**Oscilent Corporation
- Technical References**

Introduction to Quartz Frequency Standards

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

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.