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Chapter 10
Oscillators and
Synthesizers
Just say in public that oscillators are one
of the most important, fundamental build-
ing blocks in radio technology and you
will immediately be interrupted by some-
one pointing out that
tuned-RF
(
TRF
)
receivers can be built without any form of
oscillator at all. This is certainly true, but
it shows how some things can be taken for
granted. What use is any receiver without
signals to receive? All intentionally trans-
mitted signals trace back to some sort of
signal generator—an oscillator or fre-
quency synthesizer. In contrast with the
TRF receivers just mentioned, a modern,
all-mode, feature-laden MF/HF trans-
ceiver may contain in excess of a dozen
RF oscillators and synthesizers, while a
simple QRP CW transmitter may consist
of nothing more than a single oscillator.
(This chapter was written by David Stock-
ton, GM4ZNX. Frederick J. Telewski,
WA7TZY, also contributed to the Fre-
quency Synthesizers section.)
In the 1980s, the main area of progress in
the performance of radio equipment was
the recognition of receiver intermodulation
as a major limit to our ability to communi-
cate, with the consequent development of
receiver front ends with improved ability
to handle large signals. So successful was
this campaign that other areas of trans-
ceiver performance now require similar
attention. One indication of this is any
equipment review receiver dynamic range
measurement qualified by a phrase like
“limited by oscillator phase noise.” A plot
of a receiver’s effective selectivity can
provide another indication of work to be
done: An IF filter’s high-attenuation region
may appear to be wider than the filter’s
published specifications would suggest—
almost as if the filter characteristic has
grown sidebands! In fact, in a way, it has:
This is the result of local-oscillator (LO) or
synthesizer
phase noise
spoiling the
receiver’s overall performance. Oscillator
noise is the prime candidate for the next
major assault on radio performance.
The sheer number of different oscillator
circuits can be intimidating, but their great
diversity is an illusion that evaporates once
their underlying pattern is seen. Almost all
RF oscillators share one fundamental prin-
ciple of operation: an amplifier and a filter
operate in a loop (
Fig 10.1
). There are
plenty of filter types to choose from:
•
be applicable to oscillators. There is an
equally large range of amplifiers to choose
from:
•
Vacuum tubes of all types
•
Bipolar junction transistors
•
Field effect transistors (JFET, MOSFET,
GaAsFET, in all their varieties)
• Gunn diodes, tunnel diodes and other
negative-resistance generators
It seems superfluous to state that any-
thing that can amplify can be used in an
oscillator, because of the well-known pro-
pensity of all prototype amplifiers to os-
cillate! The choice of amplifier is widened
further by the option of using single- or
multiple-stage amplifiers and discrete de-
vices versus integrated circuits. Multiply
all of these options with those of filter
choice and the resulting set of combina-
tions is very large, but a long way from
complete. Then there are choices of how
to couple the amplifier into the filter and
the filter into the amplifier. And then there
are choices to make in the filter section:
Should it be tuned by variable capacitor,
variable inductor or some form of sliding
cavity or line?
Despite the number of combinations
that are possible, a manageably small
number of types will cover all but very
special requirements. Look at an oscilla-
tor circuit and “read” it: What form of fil-
ter—
resonator—
does it use? What form
of amplifier? How have the amplifier’s
input and output been coupled into the fil-
ter? How is the filter tuned? These are
simple, easily answered questions that put
oscillator types into appropriate catego-
ries and make them understandable. The
questions themselves may make more
LC
•
Quartz crystal and other piezoelectric
materials
•
Transmission line (stripline, microstrip,
troughline, open-wire, coax and so on)
• Microwave cavities, YIG spheres, di-
electric resonators
• Surface-acoustic-wave (SAW) devices
Should any new forms of filter be in-
vented, it’s a safe guess that they will also
Fig 10.1—Reduced to essentials, an
oscillator consists of a filter and an
amplifier operating in a feedback loop.
Oscillators and Synthesizers
10.1
sense if we understand the mechanics of
oscillation, in which
resonance
plays a
major role.
tion, it has some extra potential energy.
At the center of its swing, the pendulum
is at its lowest point with respect to gravity
and so has lost the extra potential energy.
At the same time, however, it is moving at
its highest speed and so has its greatest
kinetic energy. Something interesting is
happening: The pendulum’s stored energy
is continuously moving between potential
and kinetic forms. Looking at the pendu-
lum at intermediate positions shows that
this movement of energy is smooth. New-
ton provided the keys to understanding this.
It took his theory of gravity and laws of
motion to explain the behavior of a simple
weight swinging on the end of a length of
string and calculus to perform a quantita-
tive mathematical analysis. Experiments
had shown the period of a pendulum to be
very stable and predictable. Apart from side
effects of air drag and friction, the length of
the period should not be affected by the
mass of the weight, nor by the amplitude of
the swing.
A pendulum can be used for timing
events, but its usefulness is spoiled by the
action of drag or friction, which eventu-
ally stops it. This problem was overcome
by the invention of the
escapement
, a part
of a clock mechanism that senses the
position of the pendulum and applies a
small push in the right direction and at the
right time to maintain the amplitude of
its swing or oscillation. The result is a
mechanical oscillator: The pendulum acts
as the filter, the escapement acts as the
amplifier and a weight system or wound-
up spring powers the escapement.
Electrical oscillators are closely analo-
gous to the pendulum, both in operation and
in development. The voltage and current in
the tuned circuit—often called
tank circuit
because of its energy-storage ability—both
vary sinusoidally with time and are 90° out
of phase. There are instants when the cur-
rent is zero, so the energy stored in the in-
ductor must be zero, but at the same time
the voltage across the capacitor is at its
peak, with all of the circuit’s energy stored
in the electric field between the capacitor’s
plates. There are also instants when the
voltage is zero and the current is at a peak,
with no energy in the capacitor. Then, all
of the circuit’s energy is stored in the
inductor’s magnetic field.
Just like the pendulum, the energy
stored in the electrical system is swinging
smoothly between two forms; electric
field and magnetic field. Also like the
pendulum, the tank circuit has losses. Its
conductors have resistance, and the capa-
citor dielectric and inductor core are im-
perfect. Leakage of electric and magnetic
fields also occurs, inducing currents in
neighboring objects and just plain radiat-
ing energy off into space as radio waves.
The amplitudes of the oscillating voltage
and current decrease steadily as a result.
Early intentional radio transmissions,
such as those of Heinrich Hertz’s experi-
ments, involved abruptly dumping energy
into a tuned circuit and letting it oscillate,
or
ring
, as shown in
Fig 10.3
. This was
done by applying a spark to the resonator.
Hertz’s resonator was a gapped ring, a
good choice for radiating as much of
the energy as possible. Although this
looks very different from the LC tank of
Fig 10.2, it has inductance
distributed
around its length and capacitance distrib-
uted across it and across its gap, as
opposed to the
lumped
L and C values in
Fig 10.2. The gapped ring therefore works
just the same as the LC tank in terms of
oscillating voltages and currents. Like the
pendulum and the LC tank, its period, and
HOW OSCILLATORS WORK
Maintained Resonance
The pendulum, a good example of a
resonator, has been known for millennia
and understood for centuries. It is closely
analogous to an electronic resonator, as
shown in
Fig 10.2
. The weighted end of
the pendulum can store energy in two dif-
ferent forms: The
kinetic energy
of its
motion and the
potential energy
of it being
raised above its rest position. As it reaches
its highest point at the extreme of a swing,
its velocity is zero for an instant as it
reverses direction. This means that it has,
at that instant, no kinetic energy, but be-
cause it is also raised above its rest posi-
Fig 10.2—A resonator lies at the heart of every oscillatory mechanical and
electrical system. A mechanical resonator (here, a pendulum) and an electrical
resonator (here, a tuned circuit consisting of L and C in parallel) share the same
mechanism: the regular movement of energy between two forms—potential and
kinetic in the pendulum, electric and magnetic in the tuned circuit. Both of these
resonators share another trait: Any oscillations induced in them eventually die
out because of losses—in the pendulum, due to drag and friction; in the tuned
circuit, due to the resistance, radiation and inductance. Note that the curves
corresponding to the pendulum’s displacement vs velocity and the tuned circuit’s
voltage vs current, differ by one quarter of a cycle, or 90°.
10.2
Chapter 10
loops, we must revisit this concept in
order to check that
those
loops
cannot
oscillate.) Fig 10.4C
shows what happens
to the amplitude of an oscillator if the
loop gain is made a little higher or lower
than one.
The loop gain has to be precisely one if
we want a stable amplitude. Any inaccu-
racy will cause the amplitude to grow to
clipping or shrink to zero, making the oscil-
lator useless. Better accuracy will only
slow, not stop this process. Perfect preci-
sion is clearly impossible, yet there are
enough working oscillators in existence
to prove that we are missing something
important. In an amplifier, nonlinearity is a
nuisance, leading to signal distortion and
intermodulation, yet nonlinearity is what
makes stable oscillation possible. All of the
vacuum tubes and transistors used in oscil-
lators tend to reduce their gain at higher
signal levels. With such components, only
a tiny change in gain can shift the loop’s
operation between amplitude growth and
shrinkage. Oscillation stabilizes at that
level at which the gain of the active device
sets the loop gain at exactly one.
Another gain-stabilization technique
involves biasing the device so that once
some level is reached, the device starts to
turn off over part of each cycle. At higher
levels, it cuts off over more of each cycle.
This effect reduces the effective gain quite
strongly, stabilizing the amplitude. This
badly distorts the signal (true in most com-
mon oscillator circuits) in the amplifying
device, but provided the amplifier is
lightly coupled to a high-Q resonant tank,
the signal in the tank should not be badly
distorted.
Many radio amateurs now have some
form of circuit-analysis software, usually
running on a PC. Attempts to analyze oscil-
lators by this means often fail by predict-
ing growing or shrinking amplitudes, and
often no signal at all, in circuits that are
known to work. Computer analysis of os-
cillator circuits can be done, but it requires
a sophisticated program with accurate,
nonlinear, RF-valid models of the devices
used, to be able to predict operating am-
plitude. Often even these programs need
some special tricks to get their modeled
oscillators to start. Such software is likely
to be priced higher than most private users
can justify, and it still doesn’t replace the
need for the user to understand the circuit.
With that understanding, some time, some
parts and a little patience will do the job,
unassisted.
Textbooks give plenty of coverage to
the frequency-determining mechanisms
of oscillators, but the amplitude-deter-
mining mechanism is rarely covered. It
is often not even mentioned. There is a
Fig 10.3—Stimulating a resonance, 1880s style. Shock-exciting a gapped ring with
high voltage from a charged capacitor causes the ring to oscillate at its resonant
frequency. The result is a damped wave, each successive alternation of which is
weaker than its predecessor because of resonator losses. Repetitively stimulating
the ring produces trains of damped waves, but oscillation is not continuous.
therefore the frequency at which it oscil-
lates, is independent of the magnitude of
its excitation.
Making a longer-lasting signal with the
Fig 10.3
arrangement merely involves
repeating the sparks. The problem is that a
truly continuous signal cannot be made this
way. The sparks cannot be applied often
enough or always timed precisely enough
to guarantee that another spark re-excites
the circuit at precisely the right instant. This
arrangement amounts to a crude spark
transmitter, variations of which served as
the primary means of transmission for the
first generation of radio amateurs. The use
of damped waves is now entirely forbidden
by international treaty because of their
great impurity. Damped waves look a lot
like car-ignition waveforms and sound like
car-ignition interference when received.
What we need is a
continuous wave
(
CW
) oscillation—a smooth, sinusoidal
signal of constant amplitude, without
phase jumps, a “pure tone.” To get it, we
must add to our resonator an equivalent of
the clock’s escapement—a means of syn-
chronizing the application of energy and a
fast enough system to apply just enough
energy every cycle to keep each cycle at
the same amplitude.
gain can be set to exactly compensate the
tank losses and perfectly maintain the
oscillation. The amplifier usually need only
give low gain, so active devices can be used
in oscillators not far below their unity
(unity = 1) gain frequency. The amplifier’s
output must be lightly coupled into the
tank—the aim is just to replace lost energy,
not forcibly drive the tank. Similarly, the
amplifier’s input should not heavily load
the tank. It is a good idea to think of
cou-
pling
networks rather than
matching
net-
works in this application, because a
matched impedance extracts the maximum
available energy from a source, and this
would certainly spoil an oscillator.
Fig 10.4A
shows the block diagram of
an oscillator. Certain conditions must be
met for oscillation. The criteria that sepa-
rate oscillator loops from stable loops are
often attributed to Barkhausen by those
aiming to produce an oscillator and to
Nyquist by those aiming for amplifier
stability, although they boil down to the
same boundary. Fig 10.4B
shows the loop
broken and a test signal inserted. (The
loop can be broken anywhere; the ampli-
fier input just happens to be the easiest
place to do it.) The criterion for oscilla-
tion says that at a frequency at which the
phase shift around the loop is exactly
zero, the net gain around the loop must
equal or exceed unity (that is, one).
(Later, when we design phase-locked
Amplification
A sample of the tank’s oscillation can be
extracted, amplified and reinserted. The
Oscillators and Synthesizers
10.3
good treatment in Clarke and Hess,
Commu-
nications Circuits: Analysis and Design
.
Fig 10.4—The bare-
bones oscillator block
diagram of Fig 10.1
did not include two
practical essentials:
Networks to couple
power in and out of
the resonator (A).
Breaking the loop,
inserting a test signal
and measuring the
loop’s overall gain
(B) allows us to
determine whether
the system can
oscillate, sustain
oscillation or clip (C).
Start-Up
Perfect components don’t exist, but if
we could build an oscillator from them,
we would naturally expect perfect per-
formance. We would nonetheless be disap-
pointed. We could assemble from our
perfect components an oscillator that
exactly met the criterion for oscillation,
having slightly excessive gain that falls to
the correct amount at the target operating
level and so is capable of sustained, stable
oscillation. But being capable of something
is not the same as doing it, for there is an-
other stable condition. If the amplifier in
the loop shown in Fig 10.4
has no input
signal, and is perfect, it will give no output!
No signal returns to the amplifier’s input
via the resonator, and the result is a sus-
tained and stable
lack
of oscillation. Some-
thing is needed to start the oscillator.
This fits the pendulum-clock analogy:
A wound-up clock is stable with its pen-
dulum at rest, yet after a push the system
will sustain oscillation. The mechanism
that drives the pendulum is similar to a
Class C amplifier: It does not act unless it
is driven by a signal that exceeds its
threshold. An electrical oscillator based
on a Class C amplifier can sometimes be
kicked into action by the turn-on transient
of its power supply. The risk is that this
may not always happen, and also that
should some external influence stop the
oscillator, it will not restart until someone
notices the problem and cycles the power.
This can be very inconvenient!
A real-life oscillator whose amplifier
does not lose gain at low signal levels can
self-start due to noise.
Fig 10.5
shows an
oscillator block diagram with the ampli-
fier’s noise shown, for our convenience, as
a second input that adds with the true input.
The amplifier amplifies the noise. The reso-
nator filters the output noise, and this sig-
nal returns to the amplifier input. The
importance of having slightly excessive
gain until the oscillator reaches operating
amplitude is now obvious. If the loop gain
is slightly above one, the recirculated noise
must, within the resonator’s bandwidth, be
larger than its original level at the input.
More noise is continually summed in as a
noise-like signal continuously passes
around the loop, undergoing amplification
and filtering as it does. The level increases,
Fig 10.5—An oscillator with noise. Real-
world amplifiers, no matter how quiet,
generate some internal noise; this
allows real-world oscillators to self-
start.
10.4
Chapter 10
causing the gain to reduce. Eventually, it
stabilizes at whatever level is necessary to
make the net loop gain equal to one.
So far, so good. The oscillator is running
at its proper level, but something seems
very wrong. It is not making a proper sine
wave; it is recirculating and filtering a noise
signal. It can also be thought of as a Q
multiplier with a controlled (high) gain,
filtering a noise input and amplifying it to
a set level. Narrow-band filtered noise
approaches a true sine wave as the filter is
narrowed to zero width. What this means is
that we cannot make a true sine-wave sig-
nal—all we can do is make narrow-band
filtered noise as an approximation to one.
A high-quality, low-noise oscillator is
merely one that does tighter filtering. Even
a kick-started Class-C-amplifier oscillator
has noise continuously entering its circu-
lating signal, and so behaves similarly.
A small-signal gain greater than one is
absolutely critical for reliable starting, but
having too much gain can make the final
operating level unstable. Some oscillators
are designed around limiting amplifiers to
make their operation predictable. AGC sys-
tems have also been used, with an RF
detector and dc amplifier used to servo-
control the amplifier gain. It is notoriously
difficult to design reliable crystal oscilla-
tors that can be published or mass-produced
without having occasional individuals
refuse to start without some form of shock.
Mathematicians have been intrigued by
“chaotic systems” where tiny changes in
initial conditions can yield large changes in
outcome. The most obvious example is
meteorology, but much of the necessary
math was developed in the study of oscilla-
tor start-up, because it is a case of chaotic
activity in a simple system. The equations
that describe oscillator start-up are similar
to those used to generate many of the popu-
lar, chaotic fractal images.
PHASE NOISE
Viewing an oscillator as a filtered-noise
generator is relatively modern. The older
approach was to think of an oscillator
making a true sine wave with an added,
unwanted noise signal. These are just dif-
ferent ways of visualizing the same thing:
They are equally valid views, which are
used interchangeably, depending which
best makes some point clear. Thinking in
terms of the signal-plus-noise version, the
noise surrounds the carrier, looking like
sidebands and so can also be considered to
be equivalent to random-noise FM and
AM on the ideal sine-wave signal. This
gives us a third viewpoint. Strangely,
these noise sidebands are called
phase
noise
. If we consider the addition of a
noise voltage to a sinusoidal voltage, we
Fig 10.6—At A, a phasor diagram of a clean (ideal) oscillator. Noise creates a
region of uncertainty in the vector’s length and position (B). AM noise varies the
vector’s length; PM noise varies the vector’s relative angular position (C) Limiting
a signal that includes AM and PM noise strips off the AM and leaves the PM (D).
Oscillators and Synthesizers
10.5
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