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Contents
3.1 Analog Signal Processing
3.1.1 Linearity
3.1.2 Linear Operations
3.1.3 Nonlinear Operations
3.2 Analog Devices
3.2.1 Terminology
3.2.2 Gain and Transconductance
3.2.3 Characteristic Curves
3.2.4 Manufacturer’s Data Sheets
3.2.5 Physical Electronics of Semiconductors
3.2.6 The PN Semiconductor Junction
3.2.7 Junction Semiconductors
3.2.8 Field-Effect Transistors (FET)
3.2.9 Semiconductor Temperature Effects
3.2.10 Safe Operating Area (SOA)
3.3 Practical Semiconductors
3.3.1 Semiconductor Diodes
3.3.2 Bipolar Junction Transistors (BJT)
3.3.3 Field-Effect Transistors (FET)
3.3.4 Optical Semiconductors
3.3.5 Linear Integrated Circuits
3.3.6 Comparison of Semiconductor Devices for
Analog Applications
3.4 Analog Systems
3.5 Amplifiers
3.5.1 Amplifier Configurations
3.5.2 Transistor Amplifiers
3.5.3 Bipolar Transistor Amplifiers
3.5.4 FET Amplifiers
3.5.5 Buffer Amplifiers
3.5.6 Cascaded Buffers
3.5.7 Using the Transistor as a Switch
3.5.8 Choosing a Transistor
3.6 Operational Amplifiers
3.6.1 Characteristics of Practical Op-Amps
3.6.2 Basic Op Amp Circuits
3.7 Analog-Digital Conversion
3.7.1 Basic Conversion Properties
3.7.2 Analog-to-Digital Converters (ADC)
3.7.3 Digital-to-Analog Converters (DAC)
3.7.4 Choosing a Converter
3.8 Miscellaneous Analog ICs
3.8.1 Transistor and Driver Arrays
3.8.2 Voltage Regulators and References
3.8.3 Timers (Multivibrators)
3.8.4 Analog Switches and Multiplexers
3.8.5 Audio Output Amplifiers
3.8.6 Temperature Sensors
3.8.7 Radio Subsystems
3.9 Analog Glossary
3.10 References and Further Reading
3.4.1 Transfer Functions
3.4.2 Cascading Stages
3.4.3 Amplifier Frequency Response
3.4.4 Interstage Loading and Impedance Matching
3.4.5 Noise
3.4.6 Buffering
Chapter
3
Analog Basics
3.1 Analog Signal Processing
The term
analog signal
refers to voltages, currents and waves that make up ac radio and
audio signals, dc measurements, even power. The essential characteristic of an analog signal
is that the information or energy it carries is continuously variable. Even small variations of
an analog signal affect its value or the information it carries. This stands in contrast to
digital
signals
(described in the
Digital Basics
chapter) that have values only within well-defined
and separate ranges called
states
. To be sure, at the fundamental level all circuits and signals
are analog: Digital signals are created by designing circuits that restrict the values of analog
signals to those discrete states.
Analog signal processing
involves various electronic stages to perform functions on analog
signals such as amplifying, filtering, modulation and demodulation. A piece of electronic
equipment, such as a radio, is constructed by combining a number of these circuits. How these
stages interact with each other and how they affect the signal individually and in tandem is
the subject of sections later in the chapter.
The first section of this chapter
discusses a variety of methods and
techniques for working with analog
signals, called signal processing.
These basic functions are combined
to produce useful systems that
become radios, instruments, audio
recorders and so on.
Subsequent sections of this chap-
ter present several types of active
components and circuits that can be
used to manipulate analog signals.
(An active electronic component is
one that requires a power source
to function, and is distinguished in
this way from passive components
such as resistors, capacitors and
inductors that are described in the
Electrical Fundamentals
chapter.)
The chapter concludes with a
discussion of analog-digital conver-
sion by which analog signals are
converted into digital signals and
vice versa.
Material in this chapter was
updated by Ward Silver, NØAX.
It builds on work by Greg Lapin,
N9GL, with contributions by
Leonard Kay, K1NU, that appeared
in previous editions. The section
“Poles and Zeroes” was adapted
from material previously written for
the chapter on
Oscillators and
Synthesizers
by David Stockton,
GM4ZNX, and Fred Telewski,
WA7TZY.
3.1.1 Linearity
The premier properties of analog signals are
superposition
and
scaling
. Superposition is
the property by which signals are combined, whether in a circuit, in a piece of wire, or even
in air, as the sum of the individual signals. This is to say that at any one point in time, the
voltage of the combined signal is the sum of the voltages of the original signals at the same
time. In a
linear
system
any number of signals will add in this way to give a single combined
signal. (Mathematically, this is a
linear combination
.) For this reason, analog signals and
components are often referred to as
linear signals
or
linear components
. A linear system whose
characteristics do not change, such as a resistive voltage divider, is called
time-invariant
. If
the system changes with time, it is
time-varying
. The variations may be random, intermittent
(such as being adjusted by an operator) or periodic.
One of the more important features of superposition, for the purposes of signal process-
ing, is that signals that have been combined by superposition can be separated back into the
original signals. This is what allows multiple signals that have been received by an antenna
to be separated back into individual signals by a receiver.
3.1.2 Linear Operations
Any operation that modifies a signal and obeys the rules of superposition and scaling is
a
linear operation
. The following sections explain the basic linear operations from which
linear systems are made.
AMPLIFICATION AND ATTENUATION
Amplification
and
attenuation
scale signals to be larger and smaller, respectively. The
operation of
scaling
is the same as multiplying the signal at each point in time by a constant
value; if the constant is greater than one then the signal is amplified, if less than one then the
signal is attenuated.
An
amplifier
is a circuit that increases the amplitude of a signal. Schematically, a generic
Analog Basics
3.1
amplifier is signified by a triangular symbol,
its input along the left face and its output
at the point on the right (see
Fig 3.1
). The
linear amplifier multiplies every value of a
signal by a constant value. Amplifier gain
is often expressed as a multiplication factor
(× 5, for example).
Obtaining a Frequency Response
With the computer tools such as spreadsheets, it’s easy to do the calculations
and make a graph of frequency response. If you don’t have a spreadsheet program,
then use semi-log graph paper with the linear axis used for dB or phase and the
logarithmic axis for frequency. An Excel spreadsheet set up to calculate and display
frequency response is available on the CD that comes with this book. You can modify
it to meet your speciic needs.
Follow these rules whether using a spreadsheet or graph paper:
•
Measure input and output in the same units, such as volts, and use the same
conventions, such as RMS or peak-to-peak.
•
Measure phase shift from the input to the output. (The
Test Equipment and
Measurements
chapter discusses how to make measurements of amplitude and
phase.)
•
Use 10 log (P
O
/P
I
) for power ratios and 20 log (V
O
/V
I
) for voltage or current.
To make measurements that are roughly equally spaced along the logarithmic fre-
quency axis, follow the “1-2-5 rule.” Dividing a range this way, for example 1-2-5-10-
20-50-100-200-500 Hz, creates steps in approximately equal ratios that then appear
equally spaced on a logarithmic axis.
V
o
i
Gain
=
(1)
V
where V
o
is the output voltage from an am-
plifier when an input voltage, V
i
, is applied.
(Gain is often expressed in decibels (dB)
as explained in the chapter on
Electrical
Fundamentals
.)
Certain types of amplifiers for which cur-
rents are the input and output signals have
current gain
. Most amplifiers have both volt-
age and current gain.
Power gain
is the ratio
of output power to input power.
Ideal linear amplifiers have the same gain
for all parts of a signal. Thus, a gain of 10
changes 10 V to 100 V, 1 V to 10 V and –1 V
to –10 V. (Gain can also be less than one.) The
ability of an amplifier to change a signal’s level
is limited by the amplifier’s
dynamic range
,
however. An amplifier’s dynamic range is the
range of signal levels over which the amplifier
produces the required gain without distortion.
Dynamic range is limited for small signals by
noise, distortion and other nonlinearities.
Dynamic range is limited for large signals
because an amplifier can only produce out-
earity is called
slew rate
. Applied to an ampli-
fier, this term describes the maximum rate at
which a signal can change levels and still be
accurately amplified in a particular device.
In-
put slew rate
is the maximum rate of change to
which the amplifier can react linearly.
Output
slew rate
refers to the maximum rate at which
the amplifier’s output circuit can change. Slew
rate is an important concept, because there is
put voltages (and currents) that are within
the range of its power supply. (Power-supply
voltages are also called the
rails
of a circuit.)
As the amplified output approaches one of the
rails, the output can not exceed a given voltage
near the rail and the operation of the amplifier
becomes nonlinear as described below in the
section on Clipping and Rectification.
Another similar limitation on amplifier lin-
Fig 3.1 — Generic ampliier. (A) Symbol.
For the linear ampliier, gain is the
constant value, G, and the output voltage
is equal to the input voltage times G; (B)
Transfer function, input voltage along the
x-axis is converted to the output voltage
along the y-axis. The linear portion of the
response is where the plot is diagonal; its
slope is equal to the gain, G. Above and
below this range are the clipping limits,
where the response is not linear and the
output signal is clipped.
Fig 3.2 — Bode plot of (A) band-pass ilter magnitude response and (B) an RC low-
pass ilter phase response.
3.2
Chapter 3
a direct correlation between a signal level’s
rate of change and the frequency content of
that signal. The amplifier’s ability to react to
or reproduce that rate of change affects its
frequency response and dynamic range.
An
attenuator
is a circuit that reduces
the amplitude of a signal. Attenuators can
be constructed from passive circuits, such
as the attenuators built using resistors, de-
scribed in the chapter on
Test Equipment
and Measurements
. Active attenuator cir-
cuits include amplifiers whose gain is less
than one or circuits with adjustable resistance
in the signal path, such as a PIN diode attenu-
ator or amplifier with gain is controlled by an
external voltage.
POLES AND ZEROES
It’s easy to imagine frequency as stretch-
ing from zero to infinity, but let’s imagine
that complex numbers could be used. This is
pure imagination — we can’t make signals
at complex values (with real and imaginary
components) of hertz — but if complex num-
bers are used for frequency, we can gain ad-
ditional insight into how the circuit behaves.
(See the chapter on
Electrical Fundamentals
for a discussion of complex numbers.)
This is illustrated by
Fig 3.3
. The transfer
function (shown at the left of the figure) de-
scribes the behavior of the simple RC-circuit
at real-world frequencies as well as imaginary
frequencies whose values contain
j
. When
complex numbers are used for f, the trans-
fer function can describe the circuit’s phase
response, as well as amplitude. At one such
frequency, f = –
j
/2πRC, the denominator of
the transfer function is zero, and the gain
is infinite! Infinite gain is a pretty amazing
thing to achieve with a passive circuit — but
because this can only happen at an imagi-
nary frequency, it does not happen in the real
world.
Frequencies that cause the transfer func-
tion to become infinite are called
poles
. This
is shown at the bottom right of Fig 3.3 in the
graph of the circuit’s amplitude response for
imaginary frequencies shown on the horizon-
tal axis. (The pole causes the graph to extend
up “as a pole under a tent,” thus the name.)
Similarly, circuits can have
zeroes
which oc-
cur at imaginary frequencies that cause the
transfer function to be zero, a less imaginative
name, but quite descriptive.
A circuit can also have poles and zeroes at
frequencies of zero and infinity. For example,
the circuit in Fig 3.3 has a zero at infinity be-
cause the capacitor’s reactance is zero at infin-
ity and the transfer function is zero, as well. If
the resistor and capacitor were exchanged, so
that the capacitor was in series with the output,
FREQUENCY RESPONSE AND
BODE PLOTS
Another important characteristic of a cir-
cuit is its
frequency response
, a description
of how it modifies a signal of any frequency.
Frequency response can be stated in the form
of a mathematical equation called a
transfer
function
, but it is more conveniently presented
as a graph of gain vs frequency. The ratio of
output amplitude to input amplitude is often
called the circuit’s
magnitude
or
amplitude
response
. Plotting the circuit’s magnitude
response in dB versus frequency on a loga-
rithmic scale, such as in
Fig 3.2A
, is called
a
Bode plot
(after Henrik Wade Bode). The
combination of decibel and log-frequency
scales is used because the behavior of most
circuits depends on ratios of amplitude and
frequency and thus appears linear on a graph
in which both the vertical and horizontal
scales are logarithmic.
Most circuits also affect a signal’s phase
along with its amplitude. This is called
phase
shift
. A plot of phase shift from the circuit’s
input to its output is called the
phase response
,
seen in Fig 3.2B. Positive phase greater than
0° indicates that the output signal
leads
the
input signal, while
lagging
phase shift has a
negative phase. The combination of an am-
plitude and phase response plot gives a good
picture of what effect the circuit has on signals
passing through it.
TRANSFER CHARACTERISTICS
Transfer characteristics
are the ratio of an
output parameter to an input parameter, such
as output current divided by input current, h
FE
.
There are different families of transfer char-
acteristics, designated by letters such as h, s,
y or z. Each family compares parameters in
specific ways that are useful in certain design
or analysis methods. The most common
transfer characteristics used in radio are the
h-parameter family (used in transistor models)
and the s-parameter family (used in RF design,
particularly at VHF and above). See the
RF
Design Techniques
chapter for more discus-
sion of transfer characteristics.
Fig 3.3 — The transfer function for a circuit describes both the magnitude and phase
response of a circuit. The RC circuit shown at the upper left has a pole at f = 2
π
RC, the
ilter’s –3 dB or cutoff frequency, at which the phase response is a 45
°
lagging phase
shift. Poles cause an ininite response on the imaginary frequency axis.
Analog Basics
3.3
then at zero frequency (dc), the output would
be zero because the capacitor’s reactance was
infinite, creating a zero.
Complex circuits can have multiple poles
or multiple zeroes at the same frequency.
Poles and zeroes can also occur at frequencies
that are combinations of real and imaginary
numbers. The poles and zeroes of a circuit
form a pattern in the complex plane that cor-
responds to certain types of circuit behavior.
(The relationships between the pole-zero pat-
tern and circuit behavior is beyond the scope
of this book, but are covered in textbooks on
circuit theory.)
not impossible in the real world (unlike the
pole), so zeroes can be found at real-number
frequencies as well as complex-number fre-
quencies.
Each zero is associated with an
upward
bend of 6 dB per octave in a magnitude re-
sponse. Similarly to a pole, the frequency
of the zero is at the +3 dB point. Each zero
is associated with a transition on a phase-
versus-frequency plot that reduces the lag
by 90°. The zero is at the 45° leading phase
point. Multiple zeroes add their phase shifts
just as poles do.
In a circuit, a zero creates gain that in-
creases with frequency forever above the zero
frequency. This requires active circuitry that
would inevitably run out of gain at some fre-
quency, which implies one or more poles up
there. In real-world circuits, zeroes are usu-
ally not found by themselves, making the
magnitude response go up, but rather paired
with a pole of a different frequency, result-
ing in the magnitude response having a slope
between two frequencies but flat above and
below them.
Real-world circuit zeroes are only found
accompanied by a greater or equal number
of poles. Consider a classic RC high-pass
filter, such as if the resistor and capacitor in
Fig 3.3 were exchanged. The response of such
a circuit increases at 6 dB per octave from
0 Hz (so there must be a zero at 0 Hz) and
then levels off at 1/2πRC Hz. This leveling
off is due to the presence of a pole adding its
6 dB-per-octave roll-off to cancel the 6 dB-
per-octave roll-up of the zero. The transfer
function for such as circuit would equal zero
at zero frequency and infinity at the imaginary
pole frequency.
shift
compensation
network to improve the
amplifier stability.
Although negative feedback reduces am-
plifier or stage gain, the advantages of
stable
gain, freedom from unwanted oscillations and
the reduction of distortion are often key design
objectives and advantages of using negative
feedback.
The design of feedback networks depends
on the desired result. For amplifiers, which
should not oscillate, the feedback network
is customized to give the desired frequency
response without loss of stability. For oscil-
lators, the feedback network is designed to
create a steady oscillation at the desired fre-
quency.
What is a Pole?
Poles cause a specific change in the circuit’s
amplitude and phase response for real-world
frequencies, even though we can’t experience
imaginary frequencies directly. A pole is as-
sociated with a bend in a magnitude response
plot that changes the slope of the response
downward with increasing frequency by 6 dB
per octave (20 dB per decade; an octave is a
2:1 frequency ratio, a decade is a 10:1 fre-
quency ratio).
There are four ways to identify the exis-
tence and frequency of a pole as shown in
Fig 3.3:
1. For a downward bend in the magni-
tude versus frequency plot, the pole is at the
–3 dB frequency for a single pole. If the bend
causes a change in slope of more than 6 dB/
octave, there must be multiple poles at this
frequency.
2. A 90° lagging change on a phase versus
frequency plot, where the lag increases with
frequency. The pole is at the point of 45° added
lag on the S-shaped transition. Multiple poles
will add their phase lags, as above.
3. On a circuit diagram, a single pole looks
like a simple RC low-pass filter. The pole is
at the –3 dB frequency (f = 1/2πRC Hz). Any
other circuit with the same response has a pole
at the same frequency.
4. In an equation for the transfer function
of a circuit, a pole is a theoretical value of
frequency that would result in infinite gain.
This is clearly impossible, but as the value of
frequency will either be absolute zero, or will
have an imaginary component, it is impos-
sible to make an actual real-world signal at a
pole frequency.
For example, comparing the amplitude re-
sponses at top and bottom of Fig 3.3 shows
that the frequency of the pole is equal to the
circuit’s –3 dB cutoff frequency (1/2πfC)
multiplied by
j
, which is also the frequency
at which the circuit causes a –45° (lagging)
phase shift from input to output.
SUMMING
In a linear system, nature does most of
the work for us when it comes to adding sig-
nals; placing two signals together naturally
causes them to add according to the principle
of superposition. When processing signals,
we would like to control the summing op-
eration so the signals do not distort or com-
bine in a nonlinear way. If two signals come
from separate stages and they are connected
together directly, the circuitry of the stages
may interact, causing distortion of either or
both signals.
Summing amplifiers
generally use a resis-
tor in series with each stage, so the resistors
connect to the common input of the following
stage. This provides some
isolation
between
the output circuits of each stage.
Fig 3.4
il-
lustrates the resistors connecting to a summing
amplifier. Ideally, any time we wanted to com-
bine signals (for example, combining an audio
signal with a sub-audible tone in a 2 meter FM
transmitter prior to modulating the RF signal)
we could use a summing amplifier.
FEEDBACK AND OSCILLATION
The
stability
of an amplifier refers to its
ability to provide gain to a signal without
tending to oscillate. For example, an amplifier
just on the verge of oscillating is not gener-
ally considered to be “stable.” If the output
of an amplifier is fed back to the input, the
feedback can affect the amplifier stability. If
the amplified output is added to the input,
the output of the sum will be larger. This
larger output, in turn, is also fed back. As this
process continues, the amplifier output will
continue to rise until the amplifier cannot go
any higher (clamps). Such
positive feedback
increases the amplifier gain, and is called
regeneration
. (The chapter on
Oscillators
and Synthesizers
includes a discussion of
positive feedback.)
Most practical amplifiers have some intrin-
sic and unavoidable feedback either as part
of the circuit or in the amplifying device(s)
itself. To improve the stability of an amplifier,
negative feedback
can be added to counteract
any unwanted positive feedback. Negative
feedback is often combined with a phase-
FILTERING
A
filter
is a common linear stage in radio
equipment. Filters are characterized by their
ability to selectively attenuate certain frequen-
Fig 3.4 — Summing ampliier. The output
voltage is equal to the sum of the input
voltages times the ampliier gain, G. As
long as the resistance values, R, are
equal and the ampliier input impedance
is much higher, the actual value of R does
not affect the output signal.
What Is a Zero?
A zero is the complement of a pole. In
math, it is a frequency at which the transfer
function equation of a circuit is zero. This is
3.4
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