**Oscilent Corporation
- Technical References**

Introduction to Quartz Frequency Standards

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**Introduction to Quartz Frequency Standards - The Effects
of Noise**

Sometimes the suitability of oscillators for an application is limited by deterministic phenomena. In other instances, stochastic (random) processes establish the performance limitations. Except for vibration, the short-term instabilities almost always result from noise. Long-term performance of quartz and rubidium standards is limited primarily by the temperature sensitivity and the aging, but the long-term performance of cesium and some hydrogen standards is limited primarily by random processes.

Noise can have numerous adverse effects on system performance.
Among these effects are the following: (1) it limits the ability
to determine the current state and the predictability of precision
oscillators (e.g., the noise of an oscillator produces time prediction
errors of ~ ts_{y}(t)
for prediction intervals of t); (2) it limits synchronization
and syntonization accuracies; (3) it can limit a receiver's
useful dynamic range, channel spacing, and selectivity; (4) it
can cause bit errors in digital communications systems; (5) it
can cause loss of lock, and limit acquisition and reacquisition
capability in phase-locked-loop systems; and (6) it
can limit radar performance, especially Doppler radar.

It is important to have appropriate statistical measures to characterize the
random component of oscillator instability. The subject of noise characterization
has been reviewed [4,18] and is also the subject of an IEEE standard [19]. The
two-sample deviation, denoted by s_{y}(T),
is the measure of short-term instabilities in the time domain. The phase noise,
denoted by L(f), or the phase instability, denoted by S_{f}(f),
are measures of instabilities in the frequency domain; L(f) º
S_{f}(f)/2 [19].