Analysis of inductively injection locked oscillators at an integer frequency ratio

Abstract

Oscillators under inductive resonant coupling are used to reduce phase noise in frequency generation and can also be applied to implement sensor systems. Here the operation of two inductively locked oscillators at an integer frequency ratio is analysed in depth, paying attention to the locking mechanism and identifying the various kinds of steady state solutions. The injection-locked solution curve versus the parameter used for control or sensing is obtained through harmonic balance with the aid of auxiliary generators. When increasing the coupling effects, the locked-operation interval undergoes a significant shift versus the parameter, which is understood with the aid of an analytical formulation. The stability properties and phase noise are analysed by linearizing the system about the mutually injection-locked steady-state solution, through the extraction of an outer-tier Jacobian matrix. The results are validated with time-domain maps based on maxima detection and with measurements.