When it comes to characterizing an oscillator, frequency stability and accuracy are key values. Accuracy in general describes the deviation of a measurement value, be it a single value or an average, from the standard of the quantity being measured. The accuracy of an oscillator is in general given in ppm. Stability on the other hand describes the variation of measurement samples and therefore can only be calculated for a set of measurement values. Frequency stability of an oscillator is typically characterized as its phase noise. Precisely, the single side band phase noise over the offset frequency or the integrated single side band phase noise as a scalar value. The single side band (SSB) phase noise fully specifies a source, as the phase noise trace is axially symmetric with regard to the oscillator frequency. The SSB phase noise is the amount of power located in a bandwidth B around an offset frequency f that results from phase changes of the oscillator under test. The phase noise value is usually normalized to B = 1 Hz of bandwidth.
Specifying the phase noise of an oscillator is equivalent to specifying the frequency noise, as the normalized or fractional frequency (to the nominal carrier frequency) can be directly derived from the phase as the instantaneous frequency Specifying the phase noise of an oscillator is equivalent to specifying the frequency noise, as the normalized or fractional frequency (to the nominal carrier frequency) can be directly derived from the phase as the instantaneous frequency v (t) can be written as
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With Φ(t) the instantaneous phase.
A number of methods to measure phase or frequency noise exist, but most of them measure phase fluctuations. Therefore phase noise is specified for most oscillators. With regard to spectrum analyzer usage for oscillator stability measurements, the following three methods are described briefly in chapter 2.
- Beat frequency method or heterodyne frequency measuring.
- Spectrum analyzer method.
- Phase locked loop method (signal source analyzer method).
Alternatively to the spectral domain based phase noise characterization, oscillator stability can also be specified in the time domain. Stability in the time domain can be characterized using the two-sample or Allan variance. It plots the variance of two samples over the time that separates these two samples.
As both domains characterize the same property, the frequency domain representation of the oscillator stability can be converted into the time domain representation and vice versa. Formulas for the most common conversions are given in chapter 3. For a detailed view on the mathematical background, have a look at the references.