Phase Noise Measurement of Low-Noise Oscillators and Devices

Virtually all commercial instruments for the measurement of phase noise make use of the cross spectrum method. These instruments achieve high sensitivity by correlation and averaging on two equal channels, which measure the same input. Under the hypothesis that the two channels are statistically independent, the instrument rejects the background noise. However, the thermal energy inherent in the input power splitter introduces negative correlation. Other effects are present, like AM noise and impedance mismatching, which break the hypothesis that the two channels are statistically independent. Cross spectra, like covariances, are positive or negative. However, in the case of PM noise the negative outcomes are generally unnoticed because the instrument displays the absolute value in a log scale. The problem with negatives outcomes is that the result is a nonsense. Sensitivity and accuracy are better understood in terms of Type A and Type B uncertainty, well established concepts in general metrology. Most instruments use a mixer as the input phase detectors. Others detect the phase by direct digitization of the input signal, or with sophisticated Software Defined Radio techniques. The problem we discuss apply to all these technologies.