Frequency measurement using the phase-controlled oscillator

This paper describes the application of the phase-controlled oscillator to precision frequency comparison in order to improve the measurement accuracy. A relation derived between the counter readings, which measure the average frequency over time T, and the power spectrum of the added phase noise forms the basis for the design of the loop in various applications: frequency comparison, optimization of the operating parameters of frequency standards by detecting the frequency shift due to an applied parameter change, and assessment of the phase jitter generated in multiplier chains. The design procedure includes a determination of the error due to drifts in the oscillator and an estimate of the response time of the loop. An example of a loop which multiplies a noisy 5.6 kHz signal by 200 is given. In determining the mean frequency of a 9.2 MHz crystal oscillator compared to a rubidium vapor frequency standard the one-second counter readings of the multiplied beat signal are found to have a standard deviation of 1.16 × 10^-11.