Automated oscillator macromodelling techniques for capturing amplitude variations and injection locking

We present a method for extracting comprehensive amplitude and phase macromodels of oscillators from their circuit descriptions. The macromodels are based on combining a scalar, nonlinear phase equation with a small linear time-varying system to capture slowly-dying amplitude variations. The comprehensive macromodels are able to correctly predict oscillator response in the presence of interference at far lower computational cost than that of full SPICE-level simulation. We also present an efficient numerical method for capturing injection locking in oscillators, thereby improving on the classic technique of Adler (1946) in terms of accuracy and applicability to any kind of oscillator. We demonstrate the proposed techniques on LC and ring oscillators, comparing results from the macromodels against full SPICE-like simulation. Numerical experiments demonstrate speed tips of orders of magnitude, while retaining excellent accuracy.