EEE 211 ANALOG ELECTRONICS LECTURE NOTES Hayrettin Köymen

254 Pages·2004·2.9 MB·German

EEE 211
ANALOG ELECTRONICS
LECTURE NOTES
Hayrettin Köymen
BİLKENT
UNIVERSITY
© Hayrettin Köymen, rev. 3.4/2004
This work is published by Bilkent University as the texbook for EEE 211 Analog
Electronics course, taught in Bilkent University. All rights are reserved. No part
of this work may be reproduced in any form except by written permission of the
author. All rights of translation are reserved. Printed in Bilkent University,
Ankara, Turkey.
First Edition, rev. 3.4
April 2004
ANALOG ELECTRONICS BİLKENT UNIVERSITY
CONTENTS
Chapter 1: SIGNALS AND COMMUNICATIONS 1-1
1.1. Frequency 1-1
1.2. Oscillators 1-3
1.3. Modulation 1-5
1.4. Amplifiers 1-7
1.5. Mixers 1-8
1.6. Filters 1-9
1.7. Receivers 1-11
1.8. TRC-10 1-12
1.9. Bibliography 1-14
1.10. Laboratory exercises 1-14
1.11. Problems 1-15
Chapter 2: CIRCUIT THEORY PRIMER 2-1
2.1. Energy sources 2-1
2.2. Resistors 2-3
2.2.1. Resistive circuits 2-5
2.3. Analysis of electrical circuits 2-5
2.4. Capacitors 2-8
2.4.1. Power and energy in capacitors 2-10
2.4.2. RC circuits 2-11
2.5. Diodes 2-15
2.5.1. Diodes as rectifiers 2-17
2.5.1. Zener diodes as voltage sources 2-19
2.6. Inductors 2-20
2.7. Transformers 2-23
2.8. Circuit protection devices 2-24
2.8.1. Varistors 2-24
2.8.2. PTC Thermistors 2-25
2.8.3. Circuit protection 2-25
2.8. Bibliography 2-26
2.9. Laboratory exercises 2-26
2.10. Problems 2-34
Chapter 3: AUDIO CIRCUITS 3-1
3.1. Linear circuits 3-1
3.1.1. Power 3-4
3.2. Impedance and Transfer Function 3-5
3.3. Sources and Equivalent Circuits 3-10
3.4. Operational amplifiers 3-12
3.5. OPAMP circuits 3-17
3.5.1. Offset voltage in OPAMPs 3-20
3.5.2. OPAMP Linear Voltage Regulator 3-21
3.6. Bibliography 3-24
CONTENTS ©Hayrettin Köymen, rev. 3.4/2004, All rights reserved i
ANALOG ELECTRONICS BİLKENT UNIVERSITY
3.7. Laboratory exercises 3-24
3.8. Problems 3-40
Chapter 4: TUNED CIRCUITS 4-1
4.1. Parallel resonance 4-1
4.1.1. Energy in tuned circuits 4-2
4.1.2. Quality of resonance 4-4
4.2. Series tuned circuits 4-8
4.3. Equivalence of series and parallel RLC circuits 4-9
4.4. Real inductors 4-12
4.4.1. Air core inductors 4-14
4.4.2. Powdered iron core inductors 4-14
4.4.3. Core losses 4-15
4.4.4. Copper losses 4-16
4.4.5. RF choke inductors 4-17
4.5. RF Amplification using OPAMPs 4-19
4.5.1. OPAMP Open Loop Frequency Response 4-19
4.5.2. Voltage gain and power gain 4-21
4.5.3. Slew Rate 4-22
4.5.4. Input Bias Current 4-22
4.6. Maximum power transfer 4-22
4.7. Bibliography 4-24
4.8. Laboratory exercises 4-24
4.9. Problems 4-33
Chapter 5: FILTERS 5-1
5.1. Motivation 5-1
5.2. Polynomial filters 5-3
5.2.1. Butterworth filters 5-3
5.2.2. Harmonic filter 5-6
5.2.3. Butterworth HPF 5-8
5.2.4. Butterworth BPF 5-9
5.3. Impedance matching 5-10
5.3.1. Transformers 5-10
5.3.2. Real transformers 5-11
5.3.3. Matching by resonant circuits 5-14
5.3.4. Impedance inverters 5-15
5.4. Crystal filters 5-16
5.4.1. Quartz crystals 5-16
5.4.2. IF ladder filter 5-17
5.5. Bibliography 5-20
5.6. Laboratory exercises 5-20
5.7. Problems 5-30
Chapter 6: DIODES IN TELECOMMUNICATIONS 6-1
6.1. Diode detector 6-1
6.1.1. Real diodes in envelope detectors 6-3
CONTENTS ©Hayrettin Köymen, rev. 3.4/2004, All rights reserved ii
ANALOG ELECTRONICS BİLKENT UNIVERSITY
6.2. TX/RX switch 6-5
6.2.1. Diode biasing 6-6
6.2.2. PIN diode switch 6-8
6.2.3. RF gain control 6-11
6.3. Audio gain control 6-12
6.4. Bibliography 6-13
6.5. Laboratory exercises 6-14
6.6. Problems 6-19
Chapter 7: FREQUENCY CONVERSION 7-1
7.1. Amplitude modulators 7-1
7.1. Mixers in telecommunication circuits 7-2
7.1.1. Switch mixer 7-2
7.1.2. Double-balanced mixers 7-4
7.2. Analog multipliers 7-5
7.2.1. Conversion gain 7-7
7.3. Oscillators 7-7
7.3.1. Oscillator concept 7-8
7.3.2. Frequency control 7-10
7.4.3. Phase considerations in oscillators 7-11
7.4. Bibliography 7-12
7.5. Laboratory exercises 7-12
7.6. Problems 7-23
Chapter 8: ON THE AIR 8-1
8.1. Antenna concept 8-1
8.1.1. Radiation from an antenna 8-1
8.1.2. Receiving antenna 8-6
8.2. Antenna impedance 8-6
8.3.1. Self impedance 8-7
8.3.2. Mutual impedance 8-7
8.3. Half wave dipole 8-8
8.4. Monopole antenna 8-8
8.5. Antenna feeders 8-10
8.5.1. Balanced-unbalanced transformation 8-11
8.5.2. TRC-10 short dipole feeder 8-12
8.6. Using amateur frequency bands 8-14
8.7. Bibliography 8-14
8.8. Laboratory exercises 8-14
8.9. Problems 8-16
Appendix A: Circuit diagrams and PCB layout
Appendix B: List of components
Appendix C: Data sheets
Appendix D: Complex numbers
CONTENTS ©Hayrettin Köymen, rev. 3.4/2004, All rights reserved iii
ANALOG ELECTRONICS BİLKENT UNIVERSITY
Chapter 1 : SIGNALS AND COMMUNICATIONS
Electronic communications is exchanging signals. While these signals are symbolic in
many communication schemes, they are almost exact electrical replicas of original
information in analog wireless communications. Sound and vision are all such signals.
Signals are converted into a form, by a transmitter, so that they can be transmitted in
the air as part of electromagnetic spectrum, and are received by a receiver, where they
are converted back to the original form. Two communicating parties can be quite far
away from each other, and therefore the term telecommunications is used to describe
this form of communications. What follows in this chapter is a descriptive theory of
analog signal processing in communications.
Transceivers are wireless transmitters (TX) and receivers (RX) combined in a single
instrument. This book is structured around building and testing a transceiver, TRC-10,
operating in the 10-meter amateur band (28-29.7 MHz). The name is generic: TRC
stands for transceiver and 10 indicate that it works in 10-meter band.
TRC-10 is an amplitude modulation superheterodyne transceiver. We have to make
some definitions in order to understand what these terms mean.
1.1. Frequency
The two variables in any electrical circuit is voltage, V, and current, I. In electronics,
all signals are in form of a voltage or a current, physically. Both of these variables can
be time varying or constant. Voltages and currents that do not change with respect to
time are called d.c. voltages or currents, respectively. The acronym d.c. is derived
from direct current.
Voltages and currents that vary with respect to time can, of course, have arbitrary
forms. A branch of applied mathematics called Laplace analysis, or its special form
Fourier analysis, investigates the properties of such time variation, and shows that all
time varying signals can be represented in terms of linear combination (or weighted
sums) of sinusoidal waveforms.
A sinusoidal voltage and current can be written as
v(t) =V cos(ωt+θ ), and
1 v
i(t) = I cos(ωt+θ).
1 i
V and I are called the amplitude of voltage and current, and have units of Volts (V)
1 1
and Amperes (A), respectively. “ω” is the radial frequency with units of radians per
second (rps) and ω = 2πf, where “f” is the frequency of the sinusoid with units of
Hertz (Hz). “θ” is the phase angle of the waveform. These waveforms are periodic,
which means that it is a repetition of a fundamental form in every T seconds, where
T=1/f seconds (sec).
Quite often, sinusoidal waveforms are referred to by their peak amplitudes or peak-to-
peak amplitudes. Peak amplitude of v(t) is V Volts peak (or V ) and peak-to-peak
1 p
amplitude is 2 V Volts peak-to-peak (or Vpp).
1
SIGNALS AND COMMUNICATIONS ©Hayrettin Köymen, rev. 3.4/2004, All rights reserved 1-1
ANALOG ELECTRONICS BİLKENT UNIVERSITY
Now we can see that a d.c. voltage is in fact a sinusoid with f = 0 Hz. Sinusoidal
voltages and currents with non-zero frequency are commonly referred to as a.c.
voltages and currents. The acronym a.c. comes from alternating current.
If we know the voltage v(t) across any element and current i(t) through it, we can
calculate the power delivered to it as
P(t) = v(t)i(t) = V I cos(ωt+θ ) cos(ωt+θ)
1 1 v i
or
VI VI
P(t) = 1 1 cos(θ -θ )+ 1 1 cos(2ωt+θ +θ ).
2 v i 2 v i
P(t) is measured in watts (W), i.e. (1V)×(1A)=1 W.
In case of a resistor, both current and voltage have the same phase and hence we can
write the power delivered to a resistor as
VI VI
P(t) = 1 1 + 1 1 cos(2ωt+2θ ).
2 2 v
We shall see that the phase difference between voltage and current in an element or a
branch of circuit is a critical matter and must be carefully controlled in many aspects
of electronics.
P(t) is called the instantaneous power and is a function of time. We are usually
interested in the average power, P , which is the constant part of P(t):
a
VI
P = 1 1 cos(θ -θ ),
a 2 v i
in general, and
VI
P = 1 1
a 2
in case of a resistor.
We note that if the element is such that the phase difference between the voltage
across and current through it is 90o, P is zero. Inductors and capacitors are such
a
elements.
Radio waves travel at the speed of light, c. The speed of light in air is 3.0 E8 m/sec
(through out this book we shall use the scientific notation, i.e. 3.0 E8 for 3×108), to a
very good approximation. This speed can be written as
c = fλ
SIGNALS AND COMMUNICATIONS ©Hayrettin Köymen, rev. 3.4/2004, All rights reserved 1-2
ANALOG ELECTRONICS BİLKENT UNIVERSITY
where λ is the wavelength in meters. TRC-10 emits radio waves at approximately
30 MHz (actually between 28 and 29.7 MHz). The wavelength of these waves is
approximately 10 meters. The amateur frequency band in which TRC-10 operates is
therefore called 10-meter band.
1.2. Oscillators
Electronic circuits that generate voltages of sinusoidal waveform are called
“sinusoidal oscillators”. There are also oscillators generating periodic signals of other
waveforms, among which square wave generators are most popular. Square wave
oscillators are predominantly used in digital circuits to produce time references,
synchronization, etc. Oscillator symbol is shown in Figure 1.1.
Figure 1.1 Oscillator symbol
We use oscillators in communication circuits for variety of reasons. There are two
oscillators in TRC-10. The first one is an oscillator that generates a signal at 16 MHz
fixed frequency. This oscillator is a square wave crystal oscillator module.
A square wave of 2 volts peak to peak amplitude is depicted in Figure 1.2.
2
1.5
)
V
(
e
d 1
u
t
pli
m 0.5
a
time
0
T/2 T 3T/2 2T
Figure 1.2 Square wave
In fact, such a square wave can be represented in terms of sinusoids as a linear
combination:
s(t) =1+(4/π)sin(ωt)+(4/3π)sin(3ωt)+(4/5π)sin(5ωt)+(4/7π)sin(7ωt)+…..
∞
=a +∑b sin(nωt)
o n
n=1
where a is the average value of s(t), 1 in this particular case, and
o
b = (2/nπ)[1-(-1)n]
n
Note here that
SIGNALS AND COMMUNICATIONS ©Hayrettin Köymen, rev. 3.4/2004, All rights reserved 1-3
ANALOG ELECTRONICS BİLKENT UNIVERSITY
(i) there are an infinite number of sinusoids in a square wave;
(ii) the frequencies of these sinusoids are only odd multiples of ω, which is a
property of square waves with equal duration of 2’s and 0’s- we call such
square waves as 50% duty cycle square waves;
(iii) the amplitude of sinusoids in the summation decreases as their frequency
increases.
We refer to the sinusoids with frequencies 2ω, 3ω, 4ω,…, nω as harmonics of the
fundamental component, sinωt.
We can obtain an approximation to a square wave by taking a , fundamental, and only
o
few harmonics into the summation. As we increase the number of harmonics in the
summation, the constructed waveform becomes a better representative of square
wave. This successive construction of a square wave is shown in Figure 1.3.
a
2
b
V) 1.5
(
de c
u 1
t
pli
m d
a 0.5
time
0
T/2 T 3T/2 2T
Figure 1.3 Constructing a square wave from harmonics, (a) only a + fundamental, (b)
o
waveform in (a) + 3rd harmonic, (c) waveform in (b) + 5th harmonic, (d) all terms up
to 13th harmonic.
Even with only 3 terms the square wave is reasonably well delineated, although its
shape looks rather corrugated.
A common graphical representation of a signal with many sinusoidal components is to
plot the line graph of the amplitude of each component versus frequency (either f or
ω). This is called the spectrum of the square wave or its frequency domain
representation. Spectrum of this square wave is given in Figure 1.4, which clearly
illustrates the frequency components of the square wave.
Figure 1.4 clearly shows that the square wave, being a periodic signal, has energy
only at discrete frequencies.
We need sinusoidal voltages in TRC-10, not square waves. Indeed, we must avoid the
harmonics of our signals to be emitted from our transceiver, because such harmonics
will interfere with other communication systems operating at that frequency. We use
this fixed frequency square wave oscillator module, because such modules provide a
SIGNALS AND COMMUNICATIONS ©Hayrettin Köymen, rev. 3.4/2004, All rights reserved 1-4
ANALOG ELECTRONICS BİLKENT UNIVERSITY
very accurate and stable frequency of oscillation and can be obtained at a low cost.
We first filter out the harmonics of the waveform, when we use this module in our
circuit.
1.4
1.2
⏐a ⏐
o
1
⏐b ⏐0.8
n
0.6
0.4
0.2
0
ω 2ω 3ω 4ω 5ω 6ω 7ω 8ω 9ω 11ω 13ω 15ω 17ω 19ω
frequency
Figure 1.4 Spectrum of the square wave
The other oscillator is a Variable Frequency Oscillator (VFO). This oscillator
produces a sinusoid of frequency that varies between 12 MHz and 13.7 MHz. This
frequency is controlled by a d.c. voltage. We discuss the VFO in Chapter 7.
1.3. Modulation
A sinusoidal waveform does not carry any information on its own. In order to transmit
any information, in our case voice, we need to make one parameter of a sinusoid
dependent on this information.
In electronics, the information must of course be converted into an electrical signal, a
voltage or a current, first. For example, a microphone converts sound into a voltage,
which we first amplify and then use as information signal, v (t). This signal is again a
m
time varying signal, which can be represented as a linear combination of sinusoids.
The frequency band of this signal, however, is not suitable for transmission in air, as it
is. This frequency band is rather low for transmission and it is called base-band. The
information signal occupying this band is referred to as base-band signal. Converting
the information-carrying signal to a form suitable for (electromagnetic) transmission
is called modulation.
There are three parameters that we can play with in a sinusoid: amplitude, frequency
and phase. We must mount the information signal v (t) on a sinusoid of appropriate
m
high frequency, so that it can be carried on air at that radio frequency. We call this
operation, modulation. In TRC-10 we use amplitude modulation (AM), which means
that we make the amplitude of a sinusoid dependent on v (t). Note that the
m
frequencies of sinusoids that are present in a voice signal is within few kHz, while we
wish to transmit this voice signal at 30 MHz. Let us assume that v (t) is a simple
m
SIGNALS AND COMMUNICATIONS ©Hayrettin Köymen, rev. 3.4/2004, All rights reserved 1-5