The Exact Synthesis Of Distributed RC Network

144 Pages·1963·3.14 MB·English

by  Ralph W. Wyndrum, Jr.

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AFCRL-63-157
TECHNICAL REPORT 4oo-76
THE EXACT SYNTHESIS OF DISTRIBUTED RC NETWORI
Ralph W. Wyndrum, Jr.
NEW YORK UNIVERSITY
COLLEGE OF ENGINEERING
DEPARTMENT OF ELECTRICAL ENGINEERING
Laboratory for Electroscience Research
University Heights
New York 53, New York
THIRD SCIENTIFIC REPORT
Contract AF 19(628)-379
Project 5628
Task 562801
May 1963
Prepared
for
AIR FORCE CAMBRIDGE RESEARCH LABORATORIES
OFFICE OF AEROSPACE RESEARCH
UNITED STATES AIR FORCE
BEIFORD, MASSACHUSETTS
ii
NOTICE
Requests for additional copies by Agencies of the Department
of Defense, their contractors, and other Government agencies
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Department of Defense contractors must be established for DDC
services or have their "need-to-know" certified by the cognizant
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All other persons and organizations should apply to the:
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iii
The research reported herein received partial sponsorship from
both the Air Force Cambridge Research Laboratories, under contract
AF 19(628)-379, and the American Machine and Foundry Corporation.
This assistance is gratefully acknowledged.
iv
ABSMUCT
The research reported in this thesis is devoted to the develop-
ment -f network synthesis techniques which are exact and applicable to
distributed RC functions. Complex variable transformations are introduced
which greatly simplify the representation and use of the hyperbolic com-
plex frequency functions of distributed RC structures. Realizability
conditions are given for the existence of distributed RC driving point
and transfer functions, and the actual synthesis techniques are described
in detail. Ecamples of the methods introduced herein are verified by
experimental data.
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TABLE OF CONTEB
Page
CHAPTER 1: An Introduction to Distributed RC Networks 1
CHAPTER 2: The Mathematical Characterization of RC Functions 10
CHAPTER 3: The Approximation Problem 27
CHAPTER 4: The Synthesis of Y Driving Point Immittances 45
CHAPTER 5: The Synthesis of BC Transfer Functions 66
CHAPTER 6: The Design of Experimental AC' Networks 99
CHAPTER 7: Conclusions 117
REFERENCES 119
VITA 122
APPRDIX I 123
APPEDIX II 129
DISTRIBUTION LIST 134
vi
LIST OF ILLUSTRATION
Page
1-1 WC Line with Arbitrary Geometry 3
1-2 Uniform RC Line 3
1-3 Exponential RC Line 4
1-4 Notch Filters
1-5 Synthesis Procedure 6
2-1 Possible Interconnections of RC Networks 11
2-2 UfRC One Ports 13
2-3 s - S Transformations 16
2-4 RCR Line Segment 21
2-5 P' - s Mapping 22
2-6 R- Driving Point Impedance Plots 25
2-7 RCR Transfer Impedance Plots 25
3-1 Magnitude Functions for BC Synthesis 31
3-2 Magnitude Functions for RC Synthesis 32
3-3 Magnitude Functions for RC Synthesis 33
3-4 Magnitude Functions for RR Synthesis, a = 1/2 35
3-5 Magnitude Functions for RCR Synthesis, a = 1 36
3-6 Magnitude Functions for RCB Synthesis, a = 2 37
3-7 Magnitude Functions for R- Synthesis 38
3-8 Approximation of A(s) by Exponential Polynomials 39
3-9 Plot of Weighting Factor in coth 1 40
2
vii
4-1 Cascaded RC Line Segments 53
4-2 RC Network Realization 57
4-3 Illustrations of Example of Section 59
4-4 RC Network to Realize Function of Fig. 4-3 61
4-5 Experimental Verification of Example 63
5-1 A Cascade-Stub Realization 70
5-2 Cascade-Stub Extraction Cycle 70
5-3 A Brune RC Cycle Equivalence 79
5-4 Equivalent RC Networks 79
5-5 Application of Theorem IX 82
5-6 Equivalent RC Networks 82
5-7 Three RC Configurations 82
5-8 High Pass R- Network Characteristic 87
5-9 Typical RC Microelectronic Circuitry 89
5-10 Required Transfer Network Configuration 90
5-11 Required Gain Characteristic 90
5-12 Overall Network Characteristic 92
5-13 Final RC Network 93
5-14 Cascade-Stub Physical Embodiment 93
5-15 Bandpass Characteristic 97
6-1 Teledeltos RC Model 100
6-2 -CLRi ne Segment 100
6-3 Slopes of Exponential Factors 105
viii
6-4 Slopes of Second Order Ebcponential Factors 106
6-5 Theoretical Low Pass Filter Characteristic 1.11
6-6 Four Section Filter Characteristics 112
6-7 Law Pass Filter Embodiment 115
A- 2-1 LRC Segment 130