Worked Examples in Basic Electronics

285 Pages·1967·9.325 MB·English

by  P. W. Crane and N. Hiller (Auth.)

Worked Examples in
Basic Electronics
BY
P. W. CRANE,
A.M.I.E.R.E.
Lecturer in Electronics
Cambridgeshire College of Arts and Technology
PERGAMON PRESS
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Copyright © 1967 Pergamon Press Ltd.
First edition 1967
Library of Congress Catalog Card No. 66-29586
Printed in Great Britain by Bell and Bain Ltd., Glasgow
This book is sold subject to the condition
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Acknowledgements
THANKS are due to the Examinations Committee of the Institution
of Electronic and Radio Engineers for permission to use questions
from past Graduateship Examinations; the Principals of Swindon
and Corby Technical Colleges for permission to use questions
from past H.N.C. papers; Mr. N. Hiller for his help and guidance
during the preparation of the work; Mr. D. G. Brown for his
assistance in checking the typescript and many calculations.
1. In general, symbols and abbreviations used in the text are
those recommended by the British Standards Institution in
B.S. 1991, Parts 1 and 6.
2. Specimen answers given to questions from the Graduateship
Examination papers of the Institution of Electronic and Radio
Engineers are the author's and are not necessarily endorsed by the
Institution.
Vlll
Preface
ONE of the difficulties experienced by students on Engineering
Courses is that the time available for formal instruction is very
limited. Contact time with their instructors is necessarily devoted
to establishing the basic principles of the relevant technology.
Too little time is available for the important task of solving
problems and obtaining numerical answers.
To rectify this situation this book is published as one of a
series devoted entirely to Worked Examples and Problems which
will enable the student to follow through a problem step-by-step
and then to attempt to solve similar problems with a minimum of
supervision. It will be an essential aid to his formal education
and training as a potential technician or professional engineer
whether on a part-time, sandwich or full-time course.
This book contains a limited amount of material on semi-
conductors since it is intended to be directly complementary to a
book in this series entitled Worked Examples on Semiconductor
Circuits by Abrahams and Pridham.
N. HILLER
IX
K*
CHAPTER 1
Derivation of Basic Formulae
TWENTY-NINE basic formulae are derived in this chapter, and
special note is made of the circuit conditions which must exist if
any particular formula is to be valid. Where possible a basic
circuit is employed in each section, and either a constant current
equivalent circuit, or a constant voltage equivalent circuit, is used
to predict the a.c. performance of that circuit, provided the active
device is biased on the linear portion of its characteristics, and
the alternating input signal is small enough to render amplitude
distortion negligible. Hence, when either type of equivalent circuit
is used, the fact that the circuit in question is linear is not included
under the Assume heading of the relevant section—it is understood.
A knowledge of complex numbers and differentiation is
sufficient to enable the reader to follow the mathematical steps
used to arrive at any result in any of the following sections.
Electrical steps are explained in some detail and at the end of
each section a Summary is included which contains conclusions
drawn from the treatment and the derived formulae.
1.1. Voltage Amplification Factor of a Resistance-
loaded Triode Valve
BASIC CIRCUIT I l
l H.T. Supply
VinfO
BIAS
FIG. 1.1
1
2 WORKED EXAMPLES IN BASIC ELECTRONICS
CONSTANT VOLTAGE EQUIVALENT CIRCUIT
A · Anode
1
G E · Earth
Λ
Jyfl G-Grid
n< K - Cathode
?
Κ,Ε
FIG. 1.2
Assume
1. The voltage input V and resulting anode current l vary
in a
sinusoidally.
2. The valve operates either on the linear portion of its static
characteristic or with constant values of valve parameters
μ, g and r .
m a
3. H.T. and bias supplies fix the operating point of the valve and
the values of /x, g and r . In pentode applications the screen
m a
voltage is assumed fixed, and feedback at the signal frequency,
negligible.
These comments apply for each constant voltage or constant
current equivalent circuit used in this chapter and will not be
stated on future occasions.
>oof of the Gain Formula
From the equivalent circuit of Fig. 1.2,
i.=
v =
0 iaRL
-|"Vin*L
r + R
a L
DERIVATION OF BASIC FORMULAE 3
The voltage amplification factor V.A.F. is given by V/V ,
0 !n
therefore,
V.A.F. = (1.1)
r.+&L
Summary
1. The gain realized by the single valve stage must always be less
than the amplification factor μ.
2. The valve acts as a constant voltage generator which produces
an e.m.f. μ times larger than the grid input voltage, and 180 deg
out of phase with it. This phase reversal is denoted by the
minus sign in equation (1.1).
3. The constant voltage generator of the equivalent circuit of
Fig. 1.2 has an internal resistance equal to the anode slope
resistance of the valve (r).
a
4. If the anode load R is not purely resistive then V/V
L 0 in
= —/xZ /(r +Z ), where Z is the load impedance at the
L a L L
frequency of the sinusoidal input voltage.
1.2. Stage Gain of a Resistance-Capacitance Coupled
Voltage Amplifier (Low Audio-frequency Working)
BASIC CIRCUIT
— ·Η.Τ.+
Vin ©
^Η.Τ,-
FIG. 1.3
4 WORKED EXAMPLES IN BASIC ELECTRONICS
CONSTANT VOLTAGE EQUIVALENT CIRCUIT CORRECT AT ALL
FREQUENCIES
I, Cç
-—?
I
I
Φ«
I I
I I
-* -4—
FIG. 1.4
C is the coupling capacitor to a following stage.
c
R is the grid leak resistor of a following stage.
g
C is the capacitance between anode and cathode of the valve.
ak
C is the input capacitance of a following stage, including
in
inter-wiring and stray capacitance effects.
The equivalent circuit of Fig. 1.4 can be simplified over certain
limited frequency ranges.
CONSTANT VOLTAGE EQUIVALENT CIRCUIT AT Low
FREQUENCIES
FIG. 1.5
Assume
1. The bias voltage provided by C and R gives the required
K K
working point down to zero frequency with no ripple.
DERIVATION OF BASIC FORMULAE 5
2. The capacitive reactances due to C and C have negligible
ak in
shunting effect on R or R at these frequencies.
L g
Proof of the Gain Formula*
From Fig. 1.5,
° " r. + Z m
AB
Therefore
v - -^" z
And V - V .— R"
0 AB
Ra + :
r Z 1
a + ÄB
J<*>C
C
Ä (l+>C Ä )
And Z = L c g
ΛAβR l+>C (tf + iO
c L
V
0
Stage gain m = —-
* i n
m =
- * (i+>,c jy *
M L c
1
[-^^I-^Ï^SOÏÏ ^]
P ' (1.2)
*C,
*An alternative method of deriving equations (1.2) and (1.5) is by the applic-
ation of Thévenin's theorem to the equivalent circuits of Fig. 1.5 and Fig. 1.8
respectively (see Chapter 2 Example 2.)
6 WORKED EXAMPLES IN BASIC ELECTRONICS
The low-frequency voltage gain is 0*707 of its maximum value
when real and imaginary terms in the denominator of equation
(1.2) are equal.
Hence, r R + (r + R )R = {"Λ*υ
a L e L g
where ω = 2π/ radians per second, and/i cycles per second is
1 χ
the frequency at which the gain has reduced to 0*707 of its
maximum value.
Therefore f = p— = cycles per second. (1.3)
t Ki2H
Summary
1. It can be seen from equation (1.2) that the stage gain is zero
when the frequency of the applied voltage is zero.
2. As the frequency is increased from zero, the imaginary term
in the denominator of equation (1.2) reduces until the gain
reaches a maximum value (m ) given by
max
_ -μR R
L g
r RL + (r + R )R
a a L g
3. When the low-frequency response is 3 dB down (stage gain
= 0*707 m ) the frequency of the applied voltage is given
max
approximately by/j = \\2-nC R cycles per second provided
c g
r R /(r + R ) is much less than R in equation (1.3).
a L a L g
4. The low-frequency response can be improved by increasing the
time constant of the coupling components C and R (see
c g
Fig. 1.6). In this way, low frequencies down to zero cycles per
second can all be amplified equally.