Nonlinear Dynamics of an Oscillator Inductively Coupled to an External Resonator for Power Transfer and Data Transmission

Abstract

This work presents an investigation of the nonlinear dynamics of an oscillator that is inductively coupled to an external resonator for power transfer applications. Analytical expressions are derived for the oscillation frequency and output power, which provide insight into the effect of the coupled resonator on the oscillator solution. From the analytical study, criteria are derived to maximize the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> range with a high efficiency and a limited variation of the oscillation frequency. The resistor of the external resonator can be modulated for data transmission to the core oscillator. Here the sensitivity to this resistor and its dependence on the coupling factor are analyzed in detail. The methods have been applied to a Class-E oscillator that has been analyzed through a contour-intersection technique. This is based on the extraction from harmonic balance (HB) of a bi-variate nonlinear admittance function accounting for the oscillator circuit, which is combined with the passive linear admittance function of the coupled resonator. The advantage is taken of the ease of this analysis to obtain constant-efficiency contours in the oscillatory regime, traced in the plane defined by the coupling factor and any suitable analysis parameter. By means of a bifurcation analysis, various phenomena, including the oscillation extinction plus onset versus the coupling factor and the appearance of quasi-periodic solutions, are detected and avoided. Very good correspondence has been obtained between simulation and measured results.