltage. The voltage v0 across a capacitor is equal to the quotient of the charge q and the capacitance C:
vc = q/C For a constant charging current / 0 , this equation becomes V
c
I C
=_!!._ t
The rate of voltage change across the capacitor is obtained from this equation as
The slew rate is given by SR =
/max
C
where/ max is the maximum current available in the circuit of the operational amplifier to charge the capacitors. The slew rate imposes a frequency as well as an amplitude limitation. An amplifier may respond faithfully to an input sign.al of a certain frequency, but may give a distorted output in response to an input signal of the same frequency when the output voltage called · for is of a higher amplitude. A voltage of a given frequency and amplitude undergoes a higher rate of change than a voltage of the same frequency but of a lower amplitude, as is illustrated in Figure 8-8. The requirement for a large output amplitude can be caused by a larger input signal and/or by a higher closed-loop gain of the amplifier. By similar reasoning it is also easy to see that of two signals of the same amplitude, the one of the higher frequency requires a larger rate of change. The amplitude and frequency of a signal are related to the required slew rate (SR). Consider an output voltage of amplitude V0 and frequency f (angular frequency w = 2nj) given by V
= Vo sinwt
The rate of change is dv dt = w V 0 coswt
and the maximum rate of change is given when coswt
= 2nfVo ( ddv) t max
=
I:
Operational Amplifiers
60
Part II
Hence , an undistorted sine wave , of amplitude V0 and frequency fat the output, requires a slew rate, SR ,
SR> 21ITjV0 For example , if an output of 7 V peak at a frequency of 10 kHz is required, an amplifier with a slew rate of at least 0.44 V / µ s must be used. High amplitud e voltage} Low a mplitude volt age Same frequency
t Voltage
tan a
v(
Time
Figure 8-8
>
tan
/3
t
Rate of change of voltage as dependent upon amplitude .
8.13 CROSSOVER DISTORTION
In the design of equipment using operational amplifiers it is usually assumed that the gain of the amplifier is linear ov~r the operating range. This is not true for small signals near the zero crossover if the amplifier uses a class B output stage. Two requirements_for an output stage are low output impedance and high-power capabilities . An emitter-follower output stage possesses these properties, but has the drawback of high-power dissipation in the emitter resistor, which causes heating of the amplifier chip and low efficiency of the amplifier. These shortcomings are removed if the output stage is operated class B using a complementary pair (npn and pnp) of transistors, but different shortcomings are introduced. The zero crossover when one transistor turns on and the other transistor turns off is never perfect. The input-output characteristic of the amplifier is then as shown in Figure 8-9. The output is not only distorted, but also the open-loop gain (which is given by the slope of the curve) is considerably smaller for small signals than for larger signals. Since the zero crossing region is relatively narrow, it is usually of no concern. But in applications where this degree of distortion or the small gain effect cannot be tolerated, the designer must avoid the use of an operational amplifier with a class B output stage.
Chap. 8
Understanding Operational Amplifier Characteristics
v, .,,
61
t
'\.. Z e ro c ross ing region
Figure 8-9
Input-output characteristic of class B amplifier.
8.14 RATED OUTPUT The manufacturer usually specifies maximum output voltage and maximum output current. The values represent limits above which the output is distorted , or the amplifier destroyed . If the voltage is exceeded, the amplifier enters saturation. This results in distortion , and there is a lengthy recovery time. It should be noted that some amplifiersthe comparators-are used in saturated operation and are especially designed for relatively short recovery times. Many operational amplifiers are built with current overload protection. The circuit operates in the normal mode for load currents below a specified point , and enters into the overload mode when the rated current is exceeded, resulting in distortion. The user must be aware that lack of overheating does not imply normal operation.
8.15 POWER DISSIPATION Two power dissipation values can be given: device dissipation, PD• and total dissipation , PT· The device dissipation is the power that can be safely consumed by the amplifier. The total dissipation refers to the amplifier plus load dissipation. Thus , permissible load power PL = PT - PD· Any two values may be given by the manufacturer. The load power may be given in terms of maximum load voltage and maximum load current for resistive loads. The product of voltage and current gives power.
Operational Amplifiers
62
Part II
8.16 INPUT OVERLOAD PROTECTION Some amplifier have an input overload protection. For differential input voltages below a specified value , the protection circuit is inactive . For larger differential input voltages, any excess current that would damage the input transistor is redirected to bypass the transistor, resulting in distorted output. The designer must be careful to keep the signal values below levels that activate the protection circuit to maintain distortionless operation. If an application requires large differential input voltages, the ·d es!gner must use an amplifier without input overload protection.
8.17 SUPPLY CURRENT DRAIN
Since normally more than one IC is supplied from one power supply, care must be taken that the total current drain does not exceed the power-supply rating. Note that some amplifiers can be operated from a wide range of supply voltages and that the current drain may depend on the voltage. In other amplifiers, the current drain may be independent of the supply voltage.
8.18 TRANSIENT RESPONSE
When a pulse is applied to the input of the amplifier, the output responds as shown in Figure 8-10. The manufacturer may specify the percentage overshoot, rise time (10% to
Output voltage
.-""""'l:: _ _ _ _ _
100% 90%
j_ Overshoot
f-
.
10%
1-
I
•I
Rise ti me
I I
t
Time
!.~--Settling time----•~!
Figure 8-10
Transient response of amplifier.
Chap. 8
Understanding Operational Amplifier Characteristics
63
90% of final output), and settling time, as well as the slew rate discussed in Section 8-12. All these specifications are defined in the figure.
8.19 INPUT CAPACITANCE
The parasitic input capacitance is usually in the range of 1 to IO pF and is specified by the manufacturer.
8.20 AMPLIFIER NOISE Amplifier noise is an important consideration in low-level signal application. The complete design must consider noise originating from the amplifier as well as other circuit components. The noise can be expressed in terms of input voltage or input current that causes the same output voltage as that caused by the noise. Curves expressing the amplifier noise referred to the input, are supplied by the manufacturer. See, for example, the noise characteristics for the LM 741 * operational amplifier shown in Appendix A 1.
•
8.21 TEMPERATURE, FREQUENCY, SUPPLY-VOLTAGE, SOURCERESISTANCE, AND LOAD-RESISTANCE DEPENDENCIES OF AMPLIFIER CHARACTERISTICS
The characteristics of an operational amplifier are specified under certain operating or test conditions. These conditions may include load resistance, temperature, and other parameters. So that the reader can study orders of magnitudes, units, and parameter dependencies of the various characteristics, a complete set of specifications of the bipolar LM .741 * * and the FET input LH0042 amplifiers is included in Appendix A3.
*The LM 741 characteristics are given by the LM 747 data sheets. The LM 747 is a package containing two LM 741 s. The characteristics are identical. * *The LM 747 shown in the appendix is a package containing two LM 741 opamps . The characteristics shown are identical with those of the LM 741.
9 Dual- and Single-Power-Supply Amplifiers, Low-Voltage Amplifiers, and Transconductance Amplifiers 9.1 INTRODUCTION Most operational amplifiers are designed for use with dual-voltage power supplies ( + 15 V or + 12 V are typical). This permits input and output signals to swing above and below ground voltage without the n~ed for coupling capacitors. However, a dual-voltage power supply can be more expensive than a comparable single-voltage power supply of twice the voltage. Amplifiers usually supplied by a dual-voltage power supply can be operated from a single-voltage power supply) in which case an external voltage divider must be added to set the input halfway between the supply-voltage extremes.
9.2 SINGLE-VOLTAGE-POWER-SUPPLY AMPLIFIERS The CA3015 (RCA) amplifier normally operates from a + 12-V supply. It can also be operated from a 24-V supply. A diagram showing the power-supply connections is shown in Figure 9-1 (a). Note: The input and output are capacitively coupled to the amplifier. With the increased interest in applications of !Cs in the automotive industry, operational amplifiers are available that are explicitly designed for use with a single-voltage power supply. Some can also be used with a dual-voltage power supply. For example, the LM 2902 quad operational amplifier (National Semiconductor) contains four operational amplifiers in one package. These amplifiers can be operated from a wide range of power supplies from 3 V to 26 V, or from + 1. 5 V to + 13 V. Thus, the amplifier can be operated from a 5-V power supply in a digital system, eliminating the need for a separate dualvoltage power supply. This amplifier can be used to sense signals near ground. An 64
+ 24 V
2. 7 H t
1S kS1 1 µF \>----4 ~ Out
(a)
100 kS1
v+ 100 kS1
100 kS1 100 kS1 vo=v 2 - v1 v 2 )l: v 1 to keep v 0 ~ 0
( b)
R2 l MQ
-. (c)
Figure 9-1 Amplifier operated from single-voltage power supply . (a) CA 3015 (b) LM 2902 (c) LM 3900.
65
66
Operational Amplifiers
Part II
example showing the application of the device in a difference amplifier is shown in Figure 9-l(b). A popular single-polarity power-supply amplifier is the LM 3900 quad operational amplifier (National Semiconductor). This amplifier is different from the conventional amplifiers in that the input stage is not a voltage differential amplifier, but a current differential amplifier. The inverting input stage is a common emitter stage. The noninverting input stage is provided by a circuit known as a current mirror circuit. This results in an input stage in which currents are compared or differenced. It is called a Norton differential amplifier. There is no limit to the common-mode input voltage range. This is useful in high-voltage comparator applications. By making use of input resistors to convert input voltages to input currents, all of the standard operational amplifier applications can be realized. An application example is shown in Figure 9-l(c), where we show an inverting amplifier. Note that the DC level at the output is determined by a resistance ratio. In particular, the DC level can be set halfway between the power supply voltage and ground by choosing R3 = 2R 2 . An important practical advantage of this amplifier is that no voltage-dividing network is needed to establish the bias level of the input stage, which would reduce the input impedance. The noninverting input is simply connected to the power supply through a resistor. Note that the Norton amplifier is identified by two arrows, one between the inverting and noninverting terminals, and one into the noninverting terminal.
9.3 LOW-VOLTAGE AMPLIFIERS As demands for miniature, p~rtable, battery-operated instruments increase, the supply of low-voltage amplifiers becomes more pressing. For portable radios and calculators, 9-Y batteries are quite adequate, but for miniature devices such as watches and hearing aids, the conventional 9-V battery i,s much too large. Miniature batteries the size of an aspirin tablet or smaller, of about 1.4 V, are now available. Another demand for low-voltage battery-operated equipment is low current drain. The LM 4250 (National Semiconductor) opamp can be operated from voltages as low as 2 V or + 1 V. This is clearly satisfactory for operation with two batteries. An external bias current resistor controls the input bias current, input offset current, quiescent power consumption, slew rate, input noise, and the gain-bandwidth product. The standby power consumption can be adjusted to as low as 500 nW. For still lower voltages, the ICL 7641 (lntersil) opamp has been introduced. It can operate from voltages as low as 1 V or +0.5 Vandis thus suitable to operate from a single battery. It has an input impedance of 10 12 fl and a typical input current of 1 pA. The opamp is a CMOS device and consequently the output swing ranges within a few millivolts of the supply voltage. The standby quiescent current is 1 mA, the unity gain bandwidth is I MHz, and the slew rate is 1.6 V / µs. The 7641 package contains four opamps. Other versions of the same amplifier with fewer opamps per package are also available. In these, the extra available package pins are used to connect external resistors
Chap. 9
Dual- and Single-Power, Low-Voltage and Transconductance Amplifiers
67
to the amplifiers, one per amplifier, which allows the programming of the amplifier characteristics to operate at a low standby current of IO µA .
9.4 LOW-NOISE AMPLIFIERS In many cases the signal that needs to be filtered is very low and it is necessary to amplify it before filtering. It is important to have a large signal-to-noise ratio, adding as little noise as possible by the amplification stage. There are so called " low-noise" amplifiers (see Appendix AS). For proper design the right low-noise amplifier must be chosen. This requires the selection of the amplifier with the best noise characteristics relative to the signal source output resistance. Some manufacturers provide noise figure vs . source resistance curves such as shown in Figure 9-2. The noise figure is given as a function of the output resistance of the signal source connected to input terminals of the amplifier. One now compares the noise figures for the correct frequency and source resistance of several operational amplifiers and chooses the one with the lowest noise figure for these particular parameters. If the noise figure (NF) curves are not given, the best amplifier can be determined from the noise voltage and noise current curves as follows. For the desired frequency, the noise figure is calculated using the formula given below for the particular source resistance.
NF = (e~; + f?-i;Rs) + 4KTRS 4kTRS where e~; and ~; are respectively the noise voltage (in volts) and current (in amperes) and Rs is the source resistance (in ohms); Tis the absolute temperature in degrees Kelvin, and k is Boltzmann's constant (k= 1.33 x 10- 23 J/ K). The amplifier that gives the lowest noise figure for the particular source resistance will introduce least noise. 0
9.5 WIDEBAND AMPLIFIER Operational amplifiers are in general low-frequency devices. Typically, unity gain (i.e., OdB gain) occurs at about I MHz for internally compensated amplifiers and 4 or 5 MHz ·for uncompensated amplifiers. The 3 dB breakpoint is about IO Hz. When filtering must be done at higher frequencies, wideband amplifiers must be used. Some manufacturers supply special wideband amplifiers. (See Appendix A9.) The RCA CA3130 opamp, for example, has an uncompensated unity gain crossover frequency of 15 MHz; with a 4 7-pF compensation capacitor, the unity gain crossover frequency is 4 MHz. It is a BiMOS operational amplifier that combines the advantages of both CMOS and bipolar transistors on a monolithic chip. The RCA CA3 l 00 opamp has an open-loop gain of 42 dB at I MHz and a unity-
Part II
Operational Amplifiers
68
INPUT NOISE VOLTAG E AS A FUNCTION OF FREQUENCY N
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Input Noise Voltave and Current vs Frequency
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173
4. TRANSCONDUCTANCE OPERATIONAL AMPLIFIER (Reprinted by permission of RCA Solid State Division, now Harris Semiconductor)
174
Operational Transconductance Amplifier --0 5
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10 IOO 1000 AMPLIFIER BIAS MICR0AMPERES (lAec>
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181
6. LOW-VOLTAGE-POWER-SUPPLY OPERATIONAL AMPLIFIER (Reprinted by permission of Intersil.)
182
,c ,c
., ... u
ICL76XX
IIO~Oll.
p..
-
lo SETTING
INPUT STAGE
OUTPUT STAGE
STAGE
I v+ 3K
900K
3K
0
OFFSET0
8.3V
OFFSET
100K
v+
pg +INPUT CFF= 9pF
'------,l---~1---6--- OUTPUT Cc= 33pF v+
-INPUT
n9
vv+
ICL-7611 ICL-7612 ICL-7621 ICL-7631 ICL-7641 ICL-7642
8, F, H 8, F, H C, E 8, F, H C, G A, E
6.3V
6
Table of Jumpers
E
1-----+-~ F G
H
__,._4-__----4_ _ ___,._ __,.__ _L_--0y-
.__ __.,_ _--4_ _ _ _......
0307-11
NOTE 1: Offset nulling pins are not available on triple (ICL-763X) and quad (ICL-764X) versions.
Figure 2: Functional Diagram INTERSIL•s SOLE AND EXCLUSIVE WARRANTY OBLIGATION WITH RESPECT TO THIS PRODUCT SHALL BE THAT STATED IN THE WARRANTY ARTICLE OF THE CONDITION OF SALE. THE WARRANTY SHALL BE EXCLUSIVE AND SHALL BE IN LIEU OF ALL OTHER WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, INCLUDING THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR USE. NOTE· All typical values have been chsrsct8fiz6d but are not tested.
183
IIO~OIL n r
ICL76XX
... Cl
Pin A11lgnment1
Device
Deacrlptlon
ICL7621XCPA ICL7621 XCTV ICL7621 XMTV
Dual op amps with internal compensation; la fixed at 100JJ,A Pin compatible with Texas Inst. TL082 Motorola MC1458 Raytheon RC4558
TO-99 (TOP VIEW) (outline dwg TV)
• PIN DIP (TOP VIEW) (outline dwg PA)
v• OUT1 -IN 1 +IN 1 5
-IN 1 4
0307-7
0307-6
'Pin 8 connected to case.
ICL7631XCPE
Triple op amps with internal compensation. Adjustable la Same pin configuration as ICL8023.
16 PIN DIP (TOP VIEW) (outline dwgs JE, PE)
IOA SET
v·
OUTc
16
13
12
11
10
9
-INc
+INc
• 1
2
3
NC
-IN•
+IN.
6 y+
OUT,
loc SET
0307-9
Note: pins 5 and 15 are internally connected. ICL7641 XCPD ICL7642XCPD
Quad op amps with internal compensation. la fixed at 1mA (ICL7641 ).. la fixed at 10µ.A (ICL7642) Pin compatible with Texas Instr. TL084 National LM324 Harris HA4741
14 PIN DIP (TOP VIEW) (outline dwg JD, PD)
OUTo
-IN 0
+INo
v·
+INc
-INc
OUTc
-IN.
+IN.
v•
+IN,
-IN,
OUT,
14
• OUT.
0307-10
Figure 1: Pin Configurations (Cont.) INTERSIL'S SOLE AND EXCLUSIVE WARRANTY OBLIGATION WITH RESPECT TO THIS PRODUCT SHALL BE THAT STATED IN THE WARRANTY ARTICLE OF THE CONDITION OF SALE. THE WARRANTY SHALL BE EXCLUSIVE AND SHALL BE IN LIEU OF ALL OTHER WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, INCLUDING THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR USE. NOTE: All typical VSll/68 hSV9 bHn chsrscterizBd but Sf'fl not tested.
184
=
ICL76XX ICL76XX Series Low Power CMOS Operational Amplifiers GENERAL DESCRIPTION
FEATURES
The ICL761X/762X/763X/764X series is a family of monolithic CMOS operational amplifiers. These devices provide the designer with high performance operation at low supply voltages and selectable quiescent currents, and are an ideal design tool when ultra low input current and low power dissipation are desired. The basic amplifier will operate at supply voltages ranging from ± 1V to ± 8V, and may be operated from a single Lithium cell.
• Wide Operating Voltage Range ± 1V to ± ev
A unique quiescent current programming pin allows setting of standby current to 1mA, 100µA, or 10µA, with no external components. This results in power consumption as low as 20µW. Output swings range to within a few millivolts of the supply voltages. Of particular significance is the extremely low (1 pA) input current, input noise current of .01 pA/ v'Hz, and 1012n input impedance. These features optimize performance in very high source impedance applications. The inputs are internally protected and require no special handling procedures. Outputs are fully protected against short circuits to ground or to either supply. AC performance is excellent, with a slew rate of 1.6V / µs, and unity gain bandwidth of 1MHz at la= 1mA. Because of the low power dissipation, operating temperatures and drift are quite low. Applications utilizing these features may include stable instruments, extended life designs, or high density packages.
• • • • •
High Input Impedance - 10120 Programmable Power Consumption - Low As 20µ w Input Current Lower Than BIFETs - Typ 1pA Available As Singles, Duals, Triples, and Quads Output Voltage Swings to Within MIiiivoits Of v- and
v+
• Low Power Replacement for Many Standard Op Amps • Compensated and Uncompensated Versions • Input Common Mode Voltage Range Greater Than Supply Ralls (ICL7612)
APPLICATIONS • • • • • •
Portable Instruments Telephone Headsets Hearing Aid/Microphone Ampllflers Meter Ampllflers Medical Instruments High Impedance Buffers
SELECTION GUIDE DEVICE NOMENCLATURE ICL76XX
X
X
XX
L
Package Code TV - TO-99, 8 pin PA- Plastic 8 pin Minidip PD - 14 pin Plastic Dip PE - 16 pin Plastic Dip JD-14 pin CERDIP JE - 16 pin CERDIP
SPECIAL FEATURE CODES C H L M 0
p V
= = = = = = =
INTERNALLY COMPENSATED HIGH QUIESCENT CURRENT (1 mA) LOW QUIESCENT CURRENT (10µ,A) MEDIUM QUIESCENT CURRENT (1 00µA) OFFSET NULL CAPABILITY PROGRAMMABLE QUIESCENT CURRENT EXTENDED CMVR
.______ Temperature Range c = 0°c to 70°c M= -55°Cto +125°C ,...__ _ _ _ _ _ Vos Selection A=2mV B=SmV C=10mV D=15mV E=20mV INTERSIL'S SOLE AND EXCLUSIVE WARRANTY OBLIGATION WITH RESPECT TO THIS PRODUCT SHALL BE THAT STATED IN THE WARRANTY ARTICLE OF THE CONDITION OF SALE. THE WARRANTY SHALL BE EXCLUSIVE AND SHALL BE IN LIEU OF ALL OTHER WARRANTIES, EXPRESS, IMPLIED OR STATUTOR Y, INCLUDING THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR USE.
302060-002
NOT£· All typical values have bBBn characterized but are not testsd.
185
-
110~0(!. n ,-
ICL76XX
...
ABSOLUTE MAXIMUM RATINGS Total Supply Voltage v+ to v- ................. .. . 18V Input Voltage ... .. .............. v - -0.3 to v+ +0.3V Differential lnputVoltage[1] . ±[(V + +0.3) - (V - -0.3)]V Duration of Output Short Circuitl2] . . . . ......... Unlimited
Cl
Continuous Power Dissipation Above 25°C @25°C derate as below: 2mWl°C 250mW TO-99 2mWl°C 250mW 8 Lead Minidip 3mWl°C 375mW 14 Lead Plastic 4mW/°C 14 Lead Cerdip 500mW 3mWl°C 16 Lead Plastic 375mW 4mWl°C 16 Lead Cerdip 500mW Storage Temperature Range ......... . - 65°C to + 150°C Operating Temperature Range ICL76XXM . . . . . . . . . . . . . . . . . . . . . . . . - 55°C to + 125°C ICL76XXC ... .... .. ... . .. .- . ....... .... 0°C to + 70°C Lead Temperature (Soldering, 10sec) . . ........... 300°C
NOTE: Stresses above those listed undtlr "Absolute Maximum Ratings" may cause permanent damage to the device. Thess SrB stress ratings only and functions/ operation of the device st these or any other conditions above those Indicated In the operations/ sections of the specifications Is not Imp/led. Exposure to absolute maximum rating conditions for extended periods may affect device rel/ab/1/ty. NOTE 1. Long term offset voltage stability will be degraded If large input differential voltages are applied for long periods of time. 2. The outputs may be shorted to ground or to either supply. for VsuPP ~ 10V. Care must be taken to insure that the dissipation rating is not exceeded.
ELECTRICAL CHARACTERISTICS (7611/12 and 7621 ONLY) (VsuPPLY = ± 5.0V, TA= 25°C, unless otherwise specified.) Symbol
Parameter
Test Conditions
76XXA
76XXB
76XXD
Units
Min Typ Max Min Typ Max Min Typ Max
Input Offset Voltage
Vos
Rss100kn, TA=25°C TM1NsTAsTMAX
2 3
A.Vos/ AT Temperature Coefficient of Vos Rss100kn Input Offset Current
los
Input Bias Current
ls1AS
VcMR
VcMR
0.5
TA =25°C ATA=C ATA=M
1.0
15 30 300 800
0.5
50 400 4000
1.0
30 300 800
0.5
50 400 4000
1.0
±4.4 ±4.2 ±3.7
±4.4 ±4.2 ±3.7
±4.4 ±4.2 ±3.7
Extended Common Mode Voltage Range (ICL7612 Only)
la= 1'0µA
±5.3
±5.3
±5.3
la= 100µ.A
+5.3 -5.1
+5.3 -5.1
+5.3 -5.1
la=1mA
+5.3 -4.5
+5.3 -4.5
+5.3 -4.5
(1) la= 10µA, AL= 1Mn TA=25°C ±4.9 ATA=C ±4.8 ATA=M ±4.7
±4.9 ±4.8 ±4.7
±4.9 ±4.8 ±4.7
la= 100µA, AL= 100kn TA=25°C ±4.9 ATA=C ±4.8 ATA=M ±4.5
±4.9 ±4.8 ±4.5
±4.9 ±4.8 ±4.5
(1) la= 1mA, AL= 10kn TA=25°C ±4.5 ATA=C ±4.3 ATA=M ±4.0
±4.5 ±4.3 ±4.0
±4.5 ±4.3 ±4.0
Output Voltage Swing
mV µVl°C
25
Common Mode Voltage Range la= 10µA(1) (Except ICL7612) la= 100µA la=1mA(1)
'
Vour
10
TA=25°C ATA=C(2) A.TA= Mc2)
15 20
5 7
30 300 800
pA
50 400 4000
pA
V
-
V
V
INTERSIL'S SOLE AND EXCLUSIVE WARRANTY OBLIGATION WITH RESPECT TO THIS PRODUCT SHALL BE THAT STATED IN THE WARRANTY ARTICLE OF THE CONDITION OF SALE THE WARRANTY SHALL BE EXCLUSIVE AND SHALL BE IN LIEU OF ALL OTHER WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, INCLUDING THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR USE.
NOTE: All typlcsl vs/uss hsvs bssn chsrsctsrizsd but srs not tBstsd.
186
>< >
"'0
>
t
600
w
~
...C
~
0
u
S
It w c., C
!;::: ~
PEAK-TO-PEAK OUTPUT VOLTAGE AS A FUNCTION OF FREQUENCY
EQUIVALENT INPUT NOISE VOLTAGE AS A FUNCTION OF FREQUENCY
...,
C
a::
"'a::
0307-17
I
;:::
•c
■D~DIL
ICL76XX TYPICAL PERFORMANCE CHARACTERISTICS MAXIMUM PEAK-TO-PEAK OUTPUT VOLTAGE AS A FUNCTION OF SUPPLY VOLTAGE
MAXIMUM PEAK-TO-PEAK OUTPUT VOLTAGE AS A FUNCTION OF FREQUENCY
>
I
I
I
... .....,
I
I
Vwpp • 10V
fo • 1mA
.._
MAXIMUM PEAK-TO-PEAK VOLTAGE AS A FUNCTION OF FREE-AIR TEMPERATURE >
1a
12
I
(.!)
,(
Rl • 1001(!!
10
14
>
--~""' t\\
I
II I
I
"~
t\.1' ~
T,_ • +25 C
'
!
!
:
X
'
"'
100K
,(
4
!
2
Vsupp • 10 VOL TS lo • lmA
~ O z
:::)
~
I
12
6
a,-.--,---.---,--...-----~--.
\
I
14
0
VOLTAGE FOLLOWER LARGE SIGNAL PULSE RESPONSE
VsuPI' • 10V a lOK !! Rl • 100pF Cl T,. • •:IS C
I
0307-25
VOLTAGE FOLLOWER LARGE SIGNAL PULSE RESPONSE lo • 1 mA
I
v• - v- •
SUPPL V VOLT AGE - VOL TS
0307-24
' s"'...>
.... 5 ...."... ...."
16
,(
\
u
"iiiz ... i! 5...
10
•75 +100 +125
MAXIMUM PEAK-TO-PEAK OUTPUT
0
!2
6
•50
VOLTAGE AS A FUNCTION OF LOAD
(.!)
lo • 10!,A
..__' l'tt...
...z
:
- 25
FREE -AIR TEMPERATURE - "C
I
'-
1
Vi
.50
0307-22
0.01
'
2
16
MAXIMUM OUTPUT SINK CURRENT AS A FUNCTION OF SUPPLY VOLTAGE
MAXIMUM OUTPUT SOURCE CURRENT AS A FUNCTION OF SUPPLY VOLTAGE
lO
14
0 . 75
SUPPLV VOLTAGE - VOLTS
0307-21
I/
r---.._
a
FREOUENCV - H•
40
-
0..
10M
1M
I
r--......
Rl • 2K!! '
6
" ...0... ... "'...
:i
?-,~~ ,..___
I
10
........
100K
~ 0.1
100
10
100
FREQUENCY (Hz) TL/H/9300 - 7
Typical Applications
(Continued) Floating Input Meter Amplifier 100 nA Full Scale
=
1.5V
6
Rs 10M
SCALE ADJUST
=
1.5V
ZERO
ADJUST GROUND
°:L
Quiescent Po = 1.8 p.W
TL/ H/ 9300-8
'Meter movement (0-100 p.A, 2 k!l) marked for 0-100 nA full scale.
X 100 Instrumentation Amplifier 10 µ W
R2 10M
-1.5V
R3 10M
6
Note 1: Quiescent Po = 10 µW. Note 2: R2, R3, R4, R5, R6 and R7 are 1 % resistors. Note 3: R11 and C1 are for DC and AC common mode rejection adjustments.
198
TL/H/9300 - 9
8. LOW-NOISE OPERATIONAL AMPLIFIER (Reprinted by permission of RCA Solid State Division, now Harris Semiconductor)
199
Linear Integrated Circuits CA6078, CA6741 MAXIMUM RATINGS, Absolute-Maximum Values at TA = 2SoC CA6741T 44 V ±30 V ±15 V
DC Supply Voltage (between v+ and v- terminals) . . . . . . . . . . . . . . . . Differential -Mode Input Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Common-Mode DC Input Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Device Dissipation : Up to 75°C (CA6741T), Up to 1250 (CA6078AT) . . . . . . . . . . . . . . 500 mW Above 750c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Der ate linearly 5 mW/OC Temperature Range : Operating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -55 to +125 °c Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -65 to +150 °c Output Short-Circuit Duration• . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . No limitation Lead Temperature (During soldering) : . ... .............. . . .. . ... . At distance 1/16 :tl/32 inch (1.59 ±0.79 mm) from case for 10 seconds max. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 °c
.
•u Supply
CA6078AT 36 V
t6V v+ to
250mW
- 55 to + 125 oc -65 to +150 oc No limitation
J00°c
Voltage is less than ±15 volts. the Absolute Meximum Input Voltage is equal to the Supply Voltage .
•Short circuit may be applied to ground or to either supply .
TIME- IOm1/DIV.
TIME- 20m1/DIV.
92CS·20299
t2C$•20300
•· Typ. dt11tict1 with high·burst-noise _,charac• teristic.
b . Typ. dt1vict1 controlltld for burst noiu.
Fig. 1- Typ. wevt1forms of type with high burst noise and tyPfl controlled for burst noise.
V+
FAIL INOICATOA
~0-dB
AMPI..FER
I-kHz LOW-PASS F'ILTER
POS. NEG.
120 THRESHOLD S£T
!:I'%
0
R51
*
a R52
•IOOkO F'OR CA6741T ANO 200k.'1 FOA CA6078AT
CA67 ◄ 1T OR CA6078AT
92CS-19 ◄ 23
Fig.2-Block diagram of burst-noist1 "popcorn" tflSt t1quipmen t .
200
v-
Operational Ampllflers CA6078, CA6741
Operational Amplifiers CA6078AT - Micropower Type CA6741T - Gener~I-Purpose Type For Applications where Low Noise (Burst + 1/f) is a Prime Requirement 8-LEAD T0-5 with Dual-In-Line Formed L-■dl
8-LEAD TO-ti
M- 1787
Virtually free from "popcorn" (burst) noise: device rejected if any noise burst exceeds 20 µV (peak), referred to input over a 30-second time period.
H -1528
RCA-CA6078AT and CA6741T• are low-no ise linear IC operational ampl ifiers that are virtually free of " popcorn" (burst) noise. These low-noise versions of the CA:ll78A T and CA37 41 T are I result of improved processing developments and rigid burst-noise inspection criteria . A highly selective test circuit (See Fig. 2) assures that each type meets the rigid low-noise standards shown in the data sect ion . This low-burst -noise property also assures excellent performance throughout the 1/f noise spectrum. In addition the CA6078A T and CA67 41 T offer the same features incorporated in the CA:ll78AT and CA3741T respectively, including output short-circuit protection, latch-free operation, wide common-mode and differential· mode signal ranges, and low-offset null ing capability . TOI' Vl(W
For detailed data, characteristics curves, schematic diagram, dimensional outline, and test circuits, refer to the Operational Amplifier Data Bulletins File No . 531 and 535. In addition, for details of considerations in burst-noise measurements, refer to Application Note, ICAN-6732, " Measurement of Burst ("Popcorn") Noise in Linear IC's". The CA6078AT and CA6741T utilize the hermetically sealed 8-lead TO-5 type package. The CA6078AT and the CA6741T can also be supplied on requl;!st with dual-in-line formed leads. These types are identified as the CA6078AS and CA67 41 S. This formed-lead configuration conforms to that of the 8-lead dual-in -line (Mini-Dip) package. For terminal arrangements, see page 4 .
.
.
Formerly Dev. tlto. TA5807X and TA6029 re1pect1vely.
CA6741T
CA6078AT
TOI' Vl[W
Applications:
Applications: ■
■
■ v· NOT(
■
■
Low-noise AC amplifier Narrow-band or band-pass filter Integrator or differentiator DC ampiifier Summing amplifi•
11'1,_ 4 IS COtl .. [CT[O TO CASE
Portable electronics Medical electronics
■
DC ampiifier Narrow-band or band-pass filt• • lnt99"ator or differentiator • Instrumentation ■ Telemetry ■ Summing amplifier ■
v· lfQT[ PIN 4 IS CONN[CHO TO CAS[
Features:
tlCS · lotM
■ Open-loop voltage gain: 40,000 (92 dB) min.
Features: ■
Internal phase compensation ■ Input bias current: 500 nA max. • Input offset current: 200 nA max. ■ Open-foop voltage geiri : 50,000 (94 dB) min. · ■ Input offset voltage : 5 mV max.
■
Input offset voltage:3.6 mV max. • Operates with low total supply voltage: 1.6 V min.(± 0.75 ■ Low quiescent operating current: adjustable for application optimization ■ Input bias current: adjustable to below 1 nA
v,
201
O peratlonal Ampllfler1 CA6078, CA6741 ELECTRICAL CHARACTERISTICS - CA6078AT, For Equipment Design. LIMITS
TEST CONDITIONS CHARACTERISTICS
SYMBOLS Supply Volts: v+ • 6, V- • -6 TA• 250C, IQ• 20 µA
UNITS MIN.
MAX.
TYP.
NoiM Charact•istic "Popcorn"
Bandwidth = 1 kHz
(Burst) Noise
Rs1 = Rs2 .. 200 k1l
Dev ice is rejected if the total noise voltage (burst + 1/f), referred to input, exceeds 20 µ.V peak, during a 30-sec. test period.
Principal Characteristics (For detailed Electrical ct.arecteristics refer to CA3078AT Data Bulletin, File No. 536.) Input Offset Voltage
v,o
Input Offset Current
110
Input Bias Current
11B
-
Rs~10k1l
0.7
3 .5
mV
0.5
2.5
nA
7
12
nA
100,000
dB
Open-Loop
Common-Mode Input Voltage Range
VtCR
v+ = V- = 15 V
±14
-
-
Common-Mode Rejection Ratio
CMRR
R5~10k1l
80
115
-
dB
Output Voltage Swing
Vo(P-P)
RL ~ 101l
±13.7
± 14. 1
-
V
Supply Current
IQ
Differential
AQL
RL ~ 10 k1l Vo
Voltage Gain
z
40,000
±4V
92
100
RL ~ 2 k1l
-
±14
-
20
25
V
µA
ELECTRICAL CHARACTERISTICS - CA6741T, For Equipment Design.
TEST CONDITIONS CHARACTERISTICS
SYMBOLS Supply Volts;V+ • 15, V-• -15
TA• 250C
LIMITS UNITS MIN.
TYP.
MAX.
NoiN Characuristic "Popcorn"
Bandwidth= 1 kHz
(Burst-) Noise
Rs1 '"' Rs2
2
100 k1l
Device is rejected if the total noise voltage (burst + 1/ f). referred to input, exceeds 20 µ.V peak, during a 30-sec. test period.
Prindpel Characteristics (For detailed Electrical Characteristics refer to CA3741T Data Bulletin, File No. 531.) Input Offset Voltage
v,o
Input Offset Current
1,0
Input Bias Current
,,B
Rs~10k11
-
1
5
mV
20
200
nA
80
500
nA
Open-Loop Differential
AOL
Voltage Gain V1cR
Common-Mode Rejection Ratio
CMRR
Output Voltage Swing
Vo(P-P)
202
z 2 k11
Vo• ±10 V
Common-Mode Input Voltage Range
Supply Current
RL
10·
50,000
200,000
94
106
±12
±13
Rs~ 10 kn
70
90
RL.z10k11
±12
±14
RL~2k11
±10
±13
-
1.7
2.8
dB V dB
V mA
Linear Integrated Circuits CA6078, CA6741 lu~""°'-'&GI
i
i ••
t1••aiw , 11·• - 6v ,
j
AMIIC•T T(IIIH•AT\,Nlt( 1T,1 1• ts•c
------~_, - ·· , ·,··r ·-• .....
1I
4-
;}
.
'
-
I
-LT
cu•••o• llol•IC.•
i
..
I i
i
• • d NCll • -
HCl · IOIU
FiJ.3-/N 111. Fr-.qwncy for CA6078A T.
~
I
l
.. - -· ~n
! '
i
I I .I
-~+
-.-..., . ., . . Y4 •tY, Y""• • lv l _ _ , fl--6fUIO( tfa)•II•(
'
•
,......
I
:
I
-·TlCN
IIICOtL 1•1 1 llltOIS(
'ILTt•
I )
iI
•
, ... UH c ,,.. •c•o OUAlril · T(C.,.
I: I
,.,,.
j
...I,,,
°" .. [T£•
120 Q
(NT ll ""f l TOTAL 111110,,c VOLf'AGC , lll('l••to ro, .. Pvt
1•c•c,,.G oeu1 .. co
• tr
Fi1.6-EN 111. Fnqu•ncy for CA6741 T.
-,,
*''"
OUAN •
HCI ·
u c..... ,,c•,
ton•
111
[ •
1111
TUT 11.0CK OIAGH• Ola
Ill
IIIOISf ,1LTltlll
..
I
►
-L
ou... • T(CM
I
I
II-
"
I
I-+
"
I.
Fig.5-IN n . FrflquMcy for CA6741T.
'
,l 111
iiifiii'1 -11ou,1-fii j ./z .,
•• fli
("ITllfril) · TOT&t,. HOIS( VOl,.TAG(,.l,(11t•tO ff)lflP,UT
1 •c•o1NG ()l:T&IN(O WITH OUAH · T(CN
•in•
NCl · IOIII
N_,_ Fig. l - T•sr block diagram for EN·
Fig.8-Test block diagram for IN.
203
9. WIDEBAND OPERATIONAL AMPLIFIER (Reprinted by permission of RCA Solid State Division, now Harris Semiconductor)
204
0 peratlonal Amplifiers CA3130, CA3130A, CA3130B
~
H - t817 :
Mini-DIP CA3130E CA3130AE
I
With MOS/FET lnpuf/ COS/MOS Output
fi'J f' i1
AUTVPN 8-LEAD TO-& with Dual-In-line
Formed leadl CS 1uffixt H -1787
BiMOS Operational Amplifiers
FEATURES: ■ MOS /FE T input stage provides:
All l'VPN 8-LEAD T0-6
CT sufflxt H -1528
very high z, = 1.5 TO (1 .5 x 10120) typ. very low II = 5 pA typ. at 15- V operation 2 pA typ. at 5- V operation ■ Common-mode input-voltage range includes} negative supply rail; input terminals can Ideal for be swung 0.5 V below negative SLlpply rail single-supply ■ CO~/ MOS output stage permits signal swing applications to either ( or both) supply rails
RCA-CA3130T, CA3130E, CA3130S, CA-3130AT, CA 3130AS, CA3130AE , CA3130BT, and CA3130BS are Integrated-circuit operational amplifiers that combine the advantages of both COS/MOS and bipolar transistors on a monolithic chip. Gate-protected p-channel MOS/FET (PMOS) transistors are used In the Input circuit to provide very-high-input impedance. very-low-input current. and exceptional speed performance. The use of PMOS field-effect transistors in the Input stage results In common-mode input-voltage capability down to 0.5 volt below the negative-supply terminal, an important attribute in single-supply applications. A complementary-symmetry MOS (COS/MOS) transistorpair, capable of swinging the output volt!ige to within 10 millivolts of either supply-voltage terminal (at very high values of load impedance). is employed as the output circuit. The CA3130 Series circuits operate at supply voltages ranging from 5 to 16 volts. or ±2.5 to ±8 volts when using spilt supplies. They can be phase compensated with a single external capacitor. and have terminals for adjustment of offset voltage for applications requiring offset-null capability. Terminal provisions are also made to permit strobing of the output stage. The CA3130 Series is supplied in standard 8-lead TO-5 style packages (T suffix). 8-lead dual-in-line formed lead TO-5 style "OIL-CAN" packages (S suffix) . The CA3130 is available in chip form (H suffix) . The CA3130 and CA3130A are also available in the Mini-DIP 8-lead dual-in-line plastic
■ ■ ■ ■ ■
■
Low Via : 2 mV max. (CA3130B) Wide BW: 15 MHz typ. (unity-gain crossover) High SR: 10 V/µs typ. (unity-gain follower) High output current (Io): 20 mA typ. High Aoc 320,000 (110 dB) typ. Compensation with single external capacitor
APPLICATIONS: ■
Ground-referenced single -supply amplifiers Fast sample-hold amplifiers • Long-duration timers/monostables ■ High-input-impedance comparators (ideal interface with digital COS/MOS) ■ High-input-impedance wideband amplifiers ■ Voltage followers (e .g., follower for single-supply DIA converter) ■ Voltage regulators (permits control of output voltage down to zero volts) ■ Peak detectors ■ Single-supply full-wave precision rectifiers ■ Photo-diode sensor amplifiers ■
package (E suffix) . All types operate over the full militarytemperature range of -55°C to +125°C . The CA3130B is intended for applications requiring premium-grade specifications . The CA3130A offers superior input characteristics over those of the CA3130.
205
Linear Integrated Circuits CA3130, CA3130A, CA3130B ELECTRICAL CHARACTERISTICS It TA•21°C,
v•-,a V, v- • 0 V
(Uni••· othtrwi• apedfied)
LIMITS CA31308 (T,S)
CHARACTERISTIC
Min.
Typ.
Max.
2
Input Offset Voltage, Iv I ol . vt•t.7 .5 v
-
0.8
Input Offset Current, 11 ,ol, vt•t.7.5 v
-
0.5
Input Current, I I vt•t.7.5 V
-
5
Maximum Output Voltage: VoM+ At RL =2 kn VoM AtRL•OO
VoM+
12
14.99
5
-
8
16
mV
10
-
0.6
20
-
0.5
30
pA
20
-
5
30
-
5
50
pA
~
50 k
320k
-
50 k 320 k
-
VN
-
94
110
-
94
110
-
dB
-
80
90
-
70
90
-
dB
10
0
-0.5 to , 12
10
V
150
-
32
-
12
-
14.99
-0.5 10
0
!O
12 100
-
-
12
0.01
-
-
14.99
32
13.3 0.002 0.01
-
-
13.3 0.002 0.01
-
-
15 0
0.01
45
12
22
45
20
45
12
20
45
-
10
15
-
10
15
3
-
2
3
-
2
3
-
-
10
-
-
10
-
-
15 0
0.01
0.01
22
45
12
22
12
20
45
12
-
10
15
2
-
5
12
V
mA
.,
Vo a 0 V, Al= oo Input Offset Voltage Temp. Drift, 6.V10/!J.T• COMl"fNSA TIOH
v-
4 TOP YltW
TOI" VIEW
S and T Suffix.. Fig. 1 -
206
320 µVN
'
loM- (Sink)@ Vo• 15 V Supply Current, I -f: Vo•7.5 V,RLa oo
~S(
2
15 0
-
VoM Maximum Output Current: loM +(Source)@ Voz0V
13.3 0.002
Units
-
.
100 k 320k urge-Signal Voltage Gain, AoL 110 Vo•10 VP·P· RL •2 kn 100 Common-Mode 100 86 Rejection Ratio,CMAR -0.5 Common-Mode Inputto 0 Voltage Range, V ICR 12 Power-Supply Rejection 32 Ratio, 6.V10l6V± v±s:±7.5 V
CA3130A (T,S,E) · CA3130 (T,1,E) Min. Typ. Max. Min. Typ. Mix
HCl · UOH
E Suffix Function•/ di.,r•m• for rh• CA3130 •ri•1.
mA
µVf'C
0 peratlonal Ampllflers CA3130, CA3130A, CA3130B TYPIC~L VALUES INTENDED ONLY FOR DESIGN GUIDANCE TEST CONDITIONS
v+ .• +7.5 V
CHARACTERISTIC
v- • -7.5 V
CA3130B ~.(T,S)
CA3130A (T,S,E)
CA3130 (T,S,E)
UNITS
±22
±22
±22
mV
1.5 4 .3 23
1.5
1.5
4.3
4.3
Tn pf
23
23
µV
Cc= 0
15
15
15
Cc= 47 pf
4
4
4
Cc= 0
30
30
30
Cc= 56 pf
10
10
10
0 .09
0 .09
0.09
µs
10
10
10
%
1.2
1.2
1.2
µs
TA• 26°C (Unless OtherwiN Specified)
Input Offset Voltage Adjustment R1"99
10 k!l across Terms. 4 and 5 or 4 and 1
Input Resistance, R1 f = 1 MHz
Input Capacitance, C1 Equivalent Input Noise Voltage, en Unity Gain Crossover
BW • 0 .2 MHz As= 1 Mn·
Frequency , fr Slew Rate, SR : Open Loop Closed Loop Transient Response : Rise Time, tr
Cc= 56 pF CL= 25 pF AL=2kn (Voltage Follower)
Overshoot Settling Time (4 VP·P Input to (T Suffix> H-1787
H-1628
■ ■ ■
High open-loop gain at video frequencies - 42 dB typ. at 1 MHz High unity-gain cronover f requency (fr) - 38 MHz typ. Wide power bandwidth - Vo= 18 Vp-p typ. at 1.2 MHz High slew rate - 70 V/µa (typ.) in 20 dB amplifier 25 V/µs (typ.] In unity-gain amplifier Fast settling time - 0.6 µs typ . High output current - ±15 mA min. LM118, 748/LM101 pin compatibility
RCA-CA3100S, CA3100T is a large-signal wideband, highspeed operational amplifier which has a unity gain crossover frequency (fr) of approximately 38 MHz and an openloop, 3 dB corner frequency of approximately 110 kHz. It can operate at a total supply voltage of from 14 to 36 volts (±7 to ±18 volts when using split supplies) and can provide at least 18 V~p and 30 mA p-p at the output when operating from ±15 volt supplies. The CA3100 can be compensated with a single external capacitor and has de offset adjust
■ ■
Single capacitor-compensation Offset null terminals
Appllcatlon1: ■ ■ ■ ■ ■ ■ ■ ■ ■
Video amplifiers Fast peak detector, Meter-driver amplifiers High-frequency feedback amp/If/er, Video pre-drivers Oscillators Multlvibrators Voltage-controlled oscillator Fast comparators
terminals for those appl ications requiring offset null. (See Fig. 15). The CA3100 circuit contains both bipolar and P-MOS transistors on a single monolithic chip. The CA3100 is supplied in either the standard 8-lead TO-5 package ("T" suffix), or in the 8- lead TO-5 dual-in-line formed-lead "DIL'CAN" package (''S" suffix) .
116 12" 01 HOH •IHV(JITIJIIIG IN'VT
03
,ooo
♦
,.,vorn,G ~-i.--_-:._-:._--:_-_-+~----_-_-_-:._-_-_-=.-+--+-----,
OUT"VT
INPUT
,--~----,,...,....-~---4,
l
,_,
""&SL
1000 COll~-S.OTIOO,
orrsn •uLL
t-----+--+--~,
or,,n IIIULL
,::iL
COM~(IISATIOO,
92CM-218155R 1
Fig. 1 - Schematic diagram for CA3100.
208
Linear Integrated Circuits CA3100 Types ELECTRICAL CHARACTERISTICS, At TA • 25°C:
CHARACTERISTICS
TEST CONDITIONS SUPPLY VOLTAGE UNLESS OTHERWISE SPECIFIED
LIMITS
cv•.v-1-15 V
UNITS
MIN.
TYP.
MAX .
-
±1
±5
mV
0 .7
2
µA
-
±005
±0.4
µA
56
61
-
dB
± 12
+ 14 - 13
-
V
76
90
-
dB
+9
+ 11
-9
- 11
-
V
STATIC Input Ofhet Voltage, V1O
Vo • 0 ! 0 .1 V
Input Bias Current, 119 Input Offset Current, Ito
Vo = 0 ! 1 V .
Low-Frequency Open -Loop Voltage Gai n,AoL •
Vo ' ! 1 V Puk , F • 1 kHz
Common -Mode Input Voltage Range, V1cR
CMAA
Common -Mode Ae1ect1on A1t10, CMAA M11umum Output Voltagp : ♦ P0$1t1ve, VQM
Negative, VoM -
Vt Common Mode • ! 12 V Doffe rent, al Input Voltage · 0 ! 0 1 V Al
Maximum Output Curren t : Pos1t1ve, IQM '
> 76 dB
2
KU
+15
+30
- 15
- 30
-
mA
-
8 .5
10.5
mA
60
70
-
dB
-
38
-
MHz
36
42
-
dB
50
70
-
V/µ.s
25
-
0 .8
1.2
-
-
0.4
-
F • 1 MHz
-
30
-
K!l
F
-
110
-
n
-
8
-
INAMS
-
0 .6
-
µ.,
Otlterl'nt ,al lnµu1 Voltage
0 ! 0 1V
S1
Negat,ve, 'OM ·
AL
250
Supply Currt:'nt, 1•
Vo
0 ' 0 1 V , Al > 10
Power -Supply Ae1ect ,on Aat ,o, PSR A
.'\v ' = •
1
v .. \ v
_. I
KH
1V
DYNAMIC Un11y -Ga1n Crossover Frequency, 'T
Cc• 0 . Vo" 0 3 VIP -Pl
1-MHz Open -Looµ Voltage Ga,n,AOL
t ::
Slew Rate . SR : 20-dB Amplii,er
Av= 10 . Cc.a 0 , Vt~ 1 V (Pulsel
Ay • 1. Cc= 10 pF , V1
Follower Mode Power Bandwidth., PB~ : 20-dB Amplof,er
Open -Loop O,fferent,al Input Impedance, Zt
•
Zo
a
10 V (Pulse
Av= 10, Cc• 0, Vo• 18 V (P -PI Av• 1.
Follower Mode
Open-Loop Output Impedance,
1 MH, . Cc:: 0 . Vos 10 V (P -PI
s
cc•
10 pF , Vo• 18 V (P-PI
1 MHz
Widebend Noise Voltage Referred to Input, •NfTotal)
BW " 1 MHz, As = 1
Settling Time, t 1 [To Within± 50 mV of 9 V Output Swing
AL = 2 KH, CL = 20 pF
Slew Rate Power Bandwidth•---ff Vo (P -P)
d2
MHz
• Low-frequency dynamic cbaracteristic
-·"'"
E Suffix
S & T Suffixes
TERMINAL ASSIGNMENTS
209
O peratlonal Amplifiers CA3100 Types MAXIMUM RATINGS, Ablolutt1-Maximum V•lua: Supply Voltage (betWNn V♦ and v- terminals). Differential Input Voltage . Input Voltage to Ground• . Offset Terminal to v- Terminal Voltage . Output Cur,.nt . , Device Oiaipetion6 UptoTA •66f AbowTA •66 C Ambient Tampereture Range : Operating: E Type Send T Types Storage Leed Temperature (During Soldering) : At distance 1/16 ± 1/32 inch (1.59 ± 0 .79 mml from case for 10 s mu . .
36 ±12
V V V V mA.
±15
i0.6 50 63)
6.67
mwf~
-40 to +85 -55 to +125 -66 to +150
oc oc oc
+266
oc
• If the supply voltage it less then ±15 volts, the maximum input voltage to ground is equal to the supply voltage. • CA3100S, CA3100T don not contain circuitry to protect against short circuits in the output .
TYPICAL CHARACTERISTIC CURVES -NT
r!I
IILl•I 1111 I.OolD CAMCl1ANC( ICLl•20,,
U)IO IIU,STANC(
,--
I ~
~
('.. ~~
!
I
:......
'I.
'\~.~~K\; ~,,......:),'
!• ►
~
'
....
Tl-"·"'-"' llarn•c
~ y IIOl.TAll IV~ v · 1ot5 V
I I
~
..
....~ ... ,~
.....
~ ~ 0
,,,,
g•
l'z"
0
~~
~~
-,.•~
"".,
• • 101
'
►
., l
.,~ 0
1-...
I
'I \
I
0
.:1 ...,, :x
\.
~I'
I 0 .001
.,rot
•••
•••01
••
1
I
'\
10
.'
'IIIOUCIICY If 1-MHI
,,
g• I
'bi
I
l
Fig. 3 - Ot»n-loop ~in
i,1.
l
I !
I' ' I
1I
tt
' .
'
'
I
If&.
fr«lfJ•ncy •nd
I
•
L()AI) CANCITA.NC( ICL ► ZO,,
I :
i'
- -+ -~
z,
~ zo
t
,,
~
I()
~
I
~,.
~,.~ ,.,.
...,.,, ...
'
IO'°
0
~
-V!IITING GAW- ,e 0 •
00,
NVl.TtNO · - - fe ~0110-UIO" .... 1-'Q.1-•
'1111'.0UIIICY 111--
F/(J 4 - Ot»n-loop ~in
If&.
f,-quency •nd wpply
n.,
•n•c ...
LOAO ll(IIITu.cl l"'-1•21111 I..OAO ~!TA.NC( ICL I• ZO,,
: :; :
: : :; 1; ::
..... ... .. . .... ....... .. ...... . -- .: ::: : :: : : :: :: :: :: ...... ... ...
10t---+--t-·-+---lt---+--t-'- +'-· .... . f-::_: :+:_ ::__,:_::_::-+--+--+-~
:·:: =·:: :: : :::: ::::
I
.an-,.,,
I 0
:=
i ~~ev
►
,__
►
a
'
NJ~
.' . ,,._
~~~. ,.., ~ IIONIT'°"
•
~
ltl)•OtOIVOC
0
IO
IO
,0
tCW\.lTT MCIIMIO VICTOII M"IIIIUICI
.,
IO
(OW(NSATION ~-!TA.NC( ICcl'IOII I
,Ot-,,
NU · l tt••
FitJ 1 - Typical 0f»n-loop output imP«Janc. ,,.(lfHncy.
210
i,a.
-•IT T(-11.UUII( ITal•ZS•c
l
00
,.,
~ • \IOI.TAG( IV'.Y ' l•l'V
Q
I
i
!!
.,
FitJ 5 - R«,ulr.d t:Otnf»nation cap«it•nce closed-loop ~in.
lf0lt•ge. - l ( • T T(W(IIATUII( I Tai
lo
- " ' ~ i - . IT6ris•c LOAO ll(SlllUIC( IIL ► l 110
• ~
SATIOtl C&HCITAIIC[ ICc I•
'
',o
tem~tu,._ \
0
•
•ICS · lt1 7•
LOAD ll(S,Sf-'NC( IIILl•Z 1111 C&HCtTAIIC( ICLl•ZO of
--i
1
tlC'\ l •\10
FitJ 2 - Ot»n-loop ~in, 0f»n-loop pha. shift f,-quency.
0
OI
000 l
tOO
If&.
Linear Integrated Circuits CA3100 Types TYPICAL CHARACTERISTIC CURVES (Cont'd) &WMlfT TIW(IIATUII( 1,,.1,n•c a.t.HOWCT" CIWI AT t 41 • 1" " '
'w'OlTA,G( 1v•. v · 1•1Sv
_......_i .. +·
•
()
•
I()
000
SOUIIC( ll(SJST.\NCC 11151-ll
Fig. 8 - Widftband input noiu voltage vs. sourca
Fig. 9 - Typical o,-n-loop difftm1ntial input im,»danctt vs. frequttncy.
resistanca. _
l
.. , l(W(IIATUII(
n,.1,z,•c
>
~ . , VOl.TAG( tv•. v · 1.,,v
>
I
1
I
. .... 1'
_____ _.,. --
l
i
..
F
~
I I
10 I
,,f
C
~
(
~
..;
. _j
l 'O..L0,,(111
i l'
.
I
,1-I
~
J ,o ~ ,, ;
·1 , ,G l l
l()t-
~ ...C"
.i '2'
. . . _.l
CllltCUtT
I
0-
,,
-I
~
• • 1I
§ ~
.,
u
0 Q ()
l
'
I 10
I
l
4
I
i
I
•
'
I K)
4
l
0
6. I 1()0
!2'
SUPl'Ll YOLTA
I
"!~
.... tl
....r:;:.-,!~,:.r:•l,E~;u~
f-4-++ Trr.-tt: tt:{ r:;:::.:.: .... ·~
--♦
~
•• -
I ,z,
.
-..,. ,o
C
:,
& ~ !
,.-~ ~
fl+t-
~
z
--·~--
't~
25
0
!2 S
!:,
!-7'
!tO
tll !,
'+•
....
:,
u
h.!'
► ..;
!., ,
,
• i
. ,,
.µ ,_ 1-+;.. u..;.....
~
~ ~
, E
.~o•..£;n
..;
+
....
,.~c:I+- .~ .,... __
~
Ht
I ~.
C
~o
~
. ,o .. ,,
Fig. 11 - Common-mode input voltagt1 range vs. supply voltage.
W-~
--
,1
~
~ ~
~+
25
0
tl5
t2 5
!'7'
t5
ttO
tl2 5
tl5
!'115
t20
SUPl'LY VOLTAGE cv•.v-1-v
S~l"LY YOLTAG( cv•.v-1-v
F;g. 12 - Maximum output voltage vs. supply Fig. 13 - Supply currt1nt vs. supply voltage.
voltage. AIHll(NT T l ~ ~ ( CT
l•U•C
,, C
I' }
•r
I
!u
~
•. o,
'
0
Fig. 14 - Input bi• cu,,.nt
If&.
wpply ~,.,._
211
Operational Ampllflers CA3021, CA3022, CA3023
Low-Power Wideband Amplifiers
.,
1
12-Lead T0-5
Feature•: ■
Lower DC Power Drain: CA3021 4 mW typ. ( Pr CA3022 12.5 mW typ. at Vee= 6 V \ CA3023 35 mW tp. ■ Excellent frequency response : ■ Wide AGC R,:mge: 33 dB typ. CA3021 = 2.4 MHz typ. • Only one pow1:J1 :; upply (4.5 to 12 V) -3d8 CA3022 7.5 MHz typ. required BW \ CA3023 = 16 MHz fyp . ■ H1gn Voltage
w 0
91CS·144S3
AMBIENT TEMPERATURE (TA)-
•c 92C S ·- " lei
Flg.J(d)
I
AGe
IS THE CURRENT FLOWING INTO TERMINAL 2. fig . ..
215
Operational Amplifiers
-
CA3021, CA3022, CA3023 VOLTAGE GAIN VS FREQUENCY FOR CA3021
TEST SETUP FOR MEASUREMENTS OF VOLT AGE-GAIN, -JdB
BANDWIDTH, AND MAXIMUM OUTPUT VOLT AGE
(R_fil
FEE08ACI( RESISTANa CONNECTED BETWEEN INALS N~. 3 ANO 7
AMBIENT TEMPERATURE (TAl•2~•c oc SUPPLY VOLTS ( Vee) • + 6 TERMINALS No. I0,11,ANO 12 CONNECTEO TO GROUND 70
Vee +6V
-
60
..,
FEEDBACK RES15 TANC: fRg,, I ~M Kll -·9:>ra
CD
IDOi(
I ~o
Rf' VTVM
4
BOONTON
z
•er I~:~~~
la.I
,
~,
-
39K .,,.,, K
40
~
-~~.... ~ ~
IOK
4 C)
91A _L-=IVALENT
ERM-
~~
r- ~
!\ 61(
30-
C)
~.I
'\.
~
4
~>
92CS - 14◄ l0
PROCEDURES
"
20 10
Voltaae Gain:
0
(a) Set e1n = 0.5 mVat frequency specified, read eout Voltaae Gain eoot (Al = 20 Loa 10 Bandwidth: ein (a) Set e0 ut to a convenient reference voltaae at f = 100 kHz and reCOfd correspondina value of 8in•
2
0.1
4
e
6
I
6
4
2
I
10
FREQUENCY ( f) - MHz 92CS- 14421
Fig.6(a)
(b) Increase the frequency, keepina 8in constant unti I eOtJt drops 3.dB. Record Bandwidth.
Fig.5 VOLT AGE GAIN VS FREQUENCY FOR CA3022 AMBIENT TEMPERATURE (TA)• 25°C DC SUPPLY VOLTS (Vee)• +6 TERMINALS No. I0, 11,ANO 12 CONNECTEO TO GROUND
ID
.., I
z
VOLT AGE GAIM VS FREQUENCY FOR CA3023
FEEOBACt< RESISTANCE (R,g) CONNECTED BETWEEN tERMINALS No 3 ANO 7
I
AMBIENT TEMPERATURE (TA)• 2!>°C DC SUPPLY VOLTS (Vccl • +6
TERMINALS No. 10, I I, ANO 12 CONNEC TED TO GROUND
..,
FEEDBACK RES ISTANCE (R 8) CONNECTED BETWEEN TERM- j INALS No 3 ANO 7 :
ID
50
-
!>O
z
40
I
4
40
4 C)
4 C) la.I
30
C)
:!..J 0
>
IOr---r--+-;--t--t---t---+---+-++--+---+---+-~
10
1
0 2
0 .1
4
6
I I
2
4
FREQUENCY( I l -
6
9 10
2
4
6
20
0 01
910Q
MMz
I I 2
4
6
8
I
2
FREQUENCY ( ll -
4
6
i
8 10
MHz 92CS • t44-27
Flg.6(b)
Fig.6(c)
oc SUPPLY VOLTS (Vccl•+6
RJI
TYPE
'
TERMINALS No.10,11, ANO 12 CONNECTED TO GROUND
CA3021
39
I
FEEDBACK RESISTANCE (RaJ CONNECTED BETWEEN TERMINALS No. 3 ANO No.7
CA3022 10 C.0023 4.7
s
I .
-~..-- ~
C4 3021'
l
z
~
4S
.
I I C-4
3'
40 ' '
I-
5>
'
-
L
021 Lt;:
h-+-
cJ._q: ... '4.Jo + ~.J --t·t--H- .µ~t=
I
3S
.
VOLTAGE GAIN VS TEMPERATURE FOR CA3021, CA3022, AND CA3023
I
C, C)
~~
I I
~
IAI
10
....
I
~
MH1
I l l ➔~ --rt I I · - LJ 4
I
I so
K fl
I
C
I !
I
I
0
50
1~
100
I~
150
AMBIENT TEMPERATURE (TA 1-"C
Fig.6(d)
216
APPENDIX B Passive Component Values and Identification
Appendix B gives Tables, Charts, and Drawings for component values and tolerances and identification of these values and tolerances. Included in the components are resistors, capacitors, and diodes.
L 2. 3. 4. 5. 6.
Tolerance and component values of carbon-composition resistors Resistor color code Resistor types and ranges Capacitor color code Capacitor ranges on the basis of dielectric material Semiconductor diode identification
217
Appendices
218 TABLE 1 Tolerance and component values of carbon-composition resistors 20% tolerance
10% tolerance
10
IO
15
12 15 18 22
22
27 33
33
39 47
47 56
68
68 82
100
100
5% tolerance 10 12 15 16 18 20 22 24 27 30 33 36 39 43 47 51 56 62 68 75 82 91 100
Harry E. Thomas, Handbook for Electronic Engineers and Technicians, copyright 1965. Reprinted by permission of Prentice Hall, Inc.
Table 2
Resistor color code A, B, C digits ABCD R =ABX 10c, D
Example A B
Red Violet
C D
R = 27 X 103, 5% = 27 kn, 5%
Orange Gold
Black 0 Green Brown 1 Blue Red 2 Violet Orange 3 Gray Yellow 4 White Gold ( C only) Silver (C only)
5 6 7
8 9
-1
-2
Tolerance (D) code No band Silver Gold
20% 10% 5%
Bruce D. Wedlock and James K. Roberge, Electronic Components and Measurements, copyright © l 978. Reprinted by permission of Prentice Hall, Inc .
TABLE 3
Resistor types and ranges
Resister Type