Capturing oscillator injection locking via nonlinear phase-domain macromodels

Injection locking is a nonlinear dynamical phenomenon that is often exploited in electronic and optical oscillator design. Behavioral modeling techniques for oscillators that predict this phenomenon accurately are of significant scientific and practical importance. In this paper, we propose a nonlinear approach for generating small phase-domain oscillator/voltage-controlled oscillator (VCO) macromodels that capture injection locking well. Our nonlinear phase-domain macromodels are closely related to recent oscillator phase noise and jitter theories, and can be extracted efficiently by algorithm from SPICE-level descriptions of any oscillator or VCO. Using LC and ring oscillators as test cases, we confirm the ability of nonlinear phase macromodels to capture injection locking, and also obtain significant computational speedups over full SPICE-level circuit simulation. Furthermore, we show that our approach is equally effective for capturing the dynamics of transition to locking, including unlocked tones and phase jump phenomena.