Identification of Power-Law Type Oscillator Phase Noise Spectra from Measurements

In this paper we demonstrate how structure functions can be used to identify power-law type spectral density components 1/fv associated with oscillator phase noise measurements when polynomial type systematic drifts are present. The technique discussed is new and novel in that it avoids the usual errors that are introduced in the measurement due to removing systematic trends in the observed data by the usual estimation detrending techniques. Several applications of the theory are given and a convenient and expedient look-up table is provided for those who perform measurements. The paper begins by summarizing accepted frequency stability measures and places these into perspective with structure functions of oscillator instability. The paper ends by showing how the rms fractional frequency deviation differs from the Allan variance; numerical examples are given.