The specification of oscillator characteristics from measurements made in the frequency domain

Abstract

A cross-correlation technique for measuring the very short-term (milliseconds to seconds) properties of stable oscillators is described. Time-dependent functions representing signals from two separate oscillators are led to a function multiplier where the instantaneous product of the functions is made. The oscillators are either set to a given phase relation or allowed a small relative drift so that a slow beat frequency is observed. Short-term fluctuations superimposed upon the slow beat signal from the multiplier output will represent the instantaneous phase difference between the oscillators when the inputs are in quadrature. When the inputs are in and out of phase, the fluctuations represent amplitude fluctuations. The time averaging function is determined by a filter having a rectangular pass band from nearly zero frequency to a cutoff frequency v <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> . The mean square frequency deviation measured in a bandwidth ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> is obtained by differentiating, filtering, squaring, and averaging the signal from the function multiplier data being taken when the input signals are in quadrature. Mean square averages of amplitude and phase averaged over various bandwidths ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> may be obtained by bypassing the differentiator. Sample data from measurements on hydrogen masers are presented, and the effect of thermal noise is seen to be the major factor limiting the short-term frequency stability of the signals.