A Liénard Oscillator Circuit with a Memristive Bridge Rectifier

A novel Liénard oscillator design incorporating a bridge rectifier with an R-L-C output filter and negative resistance converter is presented. The bridge rectifier exhibits memristive behavior and provides the even nonlinear resistance required for Liénard oscillation in the periodic steady state. The circuit's mathematical model, including state-space equations and analysis of its nonlinear characteristics, is developed. LTSpice simulations demonstrate that at higher frequencies, the memristive bridge functions as a nonlinear resistor, enabling the circuit to operate as a Liénard oscillator. The simulation results show periodic waveforms and limit cycles characteristic of Liénard systems, though with notable deviations from ideal sinusoidal behavior due to the Schottky diodes' threshold effects and second harmonic generation. While the proposed oscillator has more state variables than traditional two-variable Liénard systems, it successfully achieves sustained oscillations using readily available components: Schottky diodes, passive elements, and an operational amplifier. The circuit's behavior is analyzed through voltage-current characteristics, limit cycles, and phase portraits, confirming its operation as a Liénard-type oscillator. This work opens new possibilities for implementing Liénard oscillators using semiconductor elements and suggests directions for future research in parametric analysis and analytical solutions.