PV-PPV: Parameter Variability Aware, Automatically Extracted, Nonlinear Time-Shifted Oscillator Macromodels

The PPV is a robust phase domain macromodel for oscillators. It has been proven to predict oscillators´ responses correctly under small signal perturbations, and capture nonlinear phase effects such as injection locking/pulling. In this work, we present a novel approach to extend the PPV macromodel to handle variability in circuit parameters. We derive a modified PPV-based phase equation in which parameter variations are modelled as special inputs. An important feature of our technique is that it avoids PPV re-extraction, this resulting in great convenience and efficiency in its use for, e.g., Monte Carlo type simulations. Using LC and ring oscillators as examples, we demonstrate the capability of the proposed technique for capturing parameter variation effects in injection locking analysis. Simulation results show that our new approach accurately predicts the maximum locking range of oscillators with speedups of two orders of magnitude over direct simulation.