The Quadrature LC Oscillator: A Complete Portrait Based on Injection Locking

Abstract

We show that the quadrature LC oscillator is best treated as two strongly coupled, nominally identical oscillators that are locked to the same frequency. Differential equations that extend Adler's description of locking to strong injection reveal the full dynamics of this circuit. With a simplifying insight, the analysis reveals all the modes of the oscillator, their stability, the effects of mismatch on quadrature phase accuracy, and through a novel use of the analysis, phase noise.