A rigorous graphical technique for predicting sub-harmonic injection locking in LC oscillators

We develop methods for simply yet rigorously analyzing sub-harmonic injection locking (SHIL) in LC oscillators. Our method respects nonlinearities while offering intuition and design insights into the underlying mechanisms of different modes of locking. It can predict the presence/absence, number, stability and oscillation amplitudes of locks, as well as lock ranges. We use practical LC oscillator topologies from integrated RF and UHF applications for demonstration, validating our technique against SPICE-level simulations while being 1-2 orders of magnitude faster. To our knowledge, this is the first technique/tool for SHIL general enough to treat any kind of nonlinearity in LC oscillators.