lc_circuits.pdf

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LC Circuits
by
Rufus P. Turner, Ph. D.
Howard W. Sams & Co., Inc.
4300 WEST 62ND ST. INDIANAPOLIS, INDIANA 46268 USA
Preface
Copyright © 1980 by Howard W. Sams & Co., Inc.
Indianapolis, Indiana 46268
FIRST EDITION
FIRST PRINTING -1980
All rights reserved. No part of this book shall be
reproduced, stored in a retrieval system, or
transmitted by any means, electronic, mechanical,
photocopying, recording, or otherwise, without
written permission from the publisher. No patent
liability is assumed with respect to the use of the
information contained herein. While every
precaution has been taken in the preparation of
this book, the publisher assumes no responsibility
for errors or omissions. Neither is any liability
assumed for damages resulting from the use of
the information contained herein.
International Standard Book Number: 0-672-21694-9
Library of Congress Catalog Card Number: 79-57616
of inductance and capacitance, the LC circuit, is the basic
selective unit of electronics. Originally delegated to the tun-
ing of radio apparatus, the LC circuit has found application
far afield in many areas of electronics.
Technologically and historically, the familiar combination
This book describes a number of practical LC circuits and
offers enough background theory to promote the understanding
of them. A sufficient amount of space has been devoted also to
resistance, since that property is inherent in practical induc-
tors and capacitors.
Although the material is addressed to the electronics stu-
dent, technician, and experimenter, more advanced readers
may find certain parts of it useful, if only for reference pur-
poses. A minimum of mathematics is employed-physical ex-
planations being preferred where feasible-and frequent il-
lustrative examples demonstrate the necessary calculations.
virtuoso.
RUFUS P. TURNER
I hope that this book will serve both the novice and the
Printed in the United States of America.
2.7
2.8
2.9
Broadband Tuning
Range Coverage
Self -Resonance
2.10 Symmetrical Circuits
2.11 DC -Tuned Circuits
2.12 Wave Traps
2.13 Wavemeters
2.14 Varactor Frequency Multiplier
50
51
53
53
54
56
57
59
CHAPTER 3
Contents
CHAPTER 1
FUNDAMENTAL THEORY
7
7
FILTERS
60
60
62
Basic Filtering Properties of L and C
Filter Sections
Wave Filters
3.4
Power -Supply Filters
3.1
3.2
3.3
64
72
CHAPTER 4
BRIDGES AND OTHER MEASURING DEVICES
4.1
.
The AC Cycle -Rate of Change
1.2
Nature of Resistance
1.3
Nature of Inductance
1.4
Nature of Inductive Reactance
1.5
Nature of Capacitance
1.6
Nature of Capacitive Reactance
1.7
Combined Reactance in LC Circuits
1.1
11
15
19
76
Figure of Merit, Q
1.10 Nature of Practical Inductor
1.11 Pure L and C in Combination
1.12 Practical L and C in Combination
1.13 Inductive Coupling
1.14 Time Constant
1.15 Oscillations in LC Circuit
1.16 Range of Application of LC Circuits
CHAPTER 2
TUNED CIRCUITS
2.1
Series -Resonant Circuit
2.2
2.3
2.4
2.5
2.6
1.8
1.9
Resonance
20
24
26
26
27
28
28
30
31
32
4.2
4.3
4.4
4.5
4.6
4.7
Anderson Bridge
Hay Bridge
Maxwell Bridge
Owen Bridge
Resonance Bridges
Bridged -T Null Network
Resonant Circuit as Measuring Device
76
77
78
79
80
82
84
APPENDIX A
ANGULAR VELOCITY (w)
35
36
86
APPENDIX B
37
37
40
42
43
45
REACTANCE OF INDUCTORS AT 1000 Hz
.
.
87
Parallel -Resonant Circuit
Resonant -Circuit Constants
Selectivity
Circuit Q
Coupled Resonant Circuits
APPENDIX C
REACTANCE OF CAPACITORS
.
.
46
88
APPENDIX D
RC TIME CONSTANTS
90
APPENDIX E
RL TIME CONSTANTS
91
CHAPTER 1
APPENDIX F
RESONANT FREQUENCY OF LC COMBINATIONS
.
.
93
Fundamental Theory
This chapter digests those parts of basic electronics that
are essential to an understanding of
inductance -capacitance
(LC) circuits. These are specific items requiring
for their
understanding a general familiarity with electrical theory
and
reader has that background.
1.1 THE AC CYCLE-RATE OF CHANGE
APPENDIX G
CONVERSION FACTORS
.
.
95
the mathematics of electronics, and it is assumed that the
Fig. 1-lA depicts a sinusoidal ac voltage in terms
of a
vector rotating at constant velocity. The magnitude of this
vector is E., the maximum value attained by the ac voltage.
As the vector moves in a counterclockwise direction from its
starting point at the horizontal axis, it generates an angle 0
which increases from initial zero to 360° (27r radians) in each
complete rotation. If the figure is drawn to scale, the instan-
taneous voltage, e, is depicted by the length of the half chord
extending from the tip of the vector to the horizontal
axis.
(Although the vector is rotating at constant angular velocity,
the length of this half chord does not change at a constant
rate; see Table 1-1.)
From Fig. 1-1A, it is easily seen that the instantaneous
voltage is zero at 0°, since here the half chord has no length
at
all, and is maximum at 90°, since here the half
chord has
its maximum length. Thus, instantaneous voltage e starts at
zero, increases to the maximum positive
value (+Emax) at 90°
(7r/2 radians), returns to zero at 180° (7r radians), increases
to
7

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