A New Class of Nonlinear Resonance Networks Modeled by Levinson–Smith and Liénard Equations

Abstract

We propose a new class of nonlinear resonance networks which are modeled by standard second-order nonlinear differential equations of the Levinson-Smith type or its subset, the Liénard type. In particular, we modify series and parallel RLC resonance networks such that the passive resistor in these networks is composed of a fixed part and a variable voltage-or current-controlled part. The variable resistor is then made controllable by one of the circuit’s state-space variables leading to an embedded self feedback control mechanism. A possible discrete component circuit realizing the proposed concept is presented along with its simulations and experimental verification. The filter response behavior of one of the modified series resonance circuits is also experimentally verified using a Field Programmable Analog Array.