PPV-HB: Harmonic Balance for Oscillator/PLL Phase Macromodels

A unique feature of oscillators is that small but sustained external perturbations lead to unboundedly large changes in phase, thereby making standard harmonic balance (HB) inapplicable to realistic oscillator phase macromodels. In this paper, we rectify this situation by presenting a novel extension of HB that is capable of handling oscillator phase macro-models. Key to the new method, termed PPV-HB, is a formulation that separates unboundedly increasing phase terms from the bounded, periodic components. PPV-HB can be used not only on individual oscillators, but it also enables the application of HB-like techniques for simulating system-level equation systems composed of higher-level macromodels of blocks. We validate PPV-HB on individual oscillators and a PLL system, demonstrating excellent matches with transient simulation using phase macromodels. Speedups of 1-2 orders of magnitude are obtained, over and above additional speedups of another 2-3 orders of magnitude that stem from using macromodels (as opposed to full circuit simulation)