Lineer Zamanla Değişmeyen Endüktörlü ve Uyumlu Kesirli Dereceli Türev ile Modellenmiş Kondansatörlü Bir Salınım Devresinin Analizi

Öz

Kesirli dereceli devre elemanları araştırmacılar tarafından aralıksız olarak incelenmektedir. Literatürde giderek daha popüler hale gelmekteler. Son on yılda Uyumlu Kesirli Türev önerilmiş ve oldukça önem kazanmıştır. Bir LC tank devresinin veya bir LC osilatörünün incelenmesi, neredeyse tüm lisans fizik kitaplarında bulunabilir. Kesirli mertebeden kondansatör devreleri üzerine çok sayıda çalışma var olmasına rağmen, bildiğimiz kadarıyla, doğrusal zamanla değişmeyen bir endüktörden ve Uyumlu Kesirli Türev ile modellenmiş bir süper kondansatörden yapılmış bir osilatörün incelenmesi literatürde bulunmamaktadır. Bu makalede, literatürde ilk defa Uyumlu Kesirli Türev ile modellenmiş bir süper kondansatör ve lineer zamanla değişmeyen bir endüktör içeren kayıpsız bir osilatör devresi incelenmiştir. Devrenin doğal tepkisi analitik olarak bulunmuştur. Devrenin davranışı, farklı başlangıç koşulları için benzetimlerle gösterilmiştir.

Anahtar Kelimeler

• Devre Analizi
• Doğal Yanıt
• Kesirli Dereceden Devreler
• Salınım devresi
• Süperkondansatör
• Uyumlu Kesirli Türev.

Analysis of an Oscillation Circuit with a Linear Time-invariant Inductor and a Capacitor Modelled with Conformal Fractional Order Derivative

Öz

Fractional order circuit elements are being examined by researchers unremittingly. They are ever becoming more popular in the literature. The Conformable Fractional Derivative has been proposed and gained importance in the last decade. Examination of an LC tank circuit or an LC oscillator can be found in almost all undergrad physics books. There’s a considerable number of studies on fractional-order capacitor circuits but, to the best of our knowledge, examination of an oscillator made of a linear time-invariant inductor and a supercapacitor modeled with Conformable Fractional Derivative has not been found in literature. In this paper, a lossless oscillator circuit containing a linear time-invariant inductor and a supercapacitor modeled with Conformable Fractional Derivative is examined for the first time in the literature. Natural response of the circuit has been found analytically. Its behavior has been illustrated with simulations for different initial conditions.

Anahtar Kelimeler

• Circuit analysis
• Conformable Fractional Derivative
• Fractional Order Circuit
• Natural response
• Oscillation circuit
• Supercapacitor.

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