On the Difference Between Two Widely Publicized Methods for Analyzing Oscillator Phase Behavior

This paper describes the similarities and differences between two widely publicized methods for analyzing oscillator phase behav-ior. The methods were presented in [3] and [6]. It is pointed out that both methods are almost alike. While the one in [3] can be shown to be, mathematically, more exact, the approximate method in [6] is somewhat simpler, facilitating its use for purposes of anal-ysis and design. In this paper, we show that, for stationary input noise sources, both methods produce equal results for the oscilla-tor’s phase noise behavior. However, when considering injection locking, it is shown that both methods yield different results, with the approximation in [6] being unable to predict the locking behav-ior. In general, when the input signal causing the oscillator phase perturbations is non-stationary, the exact model produces the cor-rect results while results obtained using approximate model break down. 1