Analysis and design of injection-locked oscillators coupled to an external resonator

Abstract

This work investigates the nonlinear dynamics of an injection-locked power oscillator inductively coupled to an external resonator. This allows a high-efficiency power transfer while ensuring a constant oscillation frequency versus the coupling factor, unlike free-running implementations. The investigation focuses on the impact of the external-resonator elements on the locking range, output power, efficiency, and phase noise. The aim is to derive a strategy for an optimum selection of these elements. Initially, the effect of the coupled resonator is theoretically studied using a simple oscillator model, based on a cubic nonlinearity. For practical oscillators, two kinds of analysis methods, compatible with the use of commercial harmonic-balance (HB) simulators, are presented. The first one is semianalytical and is based on the extraction of a phase-dependent nonlinear admittance function from HB simulations. The system response is predicted in a flexible and computationally efficient manner, but coupling effects are considered at the fundamental frequency only. The second set of methods is fully based on HB and relies on the combination of a nonlinear immittance function and a Thevenin/Norton equivalent. The impact of the external resonator on the stability properties is analyzed through bifurcation detection. The phase-noise spectrum is predicted with a semianalytical formulation that demonstrates the benefit of the injection-locked operation. For validation, the methods have been applied to a Class-E oscillator at 13.56 MHz.