Generalized analysis of systems based on two nonlinear resonators

Abstract

Circuits containing two nonlinear resonators have been recently proposed for a variety of applications, such as nonlinear isolators, robust wireless power transfer, and sensors. However, their simulation is difficult due to the presence of hysteresis phenomena, associated with turning points in the solution curve, and even disconnected curves, as will be shown in this work. Here, we will present a general analysis methodology, compatible with commercial harmonic balance (HB) and able to provide all the coexisting periodic solutions. It is based on the use of two auxiliary generators (AGs), one per nonlinear resonator. The first AG acts like an independent source and controls the second one, which also depends on the input source, unlike a previously presented formulation. This extra dependence enables a systematic and broad-scope application but demands a conceptually different analysis strategy, presented in this work. Besides its numerical capabilities (in combination with HB), the new formulation will provide insight into the complex behavior of systems composed by two nonlinear resonators. It will be illustrated through its application to a Lorentzian-Fano nonlinear isolator and a system for robust near-field wireless power transfer, in which the new formulation particularizes to the previous one.