**Introduction to Quartz Frequency Standards - Stability versus Tunability**

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In most crystal oscillator types, a variable-load capacitor
is used to adjust the frequency of oscillation to the desired
value. Such oscillators operate at the parallel resonance region
of Figure 4, where the reactance versus frequency slope (i.e.,
the "stiffness") is inversely proportional to C_{1}.
For maximum frequency stability with respect to reactance (or
phase) perturbations in the oscillator circuit, the reactance
slope (or phase slope) must be maximum. This requires that the
C_{1} be minimum. The smaller the C_{1}, however,
the more difficult it is to tune the oscillator (i.e., the smaller
is Df' for a given change in C_{L}).
The highest stability oscillators use crystal units that have
a small C_{1} (and a high Q). Since C_{1} decreases
rapidly with overtone number, high-stability oscillators
generally use third- or fifth-overtone crystal units.
Overtones higher than fifth are rarely used, because R_{1}
also increases rapidly with overtone number, and some tunability
is usually desirable in order to allow setting the oscillator
to the desired frequency.

**Figure 4.** Reactance versus frequency of a crystal unit.

Wide-tuning-range VCXOs use fundamental mode crystal
units of large C_{1}. Voltage control is used for the
following purposes: to frequency or phase lock two oscillators;
for frequency modulation; for compensation, as in a TCXO (see
below); and for calibration (i.e., for adjusting the frequency
to compensate for aging). Whereas a high-stability, ovenized
10-MHz VCXO may have a frequency adjustment range of ±5
x 10^{-7} and an aging rate of 2 x 10^{-8} per
year, a wide-tuning-range 10-MHz VCXO may have
a tuning range of ±50 parts per million (ppm) and an aging
rate of 2 ppm per year.

In general, making an oscillator tunable over a wide frequency
range degrades its stability because making an oscillator susceptible
to intentional tuning also makes it susceptible to factors that
result in unintentional tuning. For example, if an oven-controlled
crystal oscillator (OCXO) is designed to have a stability of 1
x 10^{-12} for a particular averaging time and a
tunability of 1 x 10^{-7}, then the crystal's load reactance
must be stable to 1 x 10^{-5} for that averaging
time. Achieving such load-reactance stability is difficult
because the load-reactance is affected by stray capacitances
and inductances, by the stability of the varactor's capacitance
versus voltage characteristic, and by the stability of the voltage
on the varactor. Moreover, the 1 x 10^{-5} load-reactance
stability must be maintained not only under benign conditions,
but also under changing environmental conditions (temperature,
vibration, radiation, etc.). Therefore, the wider the tuning range
of an oscillator, the more difficult it is to maintain a high
stability.

Forward to "Quartz and the Quartz Crystal Unit".

Back to "Crystal Unit Equivalent Circuit".

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