A Time-Domain Oscillator Envelope Tracking Algorithm Employing Dual Phase Conditions

Envelope-following methods face special challenges when applied to oscillators because of their fundamental property of dynamically changing frequencies. In this paper, we present a novel and robust approach for oscillator envelope following. Our method combines, unifies, and extends ideas from two prior oscillator envelope-following approaches, namely, Petzold´s method and the warped multitime partial differential equation. Our technique uses two extra system unknowns, as well as two extra ldquophase conditionrdquo equations, to track quantities related to dynamical frequency/time-period changes. These advances confer significant robustness, without appreciable computational overhead. We validate our method on LC, ring, and crystal oscillators, accurately predicting frequency and amplitude modulations, as well as transient startup envelopes. Speedups of one to two orders of magnitude are obtained over traditional alternatives.