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Ters-Paralel Bağlı Schottky Diyot Dizisi Tabanlı Van der Pol Osilatörü Devresinin Modellenmesi ve LTspice ve Simulink Kullanarak Analizi

Yıl 2021, Cilt: 11 Sayı: 21, 81 - 91, 30.06.2021

Kübra Çakır Reşat Mutlu Ertuğrul Karakulak

Öz

Van der Pol Osilatörü 1926 yılında, Philips’te çalışan elektrik mühendisi ve fizikçi Dr. Balthasar Van der Pol tarafından keşfedilmiştir. Bu osilatör çeşidinin oldukça zengin dinamikleri mevcuttur. İlk yapılan Van der Pol Osilatörü’nde bir triyot kullanılmıştır. Günümüzde Van der Pol Osilatörü, farklı yarı iletken elemanları kullanılarak yapılabilmektedir. Bu çalışmada, nonlineer devre elemanı olarak Schottky diyotlar kullanılmıştır. Bir endüktör, bir kondansatör, ters-paralel bağlı Schottky diyot dizisi ve paralel bağlanmış negatif direnç devresinden oluşan bu yeni Van der Pol Osilatörü’nün devre denklemleri türetilmiş ve benzetimi yapılarak incelenmiştir. Benzetimlerde devrenin sınır döngüsü, devre elemanlarının akımları ve devrenin gerilimi LTspice devre analizi programı ve Matlab’in Simulink paket programı kullanılarak elde edilmiştir.

Anahtar Kelimeler

Nonlineer Osilatörler Van der Pol Osilatörü Schottky Diyot Sınır Döngüsü Devre Dinamikleri Devre Modellemesi

Kaynakça

  • B. van der Pol, “A theory of the amplitude of free and forced triode vibrations”, Radio Review, 1, pp. 701–710, 754–762, 1920.
  • B. Van der Pol, LXXXVIII. On “relaxation-oscillations”, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2(11), 978-992, 1926.
  • B. Van der Pol, J. Van Der Mark, “Frequency demultiplication”, Nature, 120(3019), 363-364, 1927.
  • B. van der Pol, “The nonlinear theory of electric oscillations”, Proc. IRE, 22, pp. 1051–1086, 1934.
  • M. L. Cartwright, “Balthazar van der Pol”, J. London Math. Soc., 35, pp. 367–376, 1960.
  • 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.
  • A. Liénard, "Etude des oscillations entretenues," Revue générale de l'électricité, 23, pp. 901–912 and 946–954, 1928.
  • T. Marios, “Theoretical and Numerical Study of the Van der Pol equation”, Dissertation, 2006.
  • J. M. Ginoux, C. Letellier, “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.
  • J. Gleick, M. Berry, “Chaos-making a new science”, Nature, 330, 293, 1987.
  • S. Ahmad, “Study of Non-linear Oscillations Using Tunnel Diode”, Doctoral dissertation, 1962.
  • T. J. Slight, B. Romeira, L. Wang, J. M. Figueiredo, E. Wasige, C. N. Ironside, “A Liénard oscillator resonant tunnelling diode-laser diode hybrid integrated circuit: model and experiment”, IEEE journal of quantum electronics, 44(12), 1158-1163, 2008.
  • L. Wang, “Reliable design of tunnel diode and resonant tunnelling diode based microwave sources”, Doctoral dissertation, University of Glasgow, 2012.
  • J. Casaleiro, L. B. Oliveira, A. C. Pinto, “Van der Pol Approximation Applied to Wien Oscillators”, Procedia Technology, 17, 335-342, 2014.
  • J. Brechtl, X. Xie, P. K. Liaw, “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, 2019.
  • M. Dursun, E. Kaşifoğlu, “Design and implementation of the FPGA-based chaotic van der pol oscillator”, International Advanced Researches and Engineering Journal, 2(3), 309-314, 2018.
  • Makoto Itoh, Leon O. Chua, “Dynamics of memristor circuits”, International Journal of Bifurcation and Chaos, 24(05), 1430015, 2014.
  • J. R. M. Pone, S. Çiçek, S. T. Kingni, A. Tiedeu, M. Kom, “Passive–active integrators chaotic oscillator with anti-parallel diodes: analysis and its chaos-based encryption application to protect electrocardiogram signals”, Analog Integrated Circuits and Signal Processing, 1-15, 2019.
  • K. Srinivasan, V. K. Chandrasekar, A. Venkatesan, I. R. Mohamed, “Duffing–van der Pol oscillator type dynamics in Murali–Lakshmanan–Chua (MLC) circuit”, Chaos, Solitons & Fractals, 82, 60-71, 2016.
  • B. Bao, H. Wu, L. Xu, M. Chen, W. Hu, “Coexistence of multiple attractors in an active diode pair based Chua’s circuit”, International Journal of Bifurcation and Chaos, 28(02), 1850019, 2018.
  • T. Kanamaru, “Van der Pol oscillator”, Scholarpedia, 2(1), 2202, 2007.
  • R. L. Boylestad, L. Nashelsky, “Electronic devices and circuit theory”, Pearson Education India, 2009.
  • Electronics Tutorials, URL:https://www.electronics-tutorials.ws/diode/diode_4.html (Erişim Zamanı; Mart 9, 2021) Wilderness Labs, Electronics, General Diodes, URL:http://developer.wildernesslabs.co/Hardware/Tutorials/Electronics/Part6/General_Diodes/ (Erişim Zamanı; Mart 10, 2021)
  • Wilderness Labs, Electronics, General Diodes, URL:http://developer.wildernesslabs.co/Hardware/Tutorials/Electronics/Part6/General_Diodes/ (Erişim Zamanı; Mart 10, 2021)
  • G. Mykolaitis, A. Tamaševičius, S. Bumelienė, A. Namajūnas, K. Pyragas, V. & Pyragas, “Application of ultrafast Schottky diodes to high megahertz chaotic oscillators”, Acta Physica Polonica A, vol. 107, no. 2, p. 365, 2005.
  • Alldatasheet, URL: https://pdf1.alldatasheet.com/datasheet-pdf/view/479637/LUGUANG/1N5819.html (Erişim Zamanı; Mayıs 13,2021)

Modeling an Anti-Parallel-Connected Schottky Diode String-Based Van der Pol Oscillator Circuit and its Analysis Using LTspice and Simulink

Yıl 2021, Cilt: 11 Sayı: 21, 81 - 91, 30.06.2021

Kübra Çakır Reşat Mutlu Ertuğrul Karakulak

Öz

The Van der Pol Oscillator was discovered in 1926 by electrical engineer and physicist Dr. Balthasar Van der Pol. This oscillator type has very rich dynamics. A triode is used in the original Van der Pol Oscillator. Nowadays, a Van der Pol Oscillator can be made using different semiconductor circuit elements. In this study, Schottky diodes are used as the nonlinear circuit elements. The circuit equations of the new Van der Pol Oscillator which consists of an inductor, a capacitor, anti-parallel connected Schottky diode strings, and a negative resistor circuit connected in parallel are derived and it is examined using simulations. The limit cycle of the circuit, the currents of the circuit elements and the voltage of the circuit were obtained using LTspice circuit analysis program and Simulink toolbox of Matlab.

Anahtar Kelimeler

Nonlinear Oscillators Van der Pol Oscillator Schottky Diode Limit Cycle Circuit Dynamics Circuit Modeling

Kaynakça

  • B. van der Pol, “A theory of the amplitude of free and forced triode vibrations”, Radio Review, 1, pp. 701–710, 754–762, 1920.
  • B. Van der Pol, LXXXVIII. On “relaxation-oscillations”, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2(11), 978-992, 1926.
  • B. Van der Pol, J. Van Der Mark, “Frequency demultiplication”, Nature, 120(3019), 363-364, 1927.
  • B. van der Pol, “The nonlinear theory of electric oscillations”, Proc. IRE, 22, pp. 1051–1086, 1934.
  • M. L. Cartwright, “Balthazar van der Pol”, J. London Math. Soc., 35, pp. 367–376, 1960.
  • 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.
  • A. Liénard, "Etude des oscillations entretenues," Revue générale de l'électricité, 23, pp. 901–912 and 946–954, 1928.
  • T. Marios, “Theoretical and Numerical Study of the Van der Pol equation”, Dissertation, 2006.
  • J. M. Ginoux, C. Letellier, “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.
  • J. Gleick, M. Berry, “Chaos-making a new science”, Nature, 330, 293, 1987.
  • S. Ahmad, “Study of Non-linear Oscillations Using Tunnel Diode”, Doctoral dissertation, 1962.
  • T. J. Slight, B. Romeira, L. Wang, J. M. Figueiredo, E. Wasige, C. N. Ironside, “A Liénard oscillator resonant tunnelling diode-laser diode hybrid integrated circuit: model and experiment”, IEEE journal of quantum electronics, 44(12), 1158-1163, 2008.
  • L. Wang, “Reliable design of tunnel diode and resonant tunnelling diode based microwave sources”, Doctoral dissertation, University of Glasgow, 2012.
  • J. Casaleiro, L. B. Oliveira, A. C. Pinto, “Van der Pol Approximation Applied to Wien Oscillators”, Procedia Technology, 17, 335-342, 2014.
  • J. Brechtl, X. Xie, P. K. Liaw, “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, 2019.
  • M. Dursun, E. Kaşifoğlu, “Design and implementation of the FPGA-based chaotic van der pol oscillator”, International Advanced Researches and Engineering Journal, 2(3), 309-314, 2018.
  • Makoto Itoh, Leon O. Chua, “Dynamics of memristor circuits”, International Journal of Bifurcation and Chaos, 24(05), 1430015, 2014.
  • J. R. M. Pone, S. Çiçek, S. T. Kingni, A. Tiedeu, M. Kom, “Passive–active integrators chaotic oscillator with anti-parallel diodes: analysis and its chaos-based encryption application to protect electrocardiogram signals”, Analog Integrated Circuits and Signal Processing, 1-15, 2019.
  • K. Srinivasan, V. K. Chandrasekar, A. Venkatesan, I. R. Mohamed, “Duffing–van der Pol oscillator type dynamics in Murali–Lakshmanan–Chua (MLC) circuit”, Chaos, Solitons & Fractals, 82, 60-71, 2016.
  • B. Bao, H. Wu, L. Xu, M. Chen, W. Hu, “Coexistence of multiple attractors in an active diode pair based Chua’s circuit”, International Journal of Bifurcation and Chaos, 28(02), 1850019, 2018.
  • T. Kanamaru, “Van der Pol oscillator”, Scholarpedia, 2(1), 2202, 2007.
  • R. L. Boylestad, L. Nashelsky, “Electronic devices and circuit theory”, Pearson Education India, 2009.
  • Electronics Tutorials, URL:https://www.electronics-tutorials.ws/diode/diode_4.html (Erişim Zamanı; Mart 9, 2021) Wilderness Labs, Electronics, General Diodes, URL:http://developer.wildernesslabs.co/Hardware/Tutorials/Electronics/Part6/General_Diodes/ (Erişim Zamanı; Mart 10, 2021)
  • Wilderness Labs, Electronics, General Diodes, URL:http://developer.wildernesslabs.co/Hardware/Tutorials/Electronics/Part6/General_Diodes/ (Erişim Zamanı; Mart 10, 2021)
  • G. Mykolaitis, A. Tamaševičius, S. Bumelienė, A. Namajūnas, K. Pyragas, V. & Pyragas, “Application of ultrafast Schottky diodes to high megahertz chaotic oscillators”, Acta Physica Polonica A, vol. 107, no. 2, p. 365, 2005.
  • Alldatasheet, URL: https://pdf1.alldatasheet.com/datasheet-pdf/view/479637/LUGUANG/1N5819.html (Erişim Zamanı; Mayıs 13,2021)
Toplam 26 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Akademik ve/veya teknolojik bilimsel makale
Yazarlar

Kübra Çakır 0000-0003-4762-5780

Reşat Mutlu 0000-0003-0030-7136

Ertuğrul Karakulak 0000-0001-5937-2114

Yayımlanma Tarihi 30 Haziran 2021
Gönderilme Tarihi 16 Mart 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 11 Sayı: 21

Kaynak Göster

APA 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.
AMA Çakır K, Mutlu R, Karakulak E. Ters-Paralel Bağlı Schottky Diyot Dizisi Tabanlı Van der Pol Osilatörü Devresinin Modellenmesi ve LTspice ve Simulink Kullanarak Analizi. EMO Bilimsel Dergi. Haziran 2021;11(21):81-91.
Chicago Çakır, Kübra, Reşat Mutlu, ve Ertuğrul Karakulak. “Ters-Paralel Bağlı Schottky Diyot Dizisi Tabanlı Van Der Pol Osilatörü Devresinin Modellenmesi Ve LTspice Ve Simulink Kullanarak Analizi”. EMO Bilimsel Dergi 11, sy. 21 (Haziran 2021): 81-91.
EndNote Çakır K, Mutlu R, Karakulak E (01 Haziran 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.
IEEE K. Çakır, R. Mutlu, ve E. Karakulak, “Ters-Paralel Bağlı Schottky Diyot Dizisi Tabanlı Van der Pol Osilatörü Devresinin Modellenmesi ve LTspice ve Simulink Kullanarak Analizi”, EMO Bilimsel Dergi, c. 11, sy. 21, ss. 81–91, 2021.
ISNAD Çakır, Kübra vd. “Ters-Paralel Bağlı Schottky Diyot Dizisi Tabanlı Van Der Pol Osilatörü Devresinin Modellenmesi Ve LTspice Ve Simulink Kullanarak Analizi”. EMO Bilimsel Dergi 11/21 (Haziran 2021), 81-91.
JAMA Çakır K, Mutlu R, Karakulak E. Ters-Paralel Bağlı Schottky Diyot Dizisi Tabanlı Van der Pol Osilatörü Devresinin Modellenmesi ve LTspice ve Simulink Kullanarak Analizi. EMO Bilimsel Dergi. 2021;11:81–91.
MLA Çakır, Kübra vd. “Ters-Paralel Bağlı Schottky Diyot Dizisi Tabanlı Van Der Pol Osilatörü Devresinin Modellenmesi Ve LTspice Ve Simulink Kullanarak Analizi”. EMO Bilimsel Dergi, c. 11, sy. 21, 2021, ss. 81-91.
Vancouver Çakır K, Mutlu R, Karakulak E. Ters-Paralel Bağlı Schottky Diyot Dizisi Tabanlı Van der Pol Osilatörü Devresinin Modellenmesi ve LTspice ve Simulink Kullanarak Analizi. EMO Bilimsel Dergi. 2021;11(21):81-9.
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