Substitution Method for the Analysis of Systems based on Two Nonlinear Resonators

Circuits containing two nonlinear resonators have recently been proposed for nonreciprocal isolators, robust wireless power transfer and sensors. A fundamental characteristic is the presence of hysteresis, associated with points of infinite slope in the solution curves. However, the prediction of hysteresis in the presence of the two distinct resonators is not possible in default harmonic balance (HB) and the additional use of continuation techniques may not be exhaustive enough. Here we present a novel substitution method that enables the system control through a single excitation voltage. Taking advantage of this single control, a simple condition is provided to obtain all the existing loci of infinite-slope points. The methods are compatible with commercial HB. They will be illustrated through their application to a Lorentzian-Fano nonlinear isolator.