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 behavior. The methods were presented by Adler (1946) and Hajimiri and Lee (1998). It is pointed out that both methods are almost alike. While Alder´s one in can be shown to be, mathematically, more exact, the approximate method of Hajimiri and Lee is somewhat simpler, facilitating its use for purposes of analysis and design. In this paper, we show that, for stationary input noise sources, both methods produce equal results for the oscillator´s phase noise behavior. However, when considering injection locking, it is shown that both methods yield different results, with the approximation of Hajimiri and Lee being unable to predict the locking behavior. In general, when the input signal causing the oscillator phase perturbations is non-stationary, the exact model produces the correct results while results obtained using the approximate model break down.