- 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 C1. 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 C1 be minimum. The smaller the C1, however, the more difficult it is to tune the oscillator (i.e., the smaller is Df' for a given change in CL). The highest stability oscillators use crystal units that have a small C1 (and a high Q). Since C1 decreases rapidly with overtone number, high-stability oscillators generally use third- or fifth-overtone crystal units. Overtones higher than fifth are rarely used, because R1 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 C1. 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.