14 - 6
Cygnus 2 Operating Manual
for a number of materials, and has been found to be valid for frequency shifts
equivalent to F
f
= 0.4F
q
. Keep in mind that equation [2] was valid to only 0.02F
q
and equation [3] was valid only to ~0.05F
q
.
14.1.4 Active Oscillator
All of the instrumentation developed to date has relied on the use of an active
oscillator circuit, generally the type schematically shown in Figure 14-4. This circuit
actively keeps the crystal in resonance, so that any type of period or frequency
measurement may be made. In this type of circuit, oscillation is sustained as long
as the gain provided by the amplifiers is sufficient to offset losses in the crystal and
circuit and the crystal can provide the required phase shift. The basic crystal
oscillator’s stability is derived from the rapid change of phase for a small change in
the crystal’s frequency near the series resonance point, as shown in Figure 14-5
on page 14-7.
Figure 14-4 Active oscillator circuit
The active oscillator circuit is designed so the crystal is required to produce a phase
shift of 0 degrees, which allows it to operate at the series resonance point. Long-
and short-term frequency stabilities are a property of crystal oscillators because
very small frequency changes are needed to sustain the phase shift required for
oscillation. Frequency stability is provided by the quartz crystal even though there
are long term changes in electrical component values caused by temperature or
aging or short-term noise-induced phase jitter.
As mass is added to a crystal, its electrical characteristics change. Figure 14-6 on
page 14-8 is the same plot as Figure 14-5 overlaid with the response of a heavily
loaded crystal. The crystal has lost the steep slope displayed in Figure 14-5.
Because the phase slope is less steep, any noise in the oscillator circuit translates
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