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

Abstract

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 [2] 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. 25-5-4

Stability Analysis of Negative Resistance-Based Source Combining Power Amplifiers

“…When the current drive from the main source is increased, the fundamental and oscillation frequency spectra are visible and the oscillation frequency spectra decreases in magnitude; past a particular drive-level, however, the oscillation frequency spectra abruptly crashes below the noise floor. The abrupt suppression of the oscillation frequency spectra is consistent with injection locking, which has been observed and studied in negative-resistance-based LC oscillators [10]. For all cases, the oscillation frequency spectra falling below the noise floor of the oscilloscope corresponds to greater than 40 dB of difference between the fundamental and oscillation frequency spectra; for all practical purposes, this corresponds to oscillation being suppressed.…”