On the Behavior of a Non-Linear Bandpass Filter with Self Voltage-Controlled Resistors

In this work, we explore the behavior of a classical RLC resonance-based bandpass filter, which includes two resistors (one of which is associated with a non-ideal inductor), when either of these resistors is self voltage-controlled. In particular, self-feedback control is achieved by using the voltage developed across the inductor or the capacitor to dynamically change the value of the controlled resistor. This results in a multiplication-type non-linearity, which transforms the linear filter into a non-linear filter described by a set of non-linear differential equations. When gradually increasing the strength of the non-linearity, a notch-like behavior is observed at twice the resonance frequency. However, the non-linear filter can lose its stability with excessive feedback. Simulations and experimental results are provided to support the theory.