Understanding injection locking in negative-resistance LC oscillators intuitively using nonlinear feedback analysis

Simple, accessible and intuitive treatments of oscillator injection locking, that at the same time maintain rigour especially with regard to nonlinearities, appear to be lacking in the literature. We present a novel analysis that incorporates all these features but uses only basic mathematical and circuit theory concepts. We develop a graphical procedure for finding the nonlinear relationship between injection amplitude and lock range that is both accurate and insightful. We also provide freely downloadable MATLAB scripts implementing our analysis and graphical procedures. These scripts can be easily adapted to any negative-resistance LC oscillator and used for convenient and accurate exploration of injection locking and other properties