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Chapter 14
Receivers and
Transmitters
In this chapter, William E. Sabin,
WØIYH, discusses the “system design” of
Amateur Radio receivers and transmitters.
“A Single-Stage Building Block” reviews
briefly a few of the basic properties of the
various individual building block circuits,
described in detail in other chapters, and
the methods that are used to combine and
interconnect them in order to meet the
requirements of the completed equipment.
“The Amateur Radio Communication
Channel” describes the relationships
between the equipment system design and
the electromagnetic medium that conveys
radio signals from transmitter to receiver.
This understanding helps to put the radio
equipment mission and design require-
ments into perspective. Then we discuss
receiver, transmitter, transceiver and
transverter design techniques in general
terms. At the end of the theory discussion
is a list of references for further study on
the various topics. The projects section
contains several hardware descriptions
that are suitable for amateur construction
and use on the ham bands. They have been
selected to illustrate system-design meth-
ods. The emphasis in this chapter is on
analog design. Those functions that can be
implemented using digital signal process-
ing (DSP) can be explored in other chap-
ters, but an initial basic appreciation of
analog methods and general system design
is very valuable.
A SINGLE-STAGE BUILDING
BLOCK
We start at the very beginning with
Fig 14.1,
a generic single-stage module
that would typically be part of a system of
many stages. A signal source having an
“open-circuit” voltage V
gen
causes a cur-
rent Igen to flow through Z
gen
, the imped-
ance of the generator, and Z
in
, the input
impedance of the stage. This input current
is responsible for an open-circuit output
voltage V
d
(measured with a high-imped-
ance voltmeter) that is proportional to I
gen
.
V
d
produces a current Iout and a voltage
drop across Z
out
, the output impedance of
the stage and Z
load
, the load impedance of
the stage. Observe that the various Zs may
contain reactance and resistance in various
combinations. Let’s first look at the differ-
ent types of gain and power relationships
that can be used to describe this stage.
Actual Power Gain
Current I
gen
produces a power dissipa-
tion P
in
in the resistive component of Z
in
that is equal to I
gen2
R
in
. The current I
out
produces a power dissipation P
load
in the
resistive component of Z
load
that is equal
to I
out2
R
load
. The actual power gain in dB
is 10 log (P
load
/ P
in
). This is the conven-
tional usage of dB, to describe a power
ratio.
Voltage Gain
The current I
gen
produces a voltage drop
across Z
in
. V
d
produces a current I
out
and a
voltage drop V
out
across Z
load
. The voltage
gain is the ratio
V
out
/ V
in
In decibels (dB) it is
20 log (V
out
/ V
in
)
(2)
(1)
only. It is used in troubleshooting and other
instances where a rough indication of op-
eration is needed, but precise measurement
is unimportant. Voltage gain is often used
in high-impedance circuits such as pentode
vacuum tubes and is also sometimes con-
venient in solid-state circuits. Its improper
usage often creates errors in radio circuit
design because many calculations, for cor-
rect answers, require power ratios rather
than voltage ratios. We will see several
examples of this throughout this chapter.
Available Power
The maximum power, in watts, that can
be obtained from the generator is V
gen2
/
(4 R
gen
). To see this, suppose temporarily
that X
gen
and X
in
are both zero. Then let
R
in
increase from zero to some large value.
The maximum power in R
in
occurs when
R
in
= R
gen
and the power in R
in
then has the
value mentioned above (plot a graph of
power in R
in
vs R
in
to verify this, letting
V
gen
= 1 V and R
gen
= 50
Ω).
This is called
the “available power” (we’re assuming
sine-wave signals). If X
gen
is an inductive
(or capacitive) reactance and if X
in
is an
equal value of capacitive (or inductive)
reactance, the net series reactance is nul-
lified and the above discussion holds true.
If the net reactance is not zero the current
I
gen
is reduced and the power in R
in
is less
than maximum. The process of tuning out
the reactance and then transforming the
resistance of R
in
is called “conjugate
matching.” A common method for doing
this conjugate matching is to put an impe-
dance transforming circuit of some kind,
such as a transformer or a tuned circuit,
between the generator and the stage input
that “transforms” R
in
to the value R
gen
(as
seen by the generator) and at the same time
nullifies the reactance.
Receivers and Transmitters
14.1
This alternate usage of dB, to describe a
voltage ratio, is common practice. It is
dif-
ferent
from the power gain mentioned in
the previous section because it does
not
take
into account the power ratio or the resis-
tance values involved. It is a voltage ratio
Fig 14.1—A single-stage building-block signal processor. The properties of this stage are discussed in the text.
Fig 14.2
illustrates this idea and later
discussion gives more details about these
interstage networks. A small amount of
power is lost within any lossy elements of
the matching network. This same tech-
nique can be used between the output of
the stage in Fig 14.1 and the load imped-
ance Z
load
. In this case, the stage delivers
the maximum amount of power to the load
resistance. If both input and output are
processed in this way, the stage utilizes
the generator signal to the maximum
extent possible. It is very important to
note, however, that in many situations we
do not want this maximum utilization. We
deliberately “mismatch” in order to
achieve certain goals that will be discussed
later (Ref 1).
The dBm Unit of Power
In low-level radio circuitry, the watt
(W) is inconveniently large. Instead, the
milliwatt (mW) is commonly used as a ref-
erence level of power. The dB with
respect to 1 mW is defined as
Fig 14.2—The conjugate impedance match of a generator to a stage input. The
network input impedance is R
gen
±jX
gen
and its output impedance is R
in
±jX
in
(where either R term may represent a dynamic impedance). Therefore the
generator and the stage input are both impedance matched for maximum power
transfer.
where
dBm = 10 log (P
W
/ 0.001)
(3)
V
gen2
/ (4 R
gen
), is called the maximum
available power gain. In some cases the
circuit is adjusted to achieve this value,
using the conjugate-match method de-
scribed above. In many cases, as men-
tioned before, less than maximum gain is
acceptable, perhaps more desirable.
Available Power Gain
Consider that in Fig 14.1 the stage and
its output load Z
load
constitute an “ex-
panded” stage as defined by the dashed
box. The power available from this new
stage is determined by V
out
and by R
stage
,
the resistive part of Z
stage
. The available
power gain is then V
out2
/ (4 R
stage
) divided
by V
gen2
/ (4 R
gen
). This value of gain is
used in a number of design procedures.
Note that Z
load
can be a physical network
of some kind, or it may be partly or
dBm = Power level in dB with respect to
1 mW
P
W
= Power level, watts.
For example, 1 W is equivalent to 30 dBm.
Also
P
W
= 0.001 × 10
dBm/10
(4)
entirely the input impedance of the stage
following the one shown in Fig 14.1.
In the latter case it is sometimes conve-
nient to “detach” this input impedance
from the next stage and make it part of the
expanded first stage, as shown in Fig 14.1,
but we note that Z
out
is still the generator
(source) impedance that the input of the
next stage “sees.”
Transducer Power Gain
The transducer gain is defined as the
ratio of the power actually delivered to
R
load
in Fig 14.1 to the power that is avail-
able from the generator V
gen
and R
gen
. In
other words, how much more power does
the stage deliver to the load than the gen-
erator could deliver if the generator were
impedance matched to the load? We will
discuss how to use this kind of gain later.
Maximum Available Power Gain
The ratio of the power that is available
from the stage, V
d2
/ (4 R
out
), to the power
that is available from the generator,
14.2
Chapter 14
Feedback (Undesired)
One of the most important properties of
the single-stage building block in Fig 14.1
is that changes in the load impedance Z
load
cause changes in the input impedance Z
in
.
Changes in Z
gen
also affect Z
out
. These ef-
fects are due to reverse coupling, within
the stage, from output to input. For many
kinds of circuits (such as networks, filters,
attenuators, transformers and so on) these
effects cause no unexpected problems.
But, as the chapter on
RF Power
Amplifiers
explains in detail, in active cir-
cuits such as amplifiers this reverse cou-
pling within one stage can have a
major impact not only on that stage but
also on other stages that follow and pre-
cede. It is the effect on system perfor-
mance that we discuss here. In particular,
if a stage is expected to have certain gain,
noise factor and distortion specifications,
all of these can be changed either by
reverse coupling (undesired feedback)
within the stage or adjacent stages. For
example, internal feedback can cause the
input impedance of a certain stage “A”
(Fig 14.1) to become very large. If this
impedance is the load impedance for the
preceding stage, the gain of the preceding
stage can become excessive, creating
problems in both stages. This same feed-
back can cause the gain of stage “A” to
become greater, thereby causing the next
stage to be driven into heavy distortion. A
very common event is that stage “A” goes
into oscillation. All of these occurrences
are common in poorly designed radio
equipment. Changes in temperature and
variations in component tolerances are
major contributors to these problems.
One particular example is shown in
Fig 14.3,
a transistor amplifier, shown in
skeleton form, with sharply tuned resona-
tors at input and output.
Because of reverse coupling, the two
tuned circuits interact, making adjustments
difficult or even impossible. The likelihood
of oscillation is very high. There are two
solutions: drastically reduce the gain of the
amplifier, or use an amplifier circuit that
has very little reverse coupling. Usually,
both methods are used simultaneously (in
the right amount) in order to get predict-
able performance. The object lesson for the
system designer is that a combination of
reduced gain and low reverse coupling is
the safe way to go when designing a radio
system. More stages may be required, but
the price is well worthwhile. The cascode
amplifier, grounded-gate amplifier, dual-
gate FET and many types of IC amplifiers
are examples of circuits that have little re-
verse coupling and good stability. “Neu-
tralization” methods are used to cancel
reverse coupling that causes instability. All
such circuits are said to be “unilateral,”
which means “in one direction” and both
input and output can be independently
tuned as in Fig 14.3 if the gain is not too
high.
Feedback (Desired)
The
RF Power Amplifiers
chapter
explains how negative feedback (good
feedback) can be used to stabilize a circuit
and make it much more predictable over a
range of temperature and component tol-
erances. Here we wish to point out some
system implications of negative feedback.
One is that the gain, noise-figure and dis-
tortion performances within a stage are
made much more constant and predictable.
Therefore a system designer can put build-
ing blocks together with more confidence
and less guesswork.
There are some problems, though. In
some circuits the amount of feedback
depends on both the output impedance
of the driving circuit and the input im-
pedance of the next stage. A classic ex-
ample is the cascadable amplifier shown
in
Fig 14.4.
In this circuit, if the output load imped-
ance becomes very low the amplifier input
impedance becomes high, and vice versa
(a “teeter-totter” effect). Other amplifier
properties also can change. With amplifi-
ers of this type it is important to maintain
the correct impedances at the input and
output interfaces. Any building block
should be examined for effects of this kind.
Data sheets frequently specify the reverse
transfer values as well as those for for-
ward transfer. Often, lab measurements
are needed. Apply a signal to the output
and measure the reverse coupling to the
input. Where varying load and source im-
pedances are involved, look for a circuit
that is less vulnerable (that is, has less re-
verse coupling).
Another problem is that feedback net-
works often add thermal noise sources to a
circuit and so degrade its noise figure. In
systems where this is a consideration, use
so-called “lossless feedback” circuits.
These circuits use very efficient trans-
formers instead of resistors or lossy net-
works that introduce thermal noise into a
system.
Noise Factor and Noise Figure
The output resistance of the signal gen-
erator that drives a typical signal process-
ing block such as shown in Fig 14.4 is a
source of thermal noise power, which is a
natural phenomenon occurring in the
resistive component of any impedance. It
is caused by random motion of electrons
within a conducting (or semiconducting)
material. Note that the reactive part of an
impedance is not a source of thermal noise
power because the voltage across a pure
reactance and the current through the
reactance are in phase quadrature (90°) at
any one frequency. The average value of
the product of these two (the power) is
zero. If this is true at any frequency, then
it is true at all frequencies. Also, a purely
Fig 14.4—A
cascadable
amplifier using
feedback. The
feedback and
therefore the
amplifier
performance
depends on the
load and driving-
stage impedances.
Fig 14.3—A double tuned transistor
amplifier circuit that may oscillate due
to excessive amplification and reverse
coupling.
Receivers and Transmitters
14.3
Negative Feedback in RF Circuit Design
This sidebar shows how negative
feedback can enhance the perfor-
mance of the RF amplifier circuits
that are used in homebrew receiv-
ers, transmitters or transceivers.
The sidebar lists the advantages of
negative feedback, and presents
examples for the advantages. We
will not consider automatic gain
control (AGC) or automatic level
control (ALC) circuits, often referred
to as “envelope feedback” (see later
sections of this chapter).
1. All amplifiers have
nonlinearities that produce output
frequencies (harmonics,
intermodulation distortion and
adjacent channel interference) of a
certain amount that are not present
in the input signal. Feedback can
reduce the
percentage.
2. Feedback can be used to
increase or decrease the input
impedance or output impedance of
an amplifier stage. Actual L, C and
R values are modified by feedback
to “effective” values. The concept of
a dynamic or lossless resistance
that does not dissipate power or
create thermal noise is introduced.
3. Feedback can improve the
stability (freedom from a tendency to
oscillate) of an amplifier. This
includes the methods of feedback
network compensation and also
“neutralization” or “unilateralization”
which means the reduction of
internal feedback within the ampli-
fier.
4. Feedback can make the
frequency response, the input
impedance and the output imped-
ance of an amplifier more constant
over a wide frequency band.
5. Feedback can reduce gain and
frequency response changes due to
temperature, supply voltage, value
tolerances of inductors, capacitors
and resistors and transistor param-
eter spreads. The performance
variations over a large number of
identical circuits are greatly reduced.
6. By controlling the performance
of each stage in a multistage
system, using feedback, the overall
performance can be more accurately
predicted and maintained with little
or no “tweaking” of the individual
stages.
Feedback in an amplifier stage
nearly always reduces the gain (ratio
of output to input voltage, current or
power) to a lower value. For a
certain overall gain requirement,
more stages are required. This is in
nearly all cases a mild penalty. Each
extra stage is an additional source of
the imperfections that were enumer-
ated above. This means that the
entire chain must be designed as a
system in order to meet the system
goals. Feedback can also be applied
over two, or sometimes three
cascaded stages, but is more
difficult. In this brief overview we will
focus mainly on single-stage feed-
back.
The Negative Feedback Concept
Fig A
shows an amplifier with
negative feedback. Prior to feed-
back, the amplifier has gain G and a
phase reversal that we assume for
simplicity is 180°. A portion of the
output
voltage,
or perhaps a portion
of the output
current,
goes through a
feedback network to the input where
it combines, possibly in
series
with
or in
parallel
with the generator
signal to produce a
modified
input
signal that is smaller than it was with
no feedback. This new input consists
partly of generator signal, assumed
to be perfect, and partly of an output
signal, assumed to be imperfect.
Note that the generator signal and
the fed-back signal are in opposite
phase. When this modified input
signal is amplified (even though it is
amplified imperfectly itself) the
original imperfections that were
(continued on page 14.6)
Fig A—Block diagram of a nonlinear amplifier with feedback to improve linearity.
Fig B—Graph 1 shows the gain margin of the feedback loop when the loop phase shift is 180°. Graph 2 shows the phase
margin of the feedback look when the loop gain is 0 dB.
14.4
Chapter 14
Fig C—Part 1 is an example of voltage-series feedback. A fraction, B, of the noninverted output voltage is in series with the
input-signal voltage. Z
out
is reduced and Z
in
is increased. R
2
consists of R
ee
in parallel with R
e
(= 1/gm).
Part 2 is an example of voltage-shunt feedback. The signal generator is a constant-current source, I
g
. Current B V
out
is in
parallel with I
g
and in phase-opposition to I
g
. The two sample circuits are a one-stage trans-resistance amplifier and an op-
amp as an inverting voltage amplifier. Input impedance and output impedance are both reduced.
Part 3 is an example of current-series feedback, or a transconductance amplifier. The noninverted output current produces a
feedback voltage of V
f
= B I
out
, which is in series opposition with the signal V
g
. Z
out
is increased and Z
in
is also increased.
Part 4 is an example of current-shunt feedback. The inverted output current produces a feedback current If = B I
out
, which is
in shunt opposition with the signal I
g
. Z
out
is increased and Z
in
is decreased.
Receivers and Transmitters
14.5

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