An Optocoupler-based Biryukov Oscillator Design

Öz

A Biryukov Equation is a special case of the Liénard equation. Liénard oscillators are commonly found in scientific literature and they have so many variants. The Biryukov Equation is used to model a set of damped oscillators. Unlike other Liénard oscillators, to the best of our knowledge, there is not a Biryukov oscillator that is experimentally examined in the literature, yet. In this study, a Biryukov oscillator is made using a microcontroller-controlled hand-made optocoupler, a negative impedance converter, and a gyrator. An STM32F070RB is used for the required switching. The oscillator’s operation has been examined experimentally. The optocoupler made of an LDR and a LED placed in a box allows the resistive switching required by a Biryukov oscillator to occur. The experimental results show that the circuit operates as an oscillator and performs well. It is also shown that an underdamped or an overdamped Biryukov oscillator can be made by varying circuit parameters.

Anahtar Kelimeler

• Biryukov Equation
• Biryukov Oscillator
• Circuit Dynamics.

Bir Optokuplör Tabanlı Biryukov Osilatörü Tasarımı

Öz

Biryukov Denklemi, Liénard denkleminin özel bir halidir. Liénard osilatörleri bilimsel literatürde yaygın olarak bulunur ve pek çok çeşidi vardır. Biryukov Denklemi, sönümlü osilatörlerin bir setini modellemek için kullanılır. Bildiğimiz kadarıyla diğer Liénard osilatörlerinden farklı olarak literatürde henüz deneysel olarak incelenen bir Biryukov osilatörü yoktur. Bu çalışmada, mikrodenetleyici kontrollü el yapımı bir optokuplör, bir negatif empedans dönüştürücü ve bir jiratör kullanılarak bir Biryukov osilatörü yapılmıştır. Gerekli anahtarlama için bir STM32F070RB kullanılmıştır. Bu osilatörün çalışması deneysel olarak incelenmiştir. Kutuya yerleştirilmiş bir LDR ve bir LED'den oluşan optokuplör, Biryukov osilatörünün ihtiyaç duyduğu dirençli anahtarlamanın gerçekleşmesini sağlar. Deneysel sonuçlar, devrenin bir osilatör olarak çalıştığını ve iyi performans gösterdiğini göstermektedir. Ayrıca, devre parametrelerini değiştirerek, düşük sönümlemeli veya aşırı sönümlemeli Biryukov osilatörünün yapılabileceği gösterilmiştir.

Anahtar Kelimeler

• Biryukov Denklemi
• Biryukov Osilatörü
• Devre Dinamikleri.

Kaynakça

1. A. Liénard, Etude des oscillations entretenues, Revue générale de l'électricité, 23, pp. 901–912 and 946–954, 1928
2. B. van der Pol, A theory of the amplitude of free and forced triode vibrations, Radio Review, 1, pp. 701–710, 754–762, 1920.
3. J. M. Ginoux, C. Letellier. (2012). Van der Pol and the history of relaxation oscillations: Toward the emergence of a concept, Chaos: An Interdisciplinary Journal of Nonlinear Science, 22(2), 023120, 2012.
4. B. Van der Pol, LXXXVIII. (1926). On “relaxation oscillations”, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2(11), 978- 992.
5. B. van der Pol, The nonlinear theory of electric oscillations, Proc. IRE, 22, pp. 1051–1086, 1934.
6. M. L. Cartwright, I. Van der Pol’s Equation for Relaxation Oscillations, In Contributions to the Theory of Nonlinear Oscillations (AM-29), Volume II, Princeton University Press., (pp. 1-18), 2016.
7. J. Gleick, M. Berry. (1987). Chaos-making a new science, Nature, 330, 293. S. Ahmad, Study of Non-linear Oscillations Using Tunnel Diode, Doctoral dissertation, 1962.
8. J. Brechtl, X. Xie, P. K. Liaw. (2019). Investigation of chaos and memory effects in the Bonhoeffer-van der Pol oscillator with a non-ideal capacitor, Communications in Nonlinear Science and Numerical Simulation, 73, 195-216.

9. T. J. Slight, B. Romeira, L. Wang, J. M. Figueiredo, E. Wasige, C. N. Ironside, (2008). A Liénard oscillator resonant tunnelling diode-laser diode hybrid integrated circuit: model and experiment, IEEE Journal of Quantum Electronics, 44(12), 1158-1163.
10. Çakır, K., Mutlu, R., & Karakulak, E. (2021). Ters-Paralel Bağlı Schottky Diyot Dizisi Tabanlı Van der Pol Osilatörü Devresinin Modellenmesi ve LTspice ve Simulink Kullanarak Analizi. EMO Bilimsel Dergi, 11(21), 81-91.
11. Çakır, K., Mutlu, R. (2022). Modeling and analysis of Schottky Diode Bridge and JFET based Liénard Oscillator circuit. DOI:10.14744/sigma.2022.00082.
12. Dursun, M., Kaşifoğlu, E. (2018). Design and implementation of the FPGA-based chaotic van der pol oscillator. International Advanced Researches and Engineering Journal, 2(3), 309-314.
13. Mevsim, E., Mutlu, R. (2022). A Microcontroller-based Liénard Oscillator. European Journal of Engineering and Applied Sciences, 5(2), 80-85.
14. Pilipenko A. M., and Biryukov V. N. (2013). Investigation of Modern Numerical Analysis Methods of Self-Oscillatory Circuits Efficiency. Journal of Radio Electronics, 9 ,1-9.
15. Biryukov, V. N., Gatko. L (2012). Exact stationary solution of the oscillator nonlinear differential equation, Nonlinear World, 10(9), 613–616.
16. Gasimov, Y. S., Guseynov, S. E., & Valdés, J. E. N. (2020). On some properties of limit cycles of the Biryukov equation. Proceedings of the Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, 46(2), 321-345.
17. Tulumbacı, F., & Mutlu, R. (2021). An optoelectronic-based memristor emulator circuit with a rational memristance function. Optoelectronics and Advanced Materials, Rapid Communications. 15(9-10), 487-497.
18. Karakulak, E. Mutlu, R. (2016). Adjustable Inductor using a memristor for integrated circuits, Materials, Methods & Technologies, 10, 283-293.