Intersystem EMC Analysis, Interference, and Solutions 9781630815615

Table of contents :
1 Definitions
1.1 Introduction
1.2 Objectives
1.3 Interference
1.4 Radio Frequency Interference
1.5 Compatibility
1.6 EMC and RF Compatib
1.7 Emissions and Susceptibility
1.8 The System
1.8.1 Definition
1.8.2 System Content
1.9 External Systems
1.9.1 External System Types
1.9.2 Definition
1.10 Intrasystem and Intersystem Compatibility
1.11 Interference to and from the System
1.12 One-Way and Two-Way EMC
1.13 Electromagnetic Environment
1.14 Signal Types
1.15 Hierarchy
1.16 Device Level
1.17 Platform Level
1.18 Site Level
1.19 Arena Level

2 EMC Requirements
2.1 Objective
2.2 Device Level EMC Requirements
2.2.1 Objective
2.2.2 The Device EMC Requirement
2.2.3 Capability to Comply with the Operational Requirements
2.2.4 Definition Approaches
2.3 EMC Requirements Within and Between Platforms
2.3.1 EMC Within and Between Platforms
2.3.2 Distance Between Platforms
2.3.3 Near-Field and Far-Field
2.4 EMC Requirements at the Platform Level
2.4.1 The Platform EMC Requirement
2.4.2 Capability to Comply with the Operational Requirement
2.4.3 Inter- and Intra-EMC
2.5 EMC Requirements at the Site L
2.5.1 The Site EMC Requirement
2.5.2 Inter- and Intra-EMC
2.6 EMC Requirements at the Arena Level
2.6.1 The Arena EMC Requirement
2.6.2 The Near-Far Requirement
2.6.3 Inter- and Intra-EMC
2.7 System EMC Requirements
2.8 Requirements Sum
2.9 Relationship to MIL-STD
2.10 Maximum Allowed Interference Level
2.11 The Performance Criteria
2.12 The Affecting Parameter
2.13 Gradual Performance Degradation
2.14 Interference Threshold
2.15 Crash Threshold
2.16 Performance Degradation Region
2.17 Interference Probability Threshold
2.18 Operational Damage Level
2.18.1 Nuisances
2.18.2 Mission Effectiveness Decreases
2.18.3 Mission Failur
2.18.4 Safety Risks

3 EMC Analysis and Survey
3.1 EMC Survey Objectives
3.2 Included in the Survey
3.3 Required Survey Outcom
3.4 The Need for Handling EMC Problems
3.5 The S/I Approach
3.6 The DES Approach
3.7 The Participants in the Interfering Mechanism
3.7.1 The Interfering Transmitter
3.7.2 The Interfering Medium
3.7.3 The Interfered Receiver
3.7.4 The Desired Transmitter
3.7.5 The Desired Medium
3.8 Worst-Case and Least-Worst-Case
3.8.1 The Worst-Case Dilemma
3.8.2 Least-Worst or Easiest Case
3.8.3 Saving Calculation Time
3.8.4 Worst-Case Parameters
3.9 A Possible Structure for the EMC Survey Report
3.9.1 Executive Summary
3.9.2 General
3.9.3 Methodology
3.9.4 Systems in the Analysis
3.9.5 Device Data
3.9.6 Scenarios
3.9.7 Requirements
3.9.8 Results
3.9.9 Summary and Recommendations
3.9.10 Annexes

4 Interference Types
4.1 Interference Types Criteria
4.2 Interfering Device Types
4.3 Antenna Lobe Types
4.4 Interference Outcome Types
4.4.1 Interference—the Desired Signal Is Not Received
4.4.2 Sensitivity Degradation by X dB
4.4.3 DES
4.4.4 False Reception
4.4.5 Damage
4.4.6 Degradation of Digital Communication
4.5 Interference Bandwidth Types
4.5.1 Narrowband Interference
4.5.2 Broadband Interference
4.5.3 Full-band Interference
4.6 False Reception
4.7 Interference Types According to Their Source
4.7.1 Interference from Transmitter and Receiver Parameters
4.7.2 Interference from Transmitter Parameters
4.7.3 Interference from Receiver Parameters

5 Interference fromBoth Transmitter and Receiver
5.1 Transmitter Spectrum
5.1.1 Transmitter Spectrum Definition
5.1.2 Source of the Interference Phenomenon
5.1.3 Calculating FDR
5.1.4 The Interference Effects
5.1.5 Calculating the Received Interference Level
5.2 CCI
5.2.1 Definition
5.2.2 Source of the Phenomenon, Nonintentional Case
5.2.3 Source of the Phenomenon, Intentional Case
5.2.4 The Interference Effects
5.2.5 Calculating the Received Interference Level
5.2.6 The BWF in CCI
5.3 ACI
5.4 Splitting the FDF

6 Interference from the Transmitter
6.1 Transmitter Frequency Bands
6.1.1 Transmission Band
6.1.2 Adjacent Channels or Modulation Band
6.1.3 In-Band
6.1.4 Out-of-Band
6.2 Interference from the Transmitter Spectrum—ACI
6.2.1 The Interference Effects
6.2.2 Calculating the Received Interference Level
6.2.3 Additional Definitions of the Parameter
6.2.4 Default Value for Modulated Signals
6.2.5 Default Value for Pulsed Signals
6.3 Interference from Spurious Emission—SPR
6.3.1 Source of the Interference Phenomenon
6.3.2 Definition of the Parameter
6.3.3 The Interference Effects
6.3.4 Calculating the Received Interference Level
6.4 Interference from PHN
6.4.1 Source of the Interference Phenomenon
6.4.2 Definition of the Parameter
6.4.3 The Interference Effects
6.4.4 Calculating the Received Interference Level
6.5 Interference from BBN
6.5.1 Source of the Interference Phenomenon
6.5.2 Definition of the Parameter
6.5.3 Measuring BBN
6.5.4 Default Value
6.5.5 The Interference Effects
6.5.6 Interference Relevance
6.5.7 Calculating the Received Interference Level
6.6 Interference from HAR
6.6.1 Source of the Interference Phenomenon
6.6.2 Definition of the Parameter
6.6.3 Default Value
6.6.4 The Interference Effects
6.6.5 Checking the Harmonics Content Feasibility
6.6.6 Calculating the Received Interference Level
6.6.7 The BWF for Harmonic Interference
6.6.8 Calculating the Interference Close to Harmonics
6.7 Interference from the TIM
6.7.1 Source of the Interference Phenomenon
6.7.2 Definition of the Parameter
6.7.3 Default Value
6.7.4 The Interference Effects
6.7.5 Calculating the Received Interference Level
6.7.6 Checking Intermodulation Feasibility
6.8 Interference from LFM Radar
6.8.1 Slow Sweep
6.8.2 Fast Sweep

7 Interference from the Receiver
7.1 Receiver Frequency Bands
7.1.1 Reception Band
7.1.2 Selectivity Band
7.1.3 In-Band
7.1.4 OOB
7.2 Required (S/I )r
7.2.1 Source of the Interference Phenomenon
7.2.2 Definition of the Parameter
7.2.3 Measuring (S/I)r
7.2.4 Default Value
7.2.5 (S/I)r and Processing Gain
7.2.6 Protection Ratio
7.2.7 Jamming Ratio
7.3 General Aspects in Receiver Interference
7.3.1 Direct and Indirect Definition of the Interference Parameter
7.3.2 Interference Effects
7.3.3 Equivalent Interfering Signal Level
7.4 Interference from SEL
7.4.1 Source of the Interference Phenomenon
7.4.2 Definition of the Parameter
7.4.3 Measuring LSEL and the Indirect Definition
7.4.4 Indirect Definition of the Parameter
7.4.5 Calculating the Received Interference
7.4.6 The BWF
7.5 SAT and Desensitization
7.5.1 Amplifier Compression
7.5.2 The Interference Effect
7.5.3 Definition of the Parameter
7.5.4 Acquiring the –1-dB Compression Point
7.5.5 Comparing Interference and SAT
7.5.6 Calculating the Received Interference Level
7.6 DMG
7.6.1 Source of the Interference Phenomenon
7.6.2 Definition of the Parameter
7.6.3 Acquiring the DMG Level
7.6.4 Default Value
7.6.5 Calculating the Received Interference Level
7.7 Interference from IMR
7.7.1 Source of the Interference Phenomenon
7.7.2 Definition of the Parameter
7.7.3 Measuring the IMR
7.7.4 Calculating the Received Interference Level
7.8 Interference at the IF
7.8.1 Source of the Interference Phenomenon
7.8.2 Definition of the Parameter
7.8.3 Calculating the Received Interference Level
7.9 Interference from LO Radiation
7.9.1 Source of the Interference Phenomenon
7.9.2 Definition of the Parameter
7.9.3 Calculating the Received Interference Level
7.10 Interference from RIM
7.10.1 Source of the Interference Phenomenon
7.10.2 Definition of the Parameter
7.10.3 Measuring the Parameter
7.10.4 Default Value
7.10.5 Calculating the Intermodulation Level
7.10.6 Calculating the Intercept Point
7.10.7 Calculating the Received Interference Level
7.10.8 Checking the Intermodulation Feasibility
7.11 Harmonics and Intermodulation
7.11.1 Harmonics
7.11.2 Introduction to Intermodulation
7.11.3 The Slope of the Intermodulation
7.11.4 The Intercept Point Concept
7.11.5 The Intermodulation Spectrum
7.11.6 The Third- and nth-Order Intermodulation Equations
7.11.7 Intermodulation from Nonequal Signals
7.11.8 Intermodulation from Multiple Transmitters
7.11.9 Number of Intermodulation Products
7.12 In-Band and OOB Interference

8 Calculating the Received Interference Level
8.1 The Calculation Principle
8.2 Calculating the Received Interference Level
8.2.1 Transmitter Pow
8.2.2 Interference Level Relative to CCI
8.2.3 Transmitter External Filter
8.2.4 Transmitter Cable Loss
8.2.5 Transmitter Waveguide Loss
8.2.6 Transmitting Antenna Gain
8.2.7 Transmitting Antenna Side Lobes
8.2.8 Path Loss and Coupling
8.2.9 Polarization Loss
8.2.10 Receiving Antenna Gain
8.2.11 Receiving Antenna Sidelobes
8.2.12 Receiver Cable Loss
8.2.13 Receiver Waveguide Loss
8.2.14 Receiver External Filter
8.2.15 BWF
8.3 Power Sum of Multiple Interferers

9 Interference Margin and Its Meaning
9.1 Background
9.2 IMRG in the S/I approach
9.2.1 The Criterion
9.2.2 Procedure and Steps of IMRG Calculation
9.2.3 Desired Signal Level S Calculation
9.2.4 Interference Threshold Calculation
9.2.5 Interference Level I Calculation
9.2.6 Interference Plus Noise Calculation
9.2.7 IMRG Calculation
9.2.8 Relationship Between IMRG and Fade Margin
9.3 IMRG in the DES Approach
9.3.1 The Criterion
9.3.2 DES Calculation
9.3.3 DES versus I/N
9.3.4 Choosing the Interference Threshold
9.3.5 Procedure and Calculation Steps
9.3.6 Interference Threshold Calculation
9.3.7 IMRG Calculation
9.3.8 DES versus I
9.3.9 IMRG Impact on DES
9.4 IMRG Impact on the Range
9.4.1 Background
9.4.2 Range Degradation in the S/I Approach
9.4.3 Range Degradation in the DES Approach
9.5 Interference to Short Desired Paths
9.6 Applying the DES Approach for Interference to Radar
9.7 FM Degradation
9.8 Inverse Calculation Technique
9.9 Sensitivity Level as Wrong Threshold Level
9.10 EMC Calculation Summary

10 The Interference Range and the Reception Range
10.1 Hierarchy Level and Interference Types
10.2 Calculating the Interference Range
10.2.1 The Problem
10.2.2 Interference Range without Terrain Influence
10.2.3 Interference with Terrain Influence
10.3 Calculating the Reception Range with Interference
10.3.1 Background
10.3.2 Signal-to-Interference Plus Noise Ratio
10.3.3 Reception Range without Terrain
10.3.4 Reception Area with Terrain
Reference

11 Propagation Models for EMC
11.1 Difference Between Communication and EMC Models
11.2 Models without Terrain Influence
11.3 Models Based on DTM
11.4 Generic Terrain-Influenced Model Path-Loss Model
References

12 Coupling Between Antennas
12.1 Measurement
12.2 Scaling
12.3 Prediction by Simulation
12.4 Approximate Free-Space Calculation
12.5 Frequency Dependency

13 Relative Angles Between Antennas
13.1 The Problem
13.2 Transformation by Rotation
13.3 Calculating θ and ϕ

14 Antenna Gain in Intercardinal Angles
14.1 The Problem
14.2 The Guiding Principle
14.3 Coordinate Systems
14.4 Coordinates System Transformation
14.5 Symmetrical Antenna Pattern
14.6 The Sum in Decibels Method in the Symmetrical Case
14.7 Nonsymmetrical Antenna Pattern
14.8 The Sum in Decibels Method in the Nonsymmetrical Case
14.9 BWAZ > BWEL
14.10 BWEL > BWAZ
14.11 Reducing the Estimation Error
14.12 Real versus Envelope Pattern
14.13 Verification by Simulation
14.14 Examples
14.15 Summary

15 Near-Field
15.1 Far-Field Definition
15.2 Near-Field Definition
15.3 Near-Field Distanc
15.4 Very Small Antenna Near-Field Distance
15.5 Aperture Antenna Near-Field Distance
15.6 Wire Antenna Near-Field Distance
15.7 Near-Field Distance Between Two Antennas
15.8 Near-Field Path Loss
15.9 Near-Field Path Loss for Aperture Antennas
15.9.1 Main Lobe
15.9.2 Main Lobe Calculation Steps
15.9.3 Sidelobes’ Path Loss

16 Interference Probability
16.1 Background
16.2 Accumulated Probability from Multiple Phenomena
16.3 Accumulated Probability from Multiple Interferers

17 Interference Probability—Antenna Patterns Aspect
17.1 The Problem
17.2 Main Lobe versus Sidelobes Case
17.3 Antenna Pattern versus Fixed Antenna Case
17.4 Two Rotating Antennas Case
17.4.1 Step 1: Calculating the Antennas’ Probability Density Function
17.4.2 Step 2: Calculating the Viewing Sector
17.4.3 Step 3: The Probability of a Certain Antenna Pattern Value
17.4.4 Step 4: The Joint Probability Density Function
17.4.5 Step 5: Reference Interference Margin in the Main Lobe
17.4.6 Step 6: Interference Margin of the Event i,j
17.4.7 Step 7: Interference Probability of the Event i,j
17.4.8 Step 8: Interference Probability
17.4.9 Step 9: Interference Probability from the Range Gate A
17.4.10 Example

18 Probability of Frequency Difference
18.1 The Problem
18.2 Mathematical Background
18.3 The General Case
18.4 Continuous Frequency Allocation
18.5 Case 1: Identical Frequency Bands
18.6 Case 2: Nonoverlapping Frequency Bands
18.7 Case 3: Partially Overlapping Frequency Bands
18.8 Case 4: One Frequency Band Is Included in the Other
18.9 Fixed-Frequency and Frequency-Hopping Device
18.9.1 Fixed-Frequency Devices
18.9.2 Frequency-Hopping Devices

19 Probability of Pulse Interference
19.1 The Problem
19.2 Definitions
19.3 Calculating RMin
19.4 Calculating RMax
19.5 Calculating the RMin Probability
19.6 Calculating the RMax Probability
19.7 Summary of Interference Probability
19.8 Various Cases
19.8.1 Probabilities Reach the Extreme Zero and One Values Case
19.8.2 Probabilities Do Not Reach the Extreme Zero and One Values Case
19.8.3 a >> d Case
19.8.4 d >> a Case
19.8.5 Identical Pulse Width Case
19.8.6 Whole Number of Interfering Pulses Case
19.8.7 Additional Probability Graph Shapes
19.9 Radar Pulses Interference

20 Pulse Interference to Digital Communication
20.1 Hierarchy from Bits to Message
20.2 Group Error Rate
20.3 Symbol Error Rate
20.4 Frame Error Rate
20.5 Message Error Rate
20.6 Error Rates with Interferen
20.6.1 General Case
20.6.2 Case 1: PW > tMessage
20.6.3 Case 2: tFrame < PW < tMessage
20.6.4 Case 3: tSymbol < PW < tFrame
20.7 Group Delivery Probability
20.8 Required Number of Retransmissions

21 EMC Between Synchronous Hopping Devices
21.1 Background
21.2 Frequency-Hopping Times
21.3 Synchronous and Orthogonal Devices
21.4 Overlapping
21.5 Distances and Reception Delay
21.6 Solution and Objective
21.7 The Overlapping Portion
21.8 Conditions for Overlapping Interference

22 EMC Solutions
22.1 Background
22.2 Time-Axis Solutions
22.3 Distance-Axis Solutions
22.4 Angle-Axis Solutions
22.5 Frequency-Axis Solutions
22.6 Required Frequency Separation
22.7 Combined Distance and Frequency Separation
22.8 Changing the Specifications

23 EMC Tests
23.1 The Need
23.2 Objectives
23.2.1 Technical EMC Test Objectives
23.2.2 Operational EMC Test Objectives
23.3 IMRG Test Procedure in the DES Approach
23.3.1 Test Block Diagram
23.3.2 Deployment Instruction
23.3.3 Preliminary Tests
23.3.4 Interference Test Procedure
23.3.5 Solution and Repeated Test
23.3.6 Miscellaneous
23.4 IMRG Test Procedure in the S/I Approach
23.4.1 Test Block Diagram
23.4.2 Deployment Instruction
23.4.3 Preliminary Tests
23.4.4 Interference Test Procedure—First Method
23.4.5 Interference Test Procedure—Second Method
23.4.6 Solution and Repeated Test
23.4.7 Miscellaneous
23.5 Differences Between Anticipated and Tested Interference
23.5.1 Case 1: No, No
23.5.2 Case 2: No, Yes
23.5.3 Case 3: Yes, N
23.5.4 Case 4: Yes, Yes
Appendix Device EMC Specifications Table

Citation preview

Intersystem EMC Analysis, Interference, and Solutions

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For a complete listing of titles in the Artech House Elecromagnetics Series turn to the back of this book.

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Intersystem EMC Analysis, Interference, and Solutions Uri Vered

artechhouse.com

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Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the U.S. Library of Congress. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. Cover design by John Gomes ISBN 13: 978-1-63081-561-5 © 2018 ARTECH HOUSE 685 Canton Street Norwood, MA 02062 All rights reserved. Printed and bound in the United States of America. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher. All terms mentioned in this book that are known to be trademarks or service marks have been appropriately capitalized. Artech House cannot attest to the accuracy of this information. Use of a term in this book should not be regarded as affecting the validity of any trademark or service mark. 10 9 8 7 6 5 4 3 2 1

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To my editor, Alan M. Egger. This book would not have reached its quality without his contribution.

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Contents 1

Definitions 1 1.1 Introduction 1.2 Objectives 1.3 Interference 1.4  Radio Frequency Interference 1.5 Compatibility 1.6  EMC and RF Compatibility 1.7  Emissions and Susceptibility 1.8  The System 1.8.1 Definition 1.8.2  System Content 1.9  External Systems 1.9.1  External System Types 1.9.2 Definition 1.10  Intrasystem and Intersystem Compatibility 1.11  Interference to and from the System 1.12  One-Way and Two-Way EMC 1.13  Electromagnetic Environment 1.14  Signal Types 1.15 Hierarchy 1.16  Device Level 1.17  Platform Level 1.18  Site Level 1.19  Arena Level

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1 1 2 2 3 3 3 3 3 4 4 4 5 5 5 6 6 7 7 8 8 8 9

EMC Requirements

11

2.1 Objective 2.2  Device Level EMC Requirements 2.2.1 Objective 2.2.2  The Device EMC Requirement 2.2.3  Capability to Comply with the Operational Requirements

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Intersystem EMC Analysis, Interference, and Solutions 2.2.4  Definition Approaches 2.3  EMC Requirements Within and Between Platforms 2.3.1  EMC Within and Between Platforms 2.3.2  Distance Between Platforms 2.3.3  Near-Field and Far-Field 2.4  EMC Requirements at the Platform Level 2.4.1  The Platform EMC Requirement 2.4.2  Capability to Comply with the Operational Requirement 2.4.3  Inter- and Intra-EMC 2.5  EMC Requirements at the Site Level 2.5.1  The Site EMC Requirement 2.5.2  Inter- and Intra-EMC 2.6  EMC Requirements at the Arena Level 2.6.1  The Arena EMC Requirement 2.6.2  The Near-Far Requirement 2.6.3  Inter- and Intra-EMC 2.7  System EMC Requirements 2.8  Requirements Summary 2.9  Relationship to MIL-STD 2.10  Maximum Allowed Interference Level 2.11  The Performance Criteria 2.12  The Affecting Parameter 2.13  Gradual Performance Degradation 2.14  Interference Threshold 2.15  Crash Threshold 2.16  Performance Degradation Region 2.17  Interference Probability Threshold 2.18  Operational Damage Level 2.18.1 Nuisances 2.18.2  Mission Effectiveness Decreases 2.18.3  Mission Failures 2.18.4  Safety Risks

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EMC Analysis and Survey

23

3.1  3.2  3.3  3.4  3.5  3.6  3.7 

23 23 24 24 26 27 28 28 29 29 29 29 30 30 30

EMC Survey Objectives Included in the Survey Required Survey Outcome The Need for Handling EMC Problems The S/I Approach The DES Approach The Participants in the Interfering Mechanism 3.7.1  The Interfering Transmitter 3.7.2  The Interfering Medium 3.7.3  The Interfered Receiver 3.7.4  The Desired Transmitter 3.7.5  The Desired Medium 3.8  Worst-Case and Least-Worst-Case 3.8.1  The Worst-Case Dilemma 3.8.2  Least-Worst or Easiest Case

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Contentsix

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3.8.3  Saving Calculation Time 3.8.4  Worst-Case Parameters 3.9  A Possible Structure for the EMC Survey Report 3.9.1  Executive Summary 3.9.2 General 3.9.3 Methodology 3.9.4  Systems in the Analysis 3.9.5  Device Data 3.9.6 Scenarios 3.9.7 Requirements 3.9.8 Results 3.9.9  Summary and Recommendations 3.9.10 Annexes

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Interference Types

35

4.1  4.2  4.3  4.4 

Interference Types Criteria Interfering Device Types Antenna Lobe Types Interference Outcome Types 4.4.1  Interference—The Desired Signal Is Not Received 4.4.2  Sensitivity Degradation by X dB 4.4.3 DES 4.4.4  False Reception 4.4.5 Damage 4.4.6  Degradation of Digital Communication 4.5  Interference Bandwidth Types 4.5.1  Narrowband Interference 4.5.2  Broadband Interference 4.5.3  Full-band Interference 4.6  False Reception 4.7  Interference Types According to Their Source 4.7.1  Interference from Transmitter and Receiver Parameters 4.7.2  Interference from Transmitter Parameters 4.7.3  Interference from Receiver Parameters

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Interference from Both Transmitter and Receiver

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5.1  Transmitter Spectrum 5.1.1  Transmitter Spectrum Definition 5.1.2  Source of the Interference Phenomenon 5.1.3  Calculating FDR 5.1.4  The Interference Effects 5.1.5  Calculating the Received Interference Level 5.2 CCI 5.2.1 Definition 5.2.2  Source of the Phenomenon, Nonintentional Case 5.2.3  Source of the Phenomenon, Intentional Case 5.2.4  The Interference Effects 5.2.5  Calculating the Received Interference Level

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Intersystem EMC Analysis, Interference, and Solutions 5.2.6  The BWF in CCI 5.3 ACI 5.4  Splitting the FDF

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Interference from the Transmitter

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6.1  Transmitter Frequency Bands 6.1.1  Transmission Band 6.1.2  Adjacent Channels or Modulation Band 6.1.3 In-Band 6.1.4 Out-of-Band 6.2  Interference from the Transmitter Spectrum—ACI 6.2.1  The Interference Effects 6.2.2  Calculating the Received Interference Level 6.2.3  Additional Definitions of the Parameter 6.2.4  Default Value for Modulated Signals 6.2.5  Default Value for Pulsed Signals 6.3  Interference from Spurious Emission—SPR 6.3.1  Source of the Interference Phenomenon 6.3.2  Definition of the Parameter 6.3.3  The Interference Effects 6.3.4  Calculating the Received Interference Level 6.4  Interference from PHN 6.4.1  Source of the Interference Phenomenon 6.4.2  Definition of the Parameter 6.4.3  The Interference Effects 6.4.4  Calculating the Received Interference Level 6.5  Interference from BBN 6.5.1  Source of the Interference Phenomenon 6.5.2  Definition of the Parameter 6.5.3  Measuring BBN 6.5.4  Default Value 6.5.5  The Interference Effects 6.5.6  Interference Relevance 6.5.7  Calculating the Received Interference Level 6.6  Interference from HAR 6.6.1  Source of the Interference Phenomenon 6.6.2  Definition of the Parameter 6.6.3  Default Value 6.6.4  The Interference Effects 6.6.5  Checking the Harmonics Content Feasibility 6.6.6  Calculating the Received Interference Level 6.6.7  The BWF for Harmonic Interference 6.6.8  Calculating the Interference Close to Harmonics 6.7  Interference from the TIM 6.7.1  Source of the Interference Phenomenon 6.7.2  Definition of the Parameter 6.7.3  Default Value 6.7.4  The Interference Effects

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6.7.5  Calculating the Received Interference Level 6.7.6  Checking Intermodulation Feasibility 6.8  Interference from LFM Radar 6.8.1  Slow Sweep 6.8.2  Fast Sweep

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Interference from the Receiver

85

7.1  Receiver Frequency Bands 85 7.1.1  Reception Band 85 86 7.1.2  Selectivity Band 86 7.1.3 In-Band 87 7.1.4 OOB 7.2  Required (S/I)r 87 87 7.2.1  Source of the Interference Phenomenon 7.2.2  Definition of the Parameter 87 7.2.3  Measuring (S/I)r 87 88 7.2.4  Default Value 7.2.5 (S/I)r and Processing Gain 88 89 7.2.6  Protection Ratio 7.2.7  Jamming Ratio 89 89 7.3  General Aspects in Receiver Interference 89 7.3.1  Direct and Indirect Definition of the Interference Parameter 7.3.2  Interference Effects 90 90 7.3.3  Equivalent Interfering Signal Level 7.4  Interference from SEL 90 90 7.4.1  Source of the Interference Phenomenon 7.4.2  Definition of the Parameter 91 7.4.3  Measuring LSEL and the Indirect Definition 91 92 7.4.4  Indirect Definition of the Parameter 7.4.5  Calculating the Received Interference Level 93 93 7.4.6  The BWF 94 7.5  SAT and Desensitization 7.5.1  Amplifier Compression 94 95 7.5.2  The Interference Effect 7.5.3  Definition of the Parameter 96 7.5.4  Acquiring the –1-dB Compression Point 96 7.5.5  Comparing Interference and SAT 96 98 7.5.6  Calculating the Received Interference Level 7.6 DMG 98 7.6.1  Source of the Interference Phenomenon 98 7.6.2  Definition of the Parameter 98 7.6.3  Acquiring the DMG Level 99 7.6.4  Default Value 99 7.6.5  Calculating the Received Interference Level 99 7.7  Interference from IMR 99 7.7.1  Source of the Interference Phenomenon 99 7.7.2  Definition of the Parameter 101 7.7.3  Measuring the IMR 102

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xii

8

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Intersystem EMC Analysis, Interference, and Solutions 7.7.4  Calculating the Received Interference Level 7.8  Interference at the IF 7.8.1  Source of the Interference Phenomenon 7.8.2  Definition of the Parameter 7.8.3  Calculating the Received Interference Level 7.9  Interference from LO Radiation 7.9.1  Source of the Interference Phenomenon 7.9.2  Definition of the Parameter 7.9.3  Calculating the Received Interference Level 7.10  Interference from RIM 7.10.1  Source of the Interference Phenomenon 7.10.2  Definition of the Parameter 7.10.3  Measuring the Parameter 7.10.4  Default Value 7.10.5  Calculating the Intermodulation Level 7.10.6  Calculating the Intercept Point 7.10.7  Calculating the Received Interference Level 7.10.8  Checking the Intermodulation Feasibility 7.11  Harmonics and Intermodulation 7.11.1 Harmonics 7.11.2  Introduction to Intermodulation 7.11.3  The Slope of the Intermodulation 7.11.4  The Intercept Point Concept 7.11.5  The Intermodulation Spectrum 7.11.6  The Third- and nth-Order Intermodulation Equations 7.11.7  Intermodulation from Nonequal Signals 7.11.8  Intermodulation from Multiple Transmitters 7.11.9  Number of Intermodulation Products 7.12  In-Band and OOB Interference

102 102 102 103 103 103 103 103 103 104 104 104 105 105 105 106 106 108 109 109 112 118 118 121 123 125 126 128 131

Calculating the Received Interference Level

133

8.1  The Calculation Principle 8.2  Calculating the Received Interference Level 8.2.1  Transmitter Power 8.2.2  Interference Level Relative to CCI 8.2.3  Transmitter External Filter 8.2.4  Transmitter Cable Loss 8.2.5  Transmitter Waveguide Loss 8.2.6  Transmitting Antenna Gain 8.2.7  Transmitting Antenna Side Lobes 8.2.8  Path Loss and Coupling 8.2.9  Polarization Loss 8.2.10  Receiving Antenna Gain 8.2.11  Receiving Antenna Sidelobes 8.2.12  Receiver Cable Loss 8.2.13  Receiver Waveguide Loss 8.2.14  Receiver External Filter 8.2.15 BWF 8.3  Power Sum of Multiple Interferers

133 134 135 135 136 136 136 136 138 141 141 144 144 144 145 145 145 145

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Contentsxiii

9

10

11

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Interference Margin and Its Meaning

149

9.1 Background 9.2  IMRG in the S/I approach 9.2.1  The Criterion 9.2.2  Procedure and Steps of IMRG Calculation 9.2.3  Desired Signal Level S Calculation 9.2.4  Interference Threshold Calculation 9.2.5  Interference Level I Calculation 9.2.6  Interference Plus Noise Calculation 9.2.7 IMRG Calculation 9.2.8  Relationship Between IMRG and Fade Margin 9.3  IMRG in the DES Approach 9.3.1  The Criterion 9.3.2  DES Calculation 9.3.3  DES versus I/N 9.3.4  Choosing the Interference Threshold 9.3.5  Procedure and Calculation Steps 9.3.6  Interference Threshold Calculation 9.3.7 IMRG Calculation 9.3.8  DES versus I 9.3.9 IMRG Impact on DES 9.4  IMRG Impact on the Range 9.4.1 Background 9.4.2  Range Degradation in the S/I Approach 9.4.3  Range Degradation in the DES Approach 9.5  Interference to Short Desired Paths 9.6  Applying the DES Approach for Interference to Radar 9.7  FM Degradation 9.8  Inverse Calculation Technique 9.9  Sensitivity Level as Wrong Threshold Level 9.10  EMC Calculation Summary

149 150 150 150 151 151 151 151 152 155 156 156 157 157 159 159 160 160 161 162 163 163 164 164 165 166 166 167 168 168

The Interference Range and the Reception Range

169

10.1  Hierarchy Level and Interference Types 10.2  Calculating the Interference Range 10.2.1  The Problem 10.2.2  Interference Range without Terrain Influence 10.2.3  Interference with Terrain Influence 10.3  Calculating the Reception Range with Interference 10.3.1 Background 10.3.2  Signal-to-Interference Plus Noise Ratio 10.3.3  Reception Range without Terrain 10.3.4  Reception Area with Terrain

169 170 170 172 173 174 174 175 177 180

Propagation Models for EMC

181

11.1  Difference Between Communication and EMC Models 11.2  Models without Terrain Influence

181 182

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xiv

12

13

14

Intersystem EMC Analysis, Interference, and Solutions 11.3  Models Based on DTM 11.4  Generic Terrain-Influenced Model Path-Loss Model

183 184

Coupling Between Antennas

187

12.1 Measurement 12.2 Scaling 12.3  Prediction by Simulation 12.4  Approximate Free-Space Calculation 12.5  Frequency Dependency

187 187 188 188 189

Relative Angles Between Antennas

191

13.1  The Problem 13.2  Transformation by Rotation 13.3 Calculating θ and ϕ

191 191 195

Antenna Gain in Intercardinal Angles

197

14.1  The Problem 197 199 14.2  The Guiding Principle 14.3  Coordinate Systems 199 202 14.4  Coordinates System Transformation 203 14.5  Symmetrical Antenna Pattern 14.6  The Sum in Decibels Method in the Symmetrical Case 206 207 14.7  Nonsymmetrical Antenna Pattern 14.8  The Sum in Decibels Method in the Nonsymmetrical Case 211 14.9  BWAZ > BWEL 213 14.10  BWEL > BWAZ 217 217 14.11  Reducing the Estimation Error 14.12  Real versus Envelope Pattern 219 219 14.13  Verification by Simulation 221 14.14 Examples 14.15 Summary 222

15 Near-Field 15.1  Far-Field Definition 15.2  Near-Field Definition 15.3  Near-Field Distance 15.4  Very Small Antenna Near-Field Distance 15.5  Aperture Antenna Near-Field Distance 15.6  Wire Antenna Near-Field Distance 15.7  Near-Field Distance Between Two Antennas 15.8  Near-Field Path Loss 15.9  Near-Field Path Loss for Aperture Antennas 15.9.1  Main Lobe 15.9.2  Main Lobe Calculation Steps 15.9.3  Sidelobes’ Path Loss

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Contentsxv

16

17

18

19

Interference Probability

237

16.1 Background 16.2  Accumulated Probability from Multiple Phenomena 16.3  Accumulated Probability from Multiple Interferers

237 238 238

Interference Probability—Antenna Patterns Aspect

241

17.1  The Problem 17.2  Main Lobe versus Sidelobes Case 17.3  Antenna Pattern versus Fixed Antenna Case 17.4  Two Rotating Antennas Case 17.4.1  Step 1: Calculating the Antennas’ Probability Density Function 17.4.2  Step 2: Calculating the Viewing Sector 17.4.3  Step 3: The Probability of a Certain Antenna Pattern Value 17.4.4  Step 4: The Joint Probability Density Function 17.4.5  Step 5: Reference Interference Margin in the Main Lobe 17.4.6  Step 6: Interference Margin of the Event i,j 17.4.7  Step 7: Interference Probability of the Event i,j 17.4.8  Step 8: Interference Probability 17.4.9  Step 9: Interference Probability from the Range Gate Aspect 17.4.10 Example

241 242 245 246

Probability of Frequency Difference

253

18.1  The Problem 18.2  Mathematical Background 18.3  The General Case 18.4  Continuous Frequency Allocation 18.5  Case 1: Identical Frequency Bands 18.6  Case 2: Nonoverlapping Frequency Bands 18.7  Case 3: Partially Overlapping Frequency Bands 18.8  Case 4: One Frequency Band Is Included in the Other 18.9  Fixed-Frequency and Frequency-Hopping Devices 18.9.1  Fixed-Frequency Devices 18.9.2  Frequency-Hopping Devices

253 254 254 256 256 258 260 262 262 262 262

Probability of Pulse Interference

267

246 247 249 250 250 251 251 251 251 251

19.1  The Problem 267 19.2 Definitions 268 19.3 Calculating RMin 268 19.4 Calculating RMax 270 19.5  Calculating the RMin Probability 271 19.6  Calculating the RMax Probability 272 19.7  Summary of Interference Probability 273 19.8  Various Cases 274 19.8.1  Probabilities Reach the Extreme Zero and One Values Case 274

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xvi

20

21

22

23

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Intersystem EMC Analysis, Interference, and Solutions 19.8.2  Probabilities Do Not Reach the Extreme Zero and One Values Case 19.8.3  a >> d Case 19.8.4  d >> a Case 19.8.5  Identical Pulse Width Case 19.8.6  Whole Number of Interfering Pulses Case 19.8.7  Additional Probability Graph Shapes 19.9  Radar Pulses Interference

274 274 275 278 279 280 280

Pulse Interference to Digital Communication

285

20.1  Hierarchy from Bits to Message 20.2  Group Error Rate 20.3  Symbol Error Rate 20.4  Frame Error Rate 20.5  Message Error Rate 20.6  Error Rates with Interference 20.6.1  General Case 20.6.2  Case 1: PW > tMessage 20.6.3  Case 2: tFrame < PW < tMessage 20.6.4  Case 3: tSymbol < PW < tFrame 20.7  Group Delivery Probability 20.8  Required Number of Retransmissions

285 285 287 287 288 288 288 289 289 289 289 291

EMC Between Synchronous Hopping Devices

293

21.1 Background 21.2  Frequency-Hopping Times 21.3  Synchronous and Orthogonal Devices 21.4 Overlapping 21.5  Distances and Reception Delay 21.6  Solution and Objective 21.7  The Overlapping Portion 21.8  Conditions for Overlapping Interference

293 293 294 295 295 297 297 300

EMC Solutions

301

22.1 Background 22.2  Time-Axis Solutions 22.3  Distance-Axis Solutions 22.4  Angle-Axis Solutions 22.5  Frequency-Axis Solutions 22.6  Required Frequency Separation 22.7  Combined Distance and Frequency Separation 22.8  Changing the Specifications

301 301 301 302 302 302 303 304

EMC Tests

305

23.1  The Need 23.2 Objectives

305 306

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Contentsxvii 23.2.1  Technical EMC Test Objectives 23.2.2  Operational EMC Test Objectives 23.3  IMRG Test Procedure in the DES Approach 23.3.1  Test Block Diagram 23.3.2  Deployment Instruction 23.3.3  Preliminary Tests 23.3.4  Interference Test Procedure 23.3.5  Solution and Repeated Test 23.3.6 Miscellaneous 23.4  IMRG Test Procedure in the S/I Approach 23.4.1  Test Block Diagram 23.4.2  Deployment Instruction 23.4.3  Preliminary Tests 23.4.4  Interference Test Procedure—First Method 23.4.5  Interference Test Procedure—Second Method 23.4.6  Solution and Repeated Test 23.4.7 Miscellaneous 23.5  Differences Between Anticipated and Tested Interference 23.5.1  Case 1: No, No 23.5.2  Case 2: No, Yes 23.5.3  Case 3: Yes, No 23.5.4  Case 4: Yes, Yes

306 306 306 307 307 307 308 309 309 309 309 310 310 310 310 311 311 311 311 311 312 312

Appendix: Device EMC Specifications Table

313

About the Author

315

Index 317

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Chapter

1 Contents

Definitions

1.1 Introduction 1.2 Objectives 1.3 Interference

1.1 Introduction

1.4  Radio Frequency Interference

Attempts to design a project without initial consideration of electromagnetic compatibility (EMC) issues will make the solutions to such issues overly costly, if not impossible to solve. Consideration of EMCs is required to ensure the proper operation of transmitting and receiving systems in their operational electromagnetic environments. EMC problems arise when several factors occur simultaneously. For example, EMC will likely become a problem if the interfering device and the interfered device are physically close, use similar frequencies, and are operating at the same time, as shown in Figure 1.1. (The consideration of time can refer to measurement of time on a large scale, such as during the same hours, or on a small scale, such as the time for a single pulse.)

1.5 Compatibility 1.6  EMC and RF Compatibility 1.7  Emissions and Susceptibility 1.8  The System 1.9  External Systems 1.10 Intrasystem and Intersystem Compatibility 1.11  Interference to and from the System 1.12  One-Way and TwoWay EMC 1.13 Electromagnetic Environment 1.14  Signal Types 1.15 Hierarchy 1.16  Device Level 1.17  Platform Level

1.2 Objectives The objectives of this book are listed as follows:

1.18  Site Level

 To outline EMC requirements;

1.19  Arena Level

 To outline techniques and provide equations for performing EMC predictions and calculations; 1

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2

Intersystem EMC Analysis, Interference, and Solutions

Time

Interference

Close frequency

Close location

Location Frequency Figure 1.1  The interference generated by location, frequency, and time confluence.

 To suggest default values for missing data;  To present EMC solutions. Existing EMC books [1–5] and other publications deal mainly with the design aspects of electronic circuits and printed circuit boards (PCBs), noise, grounding, shielding, cabling, and filtering. This book analyzes the interference between deployed systems—a subject that has been less studied and one that occupies a higher level than the circuit.

1.3 Interference Interference is a condition, in which the operation of one device, the interferer, causes performance degradation (or even cessation of operation) of a second device, the interfered. The devices might also be given the names jammer and victim. Since interferer and interfered both start with the letter “i,” we will use, as subscripts, the letters “j” and “v,” respectively, to distinguish between the properties of the two devices. Intentional jamming is not regarded as interference.

1.4  Radio Frequency Interference This book is limited to a discussion of radio frequency interference (RFI) from antenna to antenna, namely in the following situations (Figure 3.2.):  When the interfering source is RF radiation coming from the interfering transmitter’s antenna;

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1.8  The System3

 When the interfering signal propagates via the medium between the antennas;  When the interference occurs due to reception of RF radiation at the interfered receiver’s antenna. RFI is part of a broader range of interferences collectively known as electromagnetic interference (EMI).

1.5 Compatibility Electromagnetic compatibility (EMC) is the opposite of interference; it describes the capability of devices to operate without interfering with each other.

1.6  EMC and RF Compatibility EMC is the capability of systems to operate with each other without EMI. RF compatability (RFC) is a component of EMC: the capability of transmitters and receivers to operate without interfering with each other due to RFI.

1.7  Emissions and Susceptibility Transmitters will always broadcast unwanted or nondesired emissions. The term refers to emissions other than those intentionally being transmitted. Examples of these unwanted transmissions include transmitter spectrum, harmonic emissions, and spurious emissions. A full list of these nondesired emissions is presented in Chapter 6. Electromagnetic susceptibility or vulnerability is a receiver attribute: It is a decrease in performance relative to the nominal desired signal reception. This susceptibility can result in interference to reception of the desired signal, the reception of a nondesired signal, sensitivity degradation, and damage. We present a full list of nondesired reception or nondesired responses in Chapter 7. Note that there may also be unwanted emission coming from the receiver’s local oscillator (LO).

1.8  The System 1.8.1 Definition The term system refers to everything included in our project from the EMC viewpoint. A definition of the elements included in the system is necessary for several reasons, listed as follows:

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4

Intersystem EMC Analysis, Interference, and Solutions

 This system definition distinguishes between those devices that are part of our system or our project and those that are part of the outside world. We require this distinction to differentiate between intersystem and intrasystem EMC as discussed in Section 1.10.  We will need to define the EMC interference requirements for all devices included in the system. 1.8.2  System Content The system may be as simple as a single device, or consist of a platform, or a most complex system, including many platforms. Some examples are described as follows:  Devices: This refers to any transmitter, receiver, or transceiver, such as a communication radio, a mobile phone, radar, a jammer, a direction finder (DF), and a GPS receiver.  Platforms: This refers to ground vehicles, aerial platforms, vessels, or even a person using a device such as a mobile phone.  Systems: This includes many devices of different types or multiple platforms of different types deployed throughout a large geographic area.  Projects: A project may refer to a development effort or to a mission having EMC aspects. Examples of projects, in addition to the development of new devices, include adding a new device to a device-populated platform and adding a platform to a site that already includes some platforms with devices. System definitions contain the complete list of components, devices, and platforms.

1.9  External Systems 1.9.1  External System Types External systems comprise all components that must be EMC-compatible with our system. External systems may belong to one of the following categories:  Friendly systems.  Enemy systems that might unintentionally interfere with our system. (Note that deliberate interference is not regarded as EMC, but as jamming.)

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1.11  Interference to and from the System5

 Neutral systems, such as civilian systems or those belonging to other forces in the arena, although not involved in the scenario. 1.9.2 Definition Defining the contents of external systems is one of the more complicated tasks in EMC activity. It isn’t possible to require EMC with the whole external world, so it is necessary to carefully determine who, or what, might be in the area in which we intend to operate the system. First, we must create an initial list of all devices and platforms that could potentially be included in external systems. Then we can try to eliminate from our consideration those devices or platforms that do not affect the system from the viewpoint of distance, frequency separation, and timing. Timing, for example, may include operational considerations and doctrine, excluding devices that are not used at the same time, or the timing of introducing new devices into service, or taking others out of service. External system definitions are created by listing all components, devices, and platforms.

1.10  Intrasystem and Intersystem Compatibility There is a clear distinction between intrasystem and intersystem compatibility. The term intrasystem compatibility refers to the requirement for EMC of all devices within the system between the devices themselves. The term intersystem compatibility refers to the requirement for EMC between all devices included in the system, and all devices included in the external systems. There is no technical distinction between intrasystem and intersystem compatibility. Calculations of the potential interference between two devices are done in the same manner, whether they are part of intrasystem or intersystem compatibility considerations. It is important to make the distinction between the two cases to be able to identify, or assign responsibility, for performing EMC surveys and applying the required EMC solutions. In the case of intersystem compatibility, the EMC requirements are divided between the direction of interference being considered (i.e., to or from the system).

1.11  Interference to and from the System EMI to the system is defined as follows: EMC is required between all transmitters defined as being included in the external system and all receivers defined as being included

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6

Intersystem EMC Analysis, Interference, and Solutions

within the system. Interference to the system is sometimes referred to as in or ingress. EMI from the system is defined as follows: EMC is required between all transmitters defined as being included within the system and all receivers defined as being included in the external system. Interference from the system is sometimes referred to as out or egress.

1.12  One-Way and Two-Way EMC Two-way EMC surveys need to be performed to assure that the required EMC is achieved in both directions (i.e., to and from the system). However, there are cases in which it is necessary to perform a one-way EMC survey first, deferring the decision to complete the two-way survey. For example, we may give consideration to the development of a new device that is to be added to an existing platform. The existing devices in the platform may degrade the reception capability of the new device. We may desire to act in steps: First, we will examine if the new device has a chance of receiving signals in the existing electromagnetic environment and complete the full two-way survey only in case of a positive outcome. Yet another example might relate to defining the areas of responsibility between two administrations whose systems have to be compatible. In this case, it may be desirable to split responsibility between the two administrations. Each group would be responsible for conducting a one-way EMC survey, only the ingress. That is, each group would check that all devices in the other system do not interfere with the devices in its own system. In many cases, the two-way EMC survey outcome is asymmetric: One of the two interference directions is dominant. Solving the EMC problem may reverse the outcome. For example, if there is severe interference from a device within the system to a device within the external system, it is necessary to implement a successful solution. As a result, the next most dominant interferer may turn out to be from the external system to the system, rather than the reverse.

1.13  Electromagnetic Environment We refer to the conditions, in which intersystem and intrasystem EMC is required, as the electromagnetic environment. An EMC requirement document may include a foreword containing a sentence such as, “The system has to be capable of fully operating in a dense electromagnetic environment.”

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1.15 Hierarchy7

If we do not quantitatively specify the electromagnetic environment in the EMC requirements document the sentence would be meaningless. Moreover, without detailing the electromagnetic environment, it is not possible to perform an acceptance test verifying that this requirement has been met. The quantitative definition of the electromagnetic environment is composed of the following:  Contents, or a list of devices and platforms in the system and in the external system.  Device EMC specifications for all the components such as transmitters, receivers, and antennas (see the appendix), and external components.  Deployment scenarios for both the system and the external system. We may define several scenarios from the viewpoint of EMC requirement severity, such as representative, mild, or stringent. From the operational viewpoint, different scenarios may be defined for experiments, testing, training, or combat.

1.14  Signal Types There are three signal types, described as follows:  Legitimate or standard signals: Signals having exactly all the desired transmission properties (e.g., having the exact digital modulation [even if transmitting different data than the desired signal]).  Desired signals: The signals from among all legitimate signals that the receiver is intended to receive from its partnered transmitter.  Interfering signals: Signals that the receiver is not intended to receive. Interfering signals may be legitimate (at a different frequency or at the same frequency due to frequency reuse), nonlegitimate (from any different transmitter), or spurious emissions.

1.15 Hierarchy We define four EMC hierarchy levels, listed as follows (Figure 1.2):  Device: includes transmitter and or receiver and antenna;  Platform: includes devices;  Site: includes platforms;  Arena: includes sites.

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8

Intersystem EMC Analysis, Interference, and Solutions Device

Platform

Site

Arena

Figure 1.2  EMC hierarchy levels: device, platform, site, and arena

1.16  Device Level A device is a transmitter and/or a receiver operating in the RF range, using an antenna. The device definition includes a list of all external components that may have an EMC impact such as:  Antennas, coaxial cables, waveguides, low-noise amplifiers (LNAs), external filters, power dividers, and power combiners;  Transmitters and receivers such as radio transceivers or radars;  Receive-only examples such as GPS receivers, radar warning receivers, interception receivers, or DFs;  Transmit-only examples such as jammers, beacons, or broadcast transmitters.

1.17  Platform Level We define the platform with a list of all its included devices (even if there is only one device). More platform aspects are detailed in Section 2.4.1.

1.18  Site Level We define the site with the list of all its included platforms and their deployment. We have provided more detail in Section 2.5.1. A site may be very

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1.19  Arena Level9

small, such as a cellular base station; medium-sized, such as a division headquarter; or very large, such as a complete military base.

1.19  Arena Level The arena is defined by the list of all included sites and single platforms and their deployment. We provide more detail in Section 2.6.1. An arena may be very large; examples include a county, a country, or several countries.

References [1] Sevgi, L., A Practical Guide to EMC Engineering, Norwood, MA: Artech House, 2017. [2] Freeman, E. R., and M. Sachs, Electromagnetic Compatibility Design Guide, Norwood, MA: Artech House, 1982. [3] Clayton, R., Paul, Introduction to Electromagnetic Compatibility, Hoboken, NJ: John Wiley and Sons, 2006. [4] Ott, W., Henry, Electromagnetic Compatibility Engineering, Hoboken, NJ: John Wiley and Sons, 2009. [5] Kaiser, B. E., Principles of Electromagnetic Compatibility, Dedham, MA: Artech House, 1987.

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Chapter

2 Contents 2.1 Objective 2.2  Device Level EMC Requirements 2.3  EMC Requirements Within and Between Platforms 2.4  EMC Requirements at the Platform Level 2.5  EMC Requirements at the Site Level 2.6  EMC Requirements at the Arena Level 2.7  System EMC Requirements 2.8 Requirements Summary 2.9  Relationship to MILSTD 2.10  Maximum Allowed Interference Level 2.11  The Performance Criteria 2.12  The Affecting Parameter 2.13 Gradual Performance Degradation 2.14 Interference Threshold 2.15  Crash Threshold 2.16 Performance Degradation Region 2.17 Interference Probability Threshold 2.18 Operational Damage Level

EMC Requirements 2.1 Objective This chapter explains the method of creating the EMC requirements within the system requirements in each of four hierarchical levels. The EMC document enables the performance of the EMC survey, the EMC tests, and the acceptance tests.

2.2  Device Level EMC Requirements 2.2.1 Objective The formal objective of the device EMC specification is to ensure compliance with the operational requirements, meaning compliance with intersystem and intrasystem EMC requirements at the platform, the site, or the arena level. However, please note that it is usually difficult to achieve this goal! Full compliance with the operational EMC requirements may not be physically realizable at the device performance level. We may eventually achieve compliance with the operational EMC requirements with a combination of solving that can be done at the device level and then seek EMC solutions outside the device. These solutions might include changes in distance separation, frequency separation, antenna redirection, and more. 11

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12

Intersystem EMC Analysis, Interference, and Solutions

Thus, the practical objective of the device EMC specification is to get as close as possible to meeting the operational EMC requirements while considering further solutions outside the device. 2.2.2  The Device EMC Requirement The device EMC requirement is a technical requirement. When we state that EMC compatibility is required at the device level, we mean that the device’s nondesired emissions and nondesired responses will not exceed the limits within the specifications. Simply put, the device EMC requirement is the device EMC specification (i.e., the list of all the device’s nondesired emissions and nondesired responses and their values). 2.2.3  Capability to Comply with the Operational Requirements Even full compliance with the device’s technical EMC requirements does not necessarily guarantee full compliance with operational EMC system requirements. There is a gap between that which is required and that which can be achieved based on the different nature of these two sets of requirements. The operational EMC requirements are derived from the electromagnetic environment in which the device must operate. However, the technical EMC requirements are derived from the realizable physical capabilities (or the amount of money one is willing to spend for improved technical performance). 2.2.4  Definition Approaches There are two opposite approaches for defining the device EMC requirements. These approaches, which depend on our starting point, are described as follows:  Approach A: We begin by defining the electromagnetic environment in which the device must operate. As an example of the electromagnetic environment, one device is required to function with no interference when placed x meters from another device. By calculating the received interfering signal strength, the nondesired emissions and nondesired responses can be calculated and then written as device EMC requirements.  Approach B: We start by defining the device EMC requirements. As an example, we define the device’s nondesired emissions and nondesired responses according to the current (or even somewhat more advanced) technology. Compliance with the EMC requirement then leads to calculating the required distance between interfering and interfered devices.

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2.3  EMC Requirements Within and Between Platforms13

Theoretically, the technical EMC requirements for the device should be derived from, rather than dictating, the operational requirements, so approach A should be used. In practice, there is a dilemma in deciding which approach to use; both have disadvantages. With approach A, the disadvantage is that if we make operational requirements too tough, there is a risk that the technical EMC requirements of the device will make no sense, or be too expensive to acquire. On the other hand, if the operational requirements are too mild, there is the risk that the device supplier will not invest enough effort to deliver a device with the best achievable current capabilities. The disadvantage in using approach B is that the operational EMC limitations may not be acceptable. For example, the approach may require impractical deployment in terms of factors such as distance, antenna direction, and frequency separation. The way we can overcome these disadvantages is to perform several iterations of both the technical and the operational requirements.

2.3  EMC Requirements Within and Between Platforms 2.3.1  EMC Within and Between Platforms From the viewpoint of the platform we have two considerations: EMC within a platform and EMC between platforms. In the first case, the EMC requirement is to have any two devices mounted in the same platform perform without interference from each other. In the second case, the EMC requirement is that any two devices mounted in the different platforms, whether the same kind or not, will perform without interference. 2.3.2  Distance Between Platforms If the two platforms are near, it is a case of EMC within a site, but if they are far, it is a case of EMC in the arena. There is obviously no quantitative measure with which we can define the terms near and far. The distinction between the cases is based on functional association of the platforms operating together in the site, rather than the measured distance. 2.3.3  Near-Field and Far-Field We should avoid using the terms near-field EMC and far-field EMC to designate platforms that are respectively physically near or far apart. The difference between the definitions is that “within or between platforms” is an operational aspect, based on functional association, whereas “near- or far-field” is a technical aspect, mainly based on frequency and antenna size.

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14

Intersystem EMC Analysis, Interference, and Solutions

Therefore, there is no overlap between the definitions. Two antennas on the platform may include one within the near-field of the other at one frequency but within the far-field at another. On the other hand, two antennas mounted on close but different platforms may be within the near-field, from the technical viewpoint.

2.4  EMC Requirements at the Platform Level 2.4.1  The Platform EMC Requirement The platform EMC requirement is an operational requirement. The statement “EMC compatibility is required in the platform level” means that devices mounted on the platform will operate without interference. Using one or more devices on the platform will not degrade the performance of the other devices on the platform (or not beyond a maximum allowed value). The platform EMC requirement may also be referred to as onboard compatibility. The platform EMC requirement includes the following:  A list of devices onboard the platform;  Antenna locations on the platform and their directions, if directional  The requirement that all devices will operate either without interference, or under a specified maximum allowed value  Additional conditions that may be specified (e.g., a requirement, for safety reasons that a certain device never be interfered by another device or platform). Also, there may be a preferred order of requirements for various devices, or there may be a requirement that bars using two devices at the same time. 2.4.2  Capability to Comply with the Operational Requirement The fact that we consider onboard EMC requirements to be reasonable or legitimate doesn’t necessarily guarantee that the operational EMC system requirements can be achieved. Sometimes it is not possible to use two devices on the platform at the same time, and we need to define an order of preference. 2.4.3  Inter- and Intra-EMC Though all devices on the list are placed in the same platform, the EMC requirement may be either intersystem or intrasystem. We define the EMC intrasystem requirement as a case in which all devices belong to the same system or project. If some devices belong to one system or project and others

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2.6  EMC Requirements at the Arena Level15

do not, we consider this case to have an intersystem EMC requirement, though in the same platform.

2.5  EMC Requirements at the Site Level 2.5.1  The Site EMC Requirement The site EMC requirement is an operational requirement as well. The statement “EMC compatibility is required in the site level” means that devices mounted on different platforms in the site will operate without interference. Using one or more devices, in one or more platforms should not degrade the performance of other devices on another platform (or not beyond a maximum allowed value). We also refer to the site EMC requirement as cosite compatibility or collocation. A site EMC requirement includes the following:  A list of platforms in the site.  Specifications for platforms deployed in the site. If the deployment is fixed, each platform’s coordinates (and height if applicable) need to be specified. If the deployment is not fixed, it is necessary to specify deployment rules, such as the typical distances between platforms in the site. We may specify deployment for several conditions such as representative, mild, or stringent.  The requirement that devices operate without interference, or under a specified maximum allowed value. As in the platform level case, additional necessary conditions may be specified. 2.5.2  Inter- and Intra-EMC Though all platforms on the list are placed in the same site, EMC requirements may be either intersystem or intrasystem. We regard the case in which all platforms belong to the same system or project as intrasystem. If some platforms belong to one system or project and others do not, then we consider the deployment as needing intersystem EMC requirement definition, though in the same site.

2.6  EMC Requirements at the Arena Level 2.6.1  The Arena EMC Requirement The EMC requirement for the arena is an operational requirement as well. The statement “EMC compatibility is required in the arena level” means that devices deployed in different sites in the arena will operate without interference. That is, the use of one or more devices in one or more platforms in a

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Intersystem EMC Analysis, Interference, and Solutions

site will not degrade the performance of another device on another platform in another site (or not beyond a maximum allowed value). We sometimes refer to the arena EMC requirement as coexistence. We typically require an arena EMC definition mainly in dynamic environments. When platforms carrying devices are in motion, deployment is never constant. Platforms may be very close together at one time and far apart at another. Typical dynamic environments include vehicles, aircraft, missiles, guided weapon systems, and naval systems. Arena EMC requirements are also necessary in the simpler case, in which all platforms have fixed locations. The arena EMC requirements include the following:  A list of sites and single platforms in the arena.  The requirement that all devices will operate without interference, or not beyond a maximum allowed value.  Site and single platform locations (and height if applicable) in the arena. If the deployment is fixed, each site’s coordinates have to be specified. If the deployment is dynamic, deployment rules must be specified. These specifications may include the path of vehicles or airframes and the flight profile of missiles. Deployment may be specified for several cases such as representative, mild, or stringent.  As in the platform level case, additional necessary conditions may be specified. 2.6.2  The Near-Far Requirement The near-far requirement is typical in a dynamic environment. On one hand, the device within a platform must fulfill its task with respect to a far platform. These tasks may include communicating with the far partner device or detecting a far target. On the other hand, an interfering device placed in another platform may be very near—hence the name near-far requirement. 2.6.3  Inter- and Intra-EMC Arena EMC requirements are usually intersystem, since the system or project rarely includes the whole arena.

2.7  System EMC Requirements EMC requirements for systems or projects may have definitions that vary from very simple to very complex. In the simplest case, two single devices are

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2.9  Relationship to MIL-STD17

involved, whereas in a complex case we may include many devices, mounted in a variety of platforms. These devices may be fixed, or in motion, on the ground or in an aerial or naval platform, and deployed in a large area. Thus, system EMC requirements include parts of all the four EMC levels: device, platform, site, and arena.

2.8  Requirements Summary Table 2.1 summarizes the EMC requirements for each of the four EMC hierarchy levels.

2.9  Relationship to MIL-STD There are many military standards that deal with EMI and EMC. The requirements in MIL-STD 461 [1], for example, separately specify various nondesired transmitter emissions and various receiver nondesired responses, but not their interaction: the main issue of this book. We must emphasize that, from the EMC viewpoint, even if the interfering transmitter fully complies with the radiated emissions (RE) requirements and the interfered receiver fully complies with the radiated susceptibility (RS) requirements, it is not a guarantee that they will operate mutually, free of interference when the devices are deployed.

Table 2.1 EMC Requirements at the Four EMC Hierarchy Levels Level

Name

Requirement

Specification

Device

EMC specification

Device’s nondesired emission and nondesired response will not exceed specifications

Nondesired emission and nondesired response specification

Platform

Onboard compatibility

Devices operating in the same platform will operate with no interference*

List of devices in the platform, antennas, locations, and directions

Site

Cosite compatibility or Collocation

Devices operating in two platforms in the site will operate with no interference*

List of platforms in the site and their deployment

Arena

Coexistence

Devices operating in two sites in the arena will operate with no interference*

List of sites and single platforms in the arena and their deployment

*Or maximum allowed interference value.

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Intersystem EMC Analysis, Interference, and Solutions

2.10  Maximum Allowed Interference Level In EMC requirements, we sometimes use the following wording: “The device is required to operate without interference.” This statement is only a general statement, and, in many cases, it is not even an accurate one. The EMC requirements often allow a certain amount of interference. It is therefore our responsibility to specify the amount of interference allowed. The allowed interference level may be examined from various viewpoints, depending both on the device type (e.g., analog communication, digital communication, and radar) and device function (e.g., data transfer, navigation, weapon system command, and alert).

2.11  The Performance Criteria Many parameters may be used as criteria. Some examples are listed as follows:  Receiver sensitivity;  Range;  Fade margin;  Communication availability or reliability;  Maximum allowed error, in terms of such factors as bit error rate (BER), frame error rate (FER), and message error rate (MER);  Communication data rate or throughput;  Base station subscriber capacity;  Number of required message repetitions until the message is properly received;  Picture or video quality;  Navigation accuracy;  Probability of detection. The implications of the first three criteria are discussed in Sections 9.3.9, 9.4, and 9.2.8 respectively. Error rates and message repetitions are discussed in Chapter 20.

2.12  The Affecting Parameter Several parameters may affect the interference, including the following:

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2.13  Gradual Performance Degradation19

 The signal level viewpoint: The interfering signal level at the receiver input, designated I (for interference), or the interference margin, IMRG.  The time viewpoint: The time portion x, above which interference exists. (For example, digital communication may be sensitive to interference even if it occurs only in the x time portion rather than continuously).  A combination of level and time viewpoints and other such factors.

2.13  Gradual Performance Degradation Generally, when the interference threshold is crossed, device performance does not immediately crash. Rather, performance gradually degrades. Figure 2.1 depicts performance degradation as a function of the affecting parameter. Figure 9.5 shows an example of gradual degradation of receiver sensitivity, where the affecting parameter is the interference to noise ratio (I/N). Figures 9.8 and 9.9 show the operational-range gradual degradation examples, where the affecting parameter is the interference margin, IMRG.

Performance criterion Nominal performance

Interference start

Minimum allowed

Affecting parameter

No interference

Performance degradation

Interference threshold

Interference: Mission failure

Crash threshold

Figure 2.1  Interference result regions.

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Intersystem EMC Analysis, Interference, and Solutions

2.14  Interference Threshold The interference threshold is the affecting parameter value beyond which, the device performance decreases and interference begins. If the interference level is less than the interference threshold, device performance degradation, even if it occurs, is regarded as no interference. Consider the following examples:  An interfering signal level lower than I = −110 dBm, causes no more than a 1-dB receiver sensitivity degradation.  An interfering signal less than x = 0.02-time portion, causes MER that does not exceed 5%.

2.15  Crash Threshold The crash threshold is the affecting parameter value beyond which the device performance drops below the minimum allowed. Consider the following examples:  An interfering signal level higher than I = −95 dBm causes more than a 10-dB receiver sensitivity degradation.  An interfering signal more than x = 0.1-time portion, causes MER in excess of 20%. Calculating the sensitivity degradation is discussed in Section 9.3, and calculating the MER is discussed in Chapter 20.

2.16  Performance Degradation Region The performance degradation region lies between the interference threshold and the crash threshold. This is the price of the existence of the interference: The device operates with less than acceptable performance but has not yet crashed. It is not mandatory that we define two threshold values and a performance degradation region between them. For many devices, we only define a single interference threshold. In this case we regard the device as either being interfered with or not.

2.17  Interference Probability Threshold We cannot use performance degradation alone to indicate a problem, since the probability of interference also must be addressed. For example, we may

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2.18  Operational Damage Level21

allow large performance degradation if the probability of such degradation is minuscule, while even small performance degradations may not be allowed, if their probability is close to 100%.

2.18  Operational Damage Level Sections 2.18.1–2.18.4 define four categories of functional interference impact, from the most benign to the most severe damage categories. 2.18.1 Nuisances If interference occurs, nuisance, inconvenience or other small performance degradations appear, having no impact on the mission. Examples of nuisances include when voice quality is poor but understandable; when video quality is low, but images are still usable; when –1-dB receiver desensitization occurs, MER is somewhat higher and messages may have to be repeated occasionally; and when squelch is sometimes breached. 2.18.2  Mission Effectiveness Decreases If interference occurs, it causes meaningful degradation to the device performance. Examples include when the device’s range is much less than nominal and when devices start decreasing their data rate. 2.18.3  Mission Failures If interference occurs and the device performance crashes, the mission will have failed. If interference occurrence can be anticipated a priori, mission cancelation might be required. Examples include when data cannot be transferred even at the lowest device data rate; when command channel of a guided weapon system does not function; and when radar or communication ranges are below any operational values. 2.18.4  Safety Risks If interference occurs, life of personnel might be endangered, or platform survivability might be at risk. Examples include interference to a radar warning receiver (RWR) alerting an incoming missile threat to a platform. Irreversible damage to receiver can also be included in this category.

Reference [1] MIL-STD 461 F, Department of Defense, Interface Standard Requirements for the Control of Electromagnetic Interference Characteristics of Subsystems and Equipment, 10 December 2007.

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Chapter

3 Contents 3.1  EMC Survey Objectives 3.2  Included in the Survey 3.3  Required Survey Outcome 3.4  The Need for Handling EMC Problems 3.5  The S/I Approach 3.6  The DES Approach 3.7  The Participants in the Interfering Mechanism 3.8  Worst-Case and Least-Worst-Case 3.9  A Possible Structure for the EMC Survey Report

EMC Analysis and Survey 3.1  EMC Survey Objectives The EMC survey objectives are listed as follows:  To analyze the system’s ability to meet the EMC requirements by analytic calculation of the anticipated interference.  To predict EMC problems at an early project stage, thereby solving problems in advance and minimizing schedule delays and cost.  To perform initial screening, enabling decision-making with respect to the order of priorities for resource investment in EMC solutions, graded by the severity of the anticipated problem.

3.2  Included in the Survey On principle, we must include all devices listed in the EMC requirements document in the survey. The scope of the survey may become enormous as the system gets larger and more complex. For example, we would have to analyze two hundred intersystem EMC interference 23

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24

Intersystem EMC Analysis, Interference, and Solutions

cases if the system included just 10 devices and the external system included 20! It is advisable for us to screen out as many cases as possible. We can justify the elimination of certain jammer-victim combinations based on experience and prior testing, or on previous survey results, or combinations of devices that will not operate at the same time.

3.3  Required Survey Outcome The required EMC survey outcome should include part, or all, of the following considerations:  Between which jammer-victim pairs do we anticipate interference?  What are the interference levels and/or interference margins?  What is the interference probability?  What operational limitations exist?  What recommendations do we make for EMC solutions?  What recommendations do we make for EMC tests?  Qualitative tests to check functionality;  Quantitative tests to measure the interference;  Comparison of alternatives.  What is a device operation range under interference?  What recommendations do we have for additional EMC steps?

3.4  The Need for Handling EMC Problems The interference outcome between jammer-victim pairs is not automatically a call for action. There are four levels in handling a problem, described as follows:  Action is not required: When no interference is anticipated, obviously nothing needs to be done.  Not worthwhile to take action: When interference risk level and/or operational damage levels are low, acting is not worthwhile.  Consider taking action: When interference risk levels and/or operational damage levels are marginal, taking action should be considered.  Taking action is mandatory: When interference risk levels and or operational damage levels are high, action is required.

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3.4  The Need for Handling EMC Problems25

We should consider the following:  Operational damage level, according to Section 2.18;  Interference margin (IMRG), according to Chapter 9;  Interference probability, according to Chapter 16. We can use the guidelines in Table 3.1 to determine how to handle EMC problems. We need to consider the question: What constitutes the quantitative values of low and high interference margins? In response, we can only give general rules of thumb since the answer is subjective and case-driven. We may consider interference levels of 6 or 10 dB as low and 20 dB as high. We can expand Table 3.1 for such considerations and include the probability of interference as well. We can assign weights to the three aspects as follows:  Operational damage level, A: 1. A = 1: Nuisance; 2. A = 2: Mission effectiveness decrease; 3. A = 3: Mission failure; 4. A = 5: Safety risk.  IMRG, B: 1. B = 0: Positive high; 2. B = 1.5: Positive low; Table 3.1 Guidelines for Handling EMC Problems Operational Damage Level

IMRG

Nuisance

Mission effectiveness decrease

Positive high

Not required

Not required

Not required

Not required

Positive low

Not Worthwhile

Not Worthwhile

Not Worthwhile

Consider

Negative low

Not Worthwhile

Not Worthwhile

Consider

Must

Negative medium

Not Worthwhile

Consider

Must

Must

Negative high

Consider

Must

Must

Must

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Mission failure

Safety risk

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Intersystem EMC Analysis, Interference, and Solutions

3. B = 2: Negative low; 4. B = 3.5: Negative medium; 5. B = 6: Negative high.  Interference probability, C: 1. C = 1: Low probability; 2. C = 2: Medium probability or probability not calculated; 3. C = 3: High probability. The final score is given by the product: D = ABC (3.1)



The proposed decision for taking action is, according to the score:  Not required if D = 0.  Not worthwhile if 0 < D ≤ 10.  Worth considering if 10 < D ≤ 15.  A must if D > 15. Example 1 The operational damage will be mission failure, A = 3. The IMRG is negative and low, B = 2. However, the interference probability is high, C = 3. The result is D = 18; thus we must treat the predicted interference problem. Example 2 The operational damage is safety risk A = 5. The IMRG is positive and low, B = 1.5. The interference probability was not calculated, C = 2. The result is D = 15. We should consider handling the anticipated interference.

3.5  The S/I Approach From the viewpoint of interference calculation, we have two approaches for performing the calculations in the EMC survey: the S/I approach and the desensitization (DES) approach.

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3.6  The DES Approach27

In the S/I approach, the interfering signal level I is compared with the desired signal S. Since calculation of the S and I levels requires knowledge of the geographic deployment in a real or test scenario, we can label this calculation as the scenario-oriented approach. The scenario must include the following: 1. The interfered device: Both the interfered receiver and its partnered transmitter (or the target in the case of radar) in order to calculate signal S. 2. The interfering transmitter, in order to calculate interfering signal level I. For each transmitter and receiver, the geographic deployment must include the following: 1. Location and height. The deployment can be defined in terms of coordinates on a map, either the real deployment or a representative one for the calculation’s sake or doctrinal deployment on a blank map. 2. (If transmitters and receivers are moving) knowledge of the path or trajectory. 3. The direction of directional antennas. 4. Operating frequencies: Either as specific frequencies or as defined in a frequency assignment doctrine.

3.6  The DES Approach In the DES approach, we compare the interfering signal level with the receiver sensitivity as defined in the receiver’s specifications. We refer to this approach as the specifications-oriented approach. The interfered receiver’s partner is not a participant in the interference calculations, since only the interference level I is calculated. The DES approach is applicable in several cases, described as follows:  When the desired signal S cannot be calculated because the transmitting partner deployment scenario and or technical specifications are not available.  When we need to acquire a generic, non-scenario-dependent outcome, since the EMC analysis outcome in the S/I approach is scenario-­ dependent.

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Intersystem EMC Analysis, Interference, and Solutions

 When we need to find the degradation of a device in a stand-alone platform in the near-far case. The receiver must perform at its utmost capability regardless of its partner deployment.  When we want to examine the worst case (since in practice, S is equal to or greater than the sensitivity).

3.7  The Participants in the Interfering Mechanism There are five participants in the S/I calculation scenario: the interfering transmitter, the medium between the interfering transmitter and interfered receiver, the interfered receiver, the interfered receiver’s partner (also referred to as the desired transmitter), and the medium between the desired transmitter and interfered receiver. Only the first three apply in the DES approach. Figures 3.1 and 3.2 show the participants and their attributes as applicable to both approaches. 3.7.1  The Interfering Transmitter The interfering transmitter is the first participant. The transmitter emits interfering electromagnetic emissions through its antenna. These unintended emissions may be at the center frequency, or at any other nondesired frequencies. The interfering properties of the transmitter are detailed in Chapter 6.

Interference channel

Desired channel

Interference medium properties

Desired medium properties

I

S

Interfering transmitter

Interfered receiver

Desired transmitter

Interfering transmitter properties

Interfered receiver vulnerability

Desired transmitter properties

Figure 3.1  The participants in the S/I approach.

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3.7  The Participants in the Interfering Mechanism29 Interference channel

Interference medium properties

Interfering transmitter

Interfering transmitter properties

I

Interfered receiver

Interfered receiver vulnerability

Figure 3.2  The participants in the DES approach.

3.7.2  The Interfering Medium The second participant in interference is the medium through which the interfering signal travels from the interfering transmitter’s antenna to the interfered receiver’s antenna. We are dealing with wave propagation between antennas when the distance over which the interference is propagated is large. If the interfering distance is very small, as in the case of two antennas onboard a single platform, then coupling between antennas is the case. The wave propagation case is dealt with in Chapter 11; the coupling is dealt with in Chapter 12. 3.7.3  The Interfered Receiver The interfered receiver is the third participant involved in the mechanism. The interference is received at the receiver’s antenna, on top of the desired signal. We detail the receiver’s vulnerability properties in Chapter 7. 3.7.4  The Desired Transmitter When the received signal level S is involved in the calculation, the next participant is the desired transmitter, transmitting the legitimate desired signal. 3.7.5  The Desired Medium The last interference participant is the medium through which the desired signal propagates, from the desired transmitter’s antenna to the interfered

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Intersystem EMC Analysis, Interference, and Solutions

receiver’s antenna. In this case we always deal with the mechanism of wave propagation.

3.8  Worst-Case and Least-Worst-Case 3.8.1  The Worst-Case Dilemma Worst-case calculation is a very common approach in EMC analysis. This makes sense since we want to be sure that interference will never occur. The approach requires checking the worst case under all conditions, such as the following:  Distances between devices;  Frequency differences between devices;  Antenna directions;  Wave propagation model. There is a dilemma in applying this approach for the following reasons:  The assumption that all interfering conditions have their worst-case value simultaneously is too strict. The probability of such an event is, or may be, very low.  The resulting technical device requirements might be theoretically impossible or too expensive to realize.  The resulting operational limitations might not be realistic. We suggest a way to overcome this dilemma by checking a variety of conditions in combination with some use of worst-case values but with other conditions not set to the worst-case value. 3.8.2  Least-Worst or Easiest Case If, even in the worst case, there is no interference, the conclusion is that there will never be interference. At that point there is no reason for further EMC analysis. If there is interference in the worst case, it is worthwhile to then analyze the easiest case before analyzing intermediate cases. Our rationale is that if interference is present in the least, or easiest set of conditions, we conclude that interference will always be present. Again, there is no point in continuing the EMC analysis.

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3.8  Worst-Case and Least-Worst-Case31

Clearly, if interference exists under worst-case conditions, and there is no interference in the easiest case, the analyst has to continue checking intermediate cases. Some examples, looking at relative antenna directions, are provided as follows:  A worst-case example: If even in the main-to-main direction (see Figure 4.2) there is no interference, it will never occur.  A best-case example: If even in the side-to-side direction (see Figure 4.5) there is interference, it will always occur.  An intermediate case example: If neither of the above outcomes occurs, we need to analyze all relative antenna directions in order to recommend the required angular separation between the antennas, solving the anticipated interference problem.

3.8.3  Saving Calculation Time In Section 3.8.2, we present an example of trying to save time and resources when conducting the EMC survey by avoiding lengthy calculations when not needed. Some EMC calculations are simple to conduct while others are more complicated. There remains another way to save effort and time: by interference denial. Example 1 Calculating the interference probability between antenna patterns or the probability of pulse interference is far more complicated than calculating the IMRG. If the IMRG is positive, we can rule out interference; conducting the other calculations would be needless. Example 2 On the other hand, we can consider a case in which there is a problem in calculating the simple IMRG because a certain mandatory parameter is missing. If pulse interference is the case, and calculation showed that the pulse interference probability is below the allowed value, it would be a wasted effort to try to acquire the missing parameter for the IMRG calculation. 3.8.4  Worst-Case Parameters There are cases where a certain technical parameter has minimum and maximum values. As an example, transmitter power may be specified as

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Intersystem EMC Analysis, Interference, and Solutions

50 ± 1 dBm, or antenna gain may be specified as a 12-dBi minimum, and a 15-dBi maximum. When we conduct EMC calculations, our worst-case values are those causing more interference: that is 51 dBm plus 15 dBi. This is opposed to communication calculations where our worst-case values are those providing the minimum communication range: 49 dBm plus 12 dBi.

3.9  A Possible Structure for the EMC Survey Report The EMC survey report may include some, or all, of the factors described in Sections 3.9.1–3.9.10. 3.9.1  Executive Summary  Background;  Objective;  Participants in the analysis;  Results;  Conclusions;  Recommendations;  Summary. 3.9.2 General  Background: Brief system description, for which the EMC survey is required;  Objective: The EMC survey purpose;  Scope: Required interferences to be analyzed, such as one- or two-way EMC, intersystem or intrasystem EMC or both;  Applicable Documents. 3.9.3 Methodology  The EMC analysis phases;  The EMC calculation methodology (for example, using the S/I or DES approach);  Basic assumptions;  Path losses;

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3.9  A Possible Structure for the EMC Survey Report33

 Coupling between antennas;  Interference thresholds;  Running conditions. 3.9.4  Systems in the Analysis  The definition of the system to be analyzed;  List of our systems;  List of the enemy systems;  List of neutral system. 3.9.5  Device Data  The sources of data;  Values used (per either device): Per specifications or measured values. This is especially important to note when there is a significant difference between them;  The default values used when data is absent. In theory, all devices’ parameters should be available, but in practice, the absence of some data is common. (This book includes proposed default values, when possible, to overcome this difficulty.) 3.9.6 Scenarios  The scenarios examined;  Operational aspects;  Frequencies used or frequency allocation doctrine. 3.9.7 Requirements  What EMC requirements must the system meet? 3.9.8 Results  The results may be presented by category, such as intersystem versus intrasystem EMC, or direction: “to” versus “from” our system, or by type of interference.  Detailed results in each case.  Summary table.

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Intersystem EMC Analysis, Interference, and Solutions

3.9.9  Summary and Recommendations  Conclusions;  Recommendations for EMC solution wherever required;  Recommendations for further action;  Summary. (It is worthwhile emphasizing which interferers are dominant, and whether the dominant interference is “to” or “from” the system.) 3.9.10 Annexes  For example: Device data.

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Chapter

4 Contents

Interference Types

4.1  Interference Types Criteria 4.2  Interfering Device Types 4.3  Antenna Lobe Types

4.1  Interference Types Criteria We can classify interference types based on various criteria, discussed as follows:

4.4 Interference Outcome Types

 Intersystem or intrasystem EMC, as discussed in Section 1.10;

4.5 Interference Bandwidth Types

 Two-way or one-way interference and its direction, as discussed in Section 1.12;

4.6  False Reception

 EMC within or between platforms, as discussed in Section 2.3;

4.7  Interference Types According to Their Source

 In-band or out-of-band interference, as discussed in Section 7.12;  The number of interfering signals and their classification, that is, one signal (as the interferer), two signals (the interfering signal and the desired signal), three signals (two interferers generating intermodulation products as well as the desired signal), or many interferers all contributing to the interference probability. Additional criteria, as discussed in Sections 4.2–4.7, are the types of interferer devices, the types of antenna lobes, interference outcome types, interference bandwidth types, and types of interference per its source. 35

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Intersystem EMC Analysis, Interference, and Solutions

4.2  Interfering Device Types In terms of the interfering device types, we can define two cases, identical and different devices, described as follows:  First, we can define interference between devices of the same type. In this case, the interfering signal is a legitimate one. Although the modulation and the interfering signal bandwidth are usually the same as those of the desired signal, there are cases in which they differ; for example, software-defined radios that occasionally change their modulation schemes or parameters or radars that may have multiple waveforms. In most cases, the interfering signal uses a different frequency than that desired, but the devices may use the same frequency, due either to frequency reuse or to the occasional confluence of frequency hops.  Second, we can deal with different device types; in these cases, the interfering signal parameters are generally different from the desired signal.

4.3  Antenna Lobe Types When considering directional antennas, it is necessary to calculate the transmitted interfering level according to the interfering antenna pattern GSL-t and the received interfering level according to the interfered antenna pattern GSL-r as shown in Figure 4.1. In many cases, we use an approximation to simplify the calculations by considering only two values, disregarding the real antenna pattern. For this

Interfered link

Interfering link

G SL-t

Interfering path

GSL-r

Figure 4.1  Interferer and interfered antenna patterns.

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4.3  Antenna Lobe Types37

calculation, we assume that the antenna has its full main-lobe gain throughout the full 3-dB beamwidth, assuming a representative value for all other angles. We commonly use 0 dBi as a representative value for all side lobes. Figures 4.2–4.5, respectively, depict the four combinations: main-tomain (MM) interference, main-to-side (MS) interference, side-to-main (SM) interference, and side-to-side (SS) interference. Interferer

Interfered

Figure 4.2  MM interference.

Interferer

Interfered

Figure 4.3  MS interference.

Interferer

Interfered

Figure 4.4  SM interference.

Interferer

Interfered

Figure 4.5  SS interference.

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Intersystem EMC Analysis, Interference, and Solutions

4.4  Interference Outcome Types Several outcomes may result once a receiver receives a signal it was not meant to receive. 4.4.1  Interference—the Desired Signal Is Not Received Interference usually has the following effect: Though the desired signal level at the receiver input is higher than the sensitivity, signal reception is not possible (or reception has lower than the nominal performance) due to the interfering signal presence. This effect applies when two signals are present at the receiver input, the interfering and the desired signals. For the purposes of calculating the interference there we need to calculate the desired signal level. This is therefore the S/I approach case. 4.4.2  Sensitivity Degradation by X dB The effect: the receiver’s sensitivity for receiving the desired signal is degraded by a fixed known amount, X dB. Typical allowed values for X are 1 dB and sometimes 3 dB. This outcome involves two signals as well, the interfering and the desired signals, such as in Section 4.4.1. The difference is that now the desired signal level S calculation is not needed since by definition, it equals the receiver’s sensitivity level. This is, therefore, the DES approach case. 4.4.3 DES The DES approach is very similar to the condition in Section 4.4.2. However, this outcome deals with a total desensitization of all signals, due to the receiver’s front-end saturation (rather than sensitivity degradation to a single desired signal). We will discuss DES in Section 7.5. 4.4.4  False Reception We define false reception as the receiver’s detection of a legitimate signal but not the desired one. This condition can exist when the receiver has poor selectivity. We can see this condition with a single received signal, but also in the case of two received signals, with the desired signal being much weaker than the interfering legitimate signal. 4.4.5 Damage This outcome is the result of a very strong interfering signal that causes irreversible damage to the front end of the receiver, or to a LNA that may be connected to the receiver input.

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4.6  False Reception39

4.4.6  Degradation of Digital Communication We can have several negative outcomes from interference in digital communication systems. Such negative results include BER degradation, throughput reduction, adaptive data rate reduction, an increased number of required retransmissions, or even complete communication collapse.

4.5  Interference Bandwidth Types Sections 4.5.1–4.5.3 examine three types of interference distinguished by the bandwidth, respectively, narrowband interference, broadband interference, and full-band interference. 4.5.1  Narrowband Interference Narrowband interference is valid for a single frequency. Examples include cochannel interference (CCI), harmonics, intermodulation, and image frequency. Mathematical relationships, using the interfering frequency or frequencies, determine the frequency at which interference occurs. The interference bandwidth is on the order of magnitude of a single channel, but spillover to nearby frequencies can also occur. 4.5.2  Broadband Interference Broadband interference is valid for many channels above and below interferers’ center frequency. The interference may even be several megahertz wide, depending on the interferer’s modulation and the filter’s shape. Broadband interference is typically the result of the relationship of transmitter spectrum and receiver selectivity. By changing the frequency, we may avoid the interference. 4.5.3  Full-band Interference Full-band interference may be seen throughout the entire reception band. This form of interference is typically the outcome of receiver saturation or transmitter broadband noise. The main difference between full-band interference and the other interference types is that once it occurs, no frequency change can overcome the interference.

4.6  False Reception When the desired signal is present, false reception will occur when the IMRG is negative. When the desired signal is not present, false reception will occur when the signal level I at the receiver input is greater than the sensitivity, minimum detectable signal (MDS).

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Intersystem EMC Analysis, Interference, and Solutions

4.7  Interference Types According to Their Source EMC problems arise from the transmitter parameters, the receiver parameters, or a combination of the two. 4.7.1  Interference from Transmitter and Receiver Parameters Interference types that arise from both transmitter and receiver parameters include frequency-dependent rejection (FDR). We will discuss these types of interference in Chapter 5. 4.7.2  Interference from Transmitter Parameters We will discuss interference types that arise from the transmitter parameters in Chapter 6. We can subdivide the interferences in the transmitter caused category into the following two groups, based on their bandwidths:

 Broadband emissions: This source of interference is specified in power density, which is in decibels referenced to carrier per hertz (dBc/Hz). These interferers include phase noise (PHN) and broadband noise (BBN).  Narrowband emissions: This source of interference is specified in terms of power, in decibels referenced to carrier (dBc). These interferers include adjacent channel interference (ACI), spurious emissions (SPR), harmonics (HAR), and transmitter intermodulation (TIM) products. 4.7.3  Interference from Receiver Parameters We will explore interference types that arise from the receiver’s parameters in Chapter 7. The interferences in this category are subdivided into the following three groups based on the viewpoint of the interference outcome:  Interference: Due to selectivity (SEL), image rejection (IMR), intermediate frequency (IF) rejection (IFR) and receiver intermodulation (RIM) products.  False reception: Due to SEL, IMR, IFR.  Saturation (SAT) and damage (DMG). We summarize these categories in Figure 4.6.

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4.7  Interference Types According to Their Source41

Interference source

Receiver parameters

Transmitter and receiver parameters

Transmitter parameters

FDR

Saturation damage

SAT DMG

False reception

SEL IMR IFR

Interference

SEL IMR IFR RIM

Broad band

Narrow band

ACI SPR HAR TIM

PHN BBN

Figure 4.6  Interference type according to source.

Tables 4.1–4.3 summarize the interference type in each category, the name or abbreviation used in this book, the affecting parameters, and more. Figure 4.7 depicts some of the types of transmitter interference mentioned in Table 4.2. Table 4.1 Interference from the Transmitter and the Receiver Affecting Parameters

Physical Source of Interference

Interference Name

Transmitter

Receiver

CCI

Bandwidth

Bandwidth, S/I

Frequency reuse

5.2

FDR

Modulation envelope

Selectivity, S/I

Product of modulation envelope and selectivity

5.1

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Section in Book

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42

Intersystem EMC Analysis, Interference, and Solutions Table 4.2 Interference from the Transmitter

Interference Name

Affecting Transmitter Parameter

Physical Source of Interference Narrowband

Section in Book

ACI

Modulation envelope

Transmitter modulation

SPR

Spurious level

Synthesizer impurity

6.3

HAR

Harmonics level

Power amplifier nonlinearity

6.6

TIM

Third-order IP in transmitter

Power amplifiers nonlinearity

6.7

PHN

Phase noise level

Synthesizer instability

BBN

Broadband noise floor

Power amplifier noise figure

Broadband

5.3

6.4 6.5

Table 4.3 Interference from the Receiver Interference Name

Interference Outcome

SEL

False reception

Physical Source of Interference IF filter shape

Interference IMR

False reception Interference

IFR

False reception

Receiver nondesired vulnerability

Section in Book 7.3 7.7

Super heterodyne mixing parameters

7.8

Interference RIM

Interference

SAT

Sensitivity degradation

DMG

Damage

Front-end nonlinearity

Front end

Front-end heating

7.10 7.5 7.6

Figure 4.7  Transmitter interference types as function of frequency.

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Chapter

5 Contents 5.1 Transmitter Spectrum 5.2 CCI

Interference from Both Transmitter and Receiver

5.3 ACI 5.4  Splitting the FDF

To simplify the description, we can base the interfering signal strength calculation on the basic equation (8.1). In practice, additional components from (8.3) must be added when relevant, such as antenna patterns and cable losses.

5.1  Transmitter Spectrum 5.1.1  Transmitter Spectrum Definition The theoretical bandwidth of an unmodulated transmitted continuous wave (CW) signal is zero. The bandwidth actually broadens due to modulation creating the transmitter spectrum. Additional names are spectral power density, spectral mask, Tx mask, and Tx skirt. The transmitter spectrum is defined as the Fourier transform of the transmitted signal (i.e., the spectral power density as a function of frequency: Pd(f), in watts per hertz [W/Hz]). We will use a relative definition rather than absolute values. The transmitter spectrum Pd is defined as the ratio between the power density at frequency 43

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Intersystem EMC Analysis, Interference, and Solutions

difference dF denoted Pd dF (watts per hertz) and the power density at the center frequency denoted Pd f0 (watts per hertz). The relative power density is Pd =

Pd dF(W/Hz) Pd f (W/Hz)

(5.1)

0

Since both the nominator and denominator use the same units, Pd is unit-less. Converting to decibels: Pd(dBc) = 10log

Pd dF Pd f

(5.2)

0

Pd (decibels relative to carrier) is negative. The transmitter spectrum data source may be as specified or as measured. Figure 5.1 shows an example of deriving the transmitter spectrum shape for EMC calculation from measurements. Lines connect the measured peak values, rather than following all peaks and valleys, since we will require a graph of monotonous transmitter spectrum for EMC calculation. In turn, we use this calculation to find the minimum required frequency separation between the interfering and the interfered device. Otherwise, an EMC recommendation might be to keep a minimum value, but at larger frequency separations, the interference will reappear. There are modulations that have nulls in their spectrum. We can sometimes use additional signals in these nulls.

Transmitter mask BBN

Figure 5.1  Transmitter spectrum specification based on measured data.

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5.1  Transmitter Spectrum45

In many cases, the measured transmitter spectrum is symmetrical. If the spectrum is not symmetrical, then we should use stricter values above and below the center frequency. We will find cases in which the specifications are very strict, and the real transmitter spectrum is much better than the specification. We show an example in Figure 5.2. We measure the transmitter spectrum using a spectrum analyzer. The spectrum analyzer does not measure (and display) the power density but rather, the power graph versus frequency, defined as the ratio between the power at frequency difference dF, denoted PdF and the power at the center frequency denoted Pf0, in decibels referenced to carrier: LACI(dBc) = 10log

PdF (5.3) Pf 0

We named this ratio LACI, since the transmitter spectrum is the source for adjacent channel interference (ACI), namely, the amount in decibels by which the nondesired emission at dF is smaller than the emission at f0. When we need to calculate the power density, (which is the spectrum’s definition!), rather than the power, then the values measured by the spectrum analyzer must be divided by the spectrum analyzer’s bandwidth. However, since the same bandwidth is used for the measurement at f0 and at dF, the bandwidths in the equation are reduced, so that (5.2) and (5.3) are identical! We can conclude that since we deal with ratios, it makes no difference if we use the power density ratio or the power ratio.

Specification

Measured

Figure 5.2  Example of a better than required transmitter spectrum.

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Intersystem EMC Analysis, Interference, and Solutions

5.1.2  Source of the Interference Phenomenon Let us denote the following: Pd: Interfering transmitter spectrum or transmitter mask; SEL: Interfered receiver selectivity or receiver mask. The full transmitter power would have been received in the receiver if the transmitter spectrum graph and the receiver selectivity graph were identical and at the same frequency, as shown in Figure 5.3. The spectral loss between the interferer and the interfered, in this case, is 0 dB. (We will ignore a rather small additional loss, which can be observed in Figure 5.6 at dF = 0.) This definition is theoretical, serving as a reference. In real-world cases, the transmitter and receiver masks are not identical, and there usually is a frequency difference between the transmitter and receiver. Because of this difference, the transmitter emits signal outside its center frequency into the receiver mask, and, likewise, the receiver selectivity also receives signals outside its center frequency, from the transmitter mask, as shown in Figure 5.4.

Pd

SEL

Figure 5.3  Identical transmitter and receiver masks at the same frequency.

Pd

SEL

Figure 5.4  Partial overlapping of the transmitter and receiver masks.

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5.1  Transmitter Spectrum47

As opposed to the identical masks situation, there is a signal loss, which grows as the frequency difference increases. We will refer to this loss as frequency dependent rejection (FDR). 5.1.3  Calculating FDR The received power at the receiver is stated as the product of the transmitter power density and the receiver selectivity, as a function of dF: ∞



Pr = ∫ Pd ( f ) ⋅ SEL( f + dF)df (5.4) −∞

This integral reminds us of the convolution integral, wherein the plus is replaced by the minus sign. However, since both Pd and SEL are symmetric functions, it makes no difference which sign is used. The received power is therefore the convolution between the transmitter’s and receiver’s masks Equation (5.4) deals only with the masks aspect, disregarding such factors as antenna patterns and path losses. We will address these other loss contributors later in the text. The total transmitted power is the integral over the spectral density: ∞

Pt = ∫ Pd ( f )df (5.5)



−∞

The FDR loss is defined as their ratio: FDR =

Pr (5.6) Pt

Inserting (5.4) and (5.5) into (5.6), we get: ∞

FDR =

∫ Pd ( f ) ⋅ SEL( f + dF)df

−∞

∞

(5.7)

∫ Pd ( f )df

−∞

Figure 5.5 demonstrates an example of Pd of an interfering transmitter, SEL of an interfered receiver, while Figure 5.6 shows the resulting FDR as a function of their frequency difference. The loss is composed of the frequency difference between the transmitter and the receiver and the difference between the masks. To be able to independently calculate each factor, we will multiply and divide (5.7) by

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48

Intersystem EMC Analysis, Interference, and Solutions 0

dBc

− 20 − 40 − 60 − 80 − 100 −6 −5 −4 −3 −2 −1

0

1

2

3

4

5

5

6

6

dF (MHz)

Pd

SEL

Figure 5.5  Example of Pd and SEL.

FDR 0 − 20

dB

− 40 − 60 − 80 − 100 −6 −5 −4 −3 −2 −1

0

1

2

3

4

dF (MHz) Figure 5.6  Example of calculated FDR.

the power received in the receiver with zero frequency difference, dF = 0, given by: ∞

∫ Pd ( f ) ⋅ SEL( f )df (5.8)



−∞

The result: ∞

FDR =

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∫ Pd ( f ) ⋅ SEL( f + dF)df

−∞

∞

∫ Pd ( f ) ⋅ SEL( f )df

−∞

∞

∫ Pd ( f ) ⋅ SEL( f )df (5.9) ⋅ −∞ ∞ ∫ Pd ( f )df −∞

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5.1  Transmitter Spectrum49

And in decibels: ∞

∫ Pd ( f ) ⋅ SEL( f + dF)df

FDR = 10log −∞

∞

∫ Pd ( f ) ⋅ SEL( f )df

−∞

∞

∫ Pd ( f ) ⋅ SEL( f )df + 10log −∞ ∞ ∫ Pd ( f )df −∞

(5.10)

The left term of (5.10) is the ratio between the received powers with and without a frequency difference. This term indicates the loss of power, in decibels, due only to the frequency difference between the transmitter and receiver. This term, designated as the frequency difference factor (FDF) equals: ∞



∫ Pd ( f ) ⋅ SEL( f + dF)df FDF = 10log −∞ ∞ (5.11) ∫ Pd ( f ) ⋅ SEL( f )df −∞

FDF is also named off-frequency rejection (OFR) [1] or off-channel rejection (OCR). The right term in (5.10) is the ratio between the power received with nonidentical masks and the total power, both using the same frequency. This term indicates the amount of power lost, in decibels, due only to the difference between the transmitter and receiver bandwidths. We call this term the bandwidth factor (BWF), which equals: ∞



∫ Pd ( f ) ⋅ SEL( f )df BWF = 10log −∞ ∞ (5.12) ∫ Pd ( f )df −∞

BWF is also named on-tuned rejection (OTR) [1]. Equation (5.10) can be simply written as:

FDR = FDF + BWF (5.13)

that is, the FDR loss equals the sum of the FDF and the bandwidth factor. We will expand upon the FDF in Section 6.2. The bandwidth factors for each type of interference (being interference-type–dependent) will be dealt with separately. Figure 5.7 is a schematic of the calculations in accordance with (5.13). We must emphasize that, by splitting the FDR calculation into the two terms,

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50

Intersystem EMC Analysis, Interference, and Solutions The accurate calculation FDR Product of Pd and SEL at dF Splitting into two factors: (still accurate) Bandwidth factor BWF: Calculation of the integral

Frequency difference factor FDF: Calculation of the integral of the products

Figure 5.7  Schematic description of the accurate calculation.

we have not yet made any approximation! The approximations that will be used later in the text are summarized in Figure 5.8. 5.1.4  The Interference Effects  Interference: If the received interfering signal of strength I is too high, the desired signal S will not be received with that minimal S/I required for nominal reception. Interference will occur.  Sensitivity degradation: If the received interfering signal of strength I equals the thermal noise, then the sensitivity will be degraded by 3 dB. 5.1.5  Calculating the Received Interference Level The received interfering signal level I at the receiver input is, per (8.1): I = Pt + Gt + Gr + L + LFDR (5.14)

Meaning:

I = Pt + Gt + Gr + L + FDF + BWF (5.15)

wherein:

Pt: Interfering transmitter power, in decibels referenced to milliwatts; Gt: Gain of the interfering antenna, in decibels relative to isotropic radiator; Gr: Gain of the interfered antenna, in decibels relative to isotropic radiator;

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5.1  Transmitter Spectrum51 The accurate calculation FDR Product of Pd and SEL at dF Splitting into two factors: (still accurate)

Bandwidth Factor BWF:

Frequency Difference Factor FDF:

Calculation of the integral

Calculation of the integral of the products

Approximation 2

Approximation 1

Bandwidth Factor BWF:

Frequency Difference Factor FDF:

Ratio of 3 dB bandwidths

Splitting to two phenomena and using the worst case

Receiver mask interference-SEL: From a transmitter with 1 Hz bandwidth

Transmitter mask interference-ACI: To a receiver with 1 Hz bandwidth

Figure 5.8  The accurate FDR calculation and the approximations.

L: Path loss between the interferer and the interfered antennas, in decibels; FDF: As defined in (5.11); BWF: As defined in (5.12). Throughout this book, we express all losses, in decibels, as negative numbers, thus the plus signs in the equations. In the unique case in which the receiver is matched to the transmitter, so their masks are identical, as shown in Figure 5.3, the BWF equals zero, and (5.15) reduces to:

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I = Pt + Gt + Gr + L + FDF (5.16)

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Intersystem EMC Analysis, Interference, and Solutions

5.2 CCI In this section we will examine cochannel interference (CCI), as this is the most severe interference. 5.2.1 Definition CCI is created when the interfering transmitter and interfered receiver use the same frequency whether intentionally or not. This may be regarded as a special case of ACI, wherein dF = 0. 5.2.2  Source of the Phenomenon, Nonintentional Case In many cases, CCI occurs unintentionally for one of the following reasons:  Due to a lack of coordination between different spectrum users;  Or, in military systems, when the enemy uses the same frequencies. 5.2.3  Source of the Phenomenon, Intentional Case On the other hand, CCI may result intentionally due to the following:  Planned allocations of the same frequency to several users of the same device (i.e., frequency reuse). A classic example is the method of frequency allocation for cellular base stations.  The assignment of the same frequency to different users, due to the shortage of available frequencies. In the case of a deliberate allocation of the same frequency bands to several users, we must assure that the allocation does not cause interference. This assurance can be done by distance separation or by allocation of separate operation times, for example.

5.2.4  The Interference Effects  Interference: If the received interfering signal of strength I is too high, the desired signal S will not be received with that minimal S/I required for nominal reception. Interference will occur.  Sensitivity degradation: If the received interfering signal of strength I equals the thermal noise, then the sensitivity will be degraded by 3 dB.

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5.2 CCI53

5.2.5  Calculating the Received Interference Level Of all the types of interference, the CCI received interference level is the most basic and most severe. Other types of interference are usually used with this received interference as a reference level, indicating the degree (in decibels) that another type of interference is related to CCI. Since both participants use the same frequency, FDF = 0 and (8.1) reduces to:

I = Pt + Gt + Gr + L + BWF (5.17)

5.2.6  The BWF in CCI We define the BWF in (5.12). It may be difficult for us to calculate the solution to (5.12) since we need to know, analytically, both the transmitter spectrum and receiver selectivity functions. (Note that numerical integration may be used as well.) Instead, without the full analytic data we use an approximation: We assume that all the transmitted power is concentrated in a rectangularshaped spectrum of width identical to the transmitter bandwidth at the 3 dB points, BWt. Similarly, we assume that the selectivity has a rectangular shape, with a width the same as the receiver bandwidth at the 3 dB points, BWr. Figure 5.9 shows both bandwidths. The approximate bandwidth factor is the bandwidths ratio: BWF = 10log

BWr (5.18) BWt

As the receiver bandwidth increases, less power will be wasted outside BWr, and more interfering power will be received. The BWF will grow until reaching 0 dB, when both bandwidths are equal. The growth of BWF has a limit: At most, all transmitted power will be received. Increasing BWr beyond BWt will not add any more received interfering power.

BWt

BWr

f

Figure 5.9  The approximate BWF in CCI.

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54

Intersystem EMC Analysis, Interference, and Solutions

Thus, the following condition must be added to (5.18): 10log

BWr ≤ 0 (5.19) BWt

If the BWF becomes positive, then the value BWF = 0 dB will be substituted. In the case in which BWr equals BWt such as when the same device types interfere with each other, then BWF = 0 dB, and (5.17) reduces to: I = Pt + Gt + Gr + L (5.20)



The case of CCI interference, in which BWF = 0 dB, is used to measure the required signal-to-interference ratio (S/I)r. This measured value is then used as a basis for other interference type calculations. As we compare the FDR calculation to the approximation we expect a difference. The inaccuracy of the approximation stems from the fact that the 3-dB receiver bandwidth refers to the IF bandwidth, disregarding the IF filter shape. For example, two receivers having the same BWr, one having a poor selectivity shape while the other has excellent selectivity, will present the same BWF value. In practice, the second receiver has an obviously better immunity to interference; this better immunity would be missed in the calculation. Similarly, differences in transmitter masks having the same BWt will also be missed. Figure 5.10 shows an example.

5.3 ACI We use the FDR between the transmitter and receiver masks given in (5.13) for our ACI calculation. Even using the approximation for the BWF, we still must calculate FDF using (5.11). Again, we confront the difficulty that, for the sake of the calculation, both transmitter spectrum and receiver selectivity 0 −5

dBc

−10 −15 −20 −25 −30 −5

−4

−3

−2

−1

0

1

2

3

4

5

dF (MHz) Poor mask

Good mask

Figure 5.10  Poor and good masks having the same bandwidth.

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5.4  Splitting the FDF55

functions have to be known analytically, and knowledge of these functions is rare. To overcome this difficulty, another approximation is used, as discussed in Section 5.4.

5.4  Splitting the FDF The common way to circumvent calculating the integral of the product of the transmitter and receiver masks is to split the real physical phenomenon into two independent nonreal physical phenomena, separately calculating each, and then choosing the worst case, discussed as follows:  As if there is a single interference, resulting only from the transmitter spectrum presented to a receiver with a 1-Hz bandwidth;  As if there is another type of interference, resulting only from the receiver selectivity, from a transmitter with a 1-Hz bandwidth. Obviously, these are not really two physical phenomena but one. Splitting the interference in this manner is only an approximation used for ease of calculation. We detail the interference resulting from the transmitter spectrum only, in Section 6.2. We discuss the interference resulting from the receiver selectivity only, in Section 7.3. Figure 5.8 summarizes the accurate and the approximate calculations.

Reference [1] Recommendation ITU-R SM.337-6, Frequency and distance separations.

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Chapter

6 Contents 6.1 Transmitter Frequency Bands 6.2 Interference from the Transmitter Spectrum—ACI 6.3  Interference from Spurious Emission—SPR 6.4  Interference from PHN 6.5  Interference from BBN 6.6  Interference from HAR 6.7  Interference from the TIM

Interference from the Transmitter This chapter details the transmitter EMC parameters’ specifications and their related interference types. To simplify the description, the interfering signal strength calculation will use the basic equation (8.1). In practice, additional components from (8.3) must be added, as relevant. Examples include antenna patterns and cable losses.

6.1  Transmitter Frequency Bands We can divide the transmitter frequency band into the following four subbands as shown in Figure 6.1:  Transmission band;  Adjacent channels or modulation band;  In-band;  Out-of-band (OOB). 6.1.1  Transmission Band The transmission band, or transmission channel, is the 3-dB bandwidth around the center 57

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58

Intersystem EMC Analysis, Interference, and Solutions

3 dB

f Min

f Max

Transmission band CCI

Modulation

ACI

Out of band

ACI band

In band

Out of band

Figure 6.1  Transmitter bands.

frequency (i.e., that is f0 ± 0.5BWt). Interference created within the transmission band is referred to as CCI. Since the necessary bandwidth for applications such as communication and radar is usually larger than the 3-dB bandwidth, we also use the term the occupied bandwidth [1] to define that bandwidth that includes 99% of the transmitter’s power. 6.1.2  Adjacent Channels or Modulation Band If it were possible for us to create an ideal rectangular spectrum, the spectrum would not have been broader than BWt. In practice, the spectrum broadens due to the modulation and is therefore referred to as the modulation band. Since the modulation envelope penetrates the neighboring channels, the related interference is known as ACI. Although this is the formal name, adjacent channel is not the best description. The term originated from cases in which the interferer and interfered devices used the same channel spacing. This condition is certainly not a necessity. Some device types (mainly older ones) are continuously variable, with no discrete channels. Finally, the interference may spread into other nonadjacent channels. While using the ACI term, we must define where this interference type starts and where it ends. We will use the definition summarized as follows:  ACI starts at the end of the transmission band (–3-dB points) or the channel spacing, whichever is larger.

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6.1  Transmitter Frequency Bands59

 ACI ends where the transmitter mask drops below the transmitter BBN, since BBN dominates at this frequency and beyond. We define the ACI limit as the off-center frequency, at which both lines in Figure 6.2 intersect, according to: LACI(dBc) = LBBN(dBc/MHz) + 10log BWt(MHz) (6.1)

6.1.3 In-Band

The expression in-band refers to the transmitter tuning range, from fMin to fMax. A similar expression, the authorized bandwidth, may also be used. This term denotes the fMin to fMax range, plus half of the occupied bandwidth in either direction. 6.1.4 Out-of-Band OOB defines every frequency below fMin or above fMax. When the authorized bandwidth definition is used, OOB refers to all frequencies outside the authorized bandwidth. Note that we may sometimes use the acronym, OOB to denote the frequencies within the mask, above and below the necessary transmitter bandwidth.

ACI

ACI Limit BBN PHN poor PHN good dF Figure 6.2  The ACI limit.

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6.2  Interference from the Transmitter Spectrum—ACI 6.2.1  The Interference Effects  Interference: If the received interfering signal of strength I is too high, the desired signal S will not be received with that minimal S/I required for nominal reception. Interference will occur.  Sensitivity degradation: If the received interfering signal of strength I equals the thermal noise, then the sensitivity will be degraded by 3 dB. 6.2.2  Calculating the Received Interference Level The received interfering signal level I at the receiver input is given in (5.15): I = Pt + Gt + Gr + L + FDF + BWF (6.2)



Rather than using the exact equation (the FDR calculation), we will use the approximations:  The BWF is the approximation defined in (5.18): BWF = 10log

BWr (6.3) BWt

 The FDF is the transmitter mask, LACI, defined in (5.3); that is: FDF = LACI = 10log

PdF (6.4) Pf 0

Inserting into (6.2) we get:



I = Pt + Gt + Gr + L + LACI + 10log

BWr (6.5) BWt

Please note that we will discuss the other part of FDF, using receiver selectivity, in Section 7.3. Figure 6.3 shows an example of LACI in decibels referenced to carrier units, indicating the −3-dB point. In addition to the approximations previously mentioned, we can define another degree of inaccuracy. In the ACI case, we tune the receiver to a different frequency than the transmitter. The transmitter mask has a slope, shown in Figure 6.4, as opposed to the flatness within the transmission band as assumed in Figure 5.8.

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6.2  Interference from the Transmitter Spectrum—ACI61

L ACI

0 − 10

dBc

− 20 − 30 − 40 − 50 − 60 − 70 − 80 0

10

20

30

40

50

60

70

dF (MHz) Figure 6.3  Example of the transmitter mask: LACI.

Thus, increasing the value of BWr, increases the received level I by less than 10log BWr. As an example, we calculated the BWF of wide and narrow SEL masks with respect to a transmitter mask, as shown in Figure 6.4. The wide mask BWr was twice that of the narrow one. Using the exact calculation I showed an increase of 2.8 dB, rather than 3 dB per the approximation. In contrast to the CCI case, in this case, BWF can have positive values! The reason is that when BWr gets larger and larger, I increases even when BWr gets larger than BWt. The growth of BWF has the same a limit as in the

Pd

Wide SEL

Narrow SEL

Figure 6.4  Narrow and wide receiver bandwidths in ACI interference.

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Intersystem EMC Analysis, Interference, and Solutions

CCI case, at which all transmitted power will be received. The condition equation is now given by: LACI + 10log



BWr ≤ 0 (6.6) BWt

If the result is larger than zero, we replace it with zero. This equation unifies the CCI and ACI cases since for the CCI case, LACI = 0. 6.2.3  Additional Definitions of the Parameter The received interfering signal level I per (6.5) has several equivalent forms, depending on the various units we can use to define LACI. There are other equations that are sometimes more convenient for us to use, described as follows:  We sometimes specify the transmitter spectrum by power density, in decibels referenced to carrier per hertz, rather than in decibels referenced to carrier. Rewriting (6.5) we get: I = Pt + Gt + Gr + L + ( LACI − 10log BWt ) + 10log BWr (6.7)



The term in parentheses is the transmitter spectrum in terms of power density in decibels referenced to carrier per hertz. The equivalent equation for I is therefore: I = Pt + Gt + Gr + L + LACI(dBc/Hz) + 10log BWr (6.8)



 Another definition we use expresses the value of the transmitter spectrum in absolute terms in decibels referenced to milliwatts per hertz. In this case the transmitter power does not participate in the equivalent equation: I = Gt + Gr + L + LACI(dBm/Hz) + 10log BWr (6.9)



 A less common definition we sometimes use expresses the value of the transmitter spectrum in terms of power density in decibels referenced to carrier/BWt. This definition uses the transmitter spectrum with respect to the transmitter bandwidth, rather than to hertz. The origin of the definition is from EMC calculations dealing with interference between identical transceivers, where BWt = BWr. In such cases, the equivalent equation for I is:

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6.2  Interference from the Transmitter Spectrum—ACI63

I = Pt + Gt + Gr + L + LACI(dBc/BW ) (6.10)



t

Modern device types can dynamically switch between several waveforms, in accordance with real-time link or radar needs. Different waveforms may use different bandwidths. The subsequent transmitter mask usually changes accordingly, as shown in Figure 6.5. In such cases, the transmitter spectrum is waveform-dependent. 6.2.4  Default Value for Modulated Signals Defining the default transmitter spectrum for modulated signals is not an easy task, since even if the modulation type is known, additional modulation parameters are needed for calculating the transmitter mask—and they are rarely available. However, for several categories, there are specifications concerning the limits of nondesired emissions [2, 3]. 6.2.5  Default Value for Pulsed Signals The spectrum of pulsed radar has spectral lines. The frequency separation between the lines equals the PRF, and the level of the spectral lines has the shape of sin X/X. When the interfering radar transmits trapezoidal pulses having a pulse width (PW) and rise and fall times tr, the theoretical envelope of the sin X/X is composed of a flat line and two slant lines. In Figure 6.6 we illustrate the envelope, and the sin X/X. We can calculate the envelope in accordance with the following equations. The envelope is flat up to the dF value marked by the dot in Figure 6.6, given by: dF =



Wide BW

1 (6.11) pPW

Narrow BW

Figure 6.5  Narrow and wide transmitter bandwidth.

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Intersystem EMC Analysis, Interference, and Solutions 0 − 10

dBc

− 20 − 30 − 40 − 50 − 60 0.1

1

10

dF in 1/PW units Figure 6.6  Envelope of a transmitter spectrum using trapezoidal pulses.

The envelope has a −20 dB/dec slope up to the dF value marked by the square in Figure 6.6, given by: dF =

1 (6.12) p tr PW

The envelope equation between the dot and square is given by: −20log(p PW dF) (6.13)



The −3-dB point, marked by the triangle, is given by:

dF3 dB =

0.45 (6.14) PW

The envelope has a −40-dB/dec slope beyond the dF value marked by the square, given by:



PW ⎞ − 40log ( p tr dF ) (6.15) −20log ⎛⎜ ⎝ tr ⎟⎠

6.3  Interference from Spurious Emission—SPR 6.3.1  Source of the Interference Phenomenon Spurious emissions of the transmitter are narrowband emissions, at discrete frequencies, generated by the impurity of the synthesizer feeding the power amplifier. To emphasize that these emissions are not harmonics, they are also

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6.3  Interference from Spurious Emission—SPR65

named nonharmonic spurious emissions. As opposed to harmonics, these emissions can appear also below the center frequency. 6.3.2  Definition of the Parameter We define the spurious emissions level, LSPR (decibels referenced to carrier) as the strongest spurious emission, in decibels referenced to carrier below the carrier power at the center frequency. We might think that there is no point in calculating the interference from broadband noise (discussed in Section 6.5), since the spurious emissions level may appear above the noise, as seen in Figure 4.7. This is not the case, as there are some basic differences between these interference types. Spurious emissions are narrowband at discrete frequencies, thus, changing the receiver frequency to an adjacent one will overcome the interference. On the other hand, broadband noise exists at all frequencies, and changing the receiver frequency will not avoid interference. Moreover, increasing BWr increases I in cases of broadband noise interference, but not in cases of spurious interference. The spurious emissions frequencies depend on the specific transmitter frequency and vary accordingly, as does the spurious emissions quantity. Interference from spurious emissions has also a statistical consideration: What is the probability that the receiver uses a frequency at which spurious emissions exist? Defining the spurious emission level is therefore not the whole story; we need to consider the question of their quantity. A transmitter emitting many spurious lines per megahertz is poorer than one having few spurious lines per megahertz, even if both have the same spurious emissions level. A more accurate definition of a transmitter’s spurious emissions is: the number of spurious emissions within a specified frequency band, whose level, LSPR (decibels referenced to carrier), is not more than X. 6.3.3  The Interference Effects  Interference: If the received interfering signal of strength I is too high, the desired signal S will not be received with that minimal S/I required for nominal reception. Interference will occur.  Sensitivity degradation: If the received interfering signal of strength I equals the thermal noise, then the sensitivity will be degraded by 3 dB. 6.3.4  Calculating the Received Interference Level We express the received interfering signal level I at the receiver input, in accordance with (8.1):

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I = Pt + Gt + Gr + L + LSPR (6.16)

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where LSPR is the highest spurious emission level, in decibels referenced to carrier. In most cases, only one spurious emission line enters the receiver bandwidth, and the whole spurious emission power enters the receiver. Thus, increasing BWr will not increase the interference level and therefore the BWF in the case of spurious emission interference does not exist: BWF = 0 dB. In those rare cases where several spurious emission lines enter the receiver bandwidth, their powers must be summed (in milliwatts, not decibels referenced to milliwatts).

6.4  Interference from PHN 6.4.1  Source of the Interference Phenomenon In theory, when we shut off the transmitter modulation, the transmitter should have no bandwidth. However, in practice, this is not the case. The actual bandwidth is a result of synthesizer instability as the signal’s phase jitter creates a form of frequency modulation (FM). 6.4.2  Definition of the Parameter As opposed to spurious emissions and harmonics, which are at discrete frequencies, here we need to specify the power density rather than power: LPHN (dBc/Hz) − PHN power density relative to carrier power, as a function of the frequency difference from center frequency (in decibels referenced to carrier per hertz). We sometimes specify PHN in absolute values, in decibels referenced to milliwatts per hertz. The translation is trivial. For example, we specify the PHN as 10 dBm/MHz or −70 dBm/Hz. If the transmitter power is 40 dBm, then LPHN = −110 dBc/Hz. 6.4.3  The Interference Effects  Interference: If the received interfering signal of strength I is too high, the desired signal S will not be received with that minimal S/I required for nominal reception. Interference will occur.  Sensitivity degradation: If the received interfering signal of strength I equals the thermal noise, then the sensitivity will be degraded by 3 dB. 6.4.4  Calculating the Received Interference Level Since we specify the PHN in terms of power density, we calculate the received power by multiplying the density by the receiver noise bandwidth (i.e., adding in terms of decibels). Based on (8.1):

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6.5  Interference from BBN67

I = Pt + Gt + Gr + L + LPHN + 10log BWN (6.17)

where:

LPHN: PHN density in decibels referenced to carrier per hertz; BWN: Receiver effective noise bandwidth in hertz. We rarely know the effective noise bandwidth. We may calculate the integral of the receiver mask, but we usually approximate the bandwidth as equal to the 3-dB bandwidth, BWr, as this parameter is virtually always known: I = Pt + Gt + Gr − L + LPHN + 10log BWr (6.18)



As BWr increases, the value of I also increases. The growth of I has a limit: At most, all transmitted power will be received. The condition is expressed as: LPHN + 10log BWr ≤ 0 (6.19)



If the result is larger than zero, we replace it with zero. The PHN decreases as a function of frequency separation from center frequency. Cases in which we must consider PHN are rare; they are cases in which the PHN is larger than the transmitter ACI and BBN levels, as shown in the poor PHN case in Figure 6.2.

6.5  Interference from BBN 6.5.1  Source of the Interference Phenomenon The source of this interference is the transmitter’s power amplifier (PA) stages. The PA produces BBN, also referred to as the noise floor (see Figure 4.7). The PA amplifies both the signal and the noise fed to its input from the signal source, which is often referred to as the low-power RF (LPRF). The PA noise figure (NF) is usually very high, (as compared to the low-noise receiver front-end amplifiers). The noise coming from the LPRF is usually negligible compared to that generated in the PA stage. 6.5.2  Definition of the Parameter There are several ways in which we can specify this transmitter’s broadband noise. We use the following abbreviations (as shown in Figure 6.7):  BBN: Absolute broadband noise density level, in decibels referenced to milliwatts per hertz.

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Intersystem EMC Analysis, Interference, and Solutions

 LBBN: Relative broadband noise density referred to the transmitter output power, in decibels referenced to carrier per hertz, defined as: LBBN dBc/Hz = BBN − Pt (6.20)



We can also use a less common, relative definition for BBN, expressed in decibels referenced to carrier/BWt. This expression would define the BBN density within the transmitter bandwidth, rather than within 1 Hz. The definition arises from EMC calculations dealing with the interference between identical transceivers, where BWt = BWr. In such cases, there is no need for BWF in the calculation. The PA BBN density is frequency-independent. Therefore, it should not be necessary to specify its PA noise density value as a function of frequency difference relative to the center frequency. Practically, though, this turns out not to be the case. The BBN level is usually defined from a floor value of dF. Although the broadband noise exists below this minimum dF, other interference types are stronger. We show this in Figure 6.2. Therefore, measuring the BBN level too close to the center frequency is impossible. We also need to specify the BBN level at OOB frequencies: Filters at the PA output can, and should, reduce the BBN level as compared to the in-band levels. 6.5.3  Measuring BBN We measure the BBN level using a spectrum analyzer. The BBN level is not flat, as shown in Figure 4.7, but rather noisy, as shown in Figure 6.7. When we extract the BBN level from the spectrum analyzer display, the peak values should be used.

L BBN(dBc) BBN (dBm)

CW

Wide BW

Narrow BW

Figure 6.7  Measuring the BBN level.

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6.5  Interference from BBN69

We can determine the absolute BBN level in decibels referenced to milliwatts per hertz, directly from the spectrum analyzer display, taking care to deduct the spectrum analyzer’s bandwidth factor used: 10 log BWSA. Additional factors, such as the attenuation of components placed in front of the spectrum analyzer, (e.g., attenuators or filters) must be part of the value determination. Finding the relative BBN level in decibels referenced to carrier per hertz is somewhat more complicated, as the reference carrier depends on the transmitter bandwidth, whereas the BBN level does not. As shown in Figure 6.7, the larger the transmitter bandwidth, the lower the reference level. There are two ways to handle this issue. One is to shut off the modulation and use the CW level as the reference level. In the second method, when the transmitter does not sustain forced CW transmission, we measure the absolute BBN level in decibels referenced to milliwatts per hertz, and calculate the value in decibels referenced to carrier per hertz. 6.5.4  Default Value The BBN level has no default value for cases where data is missing, but we can very roughly assess it. The noise level at the PA output is equal to thermal noise, kTB, plus PA gain and PA NF: BBN dBm/Hz = kTB + GPA + NFPA (6.21)

where:

GPA: Gain of the RF chain, in decibels; NFPA: RF chain’s NF, in decibels; B: By definition: 1 Hz. Typical LPRF output power is 0 ÷ 20 dBm. Thus, the GPA typical value is Pt − (0 ÷ 20). PA NFs usually fall between 10 dB in best-case amplifiers and more typically 30 dB. The gain and NF sum varies in the range:

GPA + NFPA = [ Pt − (0 ÷ 20)] + (10 ÷ 30) = Pt + (−10 ÷ 30) (6.22) Inserting this expression into (6.21) we get the absolute BBN density:



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BBN dBm/Hz ≈ Pt − 174 + (−10 ÷ 30) (6.23)

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Inserting again into (6.20) we get the relative BBN density: LBBN ≈ −184 ÷ −144 dBc/Hz LBBN ≈ −124 ÷ −84 dBc/MHz



or:

(6.24)

Note that Pt does not appear in the relative notation. Although 40 dB is a large uncertainty range, we may use it when no other choices exist. 6.5.5  The Interference Effects  Interference: If the received interfering signal of strength I is too high, the desired signal S will not be received with that minimal S/I required for nominal reception. Interference will occur.  Sensitivity degradation: If the received interfering signal of strength I equals the thermal noise, then the sensitivity will be degraded by 3 dB. 6.5.6  Interference Relevance BBN interference is quite rare when the frequency difference between the interferer and interfered is small. In these cases, ACI interference usually overrides BBN interference. When the frequency difference between the interferer and the interfered devices is large, then BBN becomes the dominant interference type, together with harmonics and spurious emission. BBN levels are usually low. The interference is therefore mainly relevant in onboard EMC cases. BBN interference is relevant in cases when BWr is very large. 6.5.7  Calculating the Received Interference Level We can specify the received interfering signal level I at the receiver input with the BBN definition in decibels referenced to milliwatts per hertz, in accordance with (8.1): I = Gt + Gr + L + BBN dBm/Hz + 10log BWN (6.25)



When the BBN is specified in decibels referenced to carrier per hertz, I is given by: I = Pt + Gt + Gr + L + LBBN + 10log BWN (6.26)



When BBN is specified in decibels referenced to carrier/BWt, I is given by:

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6.6  Interference from HAR71

I = Pt + Gt + Gr + L + LBBN + 10log



BWN (6.27) BWT

where: BWN: Receiver effective noise bandwidth in hertz. We rarely know the effective noise bandwidth. We may calculate the integral of the receiver mask, but we usually approximate the bandwidth as equal to the 3-dB bandwidth, BWr, as this parameter is virtually always known. For example, (6.26) would then become:

I = Pt + Gt + Gr + L + LBBN + 10log BWr (6.28)

As noted, the BBN interference is present mainly in onboard cases. Equation (6.28) would then become:

I = Pt + CPL + LBBN + 10log BWr (6.29)

Consider, for example, two radios onboard a platform with −20 dB coupling between antennas. Pt is 47 dBm; BWr equals 20 KHz; and the BBN level is −180 dBc/Hz. We would calculate the interference level as:

I = 47 − 20 − 180 + 43 = −110 dBm

This result is within the order of magnitude of the interference threshold level in some receivers. If BWr increases, the value of I also increases. The growth of I has a limit: At most, all transmitted power will be received. The condition’s equation is given by:

LBBN + 10log BWr ≤ 0 (6.30) When the result is greater than zero, we replace it with zero.

6.6  Interference from HAR 6.6.1  Source of the Interference Phenomenon Harmonics arise from the nonlinearity of the PAs. Thus, the transmitter emits power at frequencies that are at an integer fundamental frequency multiple. Although the PA’s nonlinearity is the main source of harmonics, it is not the only source. Harmonics generated in the LPRF and in the preamplifiers are also amplified by the PA.

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In Section 7.11.1, we detail the theoretical issue of harmonics in greater depth. 6.6.2  Definition of the Parameter The definition is as follows:  LHAR-n: nth harmonic power relative to the carrier power at the center frequency, operating at the –1-dB compression point, in decibels referenced to carrier. 6.6.3  Default Value We can show that the relationship between the nth harmonic and the nth order intermodulation at the amplifier output port is: LHAR−n = (n − 1)( P1 dB Comp − IPn ) − 20log n (6.31)

where:

n: Order of harmonic and intermodulation; P1dB Comp: –1-dB compression point; The amplifier 1-dB compression point is defined as the output power that is 1 dB less than expected in the linear region, per Figure 7.4. Note that here we define the output power compression point, whereas for a receiver we define the input power compression point. IPn: nth order intermodulation intercept point. Unfortunately, (6.31)has a rather low value in real life. The reason is that harmonic level is usually so high that filters are added between the PA output and the antenna. Since these filters have no default value, (6.31)is quite useless, even if we know IPn. Another way around the case of missing data is to use the MIL-STD definition [4]: −Min {80,( PtdBm + 20)} dBc −80 dBc



for for

HAR 2 & 3

(6.32)

HAR 4 & above

6.6.4  The Interference Effects  Interference: If the received interfering signal of strength I is too high, the desired signal S will not be received with that minimal S/I required for nominal reception. Interference will occur.

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6.6  Interference from HAR73

 Sensitivity degradation: If the received interfering signal of strength I equals the thermal noise, then the sensitivity will be degraded by 3 dB. 6.6.5  Checking the Harmonics Content Feasibility Prior to calculating interference from harmonics, we may find it worthwhile to check (mathematically) whether harmonics from the interferer at the lower frequency band fall within the interfered higher frequency band. We would name the interferer’s frequency band f1Min to f1Max, and the interfered frequency band f2Min to f2Max. The lowest possible nth harmonic is given by: ⎧ ⎞⎫ ⎛f ⎞ ⎛f nHar −Min = Min ⎨Roundup ⎜ 2Min ⎟ ,Roundup ⎜ 2Min ⎟ ⎬ (6.33) f f ⎝ 1Min ⎠ ⎝ 1Max ⎠ ⎭ ⎩



And the highest possible nth harmonic is given by: ⎧ ⎞ ⎛f ⎛f ⎞⎫ nHar −Max = Max ⎨Rounddown ⎜ 2Max ⎟ ,Rounddown ⎜ 2Max ⎟ ⎬ (6.34) ⎝ f1Min ⎠ ⎝ f1Max ⎠ ⎭ ⎩ The value n < 2 is obviously not regarded as a harmonic. Harmonics from the lower frequency band fall within the higher frequency band only when: nHar −Min ≤ nHar −Max (6.35)



The contradiction, that the minimum is larger than the maximum, means that no harmonic from band 1 can fall within band 2. Consider, for example, that the VHF band, 30–88 MHz, generates harmonics of order number 3–13 in the UHF 225–400-MHz band. 6.6.6  Calculating the Received Interference Level The received interfering signal level I at the receiver input is, per (8.1): I = Pt + Gt + Gr + L + LHAR + BWF (6.36)

where:

LHAR: The nth harmonic level, relative to the carrier power at the center frequency, operating in the –1-dB compression point, in decibels referenced to carrier. BWF: Bandwidth factor for harmonic interference.

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We specify LHAR for a transmitter using its full power level at the –1-dB compression point, but in many practical cases, the transmitter is used at a lower output power level (that is, backed off by BO(dB)). The interference level is reduced by n · BO(dB):

I = Pt + Gt + Gr + L + LHAR − n ⋅ BO + BWF (6.37)

6.6.7  The BWF for Harmonic Interference A frequency component within the fundamental frequency spectrum, whose frequency is f0 + dF, appears in the nth harmonic at the frequency, which is n times larger: n ( f0 + dF ) = nf0 + ndF (6.38)



As shown in Figure 6.8. We can clearly see that the nth harmonic bandwidth is multiplied by n. The BWF for the harmonics interference type is therefore: BWF = 10log

BWr (6.39) nBWt

When BWr increases, the value of I increases. The growth of I has a limit: At most, all transmitted power will be received. The condition equation is given by:

L ACI L HAR

L ACI

f0

f 0+dF

n−f 0

n−f 0 + n−dF

Figure 6.8  The nth harmonic spectrum.

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6.7  Interference from the TIM75

10log

BWr ≤ 0 (6.40) nBWt

If the result is larger than zero, we replace it with zero. 6.6.8  Calculating the Interference Close to Harmonics Traditionally, harmonic interference is calculated at multiples of the center frequency, ignoring the transmitter spectrum. However, we must determine the required frequency change based on the transmitter spectrum as well. Taking the spectrum into account, the interference level becomes:

I = Pt + Gt + Gr + L + LHAR + LACI + BWF (6.41)

The frequency difference, dF, is defined at the fundamental transmitting frequency fTX:



dF =

fRX − fTX (6.42) n

Consider, for example, a 500-MHz transmitter that is interfering with a receiver set at 1,500 MHz. The interference margin is IMRG = −70 dB. Based on the transmitter spectrum, the missing 70 dB can be achieved at, for example, dF = 1 MHz with respect to the fundamental transmitting frequency. We have the choices of changing the interfering frequency from 500 MHz or changing the interfered frequency from 1,500 MHz. If we choose the first option, the transmitter frequency must be changed to 500 ± 1 MHz as a minimum. However, if we choose the second option, the receiver frequency must be changed to at least 1,500 ± 3 MHz.

6.7  Interference from the TIM 6.7.1  Source of the Interference Phenomenon When we have two transmitters placed in the same vicinity, power leaks from one transmitter output port to the other, as shown in Figure 6.9. The leaking signal at f2 from transmitter 2’s antenna reaches transmitter 1’s antenna. This type of leaked signal is usually seen between close antennas onboard the same platform but may also occur between two platforms in close proximity. The power reaching transmitter 1’s antenna continues to transmitter 1’s output port and then on to the input port of transmitter 1’s PA. The desired

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Intersystem EMC Analysis, Interference, and Solutions L f1 |2f 1 -f 2| |2f 2 - f1|

Tx #1 L ct f1 CPL

Tx #2 L ct

f2

Figure 6.9  The mechanism of TIM.

signal at f1 exists in the PA input port as well. Both signals generate intermodulation as is the case for any two signals at an amplifier input. The intermodulation products appear at transmitter 1’s output port, reach transmitter 1’s antenna, and are transmitted, along with the desired signal with a path loss L to the interfered receiver. We see the same intermodulation mechanism’s effect in the opposite direction. A signal leaking from transmitter 1’s antenna reaches the antenna of transmitter 2, generating intermodulation products that are transmitted to the interfered receiver. (For simplicity, this is not depicted in Figure 6.9.) We observe the same leakage between transmitters in cases where several transmitters are connected by a multicoupler to a common antenna. We refer to the mechanism by which intermodulation products are generated in transmitters as transmitter intermodulation (TIM). 6.7.2  Definition of the Parameter The transmitter’s intermodulation value is specified by the transmitter output third-order intercept point: IP3. 6.7.3  Default Value In cases in which data is missing, but P1dB is known, we may be able to assess that IP3 is 10 dB above the output power at the –1-dB compression point (for less linear amplifiers), and 15 dB above the –1-dB compression point (for highly linear amplifiers).

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IP3 = P1 dB + (10 ÷ 15) dB (6.43)

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6.7  Interference from the TIM77

6.7.4  The Interference Effects  Interference: If the received interfering signal of strength I is too high, the desired signal S will not be received with that minimal S/I required for nominal reception. Interference will occur.  Sensitivity degradation: If the received interfering signal of strength I equals the thermal noise, then the sensitivity will be degraded by 3 dB. 6.7.5  Calculating the Received Interference Level We express the received interfering signal level I at the receiver input, per (8.1), as: I = P3 + Gt + Gr + L + BWF (6.44)

where:

P3: Third-order intermodulation product power, in decibels referenced to milliwatts. In case where both transmitters are identical, P3 is given by: P3 = 3 ( Pt + Lct ) − 2IP3 + CPL (6.45)

where:

Lct: Cable losses from each transmitter to its antenna; CPL: Coupling between the transmitters:  When we have transmitters connected to different antennas, coupling exists between the antennas input ports.  In the case of transmitters connected to a single antenna via a multicoupler, coupling exists between the multicoupler input ports. We should note that this coupling is not the same as the nominal isolation value between the multicoupler input ports when they are terminated with 50-Ω loads. The actual coupling is dependent on the voltage standing wave ratio (VSWR) of the antenna, per the following equation:



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(

)

⎡ 1 VSWR − 1 2 1 ⎤ CPL = 10log ⎢ 2 + Io ⎥ (6.46) n VSWR + 1 ⎢⎣ 1010 ⎥⎦

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where: n: Number or input ports of the multicoupler; I0: Nominal isolation, in decibels. Figure 6.10 illustrates this equation for n = 2 input ports. We see that when the multicoupler is connected to an antenna having VSWR of approximately 1.3:1 and above, the actual isolation or coupling does not depend on the nominal isolations, and is quite poor.  We must account for additional factors that will exist if the circuit also includes filters and or circulators placed between the transmitter and antenna. When nonidentical transmitters are involved, (6.45) is replaced by (6.47) and (6.48). The third-order intermodulation product radiated from transmitter 1 is: P3A = 2 ( Pt1 + Lct1 ) + ( Pt 2 + Lct 2 ) − 2IP3−1 + CPL (6.47)



and from transmitter 2, it is P3B = ( Pt1 + Lct1 ) + 2 ( Pt 2 + Lct 2 ) − 2IP3−2 + CPL (6.48)

0 − 10

dB

− 20 − 30 − 40 − 50

1

1 .5

2

2 .5

3

VSWR I0(dB) 30

40

50

Figure 6.10  Multicoupler’s actual isolation versus VSWR.

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6.8  Interference from LFM Radar79

We calculate BWF using (5.18). However, we still must know the BWt of the intermodulation products. In the most common case, third-order intermodulation, the intermodulation product bandwidth equals the fundamental frequency BWt. This relationship does not necessarily hold for higher orders of intermodulation where BWt may be (but not necessarily is) larger. 6.7.6  Checking Intermodulation Feasibility Prior to calculating the intermodulation interference, we may find it worthwhile to check (mathematically) whether intermodulation products from the interfering transmitters fall within the receiver frequency band. The calculation, explained in Section 7.10.8, is identical to the calculation for receiver intermodulation (RIM) interference.

6.8  Interference from LFM Radar Pulse interference applies, among other interferers, to pulsed radar. The case of linear frequency modulation, LFM radar, is a different and special case that deserves our attention. LFM radar is a CW or pulsed radar, sweeping its frequency over a large band, BWLFM. The revisit time T (i.e., the PRI) is the reciprocal of the PRF, as shown in Figure 6.11, depicting the CW case. When the interfered device frequency resides within BWLFM, we will see that the impact of LFM radar on the interfered receiver depends on the relation between the LFM radar PRF and the receiver bandwidth, BWr. 6.8.1  Slow Sweep We will use Figure 6.12 to explore the LFM radar impact on the interfered receiver. As the swept frequency increases, it eventually hits the lower

F T=1/PRF

BW LFM

t Figure 6.11  LFM radar frequency vs. time.

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Intersystem EMC Analysis, Interference, and Solutions

frequency of the interfered receiver bandwidth, and power starts to build up in the IF filter. After a while the swept frequency reaches the upper frequency of the interfered receiver bandwidth and from this time on, no more energy enters the IF filter. The duration of the LFM signal within the receiver bandwidth is the received pulse width, PW. The response time, that is, the build-up and decay time of a pulse in a band pass filter is approximately the reciprocal of its bandwidth, [5]: t=

1 (6.49) BWr

Figure 6.13 illustrates (in a schematic way) the build-up and decay of the power. It starts building up when the interfering pulse starts, and reaches its final level after the response time, t. The power begins to drop at the end of the PW and vanishes after the response time, t. It takes the revisit time T to repeat the process. The distinction between slow and fast sweeps depends on whether the next pulse starts a long time after t, as shown in Figure 6.13, or a short time F T=1/PRF

BW LFM

BW r

t A

t PW Figure 6.12  Slow sweeper.

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6.8  Interference from LFM Radar81

A

t

t PW T Figure 6.13  Build-up and decay of slow sweeper LFM pulse.

after the leading edge of t, respectively. The impact of slow LFM radar on the interfered receiver is equivalent to pulse radar. From Figure 6.13 we can derive the definition of slow sweeper: T >> t (6.50)



Recalling that T = 1/PRF and inserting (6.49) we find the LFM radar is a slow sweeper when

PRF BWr (6.55)



Since the revisit time is much shorter than the IF filter response time, the received power never decays. The impact of fast LFM radar on the interfered receiver is equivalent to a wide band jammer. The effect of fast sweep LFM is in the frequency domain, opposed to the slow sweep LFM, whose effect is in the time domain. We are therefore interested in the transmitted LFM spectrum. Figure 6.14 depicts a typical LFM spectrum, BWLFM = 80 MHz in this example. LFM spectrum has some oscillations, but clinging to the EMC moto of looking at the worst case, we only show the envelope of these oscillations. It is customary to treat the spectrum as rectangular, that is, being flat within the swept bandwidth. The BWF would be: BWF = 10log

BWr (6.56) BWLFM

0

dBc

− 10

− 20

− 30 − 50

− 40

− 30

− 20

− 10

0

10

20

30

40

50

dF (MHz) Figure 6.14  Typical LFM spectrum.

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6.8  Interference from LFM Radar83

References [1] Recommendation ITU-R SM.328-10, Spectra and Bandwidth of Emissions. [2] Recommendation ITU-R SM.329-8, Spurious Emissions [3] Recommendation Rec. ITU-R SM.1541-6, Unwanted Emissions in the Outof-Band Domain. [4] MIL-STD 461 F, Department of Defense, Interface Standard Requirements for the Control of Electromagnetic Interference Characteristics of Subsystems and Equipment, December 10, 2007. [5] Schwartz, M., Information Transmission Modulation and Noise, 4th ed., 1990, McGraw Hill.

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Chapter

7 Contents 7.1  Receiver Frequency Bands

Interference from the Receiver

7.2  Required (S/I)r 7.3  General Aspects in Receiver Interference 7.4  Interference from SEL 7.5  SAT and Desensitization 7.6 DMG 7.7  Interference from IMR 7.8  Interference at the IF 7.9  Interference from LO Radiation

In this chapter we will describe the receiver EMC parameters’ specifications and related types of interference. To simplify the description, we will use the basic (8.1) to calculate interfering signal strength. In practice, we will have to add any relevant components from (8.3), such as antenna patterns and cable losses.

7.1  Receiver Frequency Bands We can divide the receiver frequency band into the following four subbands as shown in Figure 7.1 (quite similar to the transmitter frequency bands):  Reception band;

7.10  Interference from RIM

 Selectivity band;

7.11  Harmonics and Intermodulation

 OOB.

7.12  In-Band and OOB Interference

 In-band;

7.1.1  Reception Band The reception band or the intentional passband is the 3-dB bandwidth around the center frequency: that is f0 ± 0.5BWr. Generally, we would 85

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Intersystem EMC Analysis, Interference, and Solutions

3dB

f Min

f Max

Reception band CCI Selectivity

SEL

Out of band

In band

SEL band

Out of band

Figure 7.1  Receiver bands.

use the IF 3-dB bandwidth (the last IF, if there is more than one) for this definition. Interference created within the transmission band is the CCI. Since the necessary bandwidth for reception is usually larger than the 3-dB bandwidth, we also use the term the “occupied bandwidth” to define that bandwidth that includes 99% of the partnered transmitter’s power. 7.1.2  Selectivity Band If it were possible for us to create an ideal rectangular filter, the bandwidth would not have been broader than BWr. In reality, the filter shape is not rectangular, but rather, is matched (as far as possible) to the transmitter spectrum it is intended to receive. In practice, the receiver selectivity graph or receiver mask penetrates the neighboring channels. We will refer to it as SEL. We must define where the selectivity band starts and ends. We will use the following definition:  The selectivity band starts at the end of the reception band (the 3-dB points) or the channel spacing, whichever is greater.  The selectivity band ends at the point at which the IF selectivity has no more capability to reduce the received interference level. 7.1.3 In-Band The expression in-band refers to the receiver tuning range, from fmin to fmax. A similar expression may also be used: the authorized bandwidth. This term

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7.2  Required (S/I)r87

denotes the fmin to fmax range, plus half of the occupied bandwidth in either direction. 7.1.4 OOB OOB defines every frequency below fmin or above fmax. When the authorized bandwidth definition is used, OOB refers to all frequencies outside the authorized bandwidth.

7.2  Required (S/I)r In this section we will explore one the most important criteria needed for EMC analysis: the required signal to interference ratio, (S/I)r. 7.2.1  Source of the Interference Phenomenon All that the desired signal must overcome without interference is the noise. The total noise is defined as the thermal noise plus external noise, when relevant. Our criterion for coping with noise is the required S/N at the receiver input, (S/N)r. In the presence of an interfering signal having the level I at the receiver input, the situation changes. When I is much larger than the noise, the signal must overcome this interference. The criterion for coping with the interference is the required S/I at the receiver input, (S/I)r, (also called the required carrier-to-interference ratio (C/I)r,). When the noise level is not negligible, the signal strength must be large enough to overcome both interference and noise. We will deal with this condition in Section 9.2.6 7.2.2  Definition of the Parameter We define (S/I)r as how many decibels the signal level requires to be stronger than the interference level, in order to restore the nominal reception (in terms of such measures, for example BER). The value of (S/I)r may differ for various interferers, depending whether they are CW or are modulated, if the interfering signal has the same or different modulation as the desired signal, and more. When we give the (S/I)r statement, we need to indicate what type of interference is involved. 7.2.3  Measuring (S/I)r We measure the (S/I)r at the center frequency, using the CCI type of interference. The measurement should be performed with the desired signal level set much higher than the sensitivity level to eliminate the thermal noise impact. The high-level interfering signal is then added, and gradually reduced, until

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Intersystem EMC Analysis, Interference, and Solutions

we reach the nominal reception level, as defined for receiver sensitivity. The test block diagram is similar to the one shown in Figure 23.1, with the interfering transmitter feeding a directional coupler via an attenuator rather than an antenna. 7.2.4  Default Value The order of magnitude of (S/I)r is close to, and in many cases, equal to (S/N)r. We might find this condition in many digital communication modulations, wherein the modem treats an interfering signal in the same way it treats thermal white noise. Therefore, in the absence of data, we may use the (S/N)r as a default value for (S/I)r. We will face a problem if the (S/N)r data is missing as well. In such cases, we can calculate the (S/N)r value if the sensitivity and NF are known:

( ) S N



r

= MDS − kT − 10log BWr − NF (7.1)

where: MDS: Minimum detectable signal, the sensitivity, in decibels referenced to milliwatts; kT: −174 dBm/Hz; BWr: Receiver bandwidth, in hertz; NF: Receiver NF, in decibels. In the worst case, where no data exists, we should assess the (S/N)r per the modulation type. (S/I)r and (S/N)r, are not necessarily the same. A good example would be found in the case of FM reception where the values greatly differ. In FM the value of (S/I)r ≈ 2 ÷ 3 dB due to the capture effect, while the (S/N)r ≈ 10 ÷ 13 dB, (or even more in the case of receiving stereo broadcasting). Several examples of the (S/I)r for fixed satellite service can be found in [1], where the C/I notation is used. 7.2.5 (S/I)r and Processing Gain Devices using direct sequence (DS), such as in CDMA, have a processing gain (PG) given by the RF-to-IF bandwidth ratio: PG = 10log

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BWRF (7.2) BWIF

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7.3  General Aspects in Receiver Interference89

In this case, the required S/I is:

() ( ) S I



r

=

S N

r

− PG (7.3)

We would find, in this case, that (S/I)r is usually a negative number, meaning that the signal can be weaker than the interference. Consider, for example, a civilian GPS PG of 43 dB. Assuming (S/N)r = 16 dB, the required (S/I)r = 16 − 43 = −27 dB. 7.2.6  Protection Ratio The protection ratio (PR) is a quite similar parameter. The difference between these similar terms is that (S/I)r is a number, defined for CCI, whereas the PR may be sometimes a function, defining the required S/I as function of the frequency difference: PR = (S/I)r f(dF). In the CCI case they are obviously the same: PR = (S/I)r. 7.2.7  Jamming Ratio Another familiar parameter, known from the EW realm, is the required jamming ratio, (J/S)r. It might seem that (S/I)r and (J/S)r are just each other’s reciprocals, (S/I)r = −(J/S)r, but this not true! Usually there is a difference of several decibels between the two. It is the underlying principle that matters, not the few decibels of difference, explained as follows:  The objective of denying interference is to not reach the interference threshold.  The objective of jamming is to reach at least the crash threshold. Both thresholds are depicted in Figure 2.1.

7.3  General Aspects in Receiver Interference 7.3.1  Direct and Indirect Definition of the Interference Parameter We can define the receiver interference, either directly or indirectly, described as follows:  The direct definition specifies the interfering signal level at the receiver input port. For example: the attenuation of an off-center frequency signal with respect to reception in the center frequency.

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Intersystem EMC Analysis, Interference, and Solutions

 The indirect definition specifies an interference effect. Usually, the interfering level at the receiver input degrading the receiver sensitivity by 3 dB. The advantage in using the direct definition is that it uses the values needed for EMC calculations. The advantage of using the indirect definition is that it indicates the procedure for the receiver EMC acceptance test. The two definitions are mathematically related and can be translated using appropriate mathematical relationships, which we discuss later in Sections 7.4.4, 7.7.2, and 7.10.5. 7.3.2  Interference Effects  Interference: If the received interfering signal of strength I is too high, the desired signal S will not be received with that minimal S/I required for nominal reception. Interference will occur.  Sensitivity degradation: If the received interfering signal strength I equals the thermal noise, sensitivity will be degraded by 3 dB.  False signal reception: If the interfering signal is legitimate, if will be received and treated as if it were the desired signal. 7.3.3  Equivalent Interfering Signal Level In cases where we have interference originating at the transmitter, the calculated interfering signal level I reaching the receiver input is the real value. However, when we have interference originating at the receiver the outcome may be quite different. The interfering signal level I may be the equivalent interfering signal level at the receiver input. We must calculate the received interfering signal level at the IF output since the IF filter’s effect on interference is only seen at the IF output. This level equals the real level at the receiver input plus the gain from the input port to the IF, or GRF to IF. We should compare this interfering level to the desired signal level that equals S + GRF to IF. Thus, the gain, GRF to IF (which, in any case in not known) is reduced.

7.4  Interference from SEL 7.4.1  Source of the Interference Phenomenon We will deal with the most important nondesired responses first: those caused by insufficient SEL. Since we only want to receive the desired signal, the receiver frequency response is usually designed to have the same bandwidth as its partner, BWr = BWt. The SEL, or the receiver’s frequency response, has

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7.4  Interference from SEL91

a broader shape than the –3-dB points, as shown in Figure 7.2. SEL is mainly governed by the IF filter (the last filter, if we are considering a multiple-conversion receiver). The interference involved with the nondesired response is continuous on the frequency axis and obviously decreases with the value of dF. This continuous interference is different than the discrete frequency interference caused by, for example, IMR, IFR, and RIM. 7.4.2  Definition of the Parameter Our definition of SEL, which can also be referred to as the SEL graph, SEL curve, receiver mask, or receiver skirt, is provided as follows:  LSEL: Off-center signal attenuation at dF(MHz), with respect to reception at the center frequency, in decibels. 7.4.3 Measuring LSEL and the Indirect Definition Measuring the receiver mask is not as easy as measuring the transmitter mask, where we connect a spectrum analyzer to the transmitter output. We cannot always measure the receiver mask directly, since connecting the test device to the receiver IF output is required: a capability that not many receivers possess. When we have access to the receiver IF output, a signal is fed to the receiver at its center frequency, and the level at the IF output is measured

LSEL

0 − 10 − 20

dBc

− 30 − 40 − 50 − 60 − 70 − 80

0

10

20

30

40

50

60

70

dF (MHz) Figure 7.2  Receiver SEL example.

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Intersystem EMC Analysis, Interference, and Solutions

for reference. We then change the input signal frequency, and remeasure the level at the IF output as function of dF. When access to the receiver IF output is not available, or the receiver is a black box, we use an indirect measurement procedure, described as follows:  We feed the desired signal to the receiver via a power combiner or directional coupler. The desired signal level is set to the sensitivity, MDS. We measure the receiver performance in terms of such factors, for example, BER.  The desired signal level is increased by 3 dB, which causes the receiver performance to improve.  A CW interfering signal at dF(MHz) off the center frequency is added to the power combiner or directional coupler. The interfering signal level is increased up to the PSEL, level, until receiver performance, as measured in the first step, is restored. 7.4.4  Indirect Definition of the Parameter The indirect definition of the phenomenon uses the parameter PSEL, described as follows:  PSEL: The level of an interfering signal, dF(MHz) off the center frequency, degrading the sensitivity by 3 dB. It’s easy to find the mathematical relationship between the two definitions. The receiver mask attenuates PSEL by LSEL(dB) to the level of: PSEL + LSEL (7.4)



Remember that LSEL is defined as a negative number, thus the plus sign. If the sensitivity is degraded by 3 dB, it means that the attenuated interfering signal level equals the thermal noise N: PSEL + LSEL = N (7.5)



The receiver sensitivity is given by:



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MDS = N +

( ) S N

r

= kT + 10log BWr + NF +

( ) S N

(7.6)

r

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7.4  Interference from SEL93

Extracting the noise parameter from (7.6), then inserting into (7.5) and rearranging, we get:



LSEL = MDS −

( ) S N

r

− PSEL (7.7)

As an example: the receiver sensitivity is MDS = −110 dBm, and requires (S/N)r = 6 dB. The interfering signal level at frequency difference dF degrades the sensitivity by 3 dB, at PSEL = −80 dBm. Therefore, the value of LSEL at this frequency difference is:

LSEL = −110 − 6 − (−80) = −36 dB

7.4.5  Calculating the Received Interference Level The received interfering signal level I at the receiver input is, per (8.1), is:

I = Pt + Gt + Gr + L + LSEL (7.8)

7.4.6  The BWF Note that that we did not include the BWF in (7.8), a point worthy of explanation. Recall that we replaced the exact calculation based on the product of the transmitter and receiver masks, by an approximation: interference only from the transmitter mask and interference only from the receiver mask. However, there is a major difference between these two physical phenomena: the transmitter mask is defined by power density, whereas the receiver mask is defined by attenuation. In ACI interference, the BWF as in (5.18) is: BWF = 10log

BWr (7.9) BWt

The upper side of Figure 7.3 describes the transmitter mask phenomenon. If we increase BWr from narrow to wide (leaving BWt unchanged), we can clearly see, from Figure 7.3 and (7.9), that a wider BWr receiver absorbs more power from the power density than a narrower BWr. The lower side of Figure 7.3 describes the receiver mask phenomenon. It can be clearly seen from Figure 7.3 that the attenuation LSEL of the signal dF(MHz) away is the same whether BWt is narrow or wide. In both phenomena, we ignore the inaccuracy due to the slope of the mask.

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94

Intersystem EMC Analysis, Interference, and Solutions Power density Tx mask

LACI

dF Narrow or wide BWr

Attenuation Rx mask

LSEL

dF Narrow or wide BWt Figure 7.3  Explanation for leaving BWF out of the SEL calculation.

7.5  SAT and Desensitization 7.5.1  Amplifier Compression Normally we set an amplifier’s working point to operate in the amplifier’s linear region, where its gain is the nominal one. We use the –1-dB compression point parameter, P1dB comp, to define the point at which the amplifier starts to saturate. We define the input –1-dB compression point as the input power level, at which the output power level drops by 1 dB, as compared to what is expected in the linear region, as shown in Figure 7.4. In other words, the gain at the –1-dB compression point is 1 dB less than nominal.

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7.5  SAT and Desensitization95

POut 1 dB

Saturation

P1 dB Out

The linear region PIn

P1 dB In Figure 7.4  Amplifier SAT definition.

7.5.2  The Interference Effect At an input signal level greater than P1dB comp, the gain will drop even more than 1 dB, until reaching SAT, where the output power doesn’t grow anymore: one of the worst types of interference. The reason is that if an amplifier is saturated, the spectrum is interfered at all frequencies, not just at the interferer’s frequency. We can illustrate the phenomenon with Figure 7.5. Normally, the desired signal level PIn, at the front-end amplifier will create a signal level, POut, at the amplifier output. In Figure 7.5, when an interfering signal, PInt at saturation > P1dB comp, appears at the amplifier input, it causes a shift of the nominal amplifier graph (dashed line), to the right POut

POut ∆G POut at saturation

PIn

PInt in at saturation

PIn

Figure 7.5  Amplifier gain reduction due to SAT by an interferer.

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Intersystem EMC Analysis, Interference, and Solutions

(solid line). At this point, the desired signal level, PIn, creates a signal level, POut at saturation, with a loss of ΔG, regardless of its frequency. The receiver thus suffers desensitization of ΔG (decibels). There is a distinction between the two related terms, SAT and desensitization, described as follows:  SAT is a physical phenomenon at the receiver’s front-end amplifier, which is the interference source.  Desensitization refers to the interference outcome caused by this interference source. When the amplifier receives many interfering signals, none strong enough alone to saturate the amplifier front end, their sum (in watts) will saturate the amplifier if it is greater than the –1-dB compression point. 7.5.3  Definition of the Parameter We define the 1-dB compression point as follows:  P1dB comp: Input level of a signal at the received center frequency, degrading the receiver’s sensitivity by 1 dB. We define this parameter for a signal at the received center frequency in order to neutralize the influence of an RF filter that is usually placed between the receiver input and the front-end amplifier. We take the effect of such filtering into account when calculating the received interference level. 7.5.4  Acquiring the –1-dB Compression Point The receiver P1dB comp is not measured, but, rather, acquired. The receiver P1dB comp is equal to the front-end amplifier 1-dB compression point (from the amplifier specification), plus all attenuation from the receiver input to the amplifier, such as that caused by cables and filters. When we place an external LNA in front of the receiver, the LNA’s 1-dB compression point is usually the decisive parameter. However, if the LNA has a very high gain, we should verify that it does not drive the receiver into SAT. In this case, the receiver is, again, the weakest point in the chain. 7.5.5  Comparing Interference and SAT Interference and SAT are two different physical phenomena. As opposed to interference caused when two signals at the receiver input compete for the S/I, front-end amplifier gain degradation involves a single interfering signal.

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7.5  SAT and Desensitization97

Seemingly so, a paradox may be raised when no interference is anticipated according to the interference margin from ACI or SEL, but SAT can still occur. Why at all is checking SAT needed if the interfering signal is very weak? The answer lies in the differences described as follows:  ACI case: The transmitter mask determines the interfering signal level at the receiver’s center frequency. This signal level may be very low and is not saturating the receiver. The interfering power of ACI is very low since it is attenuated by the amount LACI, whereas SAT is caused by the full transmitter power at the transmitter’s center frequency. Note that ACI interference calculations are performed at the receiver frequency.  SEL case: The IF filter is protecting the desired signal from interference. Note that SEL interference calculation is performed at the transmitter frequency.  SAT case: As opposed to the SEL case, the RF filter protects the receiver from SAT. As in the SEL case, the SAT interference calculation is performed at the transmitter frequency. Figure 7.6 helps answer the question as to the point at which the receiver is in danger of being saturated, on the frequency axis. We can expect SAT when the transmitter frequency is within the RF filter passband but outside the IF filter bandwidth. If the transmitter frequency is further away, the RF filter can attenuate the signal, avoiding SAT. On the other hand, if the transmitter frequency is within the selectivity band, SEL interference is expected to appear well before SAT.

RF filter

IF filter

Non saturating signal

Saturating signal

Figure 7.6  The mechanism of creating SAT: frequency viewpoint.

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Intersystem EMC Analysis, Interference, and Solutions

7.5.6  Calculating the Received Interference Level The received interfering signal level I at the receiver input, at the transmitter frequency, is, per (8.1): I = Pt + Gt + Gr + L + LFEF (7.10)

where:

LFEF: Front-end filter attenuation at the transmitter frequency. When we place an external LNA in front of the receiver, the filter at the front end of the receiver has no impact. The loss of a filter, if present in front the LNA, applies instead. In the case of a phased-array antenna, wherein each of the multiple modules acts as a receiver, the relevant gain Gr in (7.10) is the single module gain, not the gain of the entire phased array.

7.6 DMG 7.6.1  Source of the Interference Phenomenon We can have strong signals at the receiver input that may result in irreversible damage to the front-end amplifier. Continuous signals can cause overheating while very strong pulse signals may cause voltage breakdown. Such breakdown can also happen in the near field if the space impedance is much higher than the free-space value (120π ) as the electric field may be very strong. 7.6.2  Definition of the Parameter We define the damage level as follows:  PDMG: Maximum allowed input level at the received center frequency that will not cause irreversible damage. Sometimes we need to consider the temporal aspect (that is, the maximum allowed signal level may be time-limited). We define this parameter for a signal at the received center frequency to neutralize the influence of an RF filter, usually placed between the receiver input and the front-end amplifier. We take the effect of this filter into account when calculating the received interference level.

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7.7  Interference from IMR99

7.6.3  Acquiring the DMG Level The DMG level, PDMG, is not measured but, rather, acquired. The receiver PDMG is equal to the front-end amplifier DMG level (from the amplifier specification), plus all attenuation from the receiver input to the amplifier, such as that caused by cables and filters. The LNA DMG level would apply instead, when an external LNA is placed in front of the receiver. 7.6.4  Default Value If PDMG data is missing, but P1dB comp is known, it can be assumed that: PDMG = P1 dB Comp + (30 ÷ 35) dB (7.11)



7.6.5  Calculating the Received Interference Level The received interfering signal level I at the receiver input and at the transmitter frequency is, per (8.1): I = Pt + Gt + Gr + L + LFEF (7.12)

where:

LFEF: Front-end filter attenuation at the transmitter frequency. When we place an external LNA in front of the receiver, the filter at the front end of the receiver has no impact. The loss of a filter, if present in front the LNA, applies instead. In the case of a phased-array antenna, wherein each of the multiple modules acts as a receiver, the relevant gain Gr in (7.12) is the single module gain, not the gain of the entire phased array. Calculating the risk of receiver DMG is sometimes unnecessary because the vulnerability to SAT is always larger. Since we cannot ignore SAT risk, its resolution will eliminate any existing risk of DMG.

7.7  Interference from IMR 7.7.1  Source of the Interference Phenomenon Image response is created as a result of the mixing of signals in a superheterodyne receiver. We will detect a signal at the receiver input, at any frequency that when mixed will produce the IF. The most commonly known interferer thus produced is the image frequency. The image frequency is dependent on

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Intersystem EMC Analysis, Interference, and Solutions

the relationship between the LO frequency, fLO, and the desired frequency. If the desired frequency f0 is higher than the LO namely f0 = fLO + IF, the image frequency is: fImage = fLO − IF (7.13)



If the desired frequency f0 is lower than the LO, namely f0 = fLO − IF, the image frequency is: fImage = fLO + IF (7.14)



In both cases, the difference between the desired frequency and the image frequency is twice the IF: f0 − fImage = 2IF (7.15)



This is reason for using the name image, as shown in Figure 7.7: When the LO frequency is placed at the center, the desired frequency and image frequency are mirror images of each other. These spurious frequencies are therefore: fSpurious = fLO ± IF (7.16)



L IMR

f

IF f Image

IF LO

f0

Figure 7.7  The image frequency.

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7.7  Interference from IMR101

Although these two signals are the most important and best-known interferers, they are not the only ones. All frequencies that satisfy (7.17) are spurious frequencies that may interfere or be received: IF = ± mfSpurious ± nfLO (7.17)



where m and n are integers. For example, the desired frequency is lower than the LO, (f0 = fLO − IF). If m = −1 and n = 2, we get: IF = − fSpurious + 2 fLO = − fSpurious + 2 ( f0 + IF )



Extracting, we find that 2f0 + IF is a spurious frequency. Another spurious frequency is the IF itself, where m = 1 and n = 0. We will deal with this case in the next section. Most receivers have dual and triple conversion, by which we mean that there is more than one LO frequency and one IF. Equation (7.17) should be used for all LO frequencies and IFs. The number of spurious frequencies can thus be very large. Those frequencies falling in-band are the most dangerous. We often detect these spurious signals between two devices of the same type onboard a single platform, or between platforms in close proximity. We make a distinction between two related terms as follows:  Image response is the phenomenon in which a receiver responds to these spot frequencies, other than the center frequency.  Image rejection is the parameter specifying the receiver’s capability to attenuate the image frequencies. 7.7.2  Definition of the Parameter The direct definition of image rejection, as shown in Figure 7.7 is the following:  LIMR: The attenuation, in decibels, of a signal at an image frequency with respect to reception level at the center frequency. Common values are 80 dB or better. The indirect definition is the following:  PIMR: Level of an interfering signal at the image frequency degrading the sensitivity by 3 dB.

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We can find the mathematical relationship between the two definitions. The receiver mask attenuates PIMR by LIMR (dB) to the level: PIMR + LIMR



(7.18)



If the sensitivity is degraded by 3 dB, then the attenuated interfering signal level equals the thermal noise N: PIMR + LIMR = N (7.19)



Inserting the noise from (7.6) we get:



LIMR = MDS −

( ) S N

r

− PIMR (7.20)

As an example: the receiver sensitivity, MDS = −100 dBm, and requires a (S/N)r of 10 dB. The interfering signal level at the image frequency, degrading the sensitivity by 3 dB, is PIMR = −30 dBm. Therefore:

LIMR = −100 − 10 − (−30) = −80 dB

7.7.3  Measuring the IMR We perform the direct measurement, using a single signal, by feeding the receiver with a legitimate signal at the image frequency. We vary its level until the receiver performance, in terms of factors such as BER, is achieved. LIMR equals the difference between this value and the sensitivity, MDS. The indirect measurement, using two signals, is performed in much the same way as the SEL indirect measurement (Section 7.4.3). When we use the indirect measurement, we must be careful not to saturate the receiver. 7.7.4  Calculating the Received Interference Level The received interfering signal level I at the receiver input is, per (8.1):

I = Pt + Gt + Gr + L + LIMR (7.21)

7.8  Interference at the IF 7.8.1  Source of the Interference Phenomenon This interference is caused by direct leakage of a signal at the IF from the receiver input to the IF stage.

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7.9  Interference from LO Radiation103

7.8.2  Definition of the Parameter The definition of IF rejection is the following:  LIFR: IF rejection is the attenuation, in decibels, of a signal at the IF, with respect to reception at the center frequency.

7.8.3  Calculating the Received Interference Level The received interfering signal, level I at the receiver input is, per (8.1): I = Pt + Gt + Gr + L + LIFR (7.22)



7.9  Interference from LO Radiation 7.9.1  Source of the Interference Phenomenon The LO signal leaks back through the mixer and front-end amplifier to the receiver input port and to the antenna. This signal is radiated from the antenna and may interfere with other receivers. Since this transmitted power is usually very low, only very close receivers may be affected.

7.9.2  Definition of the Parameter We define the LO leakage as follows:  PLO: LO signal level, in decibels referenced to milliwatts, at the receiver input port.

7.9.3  Calculating the Received Interference Level The received interfering signal level I at the interfered receiver input is, per (8.1): I = PLO + Gr −Int + Gr + L (7.23)

where:

Gr-Int: Antenna gain at the IF, of the receiver emitting the LO radiation; Gr: Antenna gain at the IF, of the interfered receiver.

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7.10  Interference from RIM 7.10.1  Source of the Interference Phenomenon The source of RIM is the nonlinearity of the front-end amplifier. When two (or more) signals exist simultaneously at the receiver input they mix, producing unwanted signals at new frequencies. The intermodulation frequency will reach the IF output and may interfere even though no interfering signal at the intermodulation product frequency may have reached the antenna. The mechanism of RIM is shown in Figure 7.8. The main third-order intermodulation frequencies are: f0 = 2 f1 − f2



f0 = 2 f2 − f1 (7.24)

In Section 7.11.2, we detail the theoretical issue of intermodulation in greater depth, including the proof of some subsequent equations. 7.10.2  Definition of the Parameter We define the intermodulation as follows:  Direct definition: The receiver intermodulation is specified by the receiver input third order intercept point: IP3.

Tx #1

f1 f 1, f 2

2f 1-f 2 2f 2-f 1 f 1, f 2

Rx f2

Tx #2 Front-end amplifier Figure 7.8  The mechanism of RIM.

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7.10  Interference from RIM105

 Indirect definition: The level, P1, of each of two equal-level interfering signals, at f1 and f2, that degrades the receiver sensitivity by 3 dB. 7.10.3  Measuring the Parameter Using the direct definition, the receiver IP3 is not measured but acquired, since this level is well within the saturation zone. The receiver IP3 is equal to the front-end amplifier’s IP3 (from the amplifier specification), plus all attenuation from the receiver input to the amplifier, such as from cables and filters. The indirect definition can be measured as follows:  We feed the desired signal to the receiver via a power combiner or directional coupler. The desired signal level is set to the sensitivity, MDS, and the receiver performance in terms of factors, such as BER, is measured.  The desired signal level is increased by 3 dB, causing the receiver performance to improve.  Two equal-level interfering signals at f1 and f2, per (7.24), are added to the power combiner or directional coupler. The interfering signal levels are varied up to that level P1 restoring the receiver performance measured in the first step. IP3 can then be calculated using (7.29). 7.10.4  Default Value When IP3 data is missing but the receiver P1dB comp is known, we can assess IP3 as:

IP3 = P1 dB Comp + (10 ÷ 15) dB (7.25)

Based on the k coefficients (see Section 7.11), we can show that the theoretical value is 9.6 dB; however, 10–15 dB is a more real-life value. 7.10.5  Calculating the Intermodulation Level The third-order intermodulation product level is:

P3 = 3P1 − 2IP3 (7.26)

By this equation we mean that two interfering signals of level P1 presented at the receiver input at frequencies f1 and f2 will produce an intermodulation product at the IF output that is equivalent to an input signal at f0 of level P3.

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If the sensitivity is degraded by 3 dB, the equivalent interfering signal level P3 equals the thermal noise, N. Inserting the noise extracted from (7.6) we get: 3P1 − 2IP3 = MDS −



( )

S (7.27) N r

By extracting P1, we can see the mathematical relationship between the direct and indirect definitions. The level of the two interfering signals degrading the receiver sensitivity by 3 dB, based on the IP3 receiver specification is:

P1 =



MDS −

( ) S N 3

r

+ 2IP3

(7.28)

Consider, for example, a receiver sensitivity, MDS = −103 dBm and (S/N)r is 13 dB. The input intercept point, IP3 = 10 dBm. The interfering signal level degrading the sensitivity by 3 dB is:



P1 =

−103 − 13 + 2 ⋅10 = −32 dBm 3

7.10.6  Calculating the Intercept Point Extracting P3 from the last equation we get:

IP3 =



3P1 − MDS + 2

( ) S N

r

(7.29)

Consider, for example, a receiver sensitivity, MDS = −110 dBm, and (S/N)r = 8 dB. The measured level of the interfering signals that degrades the sensitivity by 3 dB is −30 dBm. The input intercept point is IP3 therefore:



IP3 =

3 ⋅(−30) − (−110) + 8 = 14 dBm 2

7.10.7  Calculating the Received Interference Level An instance wherein we have both interfering signal levels at the same level P1, used during the receiver specification and acceptance tests, would be a unique and special case. In more realistic instances, the interfering signals at the receiver input, emanating from different interfering transmitters, would

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7.10  Interference from RIM107

not be equal. If we denote the received interference level seen at f1 as P1A and the received interference level seen at f2 as P1B, then the received interfering signal levels P1A and P1B at the receiver input are, per (8.1):

P1A = Pt1 + Gt1 + Gr + L1 (7.30)



P1B = Pt 2 + Gt 2 + Gr + L2 (7.31)

Intermodulation interference occurs more commonly on a platform, where coupling replaces the path loss and antenna gains:

P1A = Pt1 + CPL1 (7.32)



P1B = Pt 2 + CPL2 (7.33) The frequency of one intermodulation product is: 2 f1 ± f2 (7.34)

and its level is:

P3A = 2P1A + P1B − 2 ⋅ IP3 (7.35)



The frequency of second intermodulation product is:

f1 ± 2 f2 (7.36)

and its level is:

P3B = P1A + 2P1B − 2 ⋅ IP3 (7.37)

For example, we calculate the received interfering signal levels as P1A = −25 dBm and P1B = −10 dBm. The receiver IP3 is +20 dBm. One intermodulation product level is:

P3A = 2(−25) + (−10) − 2 ⋅ 20 = −100 dBm

and the other is:

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P3B = −25 + 2(−10) − 2 ⋅ 20 = −85 dBm

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The higher level is used for calculating the interference margin. We don’t need to calculate both levels; one calculation is sufficient, defining the stronger and weaker levels as follows: I = P3 = 2P1Strong + P1Weak − 2 ⋅ IP3 (7.38)



7.10.8  Checking the Intermodulation Feasibility It may be worthwhile for us to calculate to see if interference from intermodulation products emanating from the interferer’s frequency bands falls within the receiver’s frequency band. We are designating the interferer’s frequency bands as f1Min–f1Max, and f2Min–f2Max, as shown in Figure 7.9. The bands may in fact overlap, but we are drawing them without overlap, for the sake of clarity. One band containing the intermodulation products is given by: FMin = Min { 2 f1Min − f2Min , 2 f1Min − f2Max , 2 f1Max − f2Min , 2 f1Max − f2Max }

FMax = Max { 2 f1Min − f2Min , 2 f1Min − f2Max , 2 f1Max − f2Min , 2 f1Max − f2Max } (7.39) and the other: fMin = Min { 2 f2Min − f1Min , 2 f2Min − f1Max , 2 f2Max − f1Min , 2 f2Max − f1Max }

fMax = Max { 2 f2Min − f1Min , 2 f2Min − f1Max , 2 f2Max − f1Min , 2 f2Max − f1Max } (7.40) However, there is one special case in (7.39) and (7.40). If a second harmonic from band 1 is included in band 2, then fMin = 2f1 − f2 =0. By comparing the resulting intermodulation product bands with the receiver band, we can determine if intermodulation interference is possible from the frequency viewpoint. Figure 7.10 exemplifies the intermodulation bands in accordance with (7.39) and (7.40). f 1Min

f 1Max

f 2Min

f 2Max

f Figure 7.9  Interferer’s frequency bands for study of intermodulation feasibility.

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7.11  Harmonics and Intermodulation109

Figure 7.10  Intermodulation product bands example.

7.11  Harmonics and Intermodulation 7.11.1 Harmonics We use an amplifier at the linear region (i.e. below the –1-dB compression point), as shown in Figure 7.4. However, the wording “linear region” is misleading. We may assume that harmonics and intermodulation are created by the curved transition from the linear region to the saturation region, but this is not the case. The harmonics and intermodulation stem from the mere fact that the linear region is not really linear. The voltage at an amplifier output can be represented as function of the input voltage, vin, using the Taylor series:

2 v out = k1v in + k2v in + k3v 3in + … (7.41)

where k represents the coefficients. Let us assume the input voltage:

v in = Acos wt (7.42)

where the amplitude A is given in volts. The output voltage becomes:

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v out = k1(Acos wt) + k2(Acos wt)2 + k3(Acos wt)3 + … (7.43)

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Rearranging we get: v out = k1Acos wt +

1 1 k A2(1 + cos2wt) + k3 A3(cos3wt + 3cos wt) + … (7.44) 2 2 4

While ignoring those components contributing to lower orders and direct current (DC) we get: v out = k1Acos wt +



1 1 k A2 cos2wt + k3 A3 cos3wt + … (7.45) 2 2 4

Note that the 3cosω t component in (7.44), which we have just ignored, is the main contributor to the amplifier’s compression. The output power in watts is: P = 10log



V2 R

(7.46)

We are interested in the output power in decibels referenced to milliwatts: PdBm = 20logV − 10log50Ω + 30 (7.47)

or:

PdBm = 20logV + 13 (7.48)



Since we will deal with power ratios rather than absolute powers, the value 13 will be reduced. Thus it will make no difference if we add 13 to all equations or not. From now on, we will refer to 20logV as if being the power in decibels referenced to milliwatts. The output power of the fundamental carrier signal, P1, is therefore: P1 = 20log k1A (7.49)

or, in decibel notation:

P1 = Pin + G (7.50)

Where the gain G:

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G = 20log k1 (7.51)

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7.11  Harmonics and Intermodulation111

The powers of second and third harmonics are:



1 HAR2 = 20log k2 A2 (7.52) 2



1 HAR3 = 20log k3 A3 (7.53) 4

and the power of nth harmonics is given by:



HARn = 20log

1 k An (7.54) 2(n−1) n

Recalling that we are interested in power ratios, we must divide the harmonics power by the carrier power, namely to subtract in decibel notation. The second harmonic power relative to the carrier power at the center frequency, in decibels referenced to carrier is:



1 1k LHAR-2 = 20log k2 A2 − 20log k1A = 20log 2 A (7.55) 2 2 k1

In much the same way, the third harmonic in decibels referenced to carrier is:



LHAR-3 = 20log

1 k3 2 A (7.56) 4 k1

and LHAR-n, the nth harmonic in decibels referenced to carrier, is:



LHAR-n = 20log

1 kn (n−1) A (7.57) k1 2 (n−1)

We learn, from (7.57), that we have a tool to find the k coefficients. All we need to do is measure LHAR-n using a spectrum analyzer and extract k from (7.57). The harmonic level of amplifiers is usually high, which requires a filter at the amplifier’s output. We obviously connect the spectrum analyzer in front of such a filter. An interesting outcome we see in (7.57) is that the harmonic level depends on the input voltage A, or said differently, the input power. From n (7.54) we see that the nth harmonic grows at the rate of A . Showing the

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output power versus the input power in decibel notation means that the slope of the nth harmonic equals n, as illustrated in Figure 7.11. It is customary to use the amplifiers at lower power than the rated –1-dB compression point to reduce intermodulation products, as will be shown in Section 7.11.6. This reduction in power has the same impact on harmonic emission. Backing off the amplifier by BO(dB), reduces the harmonic level by n × BO(dB). We show an example in Figure 7.12. The amplifier is operating with an output power P1dB − BO. The second harmonic level without BO would be: P1dB − LHAR-2 (7.58)



Using back-off reduces the harmonic level by an additional amount of 2BO; that is to say, P1dB − LHAR-2 − 2BO (7.59)



7.11.2  Introduction to Intermodulation We will now discuss the case where two signals, at different frequencies, are fed to the amplifier input: v in = A1 cos w1t + A2 cos w2t (7.60)



Inserting into (7.43) we get the following voltage at the amplifier’s output: Pout P1dB Carrier slope: 1

2nd harmonic slope: 2

L HAR -2 L HAR -3

3rd harmonic slope: 3 Pin

Figure 7.11  The slope of the harmonics.

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7.11  Harmonics and Intermodulation113

Pout P1dB

BO

P1dB-BO

L HAR -2

P1dB-L HAR -2 2BO P1dB-L HAR -2-2BO

Pin Figure 7.12  Harmonic level with back-off.

v out = k1 ( A1 cos w1t + A2 cos w2t ) + k2 ( A1 cos w1t + A2 cos w2t )

2

+ k3 ( A1 cos w1t + A2 cos w2t ) + … 3

(7.61)

We will analyze the components in this equation for the first, second, third, and nth order as follows:  The first order: We start examining the first component in (7.61): k1 ( A1 cos w1t + A2 cos w2t ) (7.62)



The output powers of the carrier signals are: 20log k1A1 = Pin1 + G 20log k1A2 = Pin2 + G



(7.63)

 The second order: Now we will examine the second component in (7.61): k2 ( A1 cos w1t + A2 cos w2t ) (7.64) 2

or:

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k2 ( A12 cos2 w1t + 2A1A2 cos w1t ⋅ cos w2t + A22 cos2 w2t ) (7.65)



The first and last components in (7.65) are the second harmonics of each carrier. We use the trigonometric identity for a cosine squared: cos2 a =



1 1 cos2a + (7.66) 2 2

Disregarding DC we get the following output voltages for the first and last components: 1 k A2 cos2w1t 2 2 1 (7.67) 1 2 k A cos2w2t 2 2 2



The power of the second harmonics is given by: 1 20log k2 A12 2 (7.68) 1 2 20log k2 A2 2



The output voltage of the middle component in (7.65) is: 2k2 A1A2 cos w1t ⋅ cos w2t (7.69)



We now use the trigonometric identity for the product of two cosines:



cosa ⋅ cos b =

1 [cos(a + b) + cos(a − b)] (7.70) 2

and get:

k2 A1A2 ⋅ ⎡⎣cos ( w1 + w2 ) t + cos ( w1 − w2 ) t ⎤⎦ (7.71)

This equation explains the source of intermodulation. The nonperfect linearity of the amplifier generates output signals at frequencies that are sums and differences of the input frequencies, which were not present at the input:

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f1 ± f2 (7.72)

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7.11  Harmonics and Intermodulation115

Their power is given by: P2 = 20log k2 A1A2 (7.73)



We use the subscript 2 of the power P to denote the second order (which we will define later in 7.87 and 7.120).  The third order: The third component in (7.61) is: k3 ( A1 cos w1t + A2 cos w2t ) (7.74) 3

or:

k3 ( A13 cos3 w1t + 3A12 cos2 w1t ⋅ A2 cos w2t + 3A1 cos w1t ⋅ A22 cos2 w2t + A23 cos3 w2t ) (7.75) For the first and last components in (7.75), we use the trigonometric 3 identity for cos :



cos3 a =

1 3 cos3a + cosa (7.76) 4 4

and get the output voltages:



3 1 k3 A13 cos3w1t + k3 A13 cos w1t 4 4 (7.77) 3 1 3 k3 A2 cos3w2t + k3 A23 cos w2t 4 4

Here we discover the third harmonic of each of the input signals, at 3f1 and 3f2, but also some power at the carrier frequencies, f1 and f2. The power of the third harmonics is given by:



1 20log k3 A13 4 (7.78) 1 3 20log k3 A2 4 The two middle components in equation (7.75) are:

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3k3 A12 cos2 w1t ⋅ A2 cos w2t 3k3 A1 cos w1t ⋅ A22 cos2 w2t



(7.79)

Using trigonometric identities and rearranging we find the following output voltages: 3 k A2 A ⋅ ⎡cos ( 2w1 + w2 ) t + cos ( 2w1 − w2 ) t ⎤⎦ 4 3 1 2 ⎣ (7.80) 3 k3 A1A22 ⋅ ⎡⎣cos ( w1 + 2w2 ) t + cos ( w1 − 2w2 ) t ⎤⎦ 4



These are the third-order intermodulation products. As we can see, their frequencies are: 2 f1 ± f2 (7.81)

and:

f1 ± 2 f2 (7.82)



The power of these third-order intermodulation products is given by: 3 P3 = 20log k3 A12 A2 4 3 P3 = 20log k3 A1A22 4



@ 2 f1 ± f2

(7.83)

@ f1 ± 2 f2

We use the subscript 3 of the power P, to denote the third order. In case of equal input signal voltages: A1 = A2 = A (7.84)



Both intermodulation products’ power is: 3 P3 = 20log k3 A3 (7.85) 4

 The nth order:

Following this calculation procedure, we can show that the output voltage of the nth intermodulation product is given by:

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7.11  Harmonics and Intermodulation117



⎛ n⎞ a b a b ⎜⎝ a ⎟⎠ ⋅ kn ⋅ A1 cos w1t ⋅ A2 cos w2t (7.86)

where n, the intermodulation order, is defined as: n = a + b (7.87)



The coefficients a and b are any two integers whose sum is n. n Using the general equation for cos x, while disregarding contributions to lower intermodulation orders and contribution to harmonics and DC, (7.86) yields:



⎛ n⎞ 1 a b ⎜⎝ a ⎟⎠ ⋅ 2(a−1) ⋅ 2(b−1) ⋅ kn A1 A2 ⋅ cosaw1t ⋅ cosbw2t (7.88) n

Note that the general equation for cos x depends whether n is even or odd. Still, the component contributing to the nth interference order is the same, whether n is even or odd. Using (7.70) for the cosines’ products we derive the output voltage:



⎛ n⎞ 1 a b ⎜⎝ a ⎟⎠ ⋅ 2(n−1) ⋅ kn A1 A2 ⋅ ⎡⎣cos ( aw1t + bw2t ) + cos ( aw1t − bw2t ) ⎤⎦ (7.89)

and the output power:



⎛ n⎞ 1 Pn = 20log ⎜ ⎟ ⋅ (a−1) ⋅ kn A1a A2b ⎝ a⎠ 2

@ a ⋅ f1 ± b ⋅ f2 (7.90)

As an example, let us find the output voltage of the fifth intermodulation order. The fifth intermodulation order may be acquired in four combinations:



a a a a

=1 =2 =3 =4

b b b b

=4 = 3 (7.91) =2 =1

As one example, let us calculate the output voltage in the second way:

10k5 ⋅ A12 cos2 w1t ⋅ A23 cos3 w2t (7.92)

Calculating the output voltage of the fifth intermodulation order of this combination, using (7.90) yields:

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5 ⋅ k A2 A3 ⋅ ⎡cos ( 2w1 + 3w2 ) t + cos ( 2w1 − 3w2 ) t ⎤⎦ (7.93) 8 5 1 2 ⎣



The output power would be: 5 P5 = 20log k5 A12 A23 8



@ 2 f1 ± 3 f2 (7.94)

7.11.3  The Slope of the Intermodulation We start with the simple case where both signals have equal amplitudes. Inserting (7.84) into (7.90), we see that power of the nth intermodulation n order is proportional to A : a

Pn



20log An (7.95)

Since the input power equals: PIn = 20log A (7.96)



The output power is proportional to n:

Pn

a

n ⋅ PIn (7.97)

Showing the output power versus the input power in decibel notation means that the slope of the nth intermodulation order equals n, as illustrated in Figure 7.13. 7.11.4  The Intercept Point Concept Using the k coefficients is essential for understanding the intermodulation mechanism and proving equations. However, using the k coefficients for daily practical calculations is not convenient at all: The equations are quite cumbersome not to mention that in most cases, the k coefficients values are not known and are difficult to measure. Our intention is to replace the k coefficients with another concept, simple to use and to measure. This is the interception point (IP). Two nonparallel lines must meet somewhere. So, let us extend the carrier and third-order lines from Figure 7.13 until both lines intercept as shown in Figure 7.14. We chose P3 for Figure 7.14. The definition of IPn Out, the output intercept point of the nth intermodulation order is: the hypothetical value of the output power where the line

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7.11  Harmonics and Intermodulation119 Pout

1st order, Carrier, slope: 1

3rd order intermodulation slope: 3

2nd order intermodulation slope: 2

Pin Figure 7.13  The slope of the intermodulation.

of the carrier power, P1, intercepts the line of the nth intermodulation order; that is to say, P1 = Pn = IPnOut (7.98)



When we deal with orders 4 and above, we note that rather than a single intercept point, there are several values for IPn Out, stemming from (7.90): Pout The intercept point IP 3 Out

P1 P3

IP 3 In

Pin

Figure 7.14  The concept of the IP.

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the power Pn depends not only on the order n; it also depends on the values of the building blocks of n (i.e., a and b, due to the difference in the binomial coefficient value). In the fifth-order example, there are two cases: (a,b) = (1,4) or (a,b) = (2,3). By inserting (7.49), (7.84), (7.90), and (7.98) into each other, we can show that the value of IPn is given by: IPn = 20log

2(n−1) k1n (7.99) (n−1) ⎛ n⎞ kn ⎜⎝ a ⎟⎠

The difference between the (1,4) and (2,3) cases is rather small:



⎛ 5⎞ ⎜⎝ 2⎟⎠ 10 20log 4 = 20log 4 = 20log 4 2 = 1.5 dB 5 5 ⎛ ⎞ ⎜⎝ 1⎟⎠

as shown in Figure 7.15. The output IP, IPn Out, is useful in cases of TIM. When we deal with receivers, we are interested in RIM (i.e., we look for the input IP, IPn In). The definition of IPn In, the input intercept point of the nth intermodulation order is: the hypothetical value of the input power required to generate IPn Out. Figure 7.14 depicts IP3 In and IP3 Out.

Pout IP 5 (2,3) 1.5 dB IP 5 (1,4)

P1

P5

P5

Pin Figure 7.15  The two IP5 values.

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7.11  Harmonics and Intermodulation121

We use the term hypothetical, since the value of the IP lies within the saturation region, thus making it impossible to feed the amplifier with the IPn In level and view the interception at the output. 7.11.5  The Intermodulation Spectrum In this section, we will inspect the intermodulation spectrum and understand why third-order intermodulation is the most important one. We will name the frequency difference between the two input frequencies, ΔF, where f2 > f1: Δf = f2 − f1 (7.100)



The frequency of one of the third-order intermodulation products is: 2 f2 − f1 = 2 f2 − ( f2 − Δf ) = f2 + Δf (7.101)



and the frequency of the other third-order intermodulation products is: 2 f1 − f2 = 2 f1 − ( f1 + Δf ) = f1 − Δf (7.102)



Note that both frequencies are laying ΔF MHz above and below the input frequencies as shown in Figure 7.16: Pout

P1

P1

P3

P3

∆f

∆f

∆f

f 2f 1-f 2

f1

f2

2f 2-f 1

Figure 7.16  Spectrum of the third-order intermodulation.

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This is the first reason for the importance of the third order: Both intermodulation products are very close to the input frequencies, thus having a high probability of being in-band. (There is another third-order intermodulation product at f1 + f2, far away from both f1 and f2). We will now examine higher intermodulation orders, obeying two rules: n is odd, and a and b differ by one: a − b = 1 (7.103)



In the fifth-order case we mean that a = 2 and b = 3 or vice versa, in the seventh-order case we mean that a = 3 and b = 4 or vice versa, and so on. The frequency of one intermodulation product equals: b ⋅ f1 − a ⋅ f1 = (a + 1) ⋅ f1 − a ⋅ ( f1 + Δf ) = f1 − a ⋅ Δf (7.104)



and symmetrically, the other frequency is: b ⋅ f2 − a ⋅ f1 = (a + 1) ⋅ f1 − a ⋅ ( f2 − Δf ) = f2 + a ⋅ Δf (7.105)



We see that all intermodulation products obeying these rules are equally spaced one from the other as shown in Figure 7.17. We do not show many additional intermodulation products in Figure 7.17.

IP3 =IP5 =IP7 P1

P3

P1

P3

P5

P7

P5

P7 f

Figure 7.17  Spectrum of odd-order intermodulation.

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7.11  Harmonics and Intermodulation123

The level of the higher-order intermodulation product decrease as n goes higher, as shown Figure 7.17. This is the second reason for the importance of the third-order intermodulation: it is the strongest. Figure 7.18 combines the power and the spectrum viewpoints, showing that the two lines connecting P1 and P3 in the spectrum diagram meet at the intercept point. This is very helpful and serves as straightforward graphical tool for measuring the IP using a spectrum analyzer, rather than the equations. Figure 7.17 shows all odd intermodulation orders having an equal IP: IP3 = IP5 = IP7. In reality they are not equal, but their values are very close to each other, up to, for example, 2–3 dB. Even intercept points are typically 10–15 dB better (i.e., higher, than the odd ones). This is because high-power amplifiers usually use push-pull schemes where even products cancel each other. 7.11.6  The Third- and nth-Order Intermodulation Equations We can observe an important relationship caused by the slopes, 1 for the carrier and 3 for third-order intermodulation, as seen in Figure 7.19. We examine the case where the output power is X dB below IP3. X is defined as follows: X = IP3 − P1 (7.106)



Pout

Pout

IP 3 P1

P3 Pin

f Spectrum

Power

Figure 7.18  Power and the spectrum viewpoints of the IP.

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Pout

IP 3

X

P1 3X

2X

P3

P1 P3

P Figure 7.19  Power referred to the intermodulation point.

Due to the slope of 3, the level of the third-order intermodulation is 3X dB below IP3: P3 = IP3 − 3X (7.107)



or equivalently, 2X dB below P1: P3 = P1 − 2X (7.108)



Inserting (7.106) into (7.107) we get:

P3 = IP3 − 3 ( IP3 − P1 ) (7.109)

Rearranging, we derive the famous third-order intermodulation equation:

P3 = 3P1 − 2IP3 (7.110)

This simple-to-use equation replaces (7.85). Knowing the input power P1 and the IP IP3, we easily calculate the third-order intermodulation product power. A useful lesson can be learned from (7.110): If we operate an amplifier at a lower power than its 1-dB compression point, namely P1 – BO, P3 will be decreased by 3BO. This approach is widely used in satellites communication.

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7.11  Harmonics and Intermodulation125

For the purpose of measuring an amplifier’s intercept point, we extract IP3: IP3 =



3P1 − P3 (7.111) 2

We measure P1 and P3 using a spectrum analyzer and find IP3 using this simple equation. In much the same way we can show that in the general case, the nth-order intermodulation product is given by: Pn = nP1 − (n − 1)IPn (7.112)



This equation replaces the cumbersome (7.90). As an example, the level of the seventh-order intermodulation product (for equal input levels) is: P7 = 7P1 − 6IP7 (7.113)



Extracting IPn from (7.112) for measurement purpose, we see that the nth-order intercept point equals: IPn =



nP1 − Pn (7.114) n −1

and yet another form:



IPn = P1 +

P1 − Pn (7.115) n −1

7.11.7  Intermodulation from Nonequal Signals A more realistic case is where the input signals, P1, are nonequal. We will name them P1A and P1B, where P1A at f1 is X dB below IP3 and P1B at f2 is Y dB below IP3; that is to say, P1A = IP3 − X

P1B = IP3 − Y

(7.116)

Figure 7.20 assists us in finding that the third-order intermodulation products are:



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P3A = IP3 − 2X − Y

@ 2 f1 ± f2

P3B = IP3 − X − 2Y

@ f1 ± 2 f2

(7.117)

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Pout

Pout

IP 3 P1A P1B

Y

P3A

2Y

X 2X

P3B Pin

f Spectrum

Power

Figure 7.20  Power and the spectrum viewpoints with nonequal signals.

Inserting (7.116) we get:



P3A = 2P1A + P1B − 2IP3

@ 2 f1 ± f2

P3B = P1A + 2P1B − 2IP3

@ f1 ± 2 f2

(7.118)

This equation replaces (7.83). These results are depicted in Figure 7.21. As in the equal-input signal levels case shown in Figure 7.18, the two lines connecting P1A and P3B, meet at the IP, though the picture in this case is asymmetric, as shown in Figure 7.22. As in the equal signal levels case, the IP can be derived in a graphical manner from the spectrum analyzer display. Comparing to Figure 7.18, we see that to the end of finding the IP, we do not have to worry whether the two input signals have equal powers or not. 7.11.8  Intermodulation from Multiple Transmitters The general intermodulation case involves more than just two interfering transmitters. The intermodulation frequencies in the general case are:

a ⋅ f1 ± b ⋅ f2 ± c ⋅ f3 ± …… ± m ⋅ fm (7.119)

All coefficients a to m, are nonnegative integers (i.e., zero is allowed). The intermodulation order is defined as:

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n = a + b + c + …… + m (7.120)

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7.11  Harmonics and Intermodulation127

Pout IP 3 P1A

X

Y P1B

2Y

2X P3A

P3B

f 2f 1-f 2

f1

f2

2f 2-f 1

Figure 7.21  Nonequal signals’ intermodulation.

Pout IP 3 P1A P1B

P3A P3B

f 2f 1-f 2

f1

f2

2f 2-f 1

Figure 7.22  Nonequal signals’ IP.

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The power of the nth intermodulation product is given by: Pn = aPA + bPB + … + mPm − (n − 1)IPn (7.121)



As an example, we have four transmitters, A, B, C, D, and one receiver onboard a platform. We are interested in finding the frequencies and level of the 7th intermodulation order that are generated by the receiver. Although we have to analyze all combinations we will demonstrate only one. For example: 7 = a + b + c + d = 2 +1+1+ 3



The intermodulation frequencies are: 2 f1 ± f2 ± f3 ± 3 f4



and the intermodulation products’ level is therefore: P7 = 2PA + PB + PC + 3PD − 6IP7



where PA through PD are powers at the receiver input from transmitters A through D. 7.11.9  Number of Intermodulation Products We see that the higher the intermodulation order n, the higher the number of intermodulation products, and that as m, the number of transmitters grows, so does the number of intermodulation products as well. We are therefore interested in calculating the number of these products. We must solve the mathematical question: How many frequencies of the order n can be generated by m transmitters in (7.119)? We will find the answer in steps. Our first concern is to find how many combinations exist in (7.120) (i.e., how many combinations the coefficients a ÷ m exist so their sum equals the order n). We must introduce another parameter: the number of transmitters involved in the intermodulation, q, since some of the a ÷ m coefficients may be zero. A single transmitter cannot generate intermodulation; therefore: 2 ≤ q ≤ m (7.122)



For two transmitters, the calculations are as follows:

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7.11  Harmonics and Intermodulation129

1. For the second order, namely q = 2 and n = 2, there is only one combination: 1 + 1 = 2. 2. For the third order, namely q = 2 and n = 3, there are two combinations: 1 + 2 = 3 and 2 + 1 = 3. 3. For the fourth order, namely q = 2 and n = 4, there are three combinations: 1 + 3 = 4, 3 + 1 = 4 and 2 + 2 = 4, and so on for higher orders. For three transmitters, the calculations are as follows: 1. For the second order, namely q = 3 and n = 2, there is no solution. 2. For the third order, namely q = 3 and n = 3, there is only one combination: 1 + 1 + 1 = 3. 3. For the fourth order, namely q = 3 and n = 4, there are three combinations: 1 + 1 + 2 = 4, 1 + 2 + 1 = 4 and 2 + 1 + 1 = 4, and so on for higher orders. Continuing in this way, we can generate Table 7.1, showing the number of combinations producing the sum n as function of q. We easily recognize the answer: the number of combinations producing exactly the order n by exactly q transmitters is given by the following binomial coefficient: ⎛ n − 1⎞ ⎜⎝ q − 1⎟⎠ (7.123)



Table 7.1 Number of Coefficients Combinations Producing the Order n Order 2

n 2

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Number of Transmitters Involved, q 3

4

5

6

7

1

3

2

1

4

3

3

1

5

4

6

4

6

5

10

10

5

1

7

6

15

20

15

6

1 1

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Our second concern is to find how many combinations exist in (7.119)? Each of the coefficients, except for a, can be either positive or negative. We must multiply the previous equation by all ± combinations. The number of intermodulation frequencies of exactly the order n generated by exactly q transmitters is given by: ⎛ n − 1⎞ q−1 (7.124) ⎜⎝ q − 1⎟⎠ ⋅ 2



This is the case of specific q transmitters (e.g., for two transmitters, 1 and 6, or 5 and 7). Since there are several combinations for selecting the q transmitters from the m available ones, we have to multiply (7.124) by the number of these combinations, as: ⎛ n − 1⎞ q−1 ⎛ m ⎞ ⎜⎝ q − 1⎟⎠ ⋅ 2 ⋅ ⎜⎝ q ⎟⎠ (7.125)



So far, we have dealt with the case of exactly q transmitters. In the next step we should take into consideration all possible values of q (e.g., 2, 3, and 4) up to the maximum value q can reach. Obviously, q cannot be greater than the number of transmitters, m. However, there is another limit: the maximum value q can reach is the order of the intermodulation, n, otherwise (7.120) has no solution, as shown in the Table 7.1 examples. The maximum value q can reach, which we will name Q, equals: Q = Max {m,n} (7.126)



The number of intermodulation frequencies for up to q transmitters, but still exactly the order n, is given by: ⎛ n − 1⎞

Q



⎛ m⎞

∑ ⎜⎝ q − 1⎟⎠ ⋅ 2q−1 ⋅ ⎜⎝ q ⎟⎠ (7.127) q=2

In the final step, the number of intermodulation frequencies for up to Q transmitters, and all intermodulation orders up to n, is given by summing: n



Q

⎛ n − 1⎞

⎛ m⎞

∑ ∑ ⎜⎝ q − 1⎟⎠ ⋅ 2q−1 ⋅ ⎜⎝ q ⎟⎠ (7.128) 2 q=2

The intermodulation frequencies‘ count may reach enormous numbers, but most of them will reside outside the receiver band. Moreover, several

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7.12  In-Band and OOB Interference131

Figure 7.23  Intermodulation products from multiple transmitters.

intermodulation frequencies may be duplicated, since the same frequency can result from more than one combination. Figure 7.23 shows an example of m = 6 transmitters in the 30–88-MHz band along with the level of all intermodulation products of the third, fourth, and fifth order, present in-band a receiver using the same frequency band. We can see that levels of various frequencies having the same order are not necessarily equal, although all six transmitters use the same power level. The level of even-order products is generally lower than odd-order products’ levels.

7.12  In-Band and OOB Interference In-band and OOB interference are commonly used expressions, but they are not new interference types, neither from the transmitter, nor from the receiver. Our objective in this section is adding some related remarks. In-band interference is usually, but not necessarily, experienced when interferer and interfered devices are the same type within the same platform. Frequency coordination is a quite common consideration for eliminating or at least, minimizing in-band interference. Frequency allocation is explicitly considered to prevent same-frequency reuse by adjacent users and, if possible, to maintain a minimum frequency difference. OOB interference is checked in cases where the interferer and interfered use different device types. Frequency coordination in the OOB case is rare, since, in most cases the interfering and interfered devices belong to different authorities.

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The most critical OOB interference case occurs when the different devices’ bands are contiguous. A good frequency band assignment should require that CCI does not occur. This end is accomplished by avoiding a common bands’ edge frequency. ACI may still be a problem. The OOB expression leaves the impression that the interfering and interfered frequencies are far away from each other, but, due to lack of frequency coordination, they may instead be very close. This condition could occur if one device uses its highest possible frequency while the other device uses the lowest. A useful way for us to avoid ACI is by assigning a guard band between the adjacent frequency bands.

Reference [1] Recommendation ITU-R S.741-2, Carrier to interference calculations between networks in the fixed satellite service.

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Chapter

8 Contents 8.1  The Calculation Principle 8.2  Calculating the Received Interference Level 8.3  Power Sum of Multiple Interferers

Calculating the Received Interference Level 8.1  The Calculation Principle The basic equation for calculating the received interfering signal level is: I = Pt + Gt + Gr + L + LX + BWF (8.1)     where: I: Received interfering signal level at the receiver input, in decibels referenced to milliwatts; Pt: Interfering transmitter power, in decibels referenced to milliwatts; Gt: Interfering transmitter antenna gain, in decibels referenced to isotropic; Gr: Interfered receiving antenna gain, in decibels referenced to isotropic; L: Path loss between the interfering and interfered antennas, in decibels; LX: Attenuation of interference type X relative to CCI interference, per the list detailed in Section 8.2.2: 133

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BWF: Bandwidth factor, in decibels. The plus (+) sign appears before all losses since they are defined as negative numbers. In cases of interference on a platform, or between platforms in close proximity, the coupling value, CPL, replaces the path loss and antenna gains: I = Pt + CPL + LX + BWF (8.2)



The received interfering signal level I is either the real or the equivalent level, per the interference type.

8.2  Calculating the Received Interference Level Equations (8.1) and (8.2) are very basic. Figure 8.1 serves to extend (8.1) and (8.2) to include additional terms, showing the RF chain, the interference types, and the components affecting the interference types. The full equation is presented as: I = Pt + LX + LFilter-t + Lct + LWGt + Gt + GSL-t + L + LPol + Gr + GSL-r + Lcr + LWGr + LFilter-r + BWF



(8.3)

In cases where the coupling replaces the antenna’s gain, antenna’s side lobes, path loss, and polarization loss: I = Pt + LX + LFilter-t + Lct + LWGt + CPL + Lcr + LWGr + LFilter-r + BWF (8.4) Gt GSL -t

Tx Pt L ACI L SPR L HAR L PHN L BBN TIM

Cable, filter, etc.

L

CPL

L ct L Filter-t

Gr GSL -r L Pol Cable, filter, etc. L cr L Filter-r

Rx L SEL SAT DMG RIM IMR IFR

Figure 8.1  The RF chain and interference types.

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8.2  Calculating the Received Interference Level135

We explain the terms in (8.3) in the following sections. Obviously, not all terms in (8.3) and (8.4) exist at all times. If the interference source is the transmitter, then we calculate the frequency-dependent terms in (8.1) to (8.4) at the receiver frequency, fRx. If the interference source is the receiver then we would calculate them at the transmitter frequency, fTx. These frequencies for EMC calculations are summarized in Table 8.1. 8.2.1  Transmitter Power Pt: Transmitter power, in decibels referenced to milliwatts. We use the peak power in cases where pulses are transmitted. If the transmitter uses less than the nominal output power, practicing back off, BO, the practical rather than the nominal value is used. 8.2.2  Interference Level Relative to CCI LX: Attenuation of interference type X relative to CCI interference. The following interference types are X: LACI: Transmitter spectrum or ACI; LSPR: Transmitter spurious emission; LPHN: Transmitter phase noise; LBBN: Transmitter broadband noise; LHAR: Transmitter harmonics; LSEL: Receiver selectivity; LIMR: Receiver image rejection; LIFR: Receiver IF rejection. The interference types are detailed in Chapters 6 and 7.

Table 8.1 Frequencies Used for the Various Interference Types

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Frequency

Interference Type

fRx

CCI, ACI, SPR, HAR, PHN, BBN, TIM

fTx

SEL, SAT, DMG, RIM, IMR

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8.2.3  Transmitter External Filter LFilter-t: Attenuation of an external filter, if placed between the transmitter and its antenna, in decibels.

8.2.4  Transmitter Cable Loss Lct: Cable and other losses between the transmitter and its antenna, such as splitters, combiners, switches, and circulators, in decibels.

8.2.5  Transmitter Waveguide Loss LWG-t: Waveguide loss, if this is the antenna feeding, in decibels. If the receiver frequency is less than the transmitter waveguide cut-off frequency, fRx < fcoTx, the waveguide loss will be high. This statement is valid for ACI, SPR, and BBN interference types. 8.2.6  Transmitting Antenna Gain Gt: Transmitting antenna gain, in decibels referenced to isotropic. The gain-frequency dependency is not always specified. Even when this factor is available, it is usually given only for in-band conditions. However, the gain-frequency dependence is a very important parameter for EMC calculations for OOB interference cases. Since the OOB antenna gain is usually not known, we must either measure it or calculate it using a simulation, or make an assessment. The more conservative and very stringent approach is for us to assume that the OOB gain, GOOB, is not less than the in-band gain. Usually, the loss caused by VSWR is one of the factors that make GOOB less than Gt. Antenna designers make every effort to keep the VSWR below its in-band maximum allowed value, justifiably disregarding the out-of-band VSWR. The VSWR loss (also named mismatch loss) is expressed by the following equation and is demonstrated in Figure 8.2.



LVSWR = −10log

(VSWR + 1)2 (8.5) 4 ⋅ VSWR

VSWR loss decreases gain, but no large values should be expected. For example, even if the OOB VSWR rises to 30:1, only 9 dB of loss is contributed to decreasing the interference level. In some types of antennas, GOOB contribution can be assessed above the effect of VSWR. For example, the gain of linear antennas at frequencies

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8.2  Calculating the Received Interference Level137 0 −1 −2 −3

Loss dB

−4 −5 −6 −7 −8 −9 − 10

0

5

10

15

20

25

30

35

VSWR Figure 8.2  VSWR loss.

lower than their intended band drops strongly as their size, measured in wavelengths, decreases. On the other hand, at frequencies higher than their intended band, the antenna may resonate at multiples of in-band frequencies. 2 The gain of a parabolic reflector antenna usually increases by f . At lower frequencies, GOOB usually drops. At higher frequencies, GOOB can increase, but loss from VSWR may partially compensate for the increase. It is important to note the following:  The out-of-band emissions of an interfering transmitter are usually measured in the lab, by connecting a spectrum analyzer to the transmitter output. However, there are transmitters that do not have an output connector, as for example, when a phased-array antenna is used. We sometimes can measure those transmitters’ OOB emissions over the air, using a spectrum analyzer connected to a receiving antenna at a distance. In such cases, the interfering antenna’s OOB gain is included in the measured response. GOOB should not be included in the equation, as it would then be taken into account twice.  When coupling between antennas is used, GOOB is included in the CPL and therefore not used as a separate factor.

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8.2.7  Transmitting Antenna Side Lobes When a directional interfering transmitter antenna is not directed toward the interfered receiver antenna, then there is additional loss as compared to the main lobe’s interference. We then define the parameter as follows: GSL-t: Sidelobes’ loss of the transmitting antenna, in decibels referenced to carrier. This text uses Gjv and G(ϕ ,θ ) as equivalent notations for this parameter. The term Gjv denotes the jamming antenna gain or pattern, in the direction toward the victim antenna. The term G(ϕ ,θ ) denotes the antenna gain or pattern in azimuth and elevation. We rarely use the real antenna pattern in EMC calculations. We normally use either the antenna pattern envelope, or a representative sidelobe level, usually at 0 dBi. There are several reasons for using the envelope pattern rather than the real pattern, described as follows:  The real pattern includes peaks and nulls. However, their location on the angle axis is highly frequency-dependent. At a certain angle, a peak may exist at one frequency but be a null at another frequency.  In mass production, repeatability concerning peak and null locations is not guaranteed. However, there is usually high repeatability within the main lobe.  While deploying devices in the field, we cannot rely on hitting a peak or a null.  EMC calculations need a monotonic gain versus angle function. Otherwise an EMC survey outcome may indicate the need to keep a minimum angular separation between jammer and victim, while interference might reappear at larger angles.  Last, we generally try to use the worst-case condition when dealing with EMC. The best way for us to derive the antenna envelope is to use the measured antenna pattern as demonstrated in Figure 8.3. (A limit may be added to the envelope value, such as −10 to −20 dBi.) When measured data is not available, we use computer simulation of the antenna pattern instead. When neither antenna data nor antenna simulation is available we can use a default equation for the antenna pattern, based on the beamwidth and first sidelobe level, such as the following equations.

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8.2  Calculating the Received Interference Level139

0

First side lobe envelope

Main lobe

dBc

−10 −20

Side lobes envelope

−30 −40 −50 −180 −150 −120 −90 −60 −30

0

30

60

90 120 150 180

Degrees Figure 8.3  Antenna envelope derived from measured pattern.

The shape of many directional antennas pattern in the main beam 2 resembles a parabola (i.e., the pattern is proportional to ϕ ):

G = K ⋅ f2 (8.6)

Inserting the case where ϕ = ϕ 3dB (i.e., half the beamwidth), where G equals −3 dB and solving (8.6), we get K = −12. The main beam pattern is thus:



G = −12

( ) f BW

2

(8.7)

This is a common equation given in [1, 2]. The slope of the sidelobes’ envelope of many directional antennas drops at a rate of −25 dB/dec [1, 2]. A common relationship is: f G = −25log BW (8.8)

2

Figure 8.4 depicts the main and sidelobes per (8.7) and (8.8). The main beam and sidelobes’ envelope lines do not intersect. Thus we have to add a flat line, which equals the peak of the first sidelobe level, SL1, to connect them. Several SL1 values are exemplified in Figure 8.4. The angle ϕ 1 where SL1 starts is found by inserting G = SL1 and ϕ = ϕ 1 into (8.7), and the angle ϕ 2 where SL1 ends is found by inserting G = SL1 and ϕ = ϕ 2 into (8.8).

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Intersystem EMC Analysis, Interference, and Solutions 0 −5 − 10

dBc

− 15 − 20 − 25 − 30 − 35 − 40

0

20

40

60

80

100

120

140

160

180

Degrees Main lobe

Side lobe

18

20

16 22

Figure 8.4  Main lobe, sidelobe and SL1.

The resulting pattern is summarized in (8.9) to (8.11):

( )

G(f)dBc

  

2 ⎧ f −12 for 0 ≤ f < f1 ⎪ BW ⎪ ⎪ =⎨ SL1 for f1 ≤ f < f2 (8.9) ⎪ ⎪ Max ⎧−25log f , Limit ⎫ for f ≤ f ≤ 180 ⎨ ⎬ 2 ⎪⎩ BW 2 ⎩ ⎭

f1 = BW



f2 =



−SL1 (8.10) 12

1 BW −SL 10 25 (8.11) 2

where: BW: Antenna beamwidth, in degrees; SL1: Antenna first sidelobe level, in decibels referenced to carrier (negative number);

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8.2  Calculating the Received Interference Level141

ϕ : Off-center azimuth angle, in degrees. For the elevation pattern, θ replaces ϕ . The method we use for finding ϕ and θ is detailed in Chapter 13. The method for determining antenna gain G(ϕ ,θ ) is detailed in Chapter 14. Another example, using these equations and adding a limit for the sidelobe level, is presented in Figure 17.3. Different equations for the sidelobes envelope levels can be found in [1–3]. When coupling between antennas is used, GSL-t is not used, as it is included in the CPL value. 8.2.8  Path Loss and Coupling L: Path loss between the interferer and the interfered antennas, in decibels. It is very important that we choose the appropriate path loss model for EMC analysis. This model may not necessarily be the same as that used for the desired signal path. We deal further with this issue in Chapter 11. In the case of onboard interference, or interference between very close platforms, we use the coupling between the antennas, (also referred to as isolation), rather than the path loss. Figure 8.1 explains the difference between the two terms: The path loss L is defined between the antennas apertures, whereas coupling CPL is defined between the antenna connectors. 8.2.9  Polarization Loss LPol: Polarization loss between the interfering and interfered antennas when they use different polarizations, in decibels. Polarization notations are defined as follows: V: Vertical; H: Horizontal; S: Slant 45°; RHC: Right-hand circular; LHC: Left-hand circular. The polarization loss between antennas using the same polarization is:

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LPol = 10log(cos0)2 = 0 dB (8.12)

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The polarization loss between antennas using the opposite polarization is: LPol = 10log(cos90)2 = −∞ dB (8.13)



Obviously, polarization loss never reaches −∞ dB, due to nonperfect physical antenna structures, the influence of nearby metallic objects, and other conditions. Some power is still radiated or received in the opposite polarization. If measured data is not available, we customarily use −20 dB as the default value for the opposite polarization. The polarization loss between antennas using V or H versus S polarization, and between linear and circular polarization is: LPol = 10log(cos45)2 = −3 dB (8.14)



Table 8.2 summarizes these values. Table 8.2 should be used with caution, even in communication, jamming, and other applications, as it applies only to antennas directed exactly toward each other. The cross-polarization term refers only to the center of the main lobe. The cross-polarization usually degrades as the off-center angle increases, even within the main lobe. The antenna polarization in the sidelobes may be the same as in the main lobe, or it may be any other polarization: opposite or elliptical for example. We should use the antenna cross-polarization data outside the main lobe if available. (In most cases the antenna manufacturer has no obligation to specify the off-boresight cross-polarization.) In EMC analyses, Table 8.2 should be used with even greater caution due to a fundamental difference in attitude (i.e., what is the worst case). In deploying communication systems, we may hope that there will be no polarization losses, but, in practice, they may exist. The worst case would be that we encounter unexpected polarization losses degrading the link power budget. Table 8.2 Polarization Loss Linear Polarization Linear

Circular

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Circular

V

H

S

RHC

LHC

V

0

−20

−3

−3

–3

H

−20

0

−3

–3

–3

S

−3

−3

0

–3

–3

RHC

−3

–3

–3

0

−20

LHC

–3

–3

–3

−20

0

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8.2  Calculating the Received Interference Level143

Conversely, in EMC, we would like to anticipate that opposite polarization losses will decrease the interfering signal level by, for example, 20 dB. In practice these losses may be smaller or even nonexistent. Therefore, the worst case for EMC consideration is that polarization losses are less than those in Table 8.2, or even that there are no polarization losses at all. Even if some relative angles between the directions of the interfering and interfered antennas exhibit high polarization losses, other angles may not. The recommended EMC polarization loss is therefore using the measured or specified value, whenever available. Several examples of crosspolarized antenna patterns are given in [1, 4]. If not available, a default cross-polarized antenna pattern may be suggested as follows. Within the main lobe, from zero up to the angle ϕ 1, the pattern Gφ–X (the x stands for the cross-polarized pattern) may be assumed to be constant:

G0-X = Gf -X = XPD (8.15) 1

At the angle ϕ 2, the end of the first side lobe, Gφ–X, may decrease by K1, typically 10–15 dB:

Gf -X = XPD − K1 (8.16) 2

The ϕ 1 and ϕ 2 angles are defined in (8.10) and (8.11), respectively, when we use the default antenna pattern. From ϕ 3, the angle where the nominal gain reaches its limit and up to 180 degrees, the cross-polarized pattern equals the nominal pattern less K2, typically 0 and sometimes up to 3 dB:

Gf -X = G180 = Gf − K2 (8.17) 3

3

We assume the interpolation between the angles to be linear. The polarization loss, LPol, is the difference between the cross-polarized pattern and the nominal pattern:

LPol = Gf-X − Gf (8.18)

There are two LPol values, that of the interferer antenna and that of the interfered antenna. Although the accurate calculation needs adding them in numerical values, as in (8.19), it is good enough to choose one: the less negative. For the elevation pattern, θ replaces ϕ . Figure 8.5 shows an example.

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144

Intersystem EMC Analysis, Interference, and Solutions 0

dBc

XPD

− 10

− 20 K1

− 30 K2

− 40

0

20

40

60

80

100

120

140

160

180

Degrees

φ3

φ1 φ2 Co -polarization

Cross polarization

LPol

Figure 8.5  Cross-polarized pattern and LPol example.

8.2.10  Receiving Antenna Gain Gr: Receiving antenna gain, in decibels referenced to isotropic. All the other issues detailed in Section 8.2.6 concerning the transmitting antenna, apply to the receiving antenna as well. 8.2.11  Receiving Antenna Sidelobes GSL-r: Sidelobes’ loss of the receiving antenna, in decibels referenced to carrier. This text uses Gvj and G(ϕ ,θ ) as equivalent notations for this parameter. The term Gvj denotes the victim antenna gain or pattern, in the direction toward the jamming antenna. The term G(ϕ ,θ ) denotes the antenna gain or pattern in azimuth and elevation. All the other issues detailed in Section 8.2.7 concerning the transmitting antenna sidelobes apply to the receiving antenna as well. 8.2.12  Receiver Cable Loss Lcr: Cable and other losses between the receiver and its antenna, such as splitters, combiners, switches, and circulators, in decibels.

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8.3  Power Sum of Multiple Interferers145

8.2.13  Receiver Waveguide Loss LWG-r: Waveguide loss, if this is the antenna feeding, in decibels. If the transmitter frequency is less than the receiver waveguide cut-off frequency, fTx < fcoRx, the waveguide loss will be very high. This statement is valid for the SEL interference type. 8.2.14  Receiver External Filter LFilter-r: Attenuation of an external filter, if placed between the receiver and its antenna, in decibels. 8.2.15 BWF The BWF is valid for CCI, ACI, and HAR interference types and is detailed in Sections 5.2.6, 6.2.2, and 6.6.7, which describe these interference types respectively.

8.3  Power Sum of Multiple Interferers We need to address the concern of the accumulated effect of all interferers when operating at the same time. This concern arises from the fact that EMC calculations in the survey individually analyze the interference from each interfering transmitter, to each interfered receiver. There is a fundamental difference between the power and the time aspects: If the interferers are pulsed, the received pulses are accumulated, and the interference probability increases. Chapter 19 details this issue. If the interferers are continuous (CW), their received powers are accumulated and increase in a process described as follows. Our basic assumption is that the multiple interferers are not coherent. The parameter we will accumulate is, therefore, the received power. (Otherwise, we would have to sum the received field strength vectors, in which the phase differences between signals would play a role.) Since the powers to be summed are given in decibels referenced to milliwatts notation, we will convert them to milliwatts, add them, and reconvert to decibels referenced to milliwatts value. To distinguish this sum from the more usual sum (in decibels), we will write this sum in square brackets:



I2 ⎡ I1 ⎤ I = [ I1 + I 2 ] = 10log ⎣1010 + 1010 ⎦ (8.19)

In Figure 8.6 we indicate the power sum, [I1 + I2] over I1, versus their difference in decibels. We see that if one signal power is negligible with

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[I 1+I 2]/ I 1 22 20 18 16

dB

14 12 10 8 6 4 2 0 −20

−15

−10

−5

0

5

10

15

20

I 1 −I 2 (dB) Power sum

Asymptote

Figure 8.6  Power sum of two signals.

respect to the other, the weaker one can be neglected, and the sum equals the stronger signal, as seen in the asymptotes. Figure 8.7 also illustrates the same issue in another form: the power sum [I1 + I2] over the stronger signal, versus their difference in decibels. Note that the sum of two signals can add, at most, 3 dB. Even this small value exists only when both signals are received with the exactly the same level: a rare situation. Our conclusion is that, in EMC calculations, the strongest interferer is the decisive one. There is usually no point in summing the individual interferers’ received powers, unless all have approximately the same received power, or if there are an enormous number of interferers.

[I 1+I 2]/ Max {I1,I2} 4

dB

3 2 1 0 − 20

− 15

− 10

−5

0

5

10

15

20

I1 −I 2 (dB) Figure 8.7  Power sum of two signals over the stronger signal.

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8.3  Power Sum of Multiple Interferers147

Note that the curve in Figure 8.7 is equal to the difference between the power sum and the asymptotes shown in Figure 8.6. In case of multiple interfering signals, their sum is given as: n

I1

10log ∑ 1010 (8.20)



1

References [1] Recommendation ITU-R F.699-7, Reference radiation patterns for fixed wireless system antennas for use in coordination studies and interference assessment in the frequency range from 100 MHz to about 70 GHz. [2] Rec. ITU-R F.1245-2, Mathematical model of average and related radiation patterns for line-of-sight point-to-point fixed wireless system antennas for use in certain coordination studies and interference assessment in the frequency range from 1 GHz to about 70 GHz. [3] ETSI EN 300 833 V1.4.1 (2002-11) Fixed Radio Systems; Point-to-point antennas; Antennas for point-to-point fixed radio systems operating in the frequency band 3 GHz to 60 GHz. [4] Arefi, R., and R. Blazing, “Recommended Antenna Specifications,” IEEE 802.16 Broadband Wireless Access Working Group, Boulder, Colorado, January 2000.

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Chapter

9 Contents 9.1 Background

Interference Margin and Its Meaning

9.2  IMRG in the S/I approach 9.3  IMRG in the DES Approach 9.4  IMRG Impact on the Range 9.5  Interference to Short Desired Paths 9.6  Applying the DES Approach for Interference to Radar 9.7  FM Degradation 9.8  Inverse Calculation Technique 9.9  Sensitivity Level as Wrong Threshold Level 9.10  EMC Calculation Summary

9.1 Background An EMC analysis outcome in yes or no terms (i.e., interference is or is not anticipated between device A and device B) is not adequate: We must quantify the analysis results. We generally express quantification in decibels. The interference margin, IMRG, is the difference between the required threshold and what we would expect, according to the EMC calculations. For example, we would like to determine how much lower or higher the received interfering signal level is than the maximum allowed level. Alternatively, we also would like to determine how much higher or lower the S/I is than the minimum requirement. We should bear in mind that the statement “no interference is anticipated” is not always accurate. More accurate wording would be, “even if interference is anticipated, it is less than the maximum allowed threshold.” For example, we can express the condition that receiver sensitivity will be degraded but by less than the acceptable value. Obviously, we need to quantify allowable interference, since having a positive 1-dB IMRG 149

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is decidedly different than having 20-dB margin. Not only is this a question of the no-interference confidence level, but it also considers the link fade margin, discussed in Section 9.2.8. In much the same way: the impact of a negative IMRG of –1 dB interference is different from –20-dB interference. This is not only a question of the interference confidence level but it takes the link operational range into account, as discussed in Section 9.4. Decibel quantification is not the only criterion. In several cases, it is possible to translate the negative IMRG value to other criteria, such as sensitivity degradation, fade margin reduction, range reduction, BER or MER degradation, and probability of detection reduction. There is a difference between the IMRG definitions in the S/I approach and the IMRG definition in the DES approach, which is discussed in Sections 9.2 and 9.3, respectively.

9.2  IMRG in the S/I approach 9.2.1  The Criterion The question we must answer, in the S/I approach is: Is interference anticipated or not? Thus, the criterion in the S/I approach is the intererence margin, IMRG. The meaning of the IMRG, as defined in the S/I approach is discussed in the following:  A positive IMRG value indicates that there will be no interference. The value indicates how much margin there is from seeing interference, in decibels.  A negative IMRG value means that there will be interference. The value indicates how many decibels are missing to prevent the interference. 9.2.2  Procedure and Steps of IMRG Calculation The five calculation steps are listed as follows: 1. Calculate S, the desired signal level, in accordance with Section 9.2.3. 2. Calculate ITh, the interference threshold in the S/I approach, as defined in Section 9.2.4. 3. Calculate I, the received interference level, per Chapter 8. 4. Calculate [I + N], which is interference plus noise, in accordance with Section 9.2.6.

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151

5. Calculate IMRG, the interference margin in the S/I approach, as in Section 9.2.7. We explain these calculations below. 9.2.3  Desired Signal Level S Calculation The desired signal level calculation is conducted using well-known link budget procedures. There are cases where we would have no need to calculate the value of S, since a nominal value is given. For example, in GPS applications, the received signal level is typically given as S = −130 dBm (or −160 dBW). We also find cases where S cannot be calculated, due to lack of data. The value needs to be assessed in other ways. For example, when only the receiver MDS is known, and the transmitter EMC data or link distance are not available, we can assume the level of S to be:

S = MDS + FM (9.1) Still, the required fade margin, FM, has to be assessed.

9.2.4  Interference Threshold Calculation To avoid interference, the interfering signal level I must be lower than the desired signal level S by the (S/I)r. Thus, we define the interference threshold ITh, as:



I Th = S −

()

S (9.2) I r

where (S/I)r is in accordance with Section 7.2. Continuing the GPS example in Section 7.2.5, we get the result: ITh = −130 − (−27) = −103 dBm. 9.2.5  Interference Level I Calculation We calculate the received interference level as shown in Chapter 8. 9.2.6  Interference Plus Noise Calculation The effective interference power is the interference I plus the noise, N. Since the interference and noise powers need to be added, but are given in decibels referenced to milliwatts notation, we need to convert their values to milliwatts, then add them, and reconvert to decibels referenced to milliwatts.

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To distinguish this sum from the regular sum in decibels, we will write it in square brackets:



⎛ ⎝

I

N

⎞ ⎠

[ I + N ] = 10log ⎜ 1010 + 1010 ⎟ (9.3)

9.2.7  IMRG Calculation The term power budget is used to describe the calculation of the desired signal level needed for finding if reception is possible. In much the same way, we use the term interference power budget for the calculation of the interference level that determines if interference will exist. The interference power budget outcome is the IMRG, defined as the difference between that which is required and that which is achieved:

I MRG = I Th − [ I + N ] (9.4)

An equivalent IMRG definition uses the signal-to-interference plus noise ratio, (SINR), defined as: S

[ I + N ] (9.5)



Inserting (9.2) and rearranging, we get an equivalent IMRG definition in the S/I approach:



I MRG =

S

[I + N ]

−

()

S (9.6) I r

SINR is also known as the carrier-to-interference plus noise ratio (CINR). Figures 9.1 and 9.2 show the interference threshold according to (9.2) and the IMRG, according to both (9.4) and (9.6). Figure 9.1 exemplifies the case in which the interference level is sufficiently strong so that IMRG is negative, and hence interference is experienced. Figure 9.2 exemplifies the opposite case, in which the interference level is so weak that IMRG is positive, and hence no interference exists. If the received interference level I is so small that the interference is negligible with respect to the noise, and if the equality (S/I)r = (S/N)r applies, then IMRG, according to (9.6) will reduce to:



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I MRG =

( )

S S − N N

r

I N there is virtually no difference if we take the noise into account or not. 12 10

I MRG (dB)

8 6 4 2 0 −2 −4 −6 −112 −110 −108 −106 −104 −102 −100

−98

−96

−94

I (dBm) Using S/[I+N]

Using S/I

N

Figure 9.3  IMRG versus I in the S/I approach.

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9.2  IMRG in the S/I approach

155

 Case 2: Interference level is just 2 dB above the noise: I = −108 dBm. IMRG is positive: IMRG = 5.9 dB. In this condition, we are almost 6 dB above the interference threshold. Now there will be a difference in the result; disregarding the noise, we get an error: IMRG = 8 dB. The dots in Figure 9.3 show these examples. 9.2.8  Relationship Between IMRG and Fade Margin The definition of fade margin is: FM =



S

[I + N ]

−

( )

S (9.8) N r

The definition of IMRG, per (9.6) is: I MRG =



S

[I + N ]

−

()

S (9.9) I r

Inserting, we get: FM = I MRG +



() ( ) S I

r

−

S N

(9.10)

r

In case of the common equality (S/I)r = (S/N)r we get: FM = I MRG (9.11)



Meaning that the interference margin amount is the fade margin in presence of interference. Even if (S/I)r ≠ (S/N)r, the difference between (9.10) and (9.11) is usually small. Please note that this statement applies only for the S/I approach. This result is very important. Even if IMRG > 0 (i.e., communication exists), there is also hidden harm to the communication: The fade margin degrades from its nominal interference-free value, FM, to IMRG. Consider, for example, a communication link with a very high nominal FM: 30 dB.  Case 1: IMRG = 20 dB. Since the IMRG is positive, there is no interference. The fade margin degraded from 30 to 20 dB, but it is still high.

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156

Intersystem EMC Analysis, Interference, and Solutions dB S S/[I+N]

If (S/I) r =(S/N) r

I Th Then: I MRG =FM (>0 ) [I+N] I

FM Deg N Figure 9.4  The FM = IMRG identity in the S/I approach.

 Case 2: IMRG = 1 dB. Since the interference margin is positive, there is no interference but now the fade margin degraded from 30 to 1 dB. Communication still exists but its availability is expected to be very poor.  Case 3: IMRG = 0 dB (i.e., the exact threshold value). By the definition, the link availability at FM = 0 dB is the median, 50%. The identity, FM = IMRG in the S/I approach, is demonstrated in Figure 9.4 wherein we have inserted (S/I)r = (S/N)r into Figure 9.2.

9.3  IMRG in the DES Approach 9.3.1  The Criterion In the DES approach, as opposed to the S/I approach, the question to be answered is not: Is interference anticipated? In the DES approach, interference always exists. In one case, it can be enormous; in another it can be negligible, but it will always be present. The question to be answered, in the DES approach, is therefore: What is the interference strength? The basic criterion in the DES approach is still the same: the interference margin IMRG. However, the much more meaningful criterion in the DES approach is desensitization (and therefore the name of this approach).

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157

The meaning of the interference margin, as defined in the DES approach is described as follows:  Positive IMRG indicates that DES is less than the maximum allowed; its value indicates how far we are from the threshold, in decibels.  Negative IMRG will indicate that DES is more than the maximum allowed; its value indicates the extent to which we miss the threshold, in decibels. 9.3.2  DES Calculation The thermal noise equals: N = kTBF (9.12)



The receiver sensitivity, without interference, equals the thermal noise, N, plus (S/N)r: MDS = N +



( )

S (9.13) N r

When an interfering signal is received, the effective noise level rises from N to [I + N]. The sensitivity is thus degraded as the (S/N)r is now added to [I + N] rather than to N. The degraded sensitivity is:



MDSDegraded = [ I + N ] +

( ) S N

(9.14)

r

Therefore, the desensitization equals the difference between N and [I + N]:

DES = N − [ I + N ] (9.15)

DES is a negative number, in decibels. We refer to its reciprocal, [I + N] − N, as the noise rise. 9.3.3  DES versus I/N We can rewrite (9.15) to express desensitization in decibels, as a function of I/N in decibels as well. Inserting (9.3), and rearranging, we get:



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⎛ (I/N) ⎞ DES = −10log ⎜ 10 10 + 1⎟ (9.16) ⎝ ⎠

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Intersystem EMC Analysis, Interference, and Solutions

DES (dB)

158 0 −1 −2 −3 −4 −5 −6 −7 −8 −9 −10 −11 − 10

−8

−6

−4

−2

0

2

4

6

8

10

I/N (dB) Figure 9.5  DES versus I/N in the DES approach.

   Figure 9.5 shows DES versus I/N in accordance with (9.16). The following examines three cases, from the I/N viewpoint:  The interference I equals the noise N. Inserting I/N = 0 into (9.16): DES = −10log 2 = −3 dB



I = N (9.17)

   When the interfering signal I equals the noise N, the desensitization is −3 dB, as can be seen in Figure 9.5. This result indicates that the desired signal level must be increased by 3 dB for us to restore the nominal performance in terms of factors such as BER.  The interference I is very strong: In this case, the 1 in (9.16) is negligible and we get: DES = −



I N

I >> N (9.18)

   This indicates that the sensitization equals the amount, in decibels, by which I is larger than N (not larger than MDS). Note that (9.18) is the equation for the dashed diagonal asymptote in Figure 9.5.  The interference I is very weak: In this case, the interference in (9.16) is negligible compared to the 1, and we get:

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DES = 0 dB

I 0: No interference

IMRG > 0: DES within limit

IMRG < 0: Interference

IMRG < 0: DES beyond limit

1. IMRG 2. Range reduction (Figure 9.8) 3. Reception range 4. FM degradation

1. IMRG 2. Range reduction (Figure 9.9) 3. Reception range 4. DES

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Chapter

10 Contents 10.1  Hierarchy Level and Interference Types

The Interference Range and the Reception Range

10.2  Calculating the Interference Range 10.3  Calculating the Reception Range with Interference

10.1  Hierarchy Level and Interference Types Some of the main parameters affecting the received interfering signal level I are given in the following equation: I = Pt + Gt + Gr + GSL-t + GSL-r + L + LX + BWF (10.1) LX is the attenuation of any interference type X, relative to CCI interference, in decibels. We can clearly see, from (10.1), that any two terms can compensate each other, in decibels, without changing the value of I. If we examine LX and the path loss L for example, for each decibel in power that the interference type X increases, an additional decibel needs to be added to the path loss, to avoid interference. This is a mathematical expression of the obvious: The stronger the interference, the greater its effect over distance. The strongest interference type, CCI, will obviously be felt at the platform, site, and arena levels. This interference may be felt at distance of the same order of magnitude as the interfered 169

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device’s range (e.g., tens of kilometers or more). We may experience much weaker interference types (such as BBN and RIM) at the platform level, but rarely at the site or arena levels. Table 10.1 summarizes the expected interference types in the various hierarchical levels, qualitatively.

10.2  Calculating the Interference Range 10.2.1  The Problem One of the more common solutions to EMC problems is to increase the distance between the interfering and interfered devices. We would need to be able to calculate the interference range, R, defined as the minimum distance between the interfering and interfered devices, which enables the victim to perform without interference. The basis for this calculation is IMRG (when negative). The basic problem is translating IMRG, from decibels, the engineering viewpoint, to kilometers, the operational viewpoint. There are some similarities between calculating the victim’s range and the interference range. We can use a communication link as an example, with the assumption that the maximum allowed system loss is, for example, 140 dB. Therefore, we would be able to state that the link communication range is 140 dB. This statement might appear an evasive answer for the range, but in fact, it is completely accurate, since the communication range, in kilometers, is any distance having a 140-dB path loss. This range may be thousands of kilometers in free space, few tens of kilometers in a terrestrial line-of-sight (LOS) path, and a few kilometers in a terrestrial path without LOS. Translating decibels to kilometers obviously depends on the frequency as well. The same behavior applies in looking at the interference range. We can use an example wherein IMRG = −60 dB; that is, a 60-dB increase in the

Table 10.1 Expected Interference Types in the Various Hierarchical Levels Strength

Interference Type

Platform

Site

Arena

Strong

CCI ACI and SEL at small dF

Yes

Yes

Yes

Medium

ACI and SEL at large dF HAR

Yes

Yes

Rarely

Weak

SPR, BBN, PHN, TIM, RIM, IMR, IFR

Yes

Rarely

Very rarely

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10.2  Calculating the Interference Range171

existing path loss between the interfering and interfered devices is required to avoid interference. Any distance providing the missing 60-dB path loss serves this requirement. This may turn out to be a large distance in free space, a medium distance in a terrestrial path with LOS, and small distance in a terrestrial path without LOS. As in the communication range case, this distance is frequency-dependent. Moreover, calculating the interference range depends on the wave propagation model used. However, the appropriate model for interference range calculation is not necessarily the same model used for the victim’s range calculation. We discuss this issue in Chapter 11. The use of the free-space propagation model for interference calculations is appropriate in many EMC cases, but not in all. We find that a common error is made in using the free-space model even when not appropriate, just because it is simple and easy to calculate. We will use the following example to demonstrate that it is inappropriate to use the same path loss exponent n for the interference calculation and for the interference range calculation. As an example, consider two terrestrial devices that are 50m apart. It is appropriate to use the free-space model, where n = 2, for the interference calculation. n When a path loss depends on R , the required range increase factor (RIF) is:



RIF = 10

− I MRG 10n

(10.2)

Using n = 2, the result for IMRG = −60 dB, as given in the example, is: 60



RIF = 1020 = 1000

In accordance with this equation, we would have to increase the distance between the devices from 50m to 50 km. This recommendation is obviously incorrect and would mislead the decision-makers. We make an error in assuming that free-space propagation conditions exist in any terrestrial 50-km path, since it is rarely the case. Although (10.2) is correct, using n = 2 is incorrect. We can achieve the missing 60 dB at much smaller ranges, especially if we can introduce LOS-blocking. In cases of great terrestrial distances, the exponent, n, may rise from 2 to 4 and even more than 5, according to Figure 11.3 in our GETIM model (see Section 11.4). As an example, at 400 MHz n = 4.5.

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Using this path loss exponent example, we get a much more reasonable recommended range increase factor: 60

RIF = 10 45 = 21.5



The interference range in this example would be roughly 1.1 km. Another similarity is between calculating the victim’s range and the interference range in terrestrial devices. When the communication range is terrain-dependent we cannot possibly give a definite answer to the question, What is the certain radio communication range? The range differs in various directions and from location to location. The question we should ask is, What is the communication coverage map? Similarly, when terrain has an impact on the path loss in the interfering path, we should ask the question, What is the interference coverage map? rather than, What is the interference range? In the following sections, we will start with simple cases and proceed to more complicated ones. 10.2.2  Interference Range without Terrain Influence The simplest cases are those in which terrain has no impact on the interfering path loss (as between high aerial devices), or if terrain has a negligible impact (as in certain terrestrial cases). The problem is simpler still if the interfered antenna is omnidirectional. In this circumstance we can define the interference range, R. The interfering device must be further away than R; accordingly, the interferer is excluded from being deployed in the circle shown in Figure 10.1. Only if the free-space propagation model applies in the interfering path, the radius, R, is calculated using (10.3): −

R = 10



I MRG +20log f +32.44 20

R

(10.3)

Area forbidden for interferer deployment

The interfered device

Figure 10.1  Interference radius for omnidirectional interfered antenna, without terrain.

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10.2  Calculating the Interference Range173

where: f: Frequency, in megahertz; R: Distance, in kilometers. For example, if IMRG = −60 dB and f = 100 MHz, we get R = 0.24 km. A somewhat more complicated case exists in which the interfered antenna is directional, such as in microwave links or in radar. Taking the interfered antenna pattern into account changes the forbidden area for deploying the interferer, to a shape similar to the antenna pattern, as in Figure 10.2. A customary way for us to handle the directional antenna case would be to use an approximation to simplify the calculations, to deal with an instance where the antenna pattern is not available. Rather than using the antenna pattern, we would assume that the antenna has its full nominal gain throughout the 3-dB beamwidth, and 0 dBi elsewhere. The forbidden area shown in Figure 10.2 reduces to Figure 10.3. 10.2.3  Interference with Terrain Influence In most terrestrial cases, the terrain has an impact on the interfering path loss. Exceptions occur when we deal with very short distances or long distances provided that the terrain is truly flat or over a large body of water. In most terrestrial cases, where the terrain has an impact, we can use wave

The interfered device

F M

Area forbidden for interferer deployment

Figure 10.2  Interference area for directional interfered antenna, without terrain.

BW

The interfered device

Area forbidden for interferer deployment

Figure 10.3  Interference area, simplified directional antenna, without terrain.

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propagation models using digital terrain map (DTM) data, regardless of the interfered antenna directionality. Figure 10.4 shows such a calculation outcome, with the result shown in terms of interference margin IMRG when negative, according to the legend in decibels. Using any of the painted area for deploying the interfering device would be forbidden. Only areas having positive IMRG (i.e., where the background map is not overlaid) are allowed for the interfering device deployment. The area can be defined by its radius if the forbidden area for deploying the interfering device has close to a circle shape, usually at short distances. Figure 10.5 shows an example in dichotomy: yes/no interference.

10.3  Calculating the Reception Range with Interference 10.3.1 Background When conducting the EMC survey, we may ask for complementary information in addition to the interference range or area: What is the interfered device’s reception range or its coverage map with interference? There is a fundamental difference between reception range calculations, with and without interference. The reception range without interference is limited by the noise level N, whereas the limiting factor in reception range with interference is the received interference level I.

The interfered device

Area forbidden for interferer deployment

Figure 10.4  Example of interference coverage map.

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10.3  Calculating the Reception Range with Interference175

Figure 10.5  Example of approximately circular interference coverage.

There are several ways that we can calculate and present the reception range with interference. Some examples follow:  The range degradation with respect to the nominal range, as described in Section 9.4;  The paths length ratio, as described in Section 10.3.3;  The reception coverage area with terrain influence, as discussed in Section 10.3.4. 10.3.2  Signal-to-Interference Plus Noise Ratio This section uses numerical rather than decibel values and employs the designation j for jammer and v for victim notations. The desired signal level is: S=

Pv Gvt Gvr (10.4) Lv

and the interfering signal level for CCI is: I =

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PjG jGvr (10.5) Lj

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where: Pv: Transmitter power of the desired channel; Gvt: Transmitting antenna gain of the desired channel; Gvr: Receiving antenna gain of the desired channel; Lv: Path loss in the desired channel, according to chosen propagation model; Pj: Transmitter power of the interferer; Gj: Antenna gain of the interferer; Lj: Path loss in the interfering path, according to chosen propagation model. Figure 10.6 shows these terms. For other interference types (e.g., ACI), we need to reduce the value of Pj according to LACI, translated to numerical value. The equation is valid for MM interference (or omnidirectional antennas). For other cases, GSL-t and GSL-r in numerical values have to be added to the equation. The signal-tointerference plus noise ratio is: Pv Gvt Gvr Lv S = (10.6) P G G I+N j j vr + kTBF Lj



This general equation serves both calculations, with or without terrain.

Gt

Interference channel

G vr

Desired channel

Lj dj Pj Interfering transmitter

G vt

Lv dv I

S

Interfered receiver

Pv Desired transmitter

Figure 10.6  Terms used in the calculation of reception range with interference.

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10.3  Calculating the Reception Range with Interference177

10.3.3  Reception Range without Terrain For calculating the reception range without terrain influence, we can examine three wave-propagation models: free-space, flat-terrain, and the generic n R model. If the free-space propagation model is valid, we will get: Pv Gvt Gvr 2 4p dv2 S l = (10.7) PjG jGvr I+N + kTBF 2 4p d 2j l

( )

( )

where:

dv: Reception range under interference, or the distance between the transmitter and receiver in the desired channel, in meters; dj: Distance between the interfering transmitter and the interfered receiver, in meters;

λ : Wavelength, in meters. If the flat-Earth propagation model is valid, we will get: Pv Gvt Gvr dv4 2 hvt2 hvr S = (10.8) PjG jGvr I+N + kTBF d 4j 2 2 hjt hvr

where:

hvt: Transmitting antenna height in the desired channel, in meters; hvr: Receiving antenna height in the desired channel, in meters; hjt: Interfering transmitting antenna height, in meters. The maximum available reception distance in the S/I approach is at the threshold point, when:

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()

S S = I r (10.9) I+N



In the case where (S/I)r = (S/N)r:

( )

S S = N r (10.10) I+N



Then inserting into (10.7) and extracting dv we get for the free-space model:

dv =

Pv Gvt Gvr 2 4p l

( )

( )



( )

⎡ PjG jGvr ⎤ S ⎢ 4p 2 + kTBF ⎥ N ⎢ ⎥ d 2j ⎣ l ⎦

(10.11)

r

Similarly, for the flat-Earth model: dv = 4



2 Pv Gvt Gvr hvt2 hvr 2 ⎛ PjG jGvr h2jt hvr ⎞ S + kTBF ⎟ 4 ⎜ d ⎝ ⎠ N j

( )

(10.12)

r

A flat-Earth condition is rarely valid in the real world, as it applies only when several conditions are fulfilled, the most important being the existence of LOS. Path-loss measurements in various types of terrain show that the exponent, n, varies significantly, usually between 2 and 5, [1]. We face a dilemma in determining how to calculate the reception range, dv, where, on one hand, the wave propagation depends on the terrain, but on the other hand, terrain data is not available. To this end, we will replace the fourth root in (10.12) with the nth root, and will assume (a practical but unproven assumption) that the height terms in the equation do not change. In Figure 10.7 we show an example in which a cellular communication receiver is the interfered device. We used three exponent values, n = 3, 4, and 5, to demonstrate the effect. We selected the interferer’s power as being higher than the mobile’s power, but lower than that of the base station. In cases of interference from a strong interferer (i.e., to the mobile), the term under the root is smaller than one. In such cases, the reception range dv increases with n. In other words, the worst case, namely shorter dv, is a smaller n value, as is seen in Figure 10.7.

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10.3  Calculating the Reception Range with Interference179

In cases of interference from a weak interferer (i.e., to the base station), the term under the root is larger than one. In such cases, the reception range dv decreases with n. In other words, the worst case, namely shorter dv, is a larger n value, as is seen in Figure 10.8. In both cases, when the received interference level is much smaller than the noise, the result is the nominal reception range (the horizontal lines in Figures 10.7 and 10.8).

1.E+06 1.E+05

dv

1.E+04 1.E+03 1.E+02 1.E+01 1.E+00 1.E−01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08

dj n 4

3

5

Figure 10.7  Mobile receiver reception range.

1.E+07 1.E+06

dv

1.E+05 1.E+04 1.E+03 1.E+02 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08

dj n 3

4

5

Figure 10.8  Base station reception range.

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When the received interference level is much higher than the noise, the equation yields the diagonal lines in both Figures 10.7 and 10.8. In this case, we can ignore the kTBF term in the equations. Several terms are reduced, and the equations can be simplified and rearranged to express a constant distances ratio: dv/dj. If the free-space propagation is valid, we get: dv = dj

Pv Gvt 1 ⋅ S PjG j N

( )

(10.13)

r

If the flat-Earth propagation is valid, we get: dv = dj

4



Pv Gvt hvt2 1 ⋅ S PjG j h2jt N

( )

(10.14)

r n

and if neither is valid, and we use the general R model: dv = dj

n

Pv Gvt hvt2 1 ⋅ S PjG j h2jt N

( )

(10.15)

r

10.3.4  Reception Area with Terrain When terrain data and the the appropriate wave-propagation program are both available, we can calculate a reception coverage map with interference in a similar way as we determine communication coverage maps.

Reference [1] Abhayawardhana, V. S., I. J. Wassell, D. Crosby, M. P. Sellars, and M. G. Brown, “Comparison of Empirical Propagation Path Loss Models for Fixed Wireless Access Systems,” in Vehicular Technology Conference, 2005. VTC 2005Spring. 2005 IEEE 61st, IEEE, Vol. 1, 2005, pp. 73–77.

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Chapter

11 Contents 11.1  Difference Between Communication and EMC Models 11.2  Models without Terrain Influence 11.3  Models Based on DTM 11.4  Generic TerrainInfluenced Model PathLoss Model

Propagation Models for EMC 11.1  Difference Between Communication and EMC Models There are many wave-propagation models, including free-space, two-rays, and DTM-based models. It seems that there would be no difference which model to choose and what parameters within the model to use, whether we deal with communication, radar and more, or EMC. In practice, however, there are fundamental differences to consider in choosing a model. The differences stem from the way in which we recognize the worst-case condition. In communications or radar, the worst case would occur given a path loss higher than expected. Communication would not be possible, and we would be unable to detect or track a target. In an EMC calculation we would consider the worst case to be that the path loss from the interferer were lower than expected, thereby causing interference. Other good examples are several ITU-R models aimed at EMC calculations expressing the anticipated field strength. In communication availability calculations, we are interested in the path loss at a much higher time 181

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percentage than the median. The high-time percentage used in communications is intended to make sure we will have communication at almost all times (e.g., 99%). In contrast, ITU-R models aimed at EMC calculations [1] consider time percentages much lower than the median, intending to assure that we will have interference no more than a small percentage of time (e.g., 1% of the time).

11.2  Models without Terrain Influence We can examine the case where LOS exists. Ground reflections play a dominant role in path loss in these cases. Common relevant models are the tworay model and its derivatives such as the flat-Earth, nulls-envelope [2], and Egli models [3]. Figure 11.1 shows the two-ray model, the peaks and nulls envelopes, and the free-space model. In a communication calculation, we will find that the worst case is one with nulls stemming from destructive interference between the direct and reflected waves, which increases the path loss. Nulls may be very deep, although they do not exist at all distances. On the other hand, there are peaks up to 6 dB with respect to the free-space loss. We cannot disregard the nulls since communication is required at all distances. Thus, the nulls envelope is a common choice for a worst-case model guaranteeing communication. In contrast to communication systems, wherein the worst case is that ground reflections cause the nulls, in EMC interference, the worst case is that

−100 −110

dB

−120 −130 −140 −150 −160 −170 10

100

d (Km) Free space

Two rays

Nulls envelope

Peaks envelope

Figure 11.1  Various LOS propagation models.

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11.3  Models Based on DTM183

we do not have ground reflections in the interfering channel (meaning an absence of nulls). We might have considered using the peak envelopes as the EMC worst case, but this would be an overly exaggerated worst-case assumption. Thus, we recommend the free-space loss model as the best model to be used in the interference channel in terrestrial devices, with LOS, given by: L = −(20log f + 20log R + 32.44) (11.1)

where:

f: Frequency, in megahertz; R: Distance, in kilometers.

11.3  Models Based on DTM Some DTM-based propagation models (e.g., the Longley-Rice model [4]) use the confidence level parameter. This parameter is based on the standard deviation of the path-loss accuracy, σ . The common value used in a communication model is 90%. The path loss used in communication planning is: L90 = L − 1.282s (11.2)

where:

L: Median path loss, in decibels. This is the path loss computed per the terrain path profile; L90: Path loss used in communication planning, in decibels;

σ : Standard deviation of the path loss accuracy, in decibels; 1.282: The normal distribution factor for 90% confidence. Consider, for example, a median predicted DTM-based path loss in the desired channel at −150 dB and σ = 10 dB. Almost 13 dB are subtracted, thus L90 = −163 dB. Using the same logic, if we want to have a 90% confidence level of noninterference, (i.e., a maximum interference probability of 10%), we use the following path loss for EMC calculations:

L10 = L + 1.282s (11.3)

For example, the median predicted path loss in the interfering channel is −140 dB with the same σ . Almost 13 dB are added, thus L10 = −127 dB.

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This attitude makes a 2.564 · σ difference between the desired and interfering paths, almost 2 · 13 = 26 dB in this example, which is an exaggeration. To avoid accumulating too many worst-case parameters, we recommend the use of the median value for the interfering path-loss calculation.

11.4  Generic Terrain-Influenced Model Path-Loss Model We encounter a problem in cases where the terrain influence cannot be ignored but we are looking for a generic path loss value (i.e., one that is not relevant to a specific point or area on the map). To this end we have developed generic terrain-influence model (GETIM). The basic model we have selected for our purposes is the log-distance model, whose median value is given as: d L = L ( d0 ) − 10nlog ⎛⎜ ⎞⎟ (11.4) ⎝ d0 ⎠

where: d: distance;

d0: reference distance; L(d0): path loss at the reference distance; n: path loss exponent. To acquire L(d0) and n, we need a model based on empirical measurements in various terrains, distances, frequencies, and antenna heights, with and without LOS. Accordingly, we base our model on the ITU-R P.1546 model [1]. Based on Figures 1, 9, and 17 in [1], we have averaged the pathloss exponent n in the 1–50-km range, where the path loss versus distance line is relatively straight. The data in [1] applies for antenna heights of 10m and above. For antenna heights below 10m, we apply the path-loss dependency on antenna heights in accordance with the flat- or plain-Earth [3] and Egli [3] models; that is,

L

a

20log ( h1h2 ) (11.5)

We have chosen d0 to equal 1 km, then adjusted L1km for 1-m antenna heights as reference, and finally translated the data in the source figures

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11.4  Generic Terrain-Influenced Model Path-Loss Model185

from field intensity in dB/μ V/m from a 1-kW EIRP transmitter to path loss in decibels. Our resulting GETIM model is given as: L = L1 Km − 10nlog d + 20log ( h1h2 ) (11.6)



We found that for f < 600 MHz:

L1 Km = −82.5 − 20.2log f (11.7)



n = 3.5 + 0.385log f (11.8) And for f ≥ 600 MHz:



L1 Km = −100.8 − 13.6log f (11.9)



n = 1.93 + 0.95log f (11.10)

Figure 11.2 illustrates the GETIM path loss for representative frequencies, where h1 = h2 = 2m. Figure 11.3 shows the path-loss exponent per

− 100 − 120

dB

− 140 − 160 − 180 − 200 − 220 − 240

1

10

100

Km MHz 30

100

200

500

1000

3000

Figure 11.2  GETIM path loss.

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n

5 .0

4.5

4 .0 10

100

1000

10000

MHz Figure 11.3  GETIM path loss exponent n.

(11.8) and (11.10). Note that for antenna heights above 10m, we can use the ITU-R P.1546 model as is.

References [1] Recommendation ITU-R P.1546-5, Method for Point-to-Area Predictions for Terrestrial Services in the Frequency Range 30 MHz to 3000 MHz, 09/2013. [2] TIREM/SEM Handbook, ECAC-HDBK-93-076, March 1994. [3] Egli, J., “Radio Propagation Above 40MC Over Irregular Terrain,” Proceedings of the IRE, October 1957, pp. 1383–1391. [4] Rice, P. L., A. G. Longley, K. A. Norton, and Barsis, NBS Technical Note 101: Transmission Loss Predictions for Tropospheric Communication Circuits, NTIS Reference AD 687 820, U.S. Department of Commerce, 1967.

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Chapter

12 Contents 12.1 Measurement

Coupling Between Antennas

12.2 Scaling 12.3  Prediction by Simulation 12.4  Approximate FreeSpace Calculation

There are several ways we can acquire coupling data. We now review these methods in descending order from the most accurate to the approximate case.

12.5 Frequency Dependency

12.1 Measurement Obviously, measuring the coupling between antennas is the most accurate way to acquire this data when both the platform and antennas are available. The measurement is performed by connecting a network analyzer to both antenna connectors.

12.2 Scaling When the platforms or antennas are not available, we can perform a reasonably accurate measurement using a technique called scaling. A downscaled model of the platform and antennas is built X times smaller than the real one, and the measurement is performed using a times-X frequency.

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12.3  Prediction by Simulation Coupling prediction by simulation is appropriate in the planning or early development stages of system development, when the platform or antennas are not available for measurement. Such simulations require a dedicated near-field program (e.g., NEC, MoM, UTD, GTD, TLM, FDTD, and FEM) and personnel experienced in using such programs. Prediction by simulation has some drawbacks, listed as follows:  Good platform modeling is required.  Antenna modeling needs to include the physical antenna structure (size is not enough), as well as the electronic antenna feed.  We should expect inaccuracies: It is a practical impossibility to take the influence of all other influencing parameters into account.  As compared to performing a free-space approximation, the performance costs are not negligible.

12.4  Approximate Free-Space Calculation When better options are not available, we can still use the least-accurate approximation. We assume that the path loss between the onboard antennas is the free-space model and that antenna gains and patterns have to be added, as depicted in Figure 12.1. The polarization loss has to be added as well, when relevant. The coupling is given by the following equation: CPL = Gt + GSL-t + L + LPol + Gr + GSL-r (12.1)



where the free-space path loss, L, is per (11.1), taking care to use kilometers, rather than meters, though small distances are involved. We should take extra care in considering a case in which one antenna is within the near field of another. The equations detailed in Chapter 15 can be used, recalling that they are approximations as well—only appropriate for some antennas. This free-space calculation has the advantages of low cost and ease of use—but at the expense of reduced accuracy. When we use this calculation, we cannot consider many influencing parameters, described as follows:  The platform existence and shape are ignored.  Additional antennas on the platform are ignored.

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12.5  Frequency Dependency189

G SL-t G SL -r Z

R

X

Y

Platform

Figure 12.1  The geometry for approximate free-space coupling calculation.

 The approximation is valid only between antennas having LOS.  Phenomena such as resonance are ignored. This approximation is valuable in cases wherein the resulting absolute value of IMRG is very high (either positively or negatively), since refining the coupling value will probably not make changes to the anticipated question: Will there be interference or not? When the absolute value of IMRG is small, we recommend the use of one of the other options for acquiring coupling data, if possible.

12.5  Frequency Dependency As opposed to path loss, where frequency dependency is usually monotonic, coupling loss may exhibit frequency fluctuations due to such factors as reflections from platforms, diffraction over platform edges, and resonance at certain frequencies. Figure 12.2 demonstrates the NEC calculated coupling onboard an aircraft using multiple antennas. The fluctuations are clearly seen, as compared to the smooth line calculation per (12.1).

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190

Intersystem EMC Analysis, Interference, and Solutions − 50 − 55

dB

− 60 − 65 − 70 − 75 − 80 100

1000

MHz Calculated

Free space

Figure 12.2  Calculated coupling onboard an aircraft versus free-space approximation

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Chapter

13 Contents 13.1  The Problem

Relative Angles Between Antennas

13.2  Transformation by Rotation 13.3 Calculating θ and ϕ

13.1  The Problem The received interference level equation (8.3) includes the transmitting and receiving antennas’ sidelobe loss terms, GSL-t and GSL-r, equivalently named G(ϕ ,θ ). Our objective is to calculate ϕ and θ . The next phase, finding the gain at the angles, G(ϕ ,θ ), is detailed in Chapter 14. We demonstrate the consideration of the relative angles between antennas in Figure 13.1. This issue involves both azimuth and elevation. However, to simplify Figure 13.1 we are showing only the azimuth.

13.2  Transformation by Rotation Initially and as a reference, the antenna direction is toward the north and the horizon. With respect to this reference, the directional antenna, a, is directed in space toward the following:  AZa: Azimuth angle;  ELa: Elevation angle.

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North

Direction of the antenna

AZ a

φ

AZ t

t-Target

a-Antenna Figure 13.1  Relative angles definition.

Consider the following examples:  A terrestrial communication link antenna is directed in azimuth toward its partner antenna in the link, and toward the horizon in elevation.  A surveillance radar antenna scans the space in azimuth and elevation.  A ground control station antenna follows an aerial platform both in azimuth and elevation. The antenna sees the other antenna deployed in the area, denoted target, t, at the following angles:  AZt: Azimuth angle from the antenna toward the target;  ELt: Elevation angle from the antenna toward the target. The four angles AZa, ELa, AZt, and ELt are defined in the Earth coordinate system. However, the antenna gain toward the target is defined in the antenna spherical coordinate system:  ϕ : Azimuth angle in the antenna coordinate system referred to the center of the main lobe;  θ : Elevation angle in the antenna coordinate system referred to the center of the main lobe.

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13.2  Transformation by Rotation193

The aim of the mathematical problem is to define ϕ and θ , the angles toward the target in the antenna coordinate system, based on AZa and ELa, the direction of the antenna in space, and AZt and ELt, the direction from the antenna toward the target in the Earth coordinate system. This mathematical issue is known as transformation by rotation. The antenna is referred as being in the origin of the X, Y, Z coordinates system, where: X: Directed to the east; Y: Directed to the north; Z: Directed upward. Figure 13.2 defines the transformation from spherical to Cartesian coordinates: The transformation equations are: X = R sin AZt cos ELt Y = R cos AZt cos ELt (13.1) Z = R sin ELt

Z

Y R

North

EL t

AZ t R Cos EL t

X Figure 13.2  Transformation from spherical to Cartesian coordinates.

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R is the target distance to the origin. In the first rotation phase, the antenna coordinate system is turned only AZa degrees in azimuth, clockwise around the Z-axis. The rotated coordinate system is: X′, Y′, Z′. The first rotation matrix, around the Z-axis is: MZ =

cos AZa sin AZa 0

− sin AZa cos AZa 0

0 0 (13.2) 1

In the second rotation phase, the antenna coordinate system is turned ELa degrees in elevation, namely upward around the turned X′-axis (not the original X-axis). The rotated coordinate system is: X″, Y″, Z″. The second rotation matrix, around the X′-axis is: 1 0 M X ′ = 0 cos ELa 0 − sin ELa



0 sin ELa (13.3) cos ELa

The rotated coordinate system X″, Y″, Z″ is given by the matrix multiplication: X X ′′ Y ′′ = M X ′ ∗ M Z ∗ Y (13.4) Z Z ′′



The multiplication result is: cos AZa X ′′ Y ′′ = sin AZa cos ELa Z ′′ − sin AZa sin ELa

− sin AZa cos AZa cos ELa − cos AZa sin ELa

0 X sin ELa ⋅ Y (13.5) Z cos ELa

These are the new coordinates, based on the coordinates prior to rotation. However, we will need to find the new coordinates based on AZt and ELt. To this end, we can perform the matrix multiplication, inserting X, Y, and Z per (13.1): X ′′ = R sin AZt cos ELt cos AZa − R cos AZt cos ELt sin AZa

Y ′′ = ( R sin AZt cos ELt sin AZa + R cos AZt cos ELt cos AZa ) cos ELa + R sin ELt sin ELa

Z ′′ = − ( R sin AZt cos ELt sin AZa + R cos AZt cos ELt cos AZa ) sin ELa + R sin ELt cos ELa

(13.6)

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13.3 Calculating θ and ϕ 195

13.3 Calculating θ and ϕ The target elevation angle, θ , from the antenna viewpoint, in the rotated coordinate system, is given by: q = sin−1



Z ′′ (13.7) R

Inserting we get: q = sin−1 ⎡⎣ − ( sin AZt cos ELt sin AZa + cos AZt cos ELt cos AZa ) sin ELa + sin ELt cos ELa ⎤⎦

(13.8) Rearranging, while using trigonometric identities, we get the value of θ : q = sin−1 ⎡⎣sin ELt cos ELa − cos ELt cos ( AZt − AZa ) sin ELa ⎤⎦ (13.9)



In the next step, we need to calculate cos ϕ . Since the antenna pattern is symmetrical (right and left, with reference to the main lobe), calculating cos ϕ is sufficient. Note that this case is different than cases where moving platforms are involved (i.e., where both cos ϕ and sin ϕ need to be calculated to find the quadrant of ϕ ). The target azimuthal angle, ϕ , from the antenna viewpoint, in the rotated coordinate system, is given by: f = cos−1



Y ′′ (13.10) R cos q

Inserting we get: f = cos−1

(sin ELt sin ELa + sin AZt cos ELt sin AZa + cos AZt cos ELt cos AZa ) cos ELa cos q

(13.11) Rearranging, while using trigonometric identities, we get the value of ϕ :



f = cos−1

sin ELt sin ELa + cos ELt cos ELa cos ( AZt − AZa ) (13.12) cos q

Example 1 An airborne antenna is directed toward AZa = 220° and ELa = −20°. An interfering or interfered ground antenna, (the target), is seen from the airborne

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platform at AZt = 170° and ELt = −50°. When we use the equations, the result is that the ground antenna is seen at ϕ = 75.6° and θ = −59.4° in the antenna coordinate system. If there is also a roll term in addition to the azimuthal and elevational tilt, the equations are more complicated. We will not detail the roll-term case in this text. Example 2 In addition to the previous example conditions, the airborne platform has a counterclockwise roll of 25°. The ground antenna is now seen at ϕ = 81.1° and θ = −34.9°. In a case where all directions have zero elevation, these complex equations reduce to the trivial case (the one shown in Figure 13.1):

f = AZt − AZa

q = 0 (13.13)

We will find that the equations in this chapter are valid for finding both GSL-t and GSL-r. First, the interfering transmitter is regarded as the antenna, and the interfered receiver is regarded as the target. Then their roles are exchanged. Even more complex equations (not detailed here) account for the general case in which the antenna is mounted on an aerial platform (for example, a plane or missile) with specified angles with respect to the platform heading, while the platform heading angles are specified with respect to the Earth coordinates.

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Chapter

14 Contents 14.1  The Problem

Antenna Gain in Intercardinal Angles

14.2  The Guiding Principle 14.3 Coordinate Systems 14.4 Coordinates System Transformation 14.5 Symmetrical Antenna Pattern 14.6  The Sum in Decibels Method in the Symmetrical Case 14.7 Nonsymmetrical Antenna Pattern 14.8  The Sum in Decibels Method in the Nonsymmetrical Case 14.9  BWAZ > BWEL 14.10  BWEL > BWAZ 14.11  Reducing the Estimation Error 14.12  Real versus Envelope Pattern 14.13  Verification by Simulation 14.14 Examples 14.15 Summary

14.1  The Problem Personnel dealing with technologies such as communication, radar, and SIGINT are interested in conditions in the antenna’s main lobe. The interfering and interfered antennas may be directed toward any angle in space. For this reason, EMC personnel are also interested in sidelobes, in which interference may be unintentionally transmitted or received. When the antenna manufacturer supplies the intercardinal antenna pattern data (e.g., as a 3-D pattern), both GSL-t and GSL-r are easily determined. Figure 14.1 demonstrates, schematically, how such antenna patterns may appear. This chapter aims to help in the calculation of the intercardinal antenna pattern in those cases where only cardinal (or principal) plane antenna patterns are available. Later in the chapter, Figures 14.23 and 14.24 exemplify the cardinal antenna patterns for a Yagi antenna. We define the antenna pattern terms as follows:  G(ϕ ): Cardinal antenna pattern in the horizontal or azimuth plane; 197

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198

Intersystem EMC Analysis, Interference, and Solutions θ

Cardinal axes

φ Inter Cardinal data: G(φ,θ)

Figure 14.1  Schematic example of intercardinal antenna pattern.

 G(θ ): Cardinal antenna pattern in the vertical or elevation plane;  G(ϕ ,θ ): Intercardinal antenna pattern in any azimuth or elevation angle. We face the problem of calculating (or, if not possible, estimating) G(ϕ ,θ ) as a function of G(ϕ ) and G(θ ) when G(ϕ ,θ ) data is not available. The common method of performing this calculation is to do the following:  Calculate G(ϕ );  Calculate G(θ ).  Find an equation that will use these values to assess G(ϕ ,θ ) = f{G(ϕ ),G(θ )}. A simple estimation is the sum in decibels method:

G(f,q) = G(f) + G(q) (14.1)

Consider, for example, a case where an antenna pattern at an azimuth angle of 20° is −12 dBc, and the antenna pattern at an elevation angle of 30° is −17 dBc. Given this estimate, the pattern at 20° in azimuth, and

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14.3  Coordinate Systems199

simultaneously at 30° elevation, is: G(20,30) = −29 dBc. Though simple to use, this equation is valid only for very small ϕ and θ angles, and provided some additional conditions apply, detailed below. We will prove the validity of this equation for small ϕ and θ angles, in Sections 14.6 and 14.8. This chapter describes a novel way for calculating the intercardinal pattern based on cardinal data, for all angles. The original paper was published by the author in [1].

14.2  The Guiding Principle The guiding principle for this technique is the opposite of the more common method: Rather than using both cardinal patterns, only one pattern, either G(ϕ ) or G(θ ), is used. The steps in the special case, in which the azimuthal and elevation patterns are identical, are described as follows:  Calculate the equivalent angle, ϕ ′ = f (ϕ ,θ ).  The intercardinal pattern is: G(f,q) = G(f ′) (14.2)



The steps in the general case, in which the azimuthal and elevation patterns are not identical, are described as follows:  Choose which cardinal pattern to use: G(ϕ ) or G(θ ).  Calculate the equivalent angle, ϕ ′ or θ ′ accordingly.  If G(ϕ ) was chosen, use (14.2).  If G(θ ) was chosen, the intercardinal pattern is:

G(f,q) = G(q ′) (14.3)

14.3  Coordinate Systems Let us assume a sphere such as the globe, surrounding an antenna at its center, as shown in Figure 14.2. This section, uses the following coordinate system. The boresight (BS) is on the X-axis. From above, the azimuth angle, ϕ , is measured clockwise. The elevation angle, θ , is measured upward from the horizon. The Y-axis is at ϕ = –90°, and the Z-axis is upward.

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Z

θ

Y X

φ

B.S.

Figure 14.2  X,Y,Z and φ ,θ coordinate systems.

In a conventional globe, the North Pole is upward, as seen in Figure 14.2. Longitude and latitude are ϕ and θ , respectively. An intercardinal angle, (ϕ ,θ ), lies on the globe at longitude ϕ and latitude θ . Figure 14.3 shows an example wherein ϕ = 45° and θ = 30°.

Figure 14.3  Example of intercardinal angle (ϕ ,θ ) = (45,30).

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14.3  Coordinate Systems201

In the antenna coordinate system, the North Pole is in the BS direction, and the longitude and latitude are α and β , respectively, as shown in Figure 14.4. We can specify an intercardinal angle either in the ϕ ,θ coordinates system, or equivalently, in the α ,β coordinate system. We show both coordinate systems in Figure 14.5. The ϕ longitude lines have been omitted so as not overload the drawing.

Figure 14.4  The α ,β coordinate systems.

Figure 14.5  The ϕ ,θ and α ,β coordinates systems.

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14.4  Coordinates System Transformation Next, we must calculate the transformation from ϕ ,θ to α ,β coordinate systems. We will accomplish the transformation in two steps: first, from ϕ ,θ to Cartesian XYZ, and then from XYZ to the α ,β coordinate system. The transformation from spherical coordinates ϕ ,θ to the equivalent Cartesian coordinates (per Figure 14.6) is given by: X = R cos q sin f Y = R cos q cos f (14.4) Z = R sin q



The second transformation is from the Cartesian coordinates, X, Y, Z, to the spherical coordinates α ,β . α is given by: a = tg −1



Z sin q = tg −1 (14.5) X cos q sin f

That is, a = tg −1



tgq (14.6) sin f

Z

R

α

β

θ φ

Y

R Cos θ X Figure 14.6  Transformation from spherical to Cartesian coordinates.

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14.5  Symmetrical Antenna Pattern203

β is given by: cos b =



Y = cos f cos q (14.7) R

That is, b = cos−1(cos f cos q) (14.8



14.5  Symmetrical Antenna Pattern We can define a special case in which the antenna is symmetrical, such as when we use a circular dish or a circular phased-array antenna. Their identical azimuthal and elevation envelope patterns, as functions of ϕ and θ , are exemplified in the right part of Figure 14.7, indicating the identical −3-dB beamwidths: BWAZ and BWEL. The left part of Figure 14.7 shows an isometric view of the antenna pattern envelope, where the BS is directed upward. The −3-dB circle is shown as an example. Looking down, we can clearly see that the locus of all points having equal gain are concentric circles in the ϕ ,θ plane as shown in Figure 14.8, (and, also in the first four circles in Figure 14.1). The locus of equal gain circles drawn on the sphere is shown in Figure 14.9. We see that these equal gain circles are identical to the latitude, β , lines. The calculation for finding the gain at an intercardinal angle (ϕ ,θ ) becomes trivial: All we need do is find the β line on which the intercardinal angle (ϕ ,θ ) lies. Since all points on the β line have equal gain, the gain

BW EL

BS

BW AZ

BW EL

θ

BW AZ

φ

(b) θ

(a)

φ

Figure 14.7  (a) and (b) Symmetrical antenna patterns.

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θ

θ' (φ,θ)

θ

φ

β1

φ'

φ

β2 β3 β4

Figure 14.8  Equal gain concentric circles in the ϕ ,θ plane.

Figure 14.9  Equal gain concentric circles drawn on the sphere.

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14.5  Symmetrical Antenna Pattern205

at (ϕ ,θ ) equals the gain where the β line meets any of the cardinal planes. The equivalent angles, both ϕ ′ and θ ′, are equal to β :

f ′ = q ′ = b (14.9) In Figure 14.8 both ϕ ′ and θ ′, are equal to β 3. According to (14.8):



f ′ = q ′ = cos−1(cos f cos q) (14.10)

The intercardinal gain, G(ϕ ,θ ), is equal to the azimuthal gain, replacing ϕ with ϕ ′, or equivalently, equal to the elevation gain, replacing θ with θ ′:

G(f,q) = G(f ′) = G(q ′) = G(b) (14.11) Inserting equation (14.8) we get:



G(f,q) = G [ cos−1(cos f cos q)] (14.12)

Figure 14.10 shows an example. We are tasked to find the gain at ϕ = 32°, θ = 18°. According to (14.12), β = 36.3°.

θ´ = β = 36.3°

β = θ´= 36.3°

Figure 14.10  Equivalent angle example, symmetrical case, acute angle.

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Figure 14.11  Equivalent angle example, symmetrical case, obtuse angle.

Therefore, G(32°,18°) = G(36.3°), as shown in Figure 14.10, whereas Figure 14.11 shows an example of an obtuse angle, where G(108°,18°) = G(107.1°).

14.6  The Sum in Decibels Method in the Symmetrical Case The equivalent angle ϕ ′ can be calculated per Figure 14.8 and the Pythagorean theorem:

f ′2 = f2 + q2 (14.13)

Obviously, this is only valid for very small ϕ and θ angles since (14.13) ignores the spherical coordinate system (as if the space is flat and not spherical). In this case, we get:

G(f,q) = G(f ′) = G

(

)

f2 + q2 (14.14)

Many (but obviously not all) directional antenna patterns within the main lobe have a parabolic shaped gain (in decibels) within the main lobe, as a function of the angle:

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G = Kf2 (14.15)

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14.7  Nonsymmetrical Antenna Pattern207

In such cases, as in (8.9) for example, we get: G(f ′) = K f ′2 = K ( f2 + q2 ) = Kf2 + Kq2 (14.16)



Namely, the sum in decibels equation: G(f,q) = G(f) + G(q) (14.17)



This equation is valid only if the following conditions apply:  ϕ and θ are within the main lobe.  The antenna pattern within the main lobe has the form noted in (14.15) (or is at least close to a parabola).  ϕ and θ are so small that the difference in ϕ ′, between the exact (14.10) and the approximate (14.13) is small. Consider, for example, that if ϕ = 4° and θ = 3°, the values of both the exact ϕ and approximate ϕ ′ are 5°. But, if ϕ = 40° and θ = 30°, the exact ϕ ′ = 48.5°, whereas the approximate ϕ ′ = 50°.

14.7  Nonsymmetrical Antenna Pattern In general, antennas are not symmetrical (e.g., Yagis, rectangular reflectors, and rectangular phased arrays). The azimuthal and elevation envelope patterns are not identical. This case is more complicated than the symmetrical pattern case. Moreover, there is a basic difference between the symmetrical and nonsymmetrical cases: Whereas the special symmetrical case is a calculation, the general nonsymmetrical case is an estimation or approximation. Two additional parameters are used in the general case:  BWAZ: The –3-dB antenna beamwidth in azimuth;  BWEL: The –3-dB antenna beamwidth in elevation. In fact, we are not interested in the beamwidths’ values, but in their ratio. Figure 14.12 repeats Figure 14.7, but, in Figure 14.12, the cardinal envelope patterns are not identical. In this example, BWEL > BWAZ. Looking downward at the BS, the −3-dB circle turns to be an ellipse.

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BWEL

BS

BWAZ

θ

φ (a)

BW EL

θ

BW AZ

φ

(b) Figure 14.12  Nonsymmetrical antenna patterns.

If we observe the −3-dB ellipse, it is clear that the ratio between the ellipse axes equals the ratio between the beamwidths. The basic rationale is that the equal gain loci are ellipses as well, with the same axes ratio for all other values, not just at the −3-dB points. This conclusion, while not a proof, makes physical sense. To demonstrate that this conclusion is a good approximation, we performed the simulation described in Section 14.13. The farther away from the BS (i.e., for larger values of ϕ and θ ), the poorer the match between the approximation and the simulation.

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14.7  Nonsymmetrical Antenna Pattern209 θ

BW EL >BWAZ

φ

θ BW AZ >BWEL

φ

Figure 14.13  Equal-gain concentric ellipses in the ϕ ,θ plane.

Figure 14.13 repeats Figure 14.8, in which concentric equal-gain ellipses replaced the equal-gain circles. We show two cases: BWEL > BWAZ and BWAZ > BWEL. Figures 14.14 and 14.15 repeat the information in Figure 14.9 but now show the equal-gain ellipses rather than circles, drawn on the sphere. In Figures 14.14 and 14.15, showing one quarter of the ellipses, the beamwidth ratios are 1:2. In a manner similar to the symmetrical case, we need to find the equalgain ellipse on which the intercardinal angle (ϕ ,θ ) is located. Two cases are examined: the BWAZ > BWEL case in Section 14.9, and the BWEL > BWAZ case in Section 14.10.

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Figure 14.14  Equal-gain concentric ellipses drawn on the sphere, BWEL > BWAZ.

Figure 14.15  Equal-gain concentric ellipses drawn on the sphere, BWAZ > BWEL.

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14.8  The Sum in Decibels Method in the Nonsymmetrical Case211

14.8  The Sum in Decibels Method in the Nonsymmetrical Case The sum in decibels method presented in (14.1) can be shown to be valid for the nonsymmetrical case as well. All points on the ellipse in Figure 14.16 have equal gain, namely:

G(f,q) = G(f ′) = G(q ′) (14.18)

Rather than the Pythagorean theorem, the following ellipse equation must be used:

( )

2 ⎛ f⎞ + q ⎜⎝ f ⎟⎠ q′ ′



2

= 1 (14.19)

where ϕ ′ and θ ′ are the axes. Rearranging:



f2 +

( ) f′ q q′

2

= f ′2 (14.20)

or: 2



⎛ BWAZ ⎞ 2 f2 + ⎜ q = f ′2 (14.21) ⎝ BWEL ⎟⎠

θ θ' θ φ

φ'

φ

Figure 14.16  Equal-gain points on the ellipse.

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In the case where the azimuth antenna pattern has a parabolic shape of the gain, in decibels, as function of ϕ , within the main lobe: G(f) = K f f2 (14.22)



and the elevation antenna pattern has a parabolic shape of the gain, in decibels, as function of θ , within the main lobe: G(q) = K q q2 (14.23)



And the K constant ratio equals the square of the beamwidth’s ratio (which is expected if both have a parabolic shape): K f ⎛ BWEL ⎞ 2 = (14.24) K q ⎜⎝ BWAZ ⎟⎠



We can add (14.22) and (14.23) and get: G(f) + G(q) = K f f2 + K q q2 (14.25)



Inserting (14.24) we get: 2

⎛ BWAZ ⎞ G(f) + G(q) = K f f2 + ⎜ K q2 (14.26) ⎝ BWEL ⎟⎠ f

or:

2 ⎛ ⎛ BWAZ ⎞ 2 ⎞ (14.27) G(f) + G(q) = K f ⎜ f2 + ⎜ q ⎟ ⎝ BWEL ⎟⎠ ⎝ ⎠



Inserting (14.21): G(f) + G(q) = K f f ′2 = G(f ′) (14.28)



Inserting (14.18) we get the sum in decibels method equation:

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G(f) + G(q) = G(f,q) (14.29)

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14.9  BWAZ > BWEL213

The validity conditions are listed as follows:  ϕ and θ are within the main lobe.  The antenna patterns within the main lobe have the form of (14.22), (14.23), and (14.24), or are at least close to them.  ϕ and θ are small enough that the difference in ϕ ′ between the exact equation (for example, [14.38]), and the approximate ([14.21]) is small. As an example: BWAZ = 2 · BWEL. If ϕ = 4° and θ = 3°, both the exact and approximate ϕ ′ are 7.2°. However, if ϕ = 40° and θ = 30°, the exact value of ϕ ′ = 42.3° whereas the approximate ϕ ′ = 72°.

14.9  BWAZ > BWEL In the cases where BWAZ > BWEL, the ellipses will be horizontal. The graphical transition from a circle to an ellipse is demonstrated in Figure 14.17; the circle is stretched to a value equal to the axes ratio, b/a. The X value of each point on the circle is multiplied by b/a, along equal Y lines. The same graphical technique is performed on the sphere as demonstrated in Figure 14.18. The X-coordinate is replaced with the ϕ coordinate, the Y-coordinate is replaced with the θ coordinate, and the b/a ratio is replaced by the beamwidth ratio, BWAZ/BWEL. That is, the ϕ value of each point on the circle is multiplied by BWAZ/BWEL, along equal θ lines.

Y

a

X

b

Figure 14.17  Transition from a circle to an ellipse in the plane.

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Figure 14.18  Transition from a circle to an ellipse on the sphere.

As in the special case, we must find the equivalent angles ϕ ′ and θ ′ based on ϕ and θ . Let us assume that we are on some intercardinal angle (ϕ ,θ ) on the ellipse in Figure 14.18. Since all points on the ellipse have equal gain, we can move along the ellipse, either upward until meeting the θ plane at angle θ ′, or downward until meeting the ϕ plane at angle ϕ ′. Finding the value of θ ′ requires two steps as described in Figure 14.19. In the first step, A, we move back from the ellipse (dashed line) to the circle (solid line)—that is, from (ϕ ,θ ) to an interim angle (ϕ 1,θ ). We do it along a constant θ line, by reducing ϕ to the interim angle, ϕ 1, that equals ϕ , divided by the BWAZ/BWEL ratio:



f1 = f

BWEL (14.30) BWAZ

The interim point, (ϕ 1,θ ), lies on the latitude β , in accordance with (14.8):

b = cos−1 ( cosf1 cos q ) (14.31)

In the second step, B, we move upward along the circle β , from the interim angle (ϕ 1,θ ), to the equivalent angle being sought, θ ′. However, θ ′ equals β . So, inserting β = θ ′ and (14.30) into (14.31), we get:

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14.9  BWAZ > BWEL215

(φ1, θ)

Figure 14.19  Reaching the equivalent angle in the elevation plane.



⎞ ⎛ ⎡ BWEL ⎤ ⋅ cos q ⎟ (14.32) q ′ = cos−1 ⎜ cos ⎢f ⎥ BW ⎠ ⎝ ⎣ AZ ⎦

Finally, the intercardinal gain G(ϕ ,θ ) is equal to the elevation gain, replacing θ with θ ′:

G(f,q) = G(q ′) (14.33)

Similarly, we can find ϕ ′, which requires three steps, as described in Figure 14.20. Step A is the same step as defined in Figure 14.9. In the second step, B, we will move downward along the β circle (solid line) from the interim angle (ϕ 1,θ ), until meeting the azimuth plane at a second interim angle (ϕ 2,0), where ϕ 2 equals β . In the third step, C, we will move from the circle back to the ellipse, that is, along the constant θ = 0 line, by increasing ϕ 2 to the equivalent angle we were looking for, ϕ ′. ϕ ′ equals ϕ 2 multiplied by the BWAZ/BWEL ratio:



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f ′ = f2

BWAZ BWEL

(14.34)

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C φ2 = β

Figure 14.20  Reaching the equivalent angle in the azimuth plane.

Using (13.30), (13.31), and (13.34), and inserting β = ϕ 2, we get: f′ =

BWAZ ⎞ ⎛ ⎡ BWEL ⎤ ⋅ cos q ⎟ (14.35) ⋅ cos−1 ⎜ cos ⎢f ⎥ BWEL BW ⎠ ⎝ ⎣ AZ ⎦

Finally, the intercardinal gain G(ϕ ,θ ) is equal to the azimuthal gain, replacing ϕ with ϕ ′:

G(f,q) = G(f ′) (14.36)

We can easily see the following relation between the two equivalent angles:



q ′ BWEL = f ′ BWAZ (14.37)

As an example: we need to find the gain at ϕ = 32°, θ = 18°, but in this case the antenna is not symmetric, and the BWAZ/BWEL ratio is 1.5. Inserting, we get the equivalent elevation angle:



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1 ⎤ ⎛ ⎞ f ′ = 1.5 ⋅ cos−1 ⎜ cos ⎡⎢32 ⋅ cos18⎟ = 41.5 ⎝ ⎠ ⎣ 1.5 ⎥⎦

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14.11  Reducing the Estimation Error217

or the equivalent azimuth angle:



1 ⎤ ⎛ ⎞ q ′ = cos−1 ⎜ cos ⎡⎢32 ⋅ cos18⎟ = 27.6 ⎝ ⎠ ⎣ 1.5 ⎦⎥

and the intercardinal gain is:

G(32,18) = G(f = 41.5) = G(q = 27.6)

14.10  BWEL > BWAZ Performing the same mathematical procedure for the case where BWEL > BWAZ, we get the equivalent azimuth angle:



⎛ ⎡ BWAZ ⎤⎞ (14.38) f ′ = cos−1 ⎜ cos f ⋅ cos ⎢ q ⎥⎟ ⎝ ⎣ BWEL ⎦⎠

and the equivalent elevation angle: q′ =

BWEL ⎛ ⎡ BWAZ ⎤⎞ ⋅ cos−1 ⎜ cos f ⋅ cos ⎢ q ⎥⎟ (14.39) BWAZ ⎝ ⎣ BWEL ⎦⎠

14.11  Reducing the Estimation Error If ϕ or θ are not too far from the BS, the loci of equal gain can be assumed to be ellipses drawn on a sphere. However, this assumption is less accurate as the off-BS angles, ϕ or θ , increase. The azimuth and elevation planes generate different ellipses, as shown in Figure 14.21. The best angle for observing the difference is at an angle halfway between the azimuth and elevation planes (i.e., at α = 45°). The example in Figure 14.21 shows that at angles close to the BS, the equal gain ellipses meet, but, as we get further away from the main lobe the difference increases. In the special symmetrical case, both intercardinal gain calculations, based on the either the azimuth or elevation planes, are identical. This is not true in the general nonsymmetrical antenna case. The estimation error can be reduced by choosing the better plane a priori, by calculating the longitude angle α on which the intercardinal angle (ϕ ,θ ) lies, using (14.5). Then, choosing the closer plane:



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−45 < a < 45 G(f,q) = G(f ′) Else G(f,q) = G(q ′) (14.40)

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Figure 14.21  The azimuth and elevation planes generate different ellipses.

This choice is shown in Figure 14.22. Both ϕ ′ and θ ′ are limited to ±180°. Therefore, if the calculated chosen angle ϕ ′ or θ ′ exceeds the limit, we use the other equivalent angle.

Figure 14.22  α = ±45° longitude as guideline for choosing the closer plane.

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14.13  Verification by Simulation219

14.12  Real versus Envelope Pattern The antenna pattern within the main lobe of an antenna is usually well defined and accurately repeatable among production units. The sidelobes include peak and nulls and, as mentioned earlier, their location on the angle axis is highly frequency-dependent. At a certain angle, a peak may exist at one frequency but become a null at another. This variation is a major reason for using the sidelobe envelope shown in Figure 8.3, rather than the real pattern, in EMC analysis. We see this to be true for both cardinal and intercardinal angles. The real cardinal patterns should not be used as inputs for the intercardinal gain calculation, and we do not expect to find the real peaks and nulls at the intercardinal angles. Instead, we use the cardinal envelope patterns as the input for the calculation, and the calculated outcome is used to assess the intercardinal envelope. Moreover, we see from Figure 14.1 that the antenna gain in the intercardinal angles is, in general, lower than in the cardinal ones. This means that in using the cardinal patterns as baseline for assessing the intercardinal gain, we are taking a stringent approach.

14.13  Verification by Simulation To examine our estimation accuracy in a nonsymmetrical case, we present an example of such a simulation. The antenna chosen is a Yagi, as shown in Figure 14.2, since it contains only few nulls. The three-dimensional antenna patterns are calculated, using a mini-NEC computer program at every 5° position in azimuth and in elevation. The two-dimensional antenna patterns (the cardinal azimuth and elevation patterns), are shown in Figures 14.23 and 14.24. The calculated beamwidths are BWAZ = 48°, BWEL = 58°. We compared the calculated intercardinal gain using the estimation equation to the simulation values. Note that the real values, rather than envelope values, are used for the calculation and comparison. The average error, Δ(dB), as well as the standard deviation, σ (dB) (i.e., the difference between the intercardinal calculation and the intercardinal simulation) were found. We made this comparison over the full sphere and, for three cases of a portion of the sphere, including only 1 × 1 BW; 2 × 2 BW; and 3 × 3 BW. Table 14.1 shows the comparison results, along with the comparison between the simulation and the sum in decibels method, per (14.1). We see that the intercardinal calculation is very accurate, with an average error of only 0.4 dB, within the full sphere. The standard deviation is not too large.

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Figure 14.23  Simulated Yagi antenna pattern in azimuth.

Figure 14.24  Simulated Yagi antenna pattern in elevation.

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14.14 Examples221 Table 14.1 Comparison of Intercardinal Calculation and Simulation Full Sphere

1 × 1 BW (48° × 58°)

2 × 2 BW (96° × 116°)

3 × 3 BW (144° × 174°)

Δ (db)

σ (db)

Δ (db)

σ (db)

Δ (db)

σ (db)

Δ (db)

σ (db)

Intercardinal

0.4

4.1

0.001

0.01

0.02

0.26

0.1

0.75

Sum in decibels

8.9

9.7

0.0001

0.001

0.05

0.5

1

3.7

Conversely, the sum in decibels method within the full sphere is a poor approximation: The error is more than 20 times larger (8.9 dB), and the standard deviation is more than doubled. Conducting the comparison, we have learned the following:  The intercardinal calculation is obviously superior to the sum in decibels approximation.  Within the main lobe, both calculations give very good results.  The shapes of the patterns within the main lobe are similar to, though not exactly, parabolic. The sum in decibels equation exhibits a very good match to the mini-NEC simulated values, up to 3 × 3 BW in this Yagi antenna example. To examine the contribution of the error-reduction technique described in Section 14.11, we repeated the simulation without using the error-reduction technique. As result, the error within the full sphere grew from 0.4 to 4.2 dB. This shows the contribution from our use of this technique.

14.14 Examples We use the Yagi antenna patterns in Figure 14.23 and Figure 14.24 for two examples. Example 1 An aerial Yagi interferes with a terrestrial Yagi, seen at ϕ = 120° (quite backward) and θ = −60° downward (in the antenna coordinates system). The longitude per (14.5):



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a = tg −1

sin(−60) = −63.4 cos(−60)sin120

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Intersystem EMC Analysis, Interference, and Solutions

We follow (14.40) to choose the elevation pattern. Since BWEL > BWAZ, (14.39) is used. The equivalent angle: q′ =



48 ⎞ 58 ⎛ ⋅ cos−1 ⎜ cos120 ⋅ cos ⎡⎢(−60) ⎤⎥⎟ = 131.6 ⎝ 58 ⎦⎠ 48 ⎣

The gain, per Figure 14.24, is G(60, −120) = G(θ = 131.6) = −10 dBc. Example 2 Conversely, the terrestrial Yagi sees the aerial Yagi at ϕ = 50° and θ = 35° (in the antenna coordinates system). The longitude per (14.5) is: a = tg −1



sin35 = 42.4 cos35sin50

Following (14.40), we choose the azimuth pattern. Since BWEL > BWAZ, (14.38) is used. The equivalent angle: 48 ⎞ ⎛ f ′ = cos−1 ⎜ cos50 ⋅ cos ⎡⎢35 ⎤⎥⎟ = 55.8 ⎝ ⎣ 58 ⎦⎠



The gain, per (14.38), is G(50,35) = G(ϕ = 55.8) = −17 dBc.

14.15 Summary  Within the main lobe, the sum in decibels approximation may be used due to its simplicity and equivalence to the intercardinal calculation.  At any other angle outside the main lobe, we should use the intercardinal calculation as it produces a very low error.  If we need to choose a single calculation method, without needing to check if we are within or outside the main lobe, we should always use the intercardinal calculation method.

Reference [1] Vered, U., “Estimation of Intercardinal Antenna Pattern Based on Cardinal Data,” 21st Convention of the Electrical and Electronic Engineering in Israel, IEEE Proceedings, April 11–12, 2000, pp. 37–41.

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Chapter

15 Contents

Near-Field

15.1  Far-Field Definition 15.2 Near-Field Definition 15.3 Near-Field Distance 15.4  Very Small Antenna Near-Field Distance 15.5  Aperture Antenna Near-Field Distance 15.6  Wire Antenna Near-Field Distance 15.7 Near-Field Distance Between Two Antennas 15.8  Near-Field Path Loss 15.9  Near-Field Path Loss for Aperture Antennas

15.1  Far-Field Definition The far-field is defined as that area where several equivalent phenomena occur, described as follows:  The distance to the antenna is much larger than the antenna size. The antenna can then be regarded as a point source. Therefore, it makes no difference whether we measure the distance to the antenna at one point on the antenna or another.  The antenna pattern does not depend on the distance to the antenna.  We can calculate the path loss to the antenna in accordance with wave propagation models.  The free-space impedance (i.e., the ratio between the electric and magnetic fields) is constant and equals:

      

Z0 =

E = 120p (15.1) H

 The field strength decreases by 1/R with distance. 223

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15.2  Near-Field Definition We define the near-field as the area in which these, or at least parts of these phenomena, do not hold. We need to answer the question, What is the nearfield distance (near-field range [RNF]) below which the far-field phenomena no longer apply? The far-field distance depends mainly on the antenna type and wave length, and, in the case of directional antennas, whether it is within, or outside of the main lobe.

15.3  Near-Field Distance Since several phenomena characterize the far-field, we need to make two decisions in order to find RNF:  Which phenomenon should be used as the criterion?  What should constitute the maximum allowed deviation from the farfield value? Since we may make these decisions on an arbitrary basis, the near-field distance may be arbitrary as well. We will use the most common definitions.

15.4  Very Small Antenna Near-Field Distance Very small antennas are those whose size, D, is very small in terms of wavelength: D 0.5

10

–3

30

–22

0.07 < p ≤ 0.1

5

–3

20

–25

0.1 < p ≤ 0.2

4

–3

14

–30

0.2 < p ≤ 0.5

3

–3

12

–30

p > 0.5

10

–5

18

–30

0.07 < p ≤ 0.1

8

–6

15

–30

0.1 < p ≤ 0.2

6

–5

11

–30

0.2 < p ≤ 0.5

4

–2

10

–30

p > 0.5

4

–3

10

–20

0.07 < p ≤ 0.1

2.5

–7

–22

0.1 < p ≤ 0.2

4

–17

—

8

—

0.2 < p ≤ 0.5

4

–16

—

—

p > 0.5

2

–1

5

–7

4

–10

6

–23

—

—

0.1 < p ≤ 0.2

1.8

–5

4

–21

—

—

0.2 < p ≤ 0.5

10

–23

0.07 < p ≤ 0.1

2

–4

4

–22

—

—

p > 0.5

2.5

–2

10

–30

—

—

0.07 < p ≤ 0.1

1.5

–8

5

–22

6.5

–30

0.1 < p ≤ 0.2

2.5

–10

5.2

–30

—

—

0.2 < p ≤ 0.5

3

–14

5.8

–30

—

—

p > 0.5

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0.5 ≤ n < 1.5

1.5 ≤ n < 3.5

n < 0.5

≥ 30

0.5 ≤ n ( j − 1)



(17.9)

The antenna pattern’s pdf is the probability of i and j: ni 360 (17.10) nj pdf j = p( j) = 360 pdfv = p(i) =

We show an example of an antenna pattern based on (8.9) and its pdf in Figure 17.4. The values we chose for this example were BW = 5.2°, SL1 = −15 dBc with a limit of −40 dBc. Figure 17.4 also shows the cumulative distribution function (cdf) (although this is not a factor in our calculation). When the antenna is also scanning in elevation (for example, in several bars), the relative probability of using each bar is added to the pdf calculation. 17.4.2  Step 2: Calculating the Viewing Sector The interferer’s viewing sector is the range of angles in which the interferer sees the interfered antenna, in its antenna coordinate system. We will denote the following:  ϕ jv-1 to ϕ jv-2: Interferer’s viewing sector.  ϕ jv: Azimuth from the interferer to the interfered.  ϕ j: Azimuth of the center of the interferer’s scanning sector.  ±ϕ Scan-j: Azimuth of the interferer scanning sector. Note that the total range is the Sectj-AZ as used in Section 17.2. If the interfering radar is scanning, the allowed scanning range is limited to 0 ≤ Sectj-AZ ≤ 90°. The interferer’s viewing sector is given by: fjv-1 = fj + fScan-j − fjv

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fjv-2 = fj − fScan-j − fjv

(17.11)

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248

Intersystem EMC Analysis, Interference, and Solutions G(φ)

0 −5 − 10

dBc

− 15 − 20 − 25 − 30 − 35 − 40 − 45 − 180 − 150 − 120 − 90 − 60 − 30

0

30

60

90

120 150 180

φ

(a) pdf

0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 − 60

− 50

− 40

− 30

− 20

− 10

0

dBc

(b) cdf

1.0 0.8 0.6 0.4 0.2 0.0 − 60

− 50

− 40

− 30 dBc

− 20

− 10

0

(c) Figure 17.4  Example of antenna pattern—its pdf and cdf.

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17.4  Two Rotating Antennas Case249

If the outcome is outside the ±180° range, it must be fitted: If: fjv < −180 then fjv-new = 360 + fjv-old If: fjv > +180 then fjv-new = 360 − fjv-old



(17.12)

Figure 17.5 shows an example. If the interfering radar is rotating, the scanning range is ±180°. The interferer’s viewing sector is given by: fjv-1 = −180 fjv-2 = 180



(17.13)

In the opposite direction, the interfered viewing sector is the range of angles in which the interfered sees the interferer, in its antenna coordinate system. Equations (17.11)–(17.13) apply by exchanging each j with v, and vice versa. 17.4.3  Step 3: The Probability of a Certain Antenna Pattern Value An interference event, Gjv-j, occurs when the interfering antenna pattern value j in the direction toward the interfered, v, is jdBc. The probability of this event, p(Gjv-j), is equal to the interferer’s probability density function, pdfj if the direction from the interferer to the interfered is within the interferer’s viewing sector. The probability is zero if the direction is outside the sector:

North

330

φjv =30

φScan-j ±45

φj = 285

Direction to interfered system

φjv-2=150 φjv-1=60

240

Interferer location

Figure 17.5  Interferer’s viewing sector example.

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Intersystem EMC Analysis, Interference, and Solutions

p (G jv-j ) =

{

fjv-1 ≤ fjv ≤ fjv-2 else

pdf j (17.14) 0

In the same manner: the interference event Gvj-i will occur when the interfered antenna pattern value v in the direction toward the interferer, j, is idBc. The probability of this event, p(Gvj-i), equals the interfered probability density function pdfv if the direction from the interfered to the interferer is within the interfered viewing sector and zero if it is outside the sector:



p (Gvj-i ) =

{

fvj-1 ≤ fvj ≤ fvj-2 else

pdfv (17.15) 0

17.4.4  Step 4: The Joint Probability Density Function The event i,j occurs when the interferer’s antenna pattern toward the interfered is Gjv-j, and the interfered antenna pattern toward the interferer is Gvj-i. The probability of this event occurrence is the joint probability that is the product of the individual probabilities:

p (G jv-j ,Gvj-i ) = p (G jv-j ) ⋅ p (Gvj-i ) (17.16)

Consider, for example, a probability of interfering radar to direct a sidelobe level of −10 dBc toward the interfered radar of 0.02. The probability of the interfered radar directing a sidelobe level of −20 dBc toward the interfering radar is 0.01. The probability of the occurrence of both events (that is a total of 30 dB needs to be added to the path loss) is the product of the probabilities: 0.0002. We then multiply this probability by the probability that the interfering radar will transmit in search mode, pS. (We can ignore the tracking mode in this calculation, as the radar antenna direction cannot be anticipated.)

p (G jv-j ,Gvj-i ) = p (G jv-j ) ⋅ p (Gvj-i ) ⋅ pS (17.17)

17.4.5  Step 5: Reference Interference Margin in the Main Lobe First, we calculate the interference level, IMM, in the MM lobes as reference:

I MM = Pt + LX + Lct + Gt + L + Gr + Lcr + BWF (17.18)

where LX is the attenuation of the relevant interference type X, relative to CCI interference. We then calculate the interference margin, IMRG-MM, in the MM lobes as reference for the next calculation steps:

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17.4  Two Rotating Antennas Case251

I MRG-MM = ITh − I MM (17.19)



17.4.6  Step 6: Interference Margin of the Event i,j We calculate the interference margin IMRG-i,j of the event i,j. (The interferer’s antenna pattern toward the interfered is Gjv-j, and the interfered antenna pattern toward the interferer is Gvj-i.) I MRG-i ,j = I MRG-MM − G jv-j − Gvj-i (17.20)



17.4.7  Step 7: Interference Probability of the Event i,j We calculate the interference probability of the event i,j for all i,j combinations. If interference exists at the i,j combinations (that is, the value of IMRG-i,j is negative), then the probability p(IMRG-i,j) is the probability of the i,j event per (17.17). If there is no interference at the i,j combinations (that is, IMRG-i,j is positive), the probability of the i,j event is zero:



⎧⎪ p (G jv-j ,Gvj-i ) if I MRG-i ,j < 0 ⎫⎪ p ( I MRG-i ,j ) = ⎨ ⎬ (17.21) 0 if I MRG-i ,j ≥ 0 ⎪⎭ ⎪⎩

17.4.8  Step 8: Interference Probability Finally, we can calculate the interference probability from the interfering device to the interfered device. This is the sum, over all i and j values, from zero to the maximum known antenna side lobe level. If, for example, this maximum value is −60 dBc, then: p=

−60 −60

∑ ∑ p ( I MRG-i ,j ) (17.22) i=0 j=0

17.4.9  Step 9: Interference Probability from the Range Gate Aspect Up to this point, we have only dealt with power interference, but we must also examine the time aspect. The results must then be multiplied by the probability that the interfering radar pulse will hit the relevant interfered radar range gate. This part of the probability calculation is detailed in Section 19.9. 17.4.10 Example Figure 17.6 shows the interference probability calculation result using this procedure, as a function of path loss between the radars. In one case, both

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Intersystem EMC Analysis, Interference, and Solutions

radars are rotating over a ±180° range. In the other case, both radars are scanning over ±60°. The technical parameters of two specific radars have been used for the calculation. For example, if the path loss between the ±60° scanning radars is −150 dB, the interference probability is 13%. If only the common 5% value is allowed, the path loss between the radars needs to be changed to at least −164 dB. Both examples are marked in Figure 17.6.

P Interference

1

0.1

0.01

0.001 − 200

− 190

− 180

− 170

− 160

− 150

− 140

− 130

L(dB) Scanning sector

60

180

Figure 17.6  Example of interference probability between radars versus the path loss.

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Chapter

18 Contents 18.1  The Problem

Probability of Frequency Difference

18.2 Mathematical Background 18.3  The General Case 18.4 Continuous Frequency Allocation 18.5  Case 1: Identical Frequency Bands 18.6  Case 2: Nonoverlapping Frequency Bands 18.7  Case 3: Partially Overlapping Frequency Bands 18.8  Case 4: One Frequency Band Is Included in the Other 18.9 Fixed-Frequency and Frequency-Hopping Devices

18.1  The Problem We will consider the case of two devices, each operating within its own frequency band. The bands may be identical, or they may be different. The probability of the frequency difference between the devices is one of the more important aspects in interference calculations. Consider the following cases:  CCI interference: If the IMRG is negative, the interference probability is the probability that both devices are using the same frequency.  ACI or SEL interference: If the IMRG is negative for a certain frequency difference, dF, or less, the interference probability is the probability that the frequency difference will be below the value: dF. Therefore, it is essential that we calculate p(dF): the probability of the frequency difference between two devices, (including zero difference). Even if the frequency bands are identical, they may be fully overlapping, partially overlapping, or not overlapping at all, depending on the frequency allocation doctrine used. 253

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The p(dF) calculation is suitable both for fixed-frequency devices with independent frequency allocations and for frequency hoppers. The hopping devices need not be of the same type.

18.2  Mathematical Background The frequency that one device uses is a random variable with a certain probability distribution. The frequency that the other device uses is also a random variable with a certain probability distribution. The two probability distributions may or may not be identical. First, we must calculate the pdf of the difference between the two random variables. Then, we need to calculate the cdf, which is the integral of the pdf. The pdf of the difference between two random variables is the convolution between the two pdfs. We can easily calculate the convolution when both pdfs have a uniform distribution between lowest and highest frequencies. However, there are cases where one or both distributions are not uniform. In these instances, an equivalent calculation technique can be used (i.e., simply counting the frequency difference values). We will use a procedure we dub the counting procedure since it is applicable for all cases. First, we can deal with the general case, in which the frequency allocation is not uniform, or the devices are not necessarily using the same channel spacing. Subsequently, we will use the same technique for the special (and more common) case of uniform frequency allocation with identical channel spacing.

18.3  The General Case In the general case, each device has a different band, a different probability distribution, and a different frequency allocation. It is also possible that the devices may not have fixed channel spacing. The calculation would be as follows:  Create a matrix with all device A frequencies in the top row and all device B frequencies in the left column.  Calculate i in each square, denoting the absolute frequency difference between devices A and B, in megahertz.  Count the number of squares, Ni, in which each frequency difference, i, appears in the matrix.  Count N, the total number of squares in the matrix, which is the product of the number of frequencies of devices A and B.

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18.3  The General Case255

 The pdf is then, the probability of each frequency difference, i: pi =



Ni (18.1) N

 p(dF), the probability that the frequency difference will be equal or less than dF is the cdf; that is, the sum:

p(dF) = p(i ≤ dF) =

dF

∑ pi (18.2) i=0

By inserting pi from (18.1) we get: p(dF) = p(i ≤ dF) =

1 dF N i (18.3) N∑ i=0

 If the devices are coordinated, so that frequency reuse is not allowed (such as in an orthogonal frequency-hopping device), all squares where i = 0 are omitted from the matrix. If the devices are coordinated to keep a minimum frequency difference, all squares where i is less than the minimum are omitted as well. The total number of squares, N, does not include the omitted squares. Table 18.1 is an example. Figure 18.1 shows the result of the calculated cdf using this procedure for the case of Link 16 versus IFF. The IFF uses two frequencies, 1030 MHz and 1090 MHz, while Link 16 hops between 51 channels, every 1 MHz from 969 to 1206 MHz, but with wide guard bands around the IFF frequencies. The Y-axis is the probability that the frequency difference is equal to, or less than, the value in the X-axis. Table 18.1 Example of a Matrix for Calculating the Frequency Difference Probability Device B Frequencies

Device A Frequencies 30

32

35

42

43

51

53

32

2

0

3

10

11

19

21

33

3

1

2

9

10

18

20

34

4

2

1

8

9

17

19

35

5

3

0

7

8

16

18

36

6

4

1

6

7

15

17

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Intersystem EMC Analysis, Interference, and Solutions

Figure 18.1  Calculated frequency difference, cdf example.

For example, the probability for a frequency difference of 60 MHz or less is 35%.

18.4  Continuous Frequency Allocation The special, but more common, case is that both devices have a uniform frequency distribution, each within its own band. Both devices use the same channel spacing. (Even if this is not the case, a common channel spacing value can be chosen for the sake of the calculation.) We will use the counting procedure in this case as well. However, to avoid the need for building the matrix from scratch, and performing the count for each individual case, we will use a shortcut using general equations, derived from the matrix. There are four cases:  Case 1: Identical frequency bands.  Case 2: Nonoverlapping frequency bands.  Case 3: Partially overlapping frequency bands.  Case 4: One frequency band is included within the other. Only cases 1 and 2 need to be calculated, since they serve as building blocks used for calculating cases 3 and 4.

18.5  Case 1: Identical Frequency Bands Figure 18.2 describes the frequency bands in case 1. We will use the following notation:

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18.5  Case 1: Identical Frequency Bands257

f Min

f Max m f

Figure 18.2  Frequency bands in Case 1, identical bands.

ChSp: Channel spacing, in megahertz; i: Absolute number of channels difference between the devices (herein i is not in megahertz); fMin: Lowest frequency of the common band; fMax: Highest frequency of the common band; m: Number of channels in the common band: m=



fMax − fMin + 1 (18.4) ChSp

Example: the lowest VHF frequency is 30 MHz, the highest one is 87.975 MHz, and the channel spacing is 0.025 MHz. The number of channels is: m=



87.975 − 30 + 1 = 2320 0.025

System A MHz 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 10.0 10.5 11.0 11.5 12.0 System B MHz 12.5 13.0 13.5 14.0 14.5 15.0

0 1 2 3 4 5 6 7 8 9 10

1 0 1 2 3 4 5 6 7 8 9

2 1 0 1 2 3 4 5 6 7 8

3 2 1 0 1 2 3 4 5 6 7

4 3 2 1 0 1 2 3 4 5 6

5 4 3 2 1 0 1 2 3 4 5

6 5 4 3 2 1 0 1 2 3 4

7 6 5 4 3 2 1 0 1 2 3

8 7 6 5 4 3 2 1 0 1 2

9 8 7 6 5 4 3 2 1 0 1

10 9 8 7 6 5 4 3 2 1 0

Figure 18.3  Example of a matrix for calculating the cdf in case 1.

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We use the next example shown in Figure 18.3 for deriving the general equations. We use 10 MHz for the lowest frequency, 15 MHz for the highest frequency, and 0.5 MHz as the channel spacing. We can see that the number of channels, m = 11. We can clearly see that equal i values exist in the diagonals. By simply counting, we can easily see that the equation for Ni (i.e., the number of squares with channel spacing, i) is given by: for i=0 ⎧⎪ m N i = ⎨ 2(m − i) for 0 < i ≤ m (18.5) 0 for i>m ⎩⎪



and that the total number of squares is: N = m2 (18.6)



The cdf, that is the p(dF) equation (18.3) changes slightly to: p(dF) =

1 dF/ChSp (18.7) Ni N ∑ i=0

Figure 18.4 is an example for a case 1 calculation. Figure 18.4’s upper part shows the frequency band in megahertz, used for the example. The middle part shows Ni as function of i, per (18.5). The number of channel spacings, i, must be reconverted to frequency in megahertz. For simplicity we have chosen ChSp = 1 MHz in this and the following figures, so that i is also the frequency difference in megahertz.

18.6  Case 2: Nonoverlapping Frequency Bands Figure 18.5 describes the frequency bands in case 2. We use the following notation, shown in Figure 18.5: f1Min: Lowest frequency of the lower band; f1Max: Highest frequency of the lower band; f2Min: Lowest frequency of the higher band; f2Max: Highest frequency of the higher band; m: Number of channels in the smaller band (regardless if it is the lower or upper band); n: Number of channels in the larger band (regardless if it is the lower or upper band).

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18.6  Case 2: Nonoverlapping Frequency Bands259

Frequency bands

5 4 3 2 1 0

Number of cases

0

F MHz

50

100

150

250

300

350

400

250

300

350

400

250

300

350

400

pdf

400 300 200 100 0

0

50

100

150 200 dF MHz cdf

1.0 p(dF)

200

0.8 0.6 0.4 0.2 0.0

0

50

100

150 200 dF MHz

Figure 18.4  Example of case 1—identical bands.

f 1Min

f 2Min

f 1Max n

d

f 2Max m f

Figure 18.5  Frequency bands in Case 2—bands

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m and n may be equal, namely: m ≤ n (18.8)



m and n are given by the following equations:



− f1Min ⎞ ⎛ f2Max − f2Min ⎞ ⎤ ⎡⎛ f m = Min ⎢⎜ 1Max ⎟⎠ , ⎜⎝ ⎟⎠ ⎥ + 1 (18.9) ChSp ChSp ⎣⎝ ⎦



− f1Min ⎞ ⎛ f2Max − f2Min ⎞ ⎤ ⎡⎛ f n = Max ⎢⎜ 1Max ⎟⎠ , ⎜⎝ ⎟⎠ ⎥ + 1 (18.10) ⎝ ChSp ChSp ⎣ ⎦ d is the number of channels in the range between the bands, given by: d=



f2Min − f1Max − 1 (18.11) ChSp

When the bands are tangent, they share the same edge-channel, which is the reason for subtracting the one in (18.11). Otherwise, this channel would be counted twice. By building the same kind of matrix as in Figure 18.4, this time using a rectangular matrix of size m · n, and then counting the various i values in the diagonals, the following equations are derived: 0 ⎧ i−d ⎪⎪ Ni = ⎨ m ⎪m+n+d −i 0 ⎪⎩



for for for for for

0≤i≤d d m+n+d

The number of squares in the matrix is obviously:

N = m ⋅ n (18.13)

The p(dF) equation (18.7) applies for case 2 as well. As we will see, Figure 18.6 is an example for case 2.

18.7  Case 3: Partially Overlapping Frequency Bands In case 3, the frequency bands are partially overlapping. We calculate the frequency difference probability by dividing the bands into three subbands, A, B, and C, as shown in Figure 18.7.

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18.7  Case 3: Partially Overlapping Frequency Bands261

Frequency bands

5 4 3 2 1 0

0

50

100

150

200

250

300

350

400

250

300

350

400

250

300

350

400

F MHz pdf

Number of cases

80 60 40 20 0

0

50

100

150

200

dF MHz cdf 1.0

p(dF)

0.8 0.6 0.4 0.2 0.0

0

50

100

150

200

dF MHz Figure 18.6  Example of case 2—nonoverlapping bands.

A

B

C f

Figure 18.7  Frequency bands in case 3—partially overlapping bands.

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There are four subband combinations to calculate. They are B alone, A and B, A and C, and B and C. The value of Ni is calculated for each combination. B is calculated using the case 1 calculation. The other combinations are calculated per case 2. Note that the A and B and B and C combinations share a common edge frequency. For each value of i, we calculate the sum of the four Ni values in the four subband combinations. In much the same way, the four values of N are calculated and summed. These sums will be used to calculate the cdf. As we will see, Figure 18.8 is an example of case 3.

18.8  Case 4: One Frequency Band Is Included in the Other Figure 18.9 shows the case in which one frequency band is included within the other. We perform this calculation as in case 3, except that the A and C combination does not exist, both subbands belonging to the same device. As we will see, Figure 18.10 is an example for case 4. The graph in the middle part of Figures 18.4, 18.6, 18.8, and 18.10 (i.e., the pdf) is composed of horizontal straight lines and slanted straight lines. The lower part of Figures 18.4, 18.6, 18.8, and 18.10 is the cdf, which is the integral of the pdf. Therefore, the cdf graph is composed of slanted straight lines and parabolas, respectively.

18.9  Fixed-Frequency and Frequency-Hopping Devices 18.9.1  Fixed-Frequency Devices Our first step in calculating the interference probability is determining the frequency separation, dF, required to avoid interference between the devices (detailed in Section 22.6). In the second step, we calculate p(dF), which is the cdf of the frequency difference. Finally, the interference probability is extracted from the graph as shown in Figure 18.11, based on the example in Figure 18.4. 18.9.2  Frequency-Hopping Devices It is not necessary for frequency-hopping devices to receive all hops. Due to protection mechanisms, such as error correction or interleaving, a certain portion of the hops can be missed. Signals will still be received without interference or with an acceptable error rate. If p(dF), which is the probability of the frequency difference between the interfered hopping device and the interfering device (whether fixed or hopping) is less than the threshold value, x, there will be no interference (and vice versa):

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18.9  Fixed-Frequency and Frequency-Hopping Devices263

Frequency Bands

5 4 3 2 1 0

0

50

100

150

200

250

300

350

400

Number of cases

F MHz pdf

200 150 100 50 0

0

50

100

150

200

250

300

350

400

250

300

350

400

dF MHz cdf 1.0

p(dF)

0.8 0.6 0.4 0.2 0.0

0

50

100

150

200

dF MHz Figure 18.8  Example of case 3—partially overlapping bands.

A

B

C f

Figure 18.9  Frequency bands in Case 4—one band included in the other.

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Frequency Bands

5 4 3 2 1 0

0

50

100

150

200

250

300

350

400

Number of cases

F MHz pdf

300 200 100 0

0

50

100

150

200

250

300

350

400

250

300

350

400

dF MHz cdf 1.0

p(dF)

0.8 0.6 0.4 0.2 0.0

0

50

100

150

200

dF MHz Figure 18.10  Example of case 4—one band included in the other.



P(dF) < x P(dF) ≥ x

Interference (18.14) No Interference

where x is the maximum portion of the hops allowed to be missed. If the interferer does not transmit continuously, but rather with a certain duty cycle, (dc), then x is replaced with:

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18.9  Fixed-Frequency and Frequency-Hopping Devices265

x dc (18.15)

Example

Two identical synchronous and orthogonal frequency hopping radios, using the same full band, are mounted on a platform. How do we calculate the interference probability between these devices? To find the probability, we need to perform the following calculations:  Calculate the probability of the frequency difference between the radios. Since they use the same band, we use case 1 equations. Since the radios are synchronous and orthogonal, they never use the same frequency. Therefore, cases in which i = 0 in (18.5) are omitted, and (18.6) changes to: N = m2 − m (18.16)



 Calculate IMRG for CCI onboard the platform, using CPL, the coupling between the antennas.  Calculate the required frequency difference as described in Section 22.6. For example, dF = 47 MHz.  Find the interference probability as shown in Figure 18.11. In this example, the probability of having a frequency difference equal or less than 47 MHz is p(dF) = 0.53.

1.0

p(dF)

0.8 0.6 0.4 0.2 0.0

0

50

100

150

200

250

300

350

400

dF MHz Figure 18.11  Finding the interference probability based on the required dF.

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 Compare this result with the interference threshold x. If, for example x = 0.3, we will experience interference. Note that the coupling onboard the platform is usually frequency-dependent. If the dependency is small, an average value can be used. If the dependency is large, the calculation needs to be repeated at several frequencies.

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Chapter

19 Contents 19.1  The Problem

Probability of Pulse Interference

19.2 Definitions 19.3 Calculating RMin 19.4 Calculating RMax 19.5  Calculating the RMin Probability 19.6  Calculating the RMax Probability 19.7  Summary of Interference Probability 19.8  Various Cases 19.9  Radar Pulses Interference

19.1  The Problem This chapter deals with cases in which both interfering and interfered devices transmit and receive pulses rather than continuous signals. For example, these devices might be radars or communication devices that occasionally send short data packages. If the interference power budget, IMRG, indicates that interference is anticipated, it may not necessarily mean that a pulse-receiving device will fail, as there are mechanisms in place such as error correction and other protection techniques. If there is a certain time overlap between the interfering and interfered pulses, during which the interfered device cannot receive, but the time portion is less than an allowed threshold x, then the interfered device can perform without any interference or with acceptable degradation. Let us denote as follows: x: Maximum pulse length portion that the interferer is permitted to overlap; R: Portion of pulse length that the interferer practically overlaps.

267

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We have task of calculating the interference probability that the practical portion of pulse overlap will exceed the maximum allowed overlap: P(R > x) (19.1)



The interfered and interfering devices may or may not be the same type. In the first case, the interfered and interfering pulses need not be identical, although they usually are.

19.2 Definitions Let us use the following parameters, shown in Figure 19.1:  a: Interfered pulse length;  c: Interfering pulse length;  d: Interfering pulse repetition period. Seemingly, one parameter, b, is missing: the interfered pulse repetition period. Parameter b does not play a part in the calculation since the dead times between the interfered pulses are of no interest, as we are not concerned if interference appears while we are not receiving.

19.3 Calculating RMin Let us denote: Σt: Sum of time periods where the interfering pulse overlaps the interfered pulse;

a

g

e c

d

d

t

d

Figure 19.1  Calculating RMin.

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19.3  Calculating RMin269

ΣtMin: Minimum value Σt can have; RMin: Minimum value R can have. RMin equals: RMin =



∑ t Min (19.2) a

To calculate ΣtMin, it is convenient to attach the beginning of the interfered pulse to the end of one of the interfering pulses, as shown in Figure 19.1. In Figures 19.1–19.4, the interfering pulses are symbolized using the thinner lines and the interfered pulse using the thicker lines. We will use two additional parameters defined as: N = Rounddown



M = Roundup



{}

a d (19.3)

{}

a (19.4) d

For example, in Figure 19.2, N = 2 and M = 3. The interfered pulse length a includes whole numbers of interfering pulses plus a portion, g, of a pulse (in gray). For calculating g we will first find e, since: g = c − e (19.5)



a

f

h c

d

d

t d

Figure 19.2  Calculating RMax.

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From Figure 19.1: e = Md − a (19.6)

Inserting we get:

g = c − Md + a (19.7)



Thus, the minimum value Σt can have is: ∑ t Min = Nc + g (19.8)



and the minimum value R can have is: RMin =



Nc + g (19.9) a

But if g is negative, it should not be added; therefore: RMin =



Nc + Max { g,0} (19.10) a

19.4 Calculating RMax Let us denote: ΣtMax: Maximum value Σt can have; RMax: Maximum value R can have. RMax equals:



RMax =

∑ t Max a (19.11)

To calculate ΣtMax, it is convenient to attach the beginning of the interfered pulse to the beginning of one of the interfering pulses as shown in Figure 19.2. The interfered pulse length, a, includes whole number of interfering pulses, after subtracting a portion h of a pulse (in gray). To calculate h, we will first find f, since:

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h = c − f (19.12)

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19.5  Calculating the RMin Probability271

From Figure 19.2: f = a − Nd (19.13)

Inserting we get:

h = c + Nd − a (19.14) The maximum value Σt can have is:



∑ t Max = Mc − h

(19.15)

Hence the maximum value R can have is:



RMax =

Mc − h (19.16) a

But, if h is negative, it should not be subtracted; therefore,



RMax =

Mc − Max {h,0} (19.17) a

19.5  Calculating the RMin Probability The maximum range that an interfering pulse can shift in time, without returning to a previous position, is d. We will first investigate the case in which g is positive. Figure 19.1 serves this purpose. The maximum range that the interfering pulse can shift in time, without changing the value of RMin is g. The probability that the interference will be longer than the minimum, RMin, is the probability that the pulse will not be within g. This means that the pulse will be within the complement, d–g. The probability that the interference length equals RMin is therefore:

P ( RMin ) =

d−g g = 1 − (19.18) d d

We will next investigate the case where g is negative. For this calculation we use Figure 19.3. The maximum range that the interfering pulse can shift in time, without changing the value of RMin, is the term U in Figure 19.3. From Figure 19.3, we can see that the value of U is:

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U = Md − a − c (19.19)

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a U

c t d d

d d

d d

Figure 19.3  Calculating P(RMin) for negative g.

The probability that the interference will be longer than the minimum, RMin, is the probability that the pulse will not be within U, meaning that it will be within the complement, d–U. The probability that the interference length equals RMin is therefore: P ( RMin ) =



d −U U = 1 − (19.20) d d

Comparing (19.19) and (19.7) we see that: U = − g (19.21)



The positive and negative cases of g can thus be combined to a single equation: P ( RMin ) = 1 −



g (19.22) d

a

V c t d

d

d

Figure 19.4  Calculating P(RMax) for negative h.

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19.7  Summary of Interference Probability273

19.6  Calculating the RMax Probability Let us first investigate the case where h is positive. Figure 19.2 serves this purpose. The maximum range that the interfering pulse can shift in time, without changing the value of RMax is h. The probability that the interference length equals RMax is therefore: P ( RMax ) =



h (19.23) d

Next, we will investigate the case where h is negative. We use Figure 19.4 to this end. The maximum range that the interfering pulse can shift in time, without changing the value of RMax is the term V in Figure 19.4. From Figure 19.4, we can observe that its value is: V = a − Nd − c (19.24)



The probability that the interference length equals RMax is therefore: P ( RMax ) =



V (19.25) d

Comparing (19.24) and (19.14) we see that: V = −h (19.26)



The positive and negative cases of h can thus be combined to a single equation: P ( RMax ) =



h (19.27) d

19.7  Summary of Interference Probability Recalling that R is the portion of time the interferer’s pulses practically overlap the interfered pulse length, and that x is the maximum allowed value, note the following:  If x is smaller than RMin, there will always be interference; the interference probability is 1.  If x is larger than RMax, interference will never occur; the interference probability is 0.

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 If x is between the minimum and maximum R values, the interference probability is per the straight line connecting RMin and RMax. Equation (19.28) summarize these three cases: ⎧ 1 if x < RMin ⎪ ⎪ P ( RMax ) − P ( RMin ) ⎪ P(R > x) = ⎨ P ( RMin ) + ( x − RMin ) if RMin ≤ x ≤ RMax RMax − RMin ⎪ ⎪ 0 if x > RMax ⎪ ⎩ (19.28)

19.8  Various Cases The resulting graph describing (19.28) can take many configurations, depending on the relationship between the three parameters, a, c, and d, as demonstrated in the following sections and figures. 19.8.1  Probabilities Reach the Extreme Zero and One Values Case In the most general case, the probabilities reach the extreme values, 0 and 1, and a straight line connects the two points {P(RMin), RMin} to {P(RMax), RMax}. We show these points as the dots in Figure 19.5. If, for example the allowed threshold is x = 0.5, the interference probability is 0.36. 19.8.2  Probabilities Do Not Reach the Extreme Zero and One Values Case Figure 19.6 shows another example, in which the probabilities do not reach the extreme values. 19.8.3  a >> d Case In the special case where a is much larger than d, many narrow interfering pulses enter the wide interfered pulse. Therefore, the overlapping portion R equals the interferer’s duty cycle:



RMin = RMax =

c d

a >> d (19.29)

This case is exemplified in Figure 19.7, in which the duty cycle was chosen as c/d = 0.25. The straight line that equals the dc is vertical.

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19.8  Various Cases275

a 13 R-Min 0.385

c 5 R-Max 0.538

d g −4 11 P(R-Min) P(R-Max) 0.636 0.273

h 3

N 1

M 2

P(R>x) 1 0.9 0.8

Probability

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

R Figure 19.5  Example of pulsed interference probability.

In this case, the interference probability is: ⎧ ⎪ 0 if P(R > x) = ⎨ ⎪ 1 if ⎩



c d (19.30) c x≥ d

x
> a Case In the opposite case, where d is much larger than a, the probability that the narrow-interfered pulse will enter the wide interfering pulse equals the interferer’s duty cycle. The interference probability is thus:



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P ( RMin ) = P ( RMax ) =

c d

d >> a (19.31)

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a 8 R-Min 0.000

c 10 R-Max 1.000

d g −22 40 P(R-Mi) P(R-Max) 0.450 0.050

h 2

N 0

M 1

P(R>x)

1 0.9

Probability

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

R Figure 19.6  Another example of pulsed interference probability.

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19.8  Various Cases277

a 1000

c 3

R-Min 0.249

R-Max 0.252

d 12

g −5

h −1

N 83

M 84

P(R-Min) P(R-Max) 0.583 0.083

P(R>x) 1 0.9

Probability

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

R Figure 19.7  Pulsed interference probability for a >> d and dc = 0.25.

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This case is exemplified in Figure 19.8, where the duty cycle was chosen, again, as c/d = 0.25, but now the straight line that equals the dc is horizontal. 19.8.5  Identical Pulse Width Case In the identical case, the interferer and interfered devices use the same pulse width, a = c. In this case, the right edge of the straight line always lies at the lower right-hand corner. The left edge of the straight lies on the Y-axis, where the probability equals twice the interferer’s duty cycle, up to dc = 0.5: 2c ⎧ ⎪ RMin = 0 , RMin = d ⎨ ⎪ RMax = 1 , P ( RMax ) = 0 ⎩



a 10 R-Min 0.000

c 2500 R-Max 1.000

d g 10000 −7490 P(R-Min) P(R-Max( 0.251 0.249

a = c,

h 2490

c ≤ 0.5 (19.32) d

N 0

M 1

P(R>x) 1 0.9

Probability

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

R Figure 19.8  Pulsed interference probability for a >> d and dc = 0.25.

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19.8  Various Cases279

Figure 19.9 shows such an example. When the duty cycle value is more than 0.5, the right edge of the straight line stays at the lower right-hand corner, but the left edge of the straight line moves to a point within the figure (somewhat similar to Figure 19.5). 19.8.6  Whole Number of Interfering Pulses Case We can encounter a special case wherein the number of overlapping interfering pulses is a whole number, (including one) (i.e., the a/d ratio has no residual content). It does not matter if the pulses are or are not synchronized. If only a portion of the first overlapping pulse enters the interfered pulse, the rest of the pulse is precisely completed by the last pulse, as shown in Figure 19.10, where the whole number of pulses is three. In this case R clearly equals the interferer’s duty cycle:

a 2

c 2

R-Min 0.000

R-Max 1.000

d 10

g −6

h 0

N 0

M 1

P(R-Min) P(R-Max) 0.400 0.000

P(R>x) 1 0.9

Probability

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

R Figure 19.9  Pulsed interference probability for equal pulse widths.

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a

c t

d

d

d

Figure 19.10  Interference from whole number of pulses.

R=



c (19.33) d

Therefore, the probability equation is identical to (19.30), and the probability graph has the same shape as in Figure 19.7. 19.8.7  Additional Probability Graph Shapes The probability graph can have more shapes, as shown in Figure 19.11.

19.9  Radar Pulses Interference We usually define the maximum allowed interference for a radar as a detection range reduction to 95% of its nominal range. We must have at least 5% of the range gates free of interference. Therefore, we must calculate the probability that the interfering pulse will hit any portion of the 5% of the range gates. In the communication case, the receiving time is identical to the pulse transmission time (a short message). In radars, the opposite occurs: The receiving time, waiting for the echo, is between the transmitted pulses. We denote: PRIv: Interfered radar pulse repetition interval; PWv: Interfered radar pulse width; PRIj: Interfering radar pulse repetition interval; PWj: Interfering radar pulse width.

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19.9  Radar Pulses Interference281

R

R

R

R

Figure 19.11  Additional typical shapes of the probability graph.

The reception time is the difference; that is, PRI v − PWv (19.34)



The noninterference time, the time duration in which interference is forbidden for the radar operation, is 5% of this value: 0.05( PRI v − PWv ) (19.35)



as shown in Figure 19.12. Three overlapping states can occur, between the interfering radar pulse and the noninterference time, as shown in Figure 19.13:  Overlapping starts: The beginning of the interfering pulse is at the beginning of the noninterference time (line a in Figure 19.13).

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PRI v PWv

Reception

t No-interference time: 0.05 (PRI v- PWv) Figure 19.12  Interfered radar times.

 After duration PWj, the end of the interfering pulse is at the beginning of the noninterference time (line b in Figure 19.13).  Overlapping ends when the end of the interfering pulse meets the end of the noninterference time (line c in Figure 19.13). The total overlapping time is:

PW j + 0.05( PRI v − PWv ) (19.36)

The interference probability is the ratio between this overlapping time and the interfering radar pulse repetition interval:



Pint =

PW j + 0.05( PRI v − PWv ) (19.37) PRI j

Example The interfering radar has a 10-μ Sec pulse width and 40-μ Sec PRI, and 5% of the interfered radar reception time is 8 μ Sec. The interference probability is:



Pint =

10 + 8 = 0.45 40

This is exactly the result shown in Figure 19.6.We entered the following values in this figure: a = 0.05(PRIv − PWv) = 8, c = PWj = 10, d = PRIj = 40.

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19.9  Radar Pulses Interference283

PRI j PW j

Interferer

a

Interferer

b

Interferer

c

Interfered

t

No -interference time: 0.05 (PRIv - PWv) Figure 19.13  Relative overlapping positions between pulses.

Since interference to the range gate is forbidden, the requirement is x = 0. As seen in Figure 19.6, the interference probability, P(RMin), for x = 0 is identical to this example: 0.45. We are accustomed to radars that often change their waveform dynamically, in accordance with real-time needs. However, radars most often use the maximum available duty cycle, while changing the duty cycle components, namely PW and PRI. The parameter appearing in radar specification is usually the PRF, rather than its reciprocal, the PRI, which we have used in the calculation. Therefore, it is preferable for us to use the dc and PRF whenever possible. The relation between these parameters is given by:



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dc =

PW = PW ⋅ PRF (19.38) PRI

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Inserting this relation, we get the interference probability: Pint = dc j + 0.05(1 − dc v )



PRFj (19.39) PRFv

where: PRFv: Interfered radar pulse repetition frequency; dcv: Interfered radar duty cycle; PRFj: Interfering radar pulse repetition frequency; dcj: Interfering radar duty cycle. We can see clearly that the interfering radar duty cycle, dcj, is the lower limit of the interference probability.

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Chapter

20 Contents 20.1  Hierarchy from Bits to Message

Pulse Interference to Digital Communication

20.2  Group Error Rate 20.3  Symbol Error Rate 20.4  Frame Error Rate 20.5  Message Error Rate 20.6  Error Rates with Interference 20.7  Group Delivery Probability 20.8  Required Number of Retransmissions

20.1  Hierarchy from Bits to Message Figure 20.1 shows a typical hierarchy where bits constitute a symbol, symbols constitute a frame, and frames constitute a message. We can use the calculation method for other schemes or names such as blocks or packets as well.

20.2  Group Error Rate Prior to examining the pulse interference to digital communication, we will review the error rates of digital communication without interference. We define a group of elements by three parameters:  Q: The quantity of elements within the group;  Element error rate (EER): The probability that a single element will be incorrect;  Q Max: The maximum number of elements within the group that are allowed to be incorrect, (since error correction can 285

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Message Frames

1

2

3

L

Frame Symbols

1

2

3

N

Symbol Bits

1

2

3

n

Figure 20.1  Hierarchy from bits to message.

overcome up to QMax errors). If the number of incorrect elements is more than QMax, then the whole group is incorrect. Our goal is to calculate the group error rate (GER) based on these three parameters. The probability that a single element will be correct is the complementary probability of it being incorrect: 1 − EER (20.1)



The probability that all Q elements will be correct is:

(1 − EER )Q (20.2)

The GER in the private case where no errors are allowed at all (i.e., QMax = 0) is the complementary to one:

GER = 1 − (1 − EER )Q (20.3)

We will now examine the general case where up to QMax errors are allowed. The probability that exactly QMax errors will occur is the binomial distribution:



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⎛ Q ⎞ Q−QMax QMax (20.4) ⎜⎝ Q ⎟⎠ EER (1 − EER ) Max

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20.4  Frame Error Rate287

The probability that no more than QMax errors will occur equals the sum: QMax

⎛ Q⎞

∑ ⎜⎝ i ⎟⎠ EERi (1 − EER )Q−i (20.5)



i=0

The GER in the general case is the complementary to one: GER = 1 −

QMax

⎛ Q⎞

∑ ⎜⎝ i ⎟⎠ EERi (1 − EER )Q−i (20.6) i=0

20.3  Symbol Error Rate In this case, the group is a symbol, and its elements are the bits. The GER becomes the symbol error rate (SER), and the three parameters are the following:  Q is replaced by n bits/symbol.  The EER is replaced by the BER.  QMax is zero, since if even one bit is incorrect, the symbol is incorrect. Therefore: SER = 1 − (1 − BER )n (20.7)



20.4  Frame Error Rate In this case the group is a frame, and its elements are the symbols. The GER becomes the FER, and the three parameters are the following:  Q is replaced by N symbols/frame.  The EER is replaced by the SER.  QMax is replaced by k, the maximum number of symbols allowed to be incorrect. Therefore:



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k ⎛ N⎞ FER = 1 − ∑ ⎜ ⎟ SERi (1 − SER )N −i (20.8) i⎠ i=0 ⎝

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Inserting k = 0, reduces (20.8) to the private case: FER = 1 − (1 − SER )N (20.9)



20.5  Message Error Rate In this case the group is a message and its elements are the frames. The GER becomes the MER. The three parameters are the following:  Q is replaced by L frames/message.  The EER is replaced by the FER.  QMax is replaced by m, the maximum number of frames allowed to be incorrect. Therefore: m L ⎛ ⎞ MER = 1 − ∑ ⎜ ⎟ FERi (1 − FER )L−i (20.10) i i=0 ⎝ ⎠



Inserting m = 0, reduces (20.10) to the private case:

MER = 1 − (1 − FER )L (20.11)

20.6  Error Rates with Interference 20.6.1  General Case In a case where the interferer’s pulse width, PW, is longer than the element length but shorter than the group length, all elements received during the pulse period are lost. The GER is roughly equal to the interferer’s duty cycle, dc:

GER = dc (20.12)

In theory, we have to add two refinements to (20.12). The first is, that during the rest of the group length (1 − dc), the GER is not zero, but the GER without interference. The second is that the pulse width usually does not overlap an integer number of elements. Thus, we have to calculate the number of failed elements and round it upward. In most real cases, the contribution of these refinements is so small that we can ignore them.

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20.7  Group Delivery Probability289

20.6.2  Case 1: PW > tMessage In cases where the interferer’s pulse width, PW, is longer than the message length, tMessage, the MER equals the interferer’s duty cycle, dc:

MER = dc (20.13)

20.6.3  Case 2: tFrame < PW < tMessage In cases where the interferer’s pulse width, PW, is shorter than tMessage, but longer than the frame length, tFrame, the FER equals the interferer’s duty cycle, dc:

FER = dc (20.14) We then calculate the MER using (20.10) or (20.11).

20.6.4  Case 3: tSymbol < PW < tFrame In cases where the interferer’s pulse width, PW, is shorter than tFrame, but longer than the symbol length, tSymbol, the SER equals the interferer’s duty cycle, dc:

SER = dc (20.15) We then calculate the FER using (20.8) or (20.9).

20.7  Group Delivery Probability Many digital communication devices recognize the failure of delivering a group (e.g., a message, block, or packet) and initiate repeating the group transmissions until successfully received, usually up to a ceiling of the allowed number of repeated trials. We are interested in finding the probability of successful group delivery in n trials, since this is a case of performance degradation due to interference. The probability of successfully delivering the group in the first time is obviously the complement to the GER:

1 − GER (20.16)

The probability of requiring exactly two transmissions equals the probability of successfully delivering the group in the second trial, which obviously equals the first trial probability, 1 − GER, times the probability of the need for a second trial, which is the failure probability of the first trial, GER:

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(1 − GER ) ⋅ GER (20.17)



The probability of requiring exactly three transmissions equals the probability of successfully delivering the group in the third trial, times the probability of the need for a third trial, which equals the failure probability of both first two trials: (1 − GER ) ⋅ GER2 (20.18)



And, in general, the probability of requiring exactly n transmissions equals the probability of successfully delivering the group in the nth trial, times the need for the nth trial, which equals the failure probability of all previous (n − 1) trials: (1 − GER ) ⋅ GERn−1 (20.19)



Finally, the probability of requiring not more than n transmissions equals the sum of all previous cases: n−1

Pn = (1 − GER ) ⋅ ∑ GERi



i=0

(20.20)

Figure 20.2 illustrates several examples per (20.20).

Figure 20.2  Group delivery probability in n trials.

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20.8  Required Number of Retransmissions291

20.8  Required Number of Retransmissions The reciprocal question to the group delivery probability in n trials is: What is the required number of retransmissions, n, per a required group delivery probability? We find the answer using the previous graph. Consider, for example, how many retransmissions are required to ensure 98% group reception probability, if GER = 0.2? According to Figure 20.2, we see that the average number of retransmissions is 2.6.

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Chapter

21 Contents 21.1 Background 21.2 FrequencyHopping Times 21.3  Synchronous and Orthogonal Devices 21.4 Overlapping 21.5  Distances and Reception Delay 21.6  Solution and Objective 21.7  The Overlapping Portion 21.8  Conditions for Overlapping Interference

EMC Between Synchronous Hopping Devices 21.1 Background Interference between synchronous and orthogonal frequency hopping devices is an intrasystem case. In principle, the synchronism and orthogonality are supposed to guarantee that interference cannot occur. Practically, there are two mechanisms that can still generate interference:  ACI types, requiring a minimum frequency difference between devices, dealt with in Chapter 18.  CCI due to equal-frequency hops overlapping one another, the issue of this chapter.

21.2  Frequency-Hopping Times Let us denote the following parameters shown in Figure 21.1:  T: Hopping period;  TH: Hop length.

293

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T TH F1

F2 t

Figure 21.1  Frequency-hopping times.

21.3  Synchronous and Orthogonal Devices Frequency-hopping devices use n frequencies that are also being simultaneously used by many users. The transmitted hop and the received hop must start at the same time, or communication within the link cannot be established. Synchronous hopping devices require synchronization at a higher level than within the single link. All links in a certain area are synchronized so that all frequency hops, of all transmitters, start and end at the same time. Adding the requirement of orthogonality to synchronism requires that we use a dedicated algorithm to avoid a situation in which two users will transmit the same frequency at the same time. Figure 21.2 shows the frequencies and timing of a synchronous and orthogonal frequency-hopping device, having full frequency utilization. That is, the n frequencies are allocated to n users. Each number in Figure 21.2 represents a different user. f 1

5

4

3

7

1

7

4

8

6

2

4

2

1

2

7

5

8

4

6

3

4

3

6

5

2

1

5

8

5

3

8

5

2

1

7

8

7

6

1

4

3

6

3

7

8

6

2

t

Figure 21.2  Synchronous and orthogonal frequency-hopping.

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21.5  Distances and Reception Delay295

21.4 Overlapping CCI virtually never occurs in synchronous and orthogonal frequency-hopping devices, since, by definition, frequencies never overlap. In practice, CCI can occur, due to electromagnetic wave propagation time. The important factor in finding that a transmitted hop meets another user’s receiving hop at the same frequency is the instant that a hop starts to be received, not the instant that the hop is transmitted. Though all transmitters may start transmitting their hops at the same time, they do not reach all receivers at the same time. This discrepancy arises from the different propagation times in the desired and interfered paths, (disregarding time differences due to clock inaccuracies). On a frequency versus time scale, a transmitted interfering hop may partially, or even fully, overlap a receiving hop, creating interference. CCI may occur during that part of the received hop during which overlapping occurred. ACI may occur during the rest of the received hop interval, but since ACI is weaker than CCI, we will ignore it in this analysis.

21.5  Distances and Reception Delay We now define the following distances, as shown in Figure 21.3:  dv: Distance between the transmitter and receiver in the desired channel, in meters;  dj: Distance between the interfering transmitter and the interfered receiver, in meters. The transmission from the desired transmitter will reach its partner: the interfered receiver, after: dv c (21.1)



Desired transmitter

Interfering transmitter

dv dj

Desired receiver

Figure 21.3  Interferer and interfered distances.

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where c is the speed of light, in meters per second. A transmission from the interfering transmitter will reach the interfered receiver after: dj c (21.2)

We further define the following:

 t: Duration of time, during which the interfering hop overlaps the interfered hop;  Δt: Absolute value of the difference between the time of arrival of the leading edge of the interfering and interfered hops: d j − dv (21.3) c

Δt =



Figure 21.4 describes the transmission and reception times of the interferer and the interfered. As seen in Figure 21.4, the hops using F1 did not overlap when leaving their transmitters. Still, overlapping time t did occur in their arrival times, due to the time difference, Δt. In this example, the reception of the leading edge of the interfering hop came after the reception

Transmission

F5

F1

F6

F7

Interferer transmission

F1

F2

F3

F4

Desired transmission

d j/c Reception

d v/c

F2

F1

∆t

t

F7

F6

F1

F5

F3

Interferer reception F4

Desired reception

Overlapping t

Figure 21.4  Transmission and reception timing.

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21.7  The Overlapping Portion297

of the leading edge of the desired hop. Therefore, overlapping happened at the end of the hop.

21.6  Solution and Objective Orthogonality only requires that we avoid using the same frequency twice in the same hop. However, when overlapping occurs, orthogonality conditions are not enough. Our solution requires that we do not use the same frequency in successive hops. The objective of this chapter is for us to find whether overlapping can occur, and if so, how many hops we are required to wait until being allowed to reuse the same frequency. Our definition follows:  N: Number of hops we need to wait until allowing frequency reuse. Figure 21.5 demonstrates three examples for N. If N = 1, we need to wait for one hop. This is the conventional orthogonality case. In the example of Figure 21.4, N = 1, which is not enough to prevent overlapping. If N = 2, we must wait two hops. If N = 3, we must wait three hops.

21.7  The Overlapping Portion Let us denote the following:  x: Maximum portion of the hop length, TH, the interfering signal is permitted to overlap;

N=1

N=2

F1

F2

F3

F4

F8

F1

F9

F7

F5

F8

F1

F9

F6

F5

F8

F1

One user

N=3

Other users

t

Figure 21.5  N, the number of hops until allowing frequency reuse.

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 R: Portion of the hop length, TH, that is practically overlapped by an interferer defined: R=

t (21.4) TH

Figures 21.6 and 21.7, in which N = 2, will be used to calculate t. Figure 21.6 shows the case in which dj > dv. In the upper part of Figure 21.6, NT > Δt, hence overlapping occurs at the beginning of the interfered hop. We can see that t equals: t = TH − (NT − Δt) (21.5)



NT>∆t : Overlapping the beginning of the hop Interferer reception

F1

d j/c

Desired reception

F1

d v/c ∆t

TH t

NT

TH

NT dv.

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21.7  The Overlapping Portion299 NT∆t : Overlapping the end of the hop F1 d j/c NT d v/c

F1

∆t

TH

Interferer reception

Desired reception

t

t Figure 21.7  Calculating the overlap t, where dj < dv.

In Figure 21.6’s lower part, NT < Δt, hence overlapping occurs at the end of the interfered hop. Here we see that t equals:

t = TH + NT − Δt (21.6) Both cases can be combined to a single equation:



t = TH − NT − Δt (21.7) The portion of the hop length TH that is being overlapped is: R=



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TH − NT − Δt (21.8) TH

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Conversely, Figure 21.7 shows the case where dj < dv. Following the timing diagram in Figure 2.17, we see that (21.8) applies to the dj < dv case as well. Note that to achieve equivalency in all cases, Δt was defined as absolute value in (21.3).

21.8  Conditions for Overlapping Interference To experience overlapping interference, the following several conditions must coexist:  IMRG is negative.  N is too small to fulfill the requirements.

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Chapter

22 Contents

EMC Solutions

22.1 Background 22.2  Time-Axis Solutions 22.3 Distance-Axis Solutions 22.4 Angle-Axis Solutions 22.5 Frequency-Axis Solutions 22.6 Required Frequency Separation 22.7 Combined Distance and Frequency Separation 22.8  Changing the Specifications

22.1 Background EMC interference occurs if several factors coexist (e.g., the interfering and interfered devices are in the same vicinity, use close frequencies, and operate at the same time). We showed a schematic of this condition in Figure 1.1. One EMC solution is to break down or avoid the confluence of such factors.

22.2  Time-Axis Solutions To prevent devices from operating in the same time, it is necessary to do the following:  Deciding, in procedures, which device has usage priority, the interferer or the interfered;  Using technical means such as a blanking matrix, synchronization of the interfering and the interfered devices, or using frequency-hopping techniques.

22.3  Distance-Axis Solutions To achieve distance separation between the interfering and the interfered devices, it is necessary to do the following: 301

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 At the platform level: Making a choice of locations with high mutual isolation onboard a platform;  Within a site: Requiring a minimum distance between platforms;  In the arena: Using deployment planning, requiring minimum path loss, or increasing distance between platforms.

22.4  Angle-Axis Solutions To prevent devices from using certain azimuth and or elevation angles, it is necessary to do the following:  In procedures: Define forbidden aiming sectors;  By technical means: Prevent antennas from being directed toward forbidden angles by hardware or software means; suppress the reception from certain angles using SLC, adaptive arrays, and other techniques.

22.5  Frequency-Axis Solutions The following solutions can be considered:  Planning frequency allocation;  Requiring a minimum frequency separation between devices;  Forbidding the use of harmonic, intermodulation, and image frequencies;  Adding filtering between a device and its antenna: 1. If the interference source is in the transmitted mask or harmonics, the addition is in the interfering device. 2. If the interference source is the receiver mask, saturation, or damage, the addition is in the interfered device.

22.6  Required Frequency Separation The calculation steps are listed as follows:  Calculate the IMRG for CCI.  Find the required frequency separation, dF, as shown in Figure 22.1. Repeat the calculation once using the interfering transmitter mask and once using the interfered receiver mask.

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22.7  Combined Distance and Frequency Separation303

I MRG

Figure 22.1  Finding the required dF according to the mask.

 Choose the worst case (which will be the case with the larger dF value).  Note that if IMRG depends on different variables such as distances between devices, antennas direction, and more, it is necessary to repeat the procedure for each case.

22.7  Combined Distance and Frequency Separation The missing power, in decibels, needed to avoid interference can be achieved by a combination of distance and frequency separation; the larger the distance R, the smaller the required dF. Figure 22.2 describes this EMC solution schematically. R

Required distance separation at dF = 0

Distance and frequency combinations

Required frequency separation at R → 0 dF

Figure 22.2  Combined distance and frequency separation.

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22.8  Changing the Specifications As a result of the EMC survey, we may need to change the device specifications by adding a missing specification, or altering the value of an existing one. Obviously, we would change the specification of the transmitter if the anticipated interference were one of the transmitter-generated interference types. Similarly, we would change the specification of the receiver if the anticipated interference were one of the receiver generated interference types.

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Chapter

23 Contents

EMC Tests

23.1  The Need 23.2 Objectives 23.3  IMRG Test Procedure in the DES Approach 23.4  IMRG Test Procedure in the S/I Approach 23.5 Differences Between Anticipated and Tested Interference

23.1  The Need In many projects, we would need to schedule an EMC operational test, as part of the development phase, regardless of EMC survey results. When the operational test is not scheduled, then we need to ask two key questions after completing the EMC survey:  Question 1: Should we rely on the EMC analysis results or should we perform a verification test?  Question 2: In the case of a positive answer to question 1, should all or only part of the analyzed cases be tested? The decision should be based on four factors, listed as follows:  Functional interference impact—nuisance, mission effectiveness decrease, mission failure, or safety risk.  The interference margin, in decibels.  The interference probability.  The dependence on estimated values used as a substitute for missing parameters. 305

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The first three factors served us as guidelines for deciding whether an interference solution is required and were discussed in Section 3.4. The same rationale can serve as a guideline for these two questions. The fourth factor is of great importance since there are many cases in which default and estimated values need to be used as replacements for missing data. The greater the doubt concerning the estimated values, the greater the necessity to perform the verification test.

23.2 Objectives 23.2.1  Technical EMC Test Objectives The objective of a technical EMC test is to obtain missing data, by measuring a required EMC parameter. The lack of data during the EMC survey phase can either postpone the survey or enforce the use of default values. The test enables completion of the survey or enables repeating the analysis with a higher confidence level. 23.2.2  Operational EMC Test Objectives An operational EMC test is aimed at answering a simple question: Does interference exist or not? We have the following objectives:  Verify or dismiss the EMC survey outcome as to whether interference is anticipated or not. However, differences between prediction and test results should be expected. This issue is explained in Section 23.5.  In case of interference (whether anticipated or not), we should do the following: 1. Quantify the interference in decibel terms, as this data is required for defining the EMC solution. 2. Suggest the EMC solution. 3. Apply the EMC solution. 4. Repeat the testing to verify that interference has disappeared. Sections 23.3 and 23.4 outline the test procedure.

23.3  IMRG Test Procedure in the DES Approach Since we can perform EMC calculations using either the DES or the S/I approach, the EMC test should follow the selected approach. In this section

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23.3  IMRG Test Procedure in the DES Approach

307

we describe the test procedure when the DES approach is used in the survey. In Section 23.4 we describe the test procedure when the S/I approach is used. 23.3.1  Test Block Diagram Figure 23.1 describes the test block diagram in the DES approach. The interfered channel includes the desired transmitter and the interfered receiver. The desired signal reaches the receiver via a cable rather than over the air. The signal passes through an attenuator, and a directional coupler, aimed at adding the interfering signal. Performance measurement devices, such as a BER tester, are included if the receiver does not have internal capability of measuring the performance. 23.3.2  Deployment Instruction The device deployments must be the same as used in the EMC survey and should include such instructions as operating frequencies, antenna directions, antennas heights, and the existence of LOS between the antennas. 23.3.3  Preliminary Tests The following several preliminary issues should to be examined prior to conducting the test itself:  Clear spectrum: The spectrum must be checked to assure that other devices, if operating in the area, will not interfere with the test. While both transmitters are not yet powered, a spectrum analyzer instead of a

Interfering transmitter

Directional coupler

Interfered receiver

Attenuator

Desired transmitter

Performance measurement

Figure 23.1  Test block diagram in the DES approach.

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directional coupler is temporarily connected to the receiving antenna. In cases of nondesired transmission reception in the area, we may require a change of frequency.  Antennas’ direction: If one or both antennas have very narrow beamwidth, and the EMC analysis is assumed to be using the main lobe, fine adjustment may be needed. We measure the received interfering signal level by temporarily connecting a spectrum analyzer instead of a directional coupler to the receiving antenna. We would then adjust the antennas’ azimuth and elevation for maximum received level.  Leakage: Since the attenuator setting will be used later in the test procedure, we must assure that the signal coming out of the desired transmitter does not bypass the attenuator by in-the-air leakage. We need to know the received signal level for the end of this test. Many receivers have received signal strength indicator (RSSI) capability, but if RSSI is not available, we would measure the received signal level by adding an external measuring device. The desired received signal level is set to the receiver sensitivity by adjusting the attenuator setting. We then assure that there is no leakage by changing the attenuation in 1-dB steps and checking that the RSSI reading changes accordingly. If the RSSI reading does not follow the changes of the attenuator settings, then leakage exists. Moving the desired transmitter further away, or putting it in a metallic enclosure, will help to mitigate the RF leakage.  Link functionality: Check the link functionality without interference.  Reference attenuation: Vary the attenuation until nominal receiver performance is achieved (in terms of such factors as BER). This attenuation setting serves as a reference, even if the RSSI does not exactly equal the nominal sensitivity. We would name this attenuation level Att1.

23.3.4  Interference Test Procedure The steps involved in the interference test procedure are described as follows:  Turn the interfering transmitter on and check if the nominal receiver performance has been degraded. If there is no performance degradation, there is no interference and vice versa.  If there is performance degradation, temporarily shut the interfering transmitter off. Check that the nominal receiver performance has been restored to confirm that the interfering transmitter is the interference source.

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309

 Turn on the interfering transmitter, and then decrease the attenuation until nominal receiver performance has been restored. That new attenuation level will be noted as Att2.  The measured IMRG (negative value) equals: I MRG = Att2 − Att1 (23.1)



23.3.5  Solution and Repeated Test In cases of interference, apply the EMC solution and repeat the test to verify that interference disappeared. Note that after solving the EMC problem, a weaker interference type, not previously noticed, may now become apparent, requiring an EMC solution as well. 23.3.6 Miscellaneous The steps discussed to this point cover the principles of the test procedure. Variations are needed for different cases. For example, if the interferer is rotating or scanning radar, the interference probability needs to be measured. Further, if the interfered device is a radar, no desired transmitter exists, so the echo will need to be simulated.

23.4  IMRG Test Procedure in the S/I Approach 23.4.1  Test Block Diagram Figure 23.2 shows the test block diagram in the S/I approach.

Desired transmitter

Interfered receiver

Interfering transmitter Figure 23.2  Test block diagram in the S/I approach.

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23.4.2  Deployment Instruction Indicate the deployment instructions, as in the DES approach test. 23.4.3  Preliminary Tests The following several preliminary issues need to be considered prior to the conducting the test itself:  Clear spectrum: Same as as in the DES approach test;  Antennas’ directions: Same as as in the DES approach test;  Receiver performance: If possible, measure the link performance. 23.4.4  Interference Test Procedure—First Method  Measure the signal level S: Switch on only the desired transmitter. Measure the desired signal level S in the interfered receiver.  Measure the interfering signal level I: Switch on only the interfering transmitter. Measure the interfering signal level I in the interfered receiver.  The measured interference margin (negative value) equals:

I MRG = S − I −



() S I

r

(23.2)

23.4.5  Interference Test Procedure—Second Method  Add an attenuator between the interfering transmitter and its antenna (not shown in Figure 23.2).  Switch on only the desired transmitter and measure link performance.  Set the attenuation to 0 dB, then switch on the interfering transmitter to check if the nominal receiver performance was degraded. If there is no performance degradation, there is no interference and vice versa.  If there is performance degradation, temporarily shut off the interfering transmitter. Check that the nominal receiver performance has been restored to confirm that the interfering transmitter is the interference source.  Switch on the interfering transmitter again; increase the attenuation until the nominal receiver performance has been restored. This attenuation level will be noted as Att3.

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23.5  Differences Between Anticipated and Tested Interference311

 The measured IMRG (negative value) equals: I MRG = −Att3 (23.3)



23.4.6  Solution and Repeated Test Follow the same steps as as in the DES approach test. 23.4.7 Miscellaneous Follow the same steps as in the DES approach test.

23.5  Differences Between Anticipated and Tested Interference We should expect differences between predicted and tested interference. There are four combinations, described in Sections 23.5.1–23.5.4. 23.5.1  Case 1: No, No The most common case is that, per the EMC survey, no interference is anticipated and no interference is experienced in the test—in other words, that the test verified the analysis. This case has higher probability to occur as opposed to case 2 in Section 23.5.2 due to many safety margins used in the analysis, such as the following:  High IMRG occurs.  Real sidelobes (versus the envelope) lead to a higher probability to be in a null than in the envelope, as seen in Figure 8.3.  When the interferer and the interfered device use opposite polarizations, cross-polarization losses may exist in unanticipated cases.  Multipath and terrain obstruction may exist in a terrestrial path between the interfering and interfered devices in contradiction to the free-space worst-case assumption. Terrain obstruction may exist in the path even though worst-case LOS has been assumed.  Device performance may be better than the specification, such as experienced in the example shown in Figure 5.2. 23.5.2  Case 2: No, Yes The second case is that, per the EMC survey, no interference is anticipated but practically interference is experienced in the test. The occurrence of such

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a case might be regarded as a surprise, given the safety margins used in the analysis. In this case, we need to conduct a thorough investigation to look for the reasons, which may include the following:  Mistakes in the device data used in the survey;  Devices not meeting their specifications, including device failure;  Differences between conditions under which analysis took place and those actually used in the test (mainly concerning device deployment). The probability of such outcomes increases as (positive) IMRG gets smaller. 23.5.3  Case 3: Yes, No The third case may be that interference was anticipated, but not experienced in the test. This outcome is also common but should not be regarded as a surprise, again due to the safety margins used in the analysis. The probability for such outcomes increases, as (negative) IMRG gets smaller. 23.5.4  Case 4: Yes, Yes The last case is that, per the EMC survey, interference is anticipated and experienced in the test—in other words, that the test verified the analysis. The chances for proving that anticipated interference exists increase as (negative) IMRG gets larger.

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Appendix

Device EMC Specifications Table The following table is an example of a device EMC specification table. Device Name Subject General

Value

Unit

FMin

Megahertz

FMax

Megahertz

Channel spacing

Megahertz

modulation Transmitter

Receiver

Power

Decibels referenced to milliwatts

Tx cable loss

Decibels

Tx bandwidth

Megahertz

Tx spectrum

Decibels @ frequency difference (megahertz)

Spurious

Decibels referenced to carrier

Harmonics

Decibels referenced to carrier

Broadband Noise

Decibels referenced to milliwatts per megahertz

Sensitivity

Decibels referenced to milliwatts

Rx cable loss

Decibels

Rx bandwidth

Megahertz

Rx selectivity

Decibels @ frequency difference (megahertz)

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Device Name Subject Receiver (Cont.)

Antenna

Value

Unit

Noise figure

Decibels

Required S/N

Decibels

Required S/I

Decibels

Pulse interference immunity

Percentage

1-dB compression point

Decibels referenced to milliwatts

Damage level

Decibels referenced to milliwatts

Gain

Decibels referenced to isotropic

Az beamwidth

Degrees

El beamwidth

Degrees

Az antenna pattern El antenna pattern First sidelobe

Decibels referenced to carrier

Polarization

Radar

Antenna size

Meters

Nominal range

Kilometers

Pulse width

Microsecond

PRF

Kilohertz

Duty cycle

Percentage

RPM

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Antenna scanning range in Az

Degrees

Antenna scanning range in EL

Degrees

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About the Author Uri Vered is an RF expert with more than 50 years of experience in EMC/RFI, wave propagation, wireless communication and EW. He has performed dozens of EMC surveys and studies, mainly for the Israeli defense industry and the Israel Defense Forces, and he summarizes his practical experience and lessons learned in this book. Uri Vered was the VP of EW and communications in a defense consulting company and is currently a freelance consultant conducting EMC analysis and seminars in EMC/RFI. He received his B.Sc.-E.E. from the Technion, Israel Institute of Technology in 1968 and his M.B.A. from Tel Aviv University in 1982.

315

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Index A Accumulated interference probabilities, 238–39 Adjacent channel interference (ACI) calculation, 54–55 default value of modulated signals, 63 default value of pulsed signals, 63 defined, 45, 58 definitions of parameter, 62–63 interference effects, 60 limit, 59 narrow and wide receiver bandwidths, 61 received interference level calculation, 60–62 Adjacent channels or modulation band, 58–59 Amplifiers compression, 110 harmonic level of, 111 input voltage, 109 at lower power, 112 output voltage, 109–10 Angle-axis solutions, 302 Antenna coupling approximate free-space calculation, 188–89 equation, 188 free-space calculation, 189 frequency dependency, 189–90

measurement, 187 prediction by simulation, 188 scaling, 187 Antenna gain in intercardinal angles, 197–222 receiving, 144 symmetrical antenna pattern, 203–5 transmitters, 136–37 Antenna lobe types, 36–37 Antenna pattern, 217–18 Antenna patterns (interference probability) fixed antenna case, 245 main lobe versus sidelobe case, 242–45 problem, 241 two rotating antennas case, 246–52 Antennas aperture, near-field distance, 225–26 aperture, near-field path loss for, 228–35 corner reflector, 226 relative angles between, 191–96 very small, near-field distance, 224–25 wire, near-field distance, 226–27 Arena level EMC requirements at, 15–16 overview, 9 Arenas defined, 9

317

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EMC requirement, 15–16 Azimuth angle, 195–96, 217

Coupling. See Antenna coupling Crash threshold, 20

B Bandwidth, 39 Bandwidth factor (BWF) in CCI, 53–54 defined, 49 for harmonic interference, 74–75 interference from receiver and, 93–94 Broadband interference, 39 Broadband noise (BBN) default value, 69–70 definition of parameter, 67–68 interference effects, 70 interference from, 67–71 interference relevance, 70 level measurement illustration, 68 measuring, 68–69 received interference level calculation, 70–71 source of phenomenon, 67 BWAZ > BWEL, 213–17 BWEL > BWAZ, 217

D Damage (DMG) default value, 99 definition of parameter, 98 as interference outcome type, 38 level acquisition, 99 received interference level calculation, 99 source of phenomenon, 98 Degradation of digital communication, 39 FM, 166–67 range, 163–65 DES approach applicability, 27–28 applying for interference to radar, 266 defined, 27 interference margin (IMRG) in, 156–63 interference margin (IMRG) test procedure in, 306–9 interference outcome type, 38 participants in, 29 range degradation in, 164–65 Desensitization (DES) calculation, 157 interference margin (IMRG) impact on, 162–63 I/N versus, 157–59 I versus, 161–62 Desired signals, 7 Device level EMC requirements, 11–13 EMC specification objective, 11–12 overview, 8 Devices defined, 4, 8 EMC requirement, 12 EMC specification table, 313–14 fixed-frequency, 262 frequency-hopping, 262–66 interfering types, 36 operational requirements compliance, 12

C Circular interference coverage, 175 Cochannel interference (CCI) BWF in, 53–54 defined, 52 interference effects, 52 interference level relative to CCI, 135 received interference level calculation, 53 sources of phenomenon, 52 Compatibility electromagnetic. see EMC intersystem, 5 intrasystem, 5 RF (RFC), 3 Continuous frequency allocation, 256 Coordinate systems illustrated, 200, 201 intercardinal angle, 199–201 North Pole in, 201 transformation, 202–3

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Index319 orthogonal, 294 synchronous, 294 synchronous hopping, 293–300 Digital terrain map (DTM) models based on, 183–84 wave propagation models, 174 Distance-axis solutions, 301–2 E Electromagnetic compatibility. See EMC Electromagnetic environment, 6–7 Element error rate (ERR), 285 Elevation angle, 195–96, 216 EMC defined, 3 hierarchy levels, 7–9 one-way, 6 problem factors, 1 propagation models for, 181–86 RF compatibility and, 3 between synchronous hopping devices, 293–300 to system, 5–6 from system, 6 two-way, 6 EMC analysis calculation steps, 168 calculation time, saving, 31 least-worst case, 30–31 worst-case dilemma, 30 worst-case parameters, 31–32 EMC problems guidelines for handling, 25 need for handling, 24–26 EMC requirements at arena level, 15–16 device, approaches, 12–13 device, operational, 12 device level, 11–13 in EMC survey report, 33 intersystem, 14–15, 16 intrasystem, 14–15, 16 near-far, 16 within and between platforms, 13–14 at site level, 15 summary, 17 system, 16–17

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EMC solutions angle-axis, 302 background, 301 changing the specifications, 304 combined distance and frequency separation, 303 distance-axis, 301–2 frequency-axis, 302 required frequency separation, 302–3 time-axis, 301 EMC specification table, 313–14 EMC survey DES approach, 27–28 inclusions, 23–24 need for handling problems and, 24–26 objectives, 23 report structure, 32–34 required outcome, 24 S/I approach, 26–27 EMC survey report structure annexes, 34 device data, 33 executive summary, 32 general, 32 methodology, 32–33 requirements for, 33 results, 33 scenarios, 33 summary and recommendations, 34 systems in analysis, 33 EMC tests difference between anticipated and tested interference, 311–12 interference margin (IMRG) procedure in DES approach, 306–9 interference margin (IMRG) procedure in S/I approach, 309–11 need for, 305–6 objectives, 306 operational objectives, 306 technical objectives, 306 Emissions, 3 Equivalent angle acute angle and, 205 in azimuth plane, 216 elevation plane, 215 obtuse angle and, 206

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Error rates FER, 287–88 GER, 285–87 with interference, 288–89 MER, 288 SER, 87 Estimation error, reducing, 217–18 External systems defining content of, 5 enemy, 4 friendly, 4 neutral, 5 types of, 4–5 F Fade margin, 155–56 False reception, 38, 39 Far-field, 13–14, 223 Fast sweep, LFM radar, 82 Fifth-order intermodulation, 122 Finite difference time domain (FDTD), 228 Finite element method (FEM), 228 First-order intermodulation, 113 Fixed-frequency devices, 262 Flat-Earth propagation model, 177, 180 FM degradation, 166–67 Frame error rate (FER), 287–88 Free-space loss, 230, 231, 232 Free-space propagation model, 172, 177, 180 Frequency-axis solutions, 302 Frequency bands identical, 256–58 nonoverlapping, 258–60 one included in the other, 262 partially overlapping, 260–62 See also Probability of frequency difference p(df) Frequency dependency, coupling, 189–90 Frequency dependent rejection (FDR) accurate calculation and approximations, 51 calculating, 47–50 defined, 47 example calculation, 48 loss, 49

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Frequency difference factor (FDF) defined, 49 splitting, 55 Frequency-hopping devices, 262–66 Frequency-hopping times, 293–94 Frequency separation combined distance and, 303 required, 302–3 Full-band interference, 39 G Generic terrain-influenced model path-loss model (GETIM) defined, 184 path loss, 185 path loss exponent n, 186 result, 185 Geometric theory of diffraction (GTD), 227–28 Group delivery probability, 289–90 Group error rate (GER), 285–87 H Harmonics calculating interference close to, 75 content feasibility, checking, 73 default value, 72 definition of parameter, 72 interference, BWF for, 74–75 interference effects, 72–73 interference from, 71–75 interference margin, 75 level with back-off, 113 linear region and, 109 nth spectrum, 74–75 received interference level calculation, 73–74 second, 111, 114 slope of, 112 source of phenomenon, 71–72 third, 111 Hierarchy from bits to message, 285, 286 Hierarchy levels defined, 7 expected interference types in, 170 overview, 7–9 See also specific levels

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Index321 I Identical frequency bands, 256–58 Image rejection (IMR) definition of parameter, 101–2 interference from, 99–102 measuring, 102 received interference level calculation, 102 source of phenomenon, 99–101 In-band interference, 59, 86–87, 131–32 Intercardinal antenna patterns antenna gain in, 197–222 BWAZ > BWEL, 213–17 BWEL > BWAZ, 217 calculation and simulation comparison, 221 coordinate systems, 199–201 coordinate system transformation, 202–3 estimation error reduction, 217–18 examples, 221–22 guiding principle, 199 nonsymmetrical, 207–13 problem, 197–99 real versus envelope pattern, 219 schematic example, 198 summary, 222 symmetrical, 203–7 verification by simulation, 219–21 Yagi, 220 Intercept point (IP) calculating, 106 concept, 118–21 concept illustration, 119 defined, 118–19 values of, 119–21 Interfered pulse length, 268, 269, 270, 273 Interference , 60–62 adjacent channel (ACI), 60–64 affecting parameters, 18–19 in-band, 59, 86–87, 131–32 broadband, 39 from broadband noise (BBN), 67–71 cochannel (CCI), 52–54 from damage (DMG), 98–99 defined, 2

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error rates with, 288–89 full-band, 39 generation illustration, 2 from harmonics, 71–75 from image rejection (IMR), 99–102 at intermediate frequency (IF), 102–3 from LFM radar, 79–82 from LO radiation, 103 MM, 37 MS, 37 narrowband, 39 out-of-band (OOB), 59, 87, 131–32 from phase noise (PHN), 66–67 probability threshold, 20–21 pulse, 267–91 radar pulses, 280–84 radio frequency (RFI), 2–3 receiver intermodulation (RIM), 79, 104–9 result regions, 19 from saturation (SAT), 94–98 from SEL, 90–94 to short desired paths, 165–66 SM, 37 from spurious emissions, 64–66 SS, 37 to and from system, 5–6 threshold, 20 threshold calculation, 151, 160 from transmitter intermodulation (TIM), 75–79 transmitter spectrum, 50 Interference coverage map, 174 Interference from receiver in-band and OOB, 131–32 direct/indirect definition of interference parameter and, 89–90 DMG, 98–99 equivalent interfering signal level, 90 general aspects of, 89–90 harmonics and intermodulation, 109–31 IF, 102–3 IMR, 99–102 interference effects, 90 LO radiation, 103

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322

Intersystem EMC Analysis, Interference, and Solutions

Interference from receiver (Cont.) parameters, 40–41, 42 receiver frequency bands, 85–87 required signal to interference ratio, 87–89 RIM, 104–9 SAT and desensitization, 94–98 SEL, 90–94 Interference from transmitter ACI, 60–64 BBN, 67–71 HAR, 71–75 LFM radar, 79–82 parameters, 40, 42 PHN, 66–67 SPR, 64–66 TIM, 75 transmitter frequency bands, 57–59 Interference from transmitter and receiver ACI, 54–55 CCI, 52–54 parameters, 40 splitting FDF and, 55 transmitter spectrum, 43–51 Interference level maximum allowed, 18 received, calculating, 133–47 relative to CCI, 135 Interference margin (IMRG) background, 149–50 calculation, 152–55, 160–61 calculation steps (DES), 159–60 criterion, 150, 156–57 in DES approach, 156–63 DES calculation, 157 desired signal level I calculation, 151 DES versus I, 161–62 DES versus I/N, 157–59 EMC calculation summary, 168 of event i,j, 251 fade margin relationship, 155–56 impact on DES, 162–63 impact on range, 163–65 interference level I calculation, 151 interference plus noise calculation, 151–52 interference threshold calculation, 151, 160

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interference threshold selection, 159 inverse calculation technique, 167–68 in main lobe, 250–51 procedures and steps of calculation, 150–51 sensitivity level as wrong threshold level and, 168 in S/I approach, 150 translating from decibels, 170 Interference margin (IMRG) test procedure (DES approach) deployment instruction, 307 interference test procedure, 308–9 overview, 306–7 preliminary tests, 307–8 solution and repeated test, 309 test block diagram, 307 Interference margin (IMRG) test procedure (S/I approach) deployment instruction, 310 interference test procedure (1st method), 310 interference test procedure (2nd method), 310–11 preliminary tests, 310 solution and repeated test, 311 test block diagram, 309 Interference outcome types according to their sources, 40–42 antenna lobe, 36–37 bandwidth, 39 criteria, 35 device, 36 false reception, 39 hierarchy levels and, 169–70 outcome, 38–39 RF chain and, 134 Interference plus noise, 151–52 Interference probability antenna pattern aspect, 241 antenna pattern versus fixed antenna case, 245–46 background, 237–38 of event i,j, 251 frequency allocation and, 237–38 main lobe versus sidelobes case, 242–45 MM, 242–43

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Index323 MS, 242 from multiple interferers, 238–39 from multiple phenomena, 238 from range gate aspect, 251 RMax, 273 RMin, 271–72 SM, 242 SS, 243 two rotating antennas case, 246–52 Interference range calculating, 170–74 problem, 170–72 with terrain influence, 173–74 without terrain influence, 172–73 See also Range; Reception range Interfering mechanism desired medium, 29–30 desired transmitter, 29 medium, 29 participants in, 28–30 receiver, 29 transmitter, 28 Interfering pulse length, 268 Interfering pulse repetition period, 268 Interfering signals, 7 Intermediate frequency (IF) definition of parameter, 103 interference from, 102–3 received interference level calculation, 103 source of phenomenon, 102 Intermodulation feasibility, checking, 79, 108–9 fifth-order, 122 first order, 113 higher-order, 123 intercept point (IP) and, 118–21 introduction to, 112–18 level, calculating, 105–6 from multiple transmitters, 126–28, 131 from nonequal signals, 125–26 nth-order, 116–18 nth-order equation, 123–25 number of frequencies, 130 number of products, 128–31 odd order, 122 product bands example, 109

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second order, 113–15 second product, 107 slope of, 118, 119 source of, 114 spectrum, 121–23 third order, 115–16, 121 third-order equation, 123–25 three transmitter calculation, 129 two transmitter calculation, 128–29 Intersystem compatibility, 5 Intrasystem compatibility, 5 J Jamming ratio, 89 Joint probability density function, 250 L Least-worst case, 30–31 Legitimate signals, 7 Linear frequency modulation (LFM) radar fast sweep, 82 frequency versus time, 79 interference from, 79–82 overview, 79 signal duration, 80 slow sweep, 79–82 typical spectrum, 82 LO radiation, interference from, 103 M Main lobe calculation steps, 230–32 interference probability, 242–45 near-field path loss, 228–30 reference interference margin in, 250–51 Main-to-main (MM) interference, 37 Main-to-side (MS) interference, 37 Medium desired, 29–30 interfering, 29 Message error rate (MER), 288 Method of moments (MoM), 227 MIL-STD, 17 Mission effectiveness, 21 Mission failures, 21 Mobile receiver reception range, 179

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324

Intersystem EMC Analysis, Interference, and Solutions

N Narrowband interference, 39 Near-field defined, 224 EMC, 13–14 of Hertzian dipole, 225 Near-field distance aperture antenna, 225–26 calculating for large antenna, 225 corner reflector antennas, 226 defined, 224 between two antennas, 227 very small antenna, 224 wire antenna, 225–26 Near-field path loss for aperture antennas, 228–35 CF envelope, 229 correction factor, 229 defined, 227–28 envelope versus sidelobe level and free-space loss, 231 main lobe, 228–30 main lobe calculation steps, 230–32 sidelobes, 232–35 Nonequal signals illustrated, 127 intermodulation from, 125–26 intermodulation illustration, 127 power and spectrum viewpoints, 126 Nonoverlapping frequency bands, 258–60 Nonsymmetrical antenna pattern additional parameters, 207 equal-gain concentric ellipses, 209, 210 illustrated, 208 sum in decibels method, 211–12 symmetrical case differences, 207 See also Intercardinal antenna patterns Normalized distance, 228, 231 North Pole, 200, 201 Nth-order intermodulation, 123–25, 128 Numerical electromagnetic code (NEC), 228 O Objectives, this book, 1–2

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Off-channel rejection (OCR), 49 Off-frequency rejection (OFR), 49 One-way EMC, 6 Operational damage level, 21 Operational EMC test objectives, 306 Orthogonal devices, 294 Outcome interference types, 38–39 required, EMC survey, 24 Out-of-band (OOB) interference, 59, 87, 131–32 Overlapping conditions for interference, 300 interference, 295 overlap calculation, 298, 299 portion, 297–300 P Partially overlapping frequency bands, 260–62 Path loss, 141, 227–35 Performance criteria, 18 degradation region, 20 gradual degradation, 19 Phase noise (PHN) definition of parameter, 66 interference effects, 66 received interference level calculation, 66–67 source of phenomenon, 66 Platform level EMC requirements at, 14–15 overview, 8 Platforms defined, 4, 8 distance between, 13 EMC requirement, 14 EMC within and between, 13 intermodulation interference on, 107 operational requirements compliance, 14 Polarization loss antennas using opposite polarization, 142 antennas using same polarization, 141 cross-polarized pattern example, 144

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Index325 EMC, recommended, 143 notations, 141 table, 142 Power density, 228 Power ratios, 111 Power sum of multiple interferers, 145–47 of two signals, 146 of two signals over stronger signal, 146 Probability of frequency difference p(df) continuous frequency allocation, 256 fixed-frequency devices, 262 frequency-hopping devices, 262–66 general case, 254–56 identical frequency bands case, 256–58 mathematical background, 254 matrix for calculating, 255 need for calculation, 253–54 nonoverlapping frequency bands case, 258–60 one frequency band is included in the other case, 262 partially overlapping frequency bands case, 260–62 problem, 253 Probability of pulse interference a >> d case, 274–75 additional graph shapes, 280, 281 calculating RMin, 268–70 cases, 274–80 d >> a case, 275–78 definitions, 268 for equal pulse widths, 279 examples, 275, 276 group delivery, 289–90 identical pulse width case, 278–79 probabilities do not reach extreme zero and one values case, 274 probabilities reach extreme zero and one values case, 274 problem, 267–68 radar pulses interference, 280–84 RMax, 270–71 RMax probability, calculating, 273 RMin probability, calculating, 271–72

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summary of, 273–74 whole number of interfering pulses case, 279–80 Projects defined, 4 EMC requirements for, 16–17 Propagation models based on DTM, 183–84 communication versus EMC, 181–82 flat-Earth, 177, 180 free-space, 172, 177 GETIM, 184–86 LOS, 182 without terrain influence, 182–83 Protection ratio (PR), 89 Pulse interference to digital communication, 285–91 frame error rate (FER), 287–88 group delivery probability, 289–90 group error rate (GER), 285–87 message error rate (MER), 288 probability of, 267–84 required number of retransmissions, 291 symbol error rate (SER), 287 R Radar interference to, 166 LFM, 79–82 scanning, 241 Radar pulses example, 282–84 interfered radar times, 280–81, 282 interference, 280–84 noninterference time, 281 overlapping states, 281–82 receiving time, 280 reception time, 281 relative overlapping positions, 283 total overlapping time, 282 See also Probability of pulse interference Radio frequency interference (RFI), 2–3 Range background, 163 degradation in DES approach, 164–65

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326

Intersystem EMC Analysis, Interference, and Solutions

Range (Cont.) degradation in S/I approach, 163, 164 interference, 170–74 interference margin (IMRG) impact on, 163–65 reception, 174–80 relative, 194 Range increase factor (RIF), 171 Received interference level calculation BWF, 145 path loss and coupling, 141 polarization loss, 141–44 power sum of multiple interferers, 145–47 principle, 133–34 receiver cable loss, 144 receiver external filter, 145 receiver waveguide loss, 145 receiving antenna gain, 144 receiving antenna sidelobes, 144 relative to CCI, 135 transmitter antenna gain, 136–37 transmitter cable loss, 136 transmitter external filter, 136 transmitter power, 135 transmitter waveguide loss, 136 transmitting antenna side lobes, 138–41 Receiver bands in-band, 86–87 illustrated, 86 out-of-band, 87 reception band, 85–86 selectivity band, 86 types of, 85 Receiver intermodulation (RIM) interference default value, 105 definition of parameter, 104–5 intercept point calculation, 106 intermodulation feasibility, checking, 108–9 intermodulation level calculation, 105–6 measuring the parameter, 105 mechanism of, 104 received interference level calculation, 106–8

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source of phenomenon, 104 Receivers cable loss, 144 external filter, 145 interfered, 29 interference from, 40–41, 42, 85–132 waveguide loss, 145 Receiving antenna gain, 144 Receiving antenna sidelobes, 144 Reception band, 85–86 Reception range background, 174 base station, 179 calculating, 174–80 difference between calculations, 174 mobile receiver, 179 signal-to-interference plus noise ratio, 175–76 terms used in calculation of, 176 with terrain, 180 without terrain, 177–80 See also Interference range; Range Relative angles between antennas, 191–96 azimuth angle, 195–96 definition illustration, 192 elevation angle, 195–96 problem, 191 transformation by rotation, 191–94 types of, 192 Required signal (S/I)r default value, 88 definition of parameter, 87 jamming ratio, 89 measuring, 87–88 processing gain and, 88–89 protection ratio (PR), 89 source of phenomenon, 87 Retransmissions, required number of, 291 RF compatibility (RFC), 3 RMax calculating, 270–71 calculating for negative, 272 probability, calculating, 273 RMin calculating, 268–70

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Index327 calculating for negative, 272 minimum, 271 probability, calculating, 271–72 S Safety risks, 21 Saturation (SAT) acquiring −1-dB compression point and, 96 amplifier compression and, 94 comparing interference and, 96–97 defined, 95 definition of parameter, 96 desensitization and, 94–98 gain reduction due to, 95 interference effect, 95–96 mechanism for creating, 97 need to check, 97 received interference level calculation, 98 Scaling, 187 Scanning radars, 241 Second-order intermodulation, 113–15 SEL defined, 86 definition of parameter, 91 example, 91 indirect definition of parameter, 92–93 interference from, 90–94 received interference level calculation, 93 receiver mask measurement and, 91–92 source of phenomenon, 90–91 Selectivity band, 86 Sensitivity degradation, 38 S/I approach defined, 26–27 geographic deployment, 27 interference margin (IMRG) test procedure in, 309–11 participants in, 28 range degradation in, 163, 164 survey, 26–27 Sidelobe correction factor (CFSL) calculation steps, 233 defined, 232 illustrated, 233

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values for, 234 Sidelobes interference probability, 242–45 path loss, 232–35 Side-to-main (SM) interference, 37 Side-to-side (SS) interference, 37 Signal level viewpoint, 19 Signals desired, 7 interfering, 7 legitimate, 7 nonequal, 125–27 types of, 7 Signal-to-interference plus noise ratio, 175–76 Site level EMC requirements at, 15 overview, 8–9 Sites defined, 8–9 EMC requirement, 15 Slow sweep, LFM radar, 79–82 Spurious emissions definition of parameter, 65 interference effects, 65 interference from, 64–66 received interference level calculation, 65–66 source of phenomenon, 64–65 Sum in decibels method nonsymmetrical antenna pattern, 211–12 symmetrical antenna pattern, 206–7 Susceptibility, 3 Symbol error rate (SER), 287 Symmetrical antenna pattern equal gain concentric circles, 204 equivalent angle example, acute angle, 205 equivalent angle example, obtuse angle, 206 gain calculation, 203–5 illustrated, 203 nonsymmetrical case differences, 207 sum in decibels method, 206–7 See also Intercardinal antenna patterns

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328

Intersystem EMC Analysis, Interference, and Solutions

Synchronous hopping devices background, 293 conditions for overlapping interference, 300 distances and reception delay, 295–97 EMC between, 293–400 frequency-hopping times, 293–94 orthogonal devices and, 294 overlapping, 295 overlapping portion, 297–300 solution and objective, 297 synchronous devices and, 294 transmission and reception timing, 298 Systems content, 4 defined, 3–4 EMC from, 5–6 EMC requirements for, 16–17 EMC to, 5–6 environment, 6–7 external, 4–5 interference to and from, 5–6 T Technical EMC test objectives, 306 Third-order intermodulation defined, 115–16 equation, 123–25 spectrum of, 121 Thresholds crash, 20 interference, 20 interference probability, 20–21 Time-axis solutions, 301 Time viewpoint, 19 Transformation by rotation angles, 192 antenna spherical coordination system, 192 directional antenna, 191 equations of motion, 193–94 spherical to Cartesian coordinates, 193 Transition from circle to ellipse in the plane, 213 from circle to ellipse on the sphere, 214

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Transmission band, 57–58 Transmission line model (TLM), 228 Transmitter frequency bands adjacent channels or modulation band, 58–59 in-band, 59 illustrated, 58 out-of-band, 59 transmission band, 57–58 types of, 57 Transmitter intermodulation (TIM) default value, 76 definition of parameter, 76 interference effects, 77 interference from, 75–79 intermodulation feasibility, checking, 79 mechanism of, 76 multicoupler’s isolation versus VSWR and, 78 received interference level calculation, 77–79 source of, 75–76 Transmitters antenna gain, 136–37 cable loss, 136 desired, 29 emissions, 3 external filter, 136 interference from, 40, 42, 57–82 interfering, 28 multiple, intermodulation from, 126–28 power, 135 waveguide loss, 136 Transmitter spectrum definition, 43–45 envelope, using trapezoidal pulses, 64 FDR calculation, 47–50 interference effects, 50 received interference level calculation, 50–51 requirement example, 45 source of interference phenomenon, 46–47 specification based on measured data, 44 Transmitting antenna side lobes, 138–41

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Index329 Two rotating antennas antenna pattern examples, 248 certain antenna pattern value, 249–50 density function calculation, 246– 47 example, 251–52 interference margin of event i,j, 251 interference probability, 251 interference probability from range gate aspect, 251 interference probability of event i,j, 251 interferer’s viewing sector example, 249

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joint probability density function, 250 reference interference margin in main lobe, 250–51 viewing sector calculation, 247–49 See also Interference probability Two-way EMC, 6 W Wire antennas, 226–27 Worst-case dilemma, 30 Worst-case parameters, 31–32 Y Yagi antenna pattern, 220

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Recent Titles in the Artech House Electromagnetics Series Tapan K. Sarkar, Series Editor

Advanced FDTD Methods: Parallelization, Acceleration, and Engineering Applications, Wenhua Yu, et al. Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method, Allen Taflove, editor Analysis Methods for Electromagnetic Wave Problems, Volume 2, Eikichi Yamashita, editor Analytical and Computational Methods in Electromagnetics, Ramesh Garg Analytical Modeling in Applied Electromagnetics, Sergei Tretyakov Applications of Neural Networks in Electromagnetics, Christos Christodoulou and Michael Georgiopoulos CFDTD: Conformal Finite-Difference Time-Domain Maxwell’s Equations Solver, Software and User’s Guide, Wenhua Yu and Raj Mittra The CG-FFT Method: Application of Signal Processing Techniques to Electromagnetics, Manuel F. Cátedra, et al. Computational Electrodynamics: The Finite-Difference Time-Domain Method, Second Edition, Allen Taflove and Susan C. Hagness Electromagnetic Waves in Chiral and Bi-Isotropic Media, I. V. Lindell, et al. Engineering Applications of the Modulated Scatterer Technique, Jean-Charles Bolomey and Fred E. Gardiol Fast and Efficient Algorithms in Computational Electromagnetics, Weng Cho Chew, et al., editors Fresnel Zones in Wireless Links, Zone Plate Lenses and Antennas, Hristo D. Hristov

Grid Computing for Electromagnetics, Luciano Tarricone and Alessandra Esposito High Frequency Electromagnetic Dosimetry, David A. Sánchez-Hernández, editor Intersystem EMC Analysis, Interference, and Solutions, Uri Vered Iterative and Self-Adaptive Finite-Elements in Electromagnetic Modeling, Magdalena Salazar-Palma, et al. Numerical Analysis for Electromagnetic Integral Equations, Karl F. Warnick Parallel Finite-Difference Time-Domain Method, Wenhua Yu, et al. Practical Applications of Asymptotic Techniques in Electromagnetics, Francisco Saez de Adana, et al. A Practical Guide to EMC Engineering, Levent Sevgi Quick Finite Elements for Electromagnetic Waves, Giuseppe Pelosi, Roberto Coccioli, and Stefano Selleri Understanding Electromagnetic Scattering Using the Moment Method: A Practical Approach, Randy Bancroft Wavelet Applications in Engineering Electromagnetics, Tapan K. Sarkar, Magdalena Salazar-Palma, and Michael C. Wicks For further information on these and other Artech House titles, including previously considered out-of-print books now available through our In-Print- Forever® (IPF®) program, contact: Artech House Publishers 685 Canton Street Norwood, MA 02062 Phone: 781-769-9750 Fax: 781-769-6334 e-mail: [email protected]

Artech House Books 16 Sussex Street London SW1V 4RW UK Phone: +44 (0)20 7596 8750 Fax: +44 (0)20 7630 0166 e-mail: [email protected]

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