A Microcontroller-based Liénard Oscillator

Öz

Van der Pol Equation is a special case of Liénard equations. Both oscillators have significant historical importance. There are lots of different circuit topologies for Van der Pol and Liénard oscillators. Such oscillators can be made using vacuum tubes, diodes, etc. Some oscillators are made using microcontrollers, which are cheap and easy-to-use devices. They provide accurate adjustability of the frequency and magnitude of the waveforms. Arduino Nano Klon V3.0 microcontroller is a commonly used microcontroller. In this study, to the best of our knowledge, for the first time in literature, a Liénard Oscillator has been made with the Direct digital synthesis (DDS) method using the Arduino Nano Klon V3.0 microcontroller and two DACs. The experimental results of the oscillator are given. The circuit is able to produce the state variables of the oscillator, the effect of quantization can be seen on the waveforms, and it is shown that it performs well. The two variable outputs of the system let its phase portrait be examined easily. Also, using a microcontroller helps to design the oscillator in mere a few days.

Anahtar Kelimeler

• Microcontroller-based circuit design
• Liénard Equation
• Liénard Oscillator
• Van der Pol oscillator
• Digital Circuit Synthesis
• Limit Cycle
• Circuit Dynamics.

Mikrodenetleyici Tabanlı Bir Liénard Osilatörü

Öz

Van der Pol Denklemi, Liénard denklemlerinin özel bir halidir. Her iki osilatör de önemli bir tarihsel öneme sahiptir. Pek çok farklı Van der Pol ve Liénard osilatör devreleri mevcuttur. Bu tür osilatörler vakum tüpleri, diyotlar vb. kullanılarak yapılabilmektedir. Bazı osilatörler, ucuz ve kullanımı kolay cihazlar olan mikrodenetleyiciler kullanılarak yapılmaktadır. Mikrodenetleyiciler dalga biçimlerinin frekansının ve büyüklüğünün doğru şekilde ayarlanabilmesini sağlarlar. Arduino Nano Klon V3.0 mikrodenetleyici yaygın olarak kullanılan bir mikrodenetleyicidir. Bu çalışmada bildiğimiz kadarıyla literatürde ilk defa Arduino Nano Klon V3.0 mikrodenetleyici ve iki DAC denetleyici kullanılarak direct dijital sentezleme (DDS) yöntemi ile bir Liénard Osilatörü yapılmıştır. Çıkış akımını artırmak için bir tampon opamp kullanılmıştır. Osilatörün deneysel sonuçları verilmiştir. Devre, osilatörün durum değişkenlerini üretebilir, kuantalama hatasının dalga biçimleri üzerindeki etkisi görülebilmektedir ve bu devrenin iyi performans gösterdiği gösterilmiştir. Sistemin iki değişken çıkışı, faz portresinin kolayca incelenmesini sağlar. Ayrıca, bir mikrodenetleyici kullanmak, osilatörün sadece birkaç gün içinde tasarlanmasını sağlmaktadır.

Anahtar Kelimeler

• Mikrodenetleyici tabanlı devre tasarımı
• Liénard Denklemi
• Liénard Osilatörü
• Van der Pol osilatörü
• Dijital Devre Sentezi
• Limit Döngüsü
• Devre Dinamiği

Kaynakça

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