A Liénard Oscillator Circuit with a Memristive Bridge Rectifier

Abstract

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.

Keywords

• Liénard Oscillator
• Schottky Diode Bridge Rectifier
• R-L-C Filter
• Limit Cycle
• Circuit Dynamics.

Ethical Statement

The authors declared no conflicts of interest with respect to the research, authorship, and/or publication of this article.

Memristif Köprü Doğrultuculu Bir Liénard Osilatör Devresi

Abstract

Bu çalışmada köprü doğrultucu ve R-L-C çıkış filtresi ile negatif direnç dönüştürücü içeren yeni bir Liénard osilatör tasarımı önerilmiştir. Köprü doğrultucu, memristif davranış sergilemekte ve periyodik kararlı durumda Liénard salınımı için gerekli olan çift doğrusal olmayan direnci sağlamaktadır. Devrenin matematiksel modeli, durum-uzay denklemleri ve doğrusal olmayan özelliklerinin analizi dahil olmak üzere geliştirilmiştir. LTSpice simülasyonları, daha yüksek frekanslarda memristif köprünün doğrusal olmayan bir direnç olarak işlev gördüğünü ve devrenin bir Liénard osilatörü olarak çalışmasını sağladığını göstermektedir. Simülasyon sonuçları, Liénard sistemlerine özgü periyodik dalga formları ve limit döngüleri göstermektedir, ancak Shottky diyotlarının eşik etkileri ve ikinci harmonik üretimi nedeniyle ideal sinüzoidal davranıştan kayda değer sapmalar görülmektedir. Önerilen osilatör, geleneksel iki değişkenli Liénard sistemlerinden daha fazla durum değişkenine sahip olmasına rağmen, kolayca temin edilebilen bileşenler kullanarak (Schottky diyotları, pasif elemanlar ve bir işlemsel yükselteç) sürekli salınımları başarıyla elde etmektedir. Devrenin davranışı, gerilim-akım karakteristikleri, limit döngüleri ve faz portreleri aracılığıyla analiz edilmiş, Liénard tipi bir osilatör olarak çalıştığı doğrulanmıştır. Bu çalışma, Liénard osilatörlerinin yarı iletken elemanlar kullanılarak uygulanması için yeni olanaklar sunmakta ve parametrik analiz ve analitik çözümler konusunda gelecekteki araştırmalar için farklı bakış açıları önermektedir.

Keywords

• Liénard Osilatörü
• Schottky Diyot Köprü Doğrultucu
• R-L-C Filtresi
• Limit Döngüsü
• Devre Dinamikleri

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