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Memristör tabanlı bir Liénard Osilatörü tasarımı

Yıl 2025, Cilt: 40 Sayı: 2, 1183 - 1196
https://doi.org/10.17341/gazimmfd.1273399

Öz

Yeni devre elemanı memristör sensör yapımında, hücresel sinir ağları, kaotik sistemler, programlanabilir analog devreler, kalıcı bellek cihazları gibi devre uygulamalarında kullanılabilmektedir. 1928’de salınımlı devrelerin modellenmesi için Alfred-Marie Liénard tarafından Liénard denklemleri önerilmiştir. İlk Liénard Osilatörü yapıldığında yarı iletken teknolojisi mevcut değildi ancak günümüzde çeşitli yarı iletken devre elemanları yeni tür Liénard Osilatörlerinin yapımında kullanılmaktadır. Günümüzde Knowm firmasının ürettiği ve piyasada satılan Karbon tabanlı memristörler mevcuttur. Yapılan literatür çalışmasına göre, henüz yapılmış Karbon Knowm memristör tabanlı bir Liénard Osilatörü bulunmamaktadır. Bu çalışmanın amacı iki adet Karbon tabanlı Knowm memristör kullanarak literatüre yeni bir Liénard Osilatör çeşidi kazandırmaktır. Bu çalışmada önce memristör tabanlı bir Liénard Osilatörü devre topolojisi önerilmiş, devreyi tanımlayan denklemler verilmiş, ardından Karbon tabanlı bir memristör entegresi kullanılarak devre kurulmuş ve kurulan osilatör üzerinde gerçekleştirilen deneyler sayesinde literatürde bir ilk olarak iki tane ters-paralel bağlı Karbon Knowm memristör kullanarak bir Liénard Osilatörü yapılabileceği gösterilmiştir.

Destekleyen Kurum

Tekirdağ Namık Kemal Üniversitesi Bilimsel Araştırma Projeleri Koordinasyon Birimi

Proje Numarası

NKUBAP.42.GA.19.206

Teşekkür

Bu çalışmada kullanılan memristörler Tekirdağ Namık Kemal Üniversitesi Bilimsel Araştırma Projeleri Koordinasyon Birimi tarafından finanse edilmiştir. Proje numarası: NKUBAP.42.GA.19.206.

Kaynakça

  • 1. Chua L.O, Memristor—The Missing Circuit Element, IEEE Transactions on Circuit Theory, 18 (5), 507–519, 1971.
  • 2. Chua L. O., Kang S. M., Memristive devices and systems, Proc. IEEE, 64, 209- 223, 1976.
  • 3. Strukov D. B., Snider G. S., Stewart D. R., Williams R. S., The missing memristor found, Nature (London), 453, 80-83, 2008.
  • 4. Chua L.O, If it’s pinched it’s a memristor, Semiconductor Science and Technology, 29, 104001, 2014.
  • 5. Pershin Y.V., Martinez-Rincon J., Di Ventra M., Memory circuit elements: from systems to applications, Journal of Computational and Theoretical Nanoscience, 8 (3), 441-448, 2011.
  • 6. Pershin Y. V., Di Ventra M., Memory effects in complex materials and nanoscale systems, Adv. Phys., 60, 145–227, 2011.
  • 7. Chua L.O., Resistance switching memories are memristors, Applied Physics A, 102, 765–783, 2011.
  • 8. Marani R., Gelao G., Perri A. G., A review on memristor applications, arXiv preprint arXiv:1506.06899 (2015).
  • 9. Karakulak E., Mutlu R., Erdem U., Reconstructive sensing circuit for complementary resistive switches-based crossbar memories, Turkish Journal of Electrical Engineering & Computer Sciences, 24 (3), 1371-1383, 2016.
  • 10. Rosezin R., Linn E., Nielen L., Kügeler C., Bruchhaus R., Waser R., Integrated Complementary Resistive Switches for Passive High-Density Nanocrossbar Arrays, Electron Device Letters, 32 (2), 191-193, 2011.
  • 11. Zheng J., Zeng Z., Zhu Y., Memristor-based nonvolatile synchronous flip-flop circuits, Seventh International Conference on Information Science and Technology (ICIST), 504-508, 2017.
  • 12. Sangho S., Kim K., Kang S. M., Memristor applications for programmable analog ICs, IEEE Transactions on Nanotechnology, 10 (2), 266-274, 2011.
  • 13. Prodromakis T., Toumazou C., A review on memristive devices and applications, 17th IEEE International Conference on Electronics, Circuits and Systems, 934-937, 2010.
  • 14. Yener Ş. Ç., Memristörün Analog Devre Tasarımına Katacağı Yeni Olanaklar, İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, Doktora Tezi, 2014.
  • 15. Pershin Y., Di Ventra M., Practical Approach to Programmable Analog Circuits With Memristors, IEEE Transactions on Circuits and Systems I: Regular Papers, 57, 1857 – 1864, 2010.
  • 16. Wey T. A., Jemison W.D, Variable gain amplifier circuit using titanium dioxide memristors, IET Circuits, Devices & Systems, 5, 59–65, 2011.
  • 17. Ascoli A., Tetzlaff R., Corinto F., Mirchev M., Gilli M., Memristor-based filtering applications, LATW 2013 - 14th IEEE Latin-American Test Workshop, 1-6, 2013.
  • 18. Yener Ş., Mutlu R., Kuntman H. H., Performance Analysis of a Memristor – Based Biquad Filter Using a Dynamic Model, Journal of Microelectronics, Electronic Components and Materials, 44, 109-118, 2014.
  • 19. Yener Ş.Ç., Mutlu R., Kuntman H.H., Memristor Based Sallen-Key Filters, Journal of the Faculty of Engineering and Architecture of Gazi University, 30 (2), 173–184, 2015.
  • 20. Wey T., Benderli S., Amplitude modulator circuit featuring TiO2 memristor with linear dopant drift, Electronics Letters, 45, 1103-1104, 2019.
  • 21. Mutlu R. Karakulak E., Memristor-Based Phase Shifter, ISMSIT 2018 - 2nd International Symposium on Multidisciplinary Studies and Innovative Technologies, Proceedings, Dec. 2018.
  • 22. Parlar İ., Almalı M.N., A new operational amplifier model using a memristor emulator circuit and application to a phase-shifted oscillator circuit, Journal of the Faculty of Engineering and Architecture of Gazi University, 39 (3), 1963–1972, 2024.
  • 23. Mutlu R., Solution of TiO2 memristor-capacitor series circuit excited by a constant voltage source and its application to calculate operation frequency of a programmable TiO2 memristor-capacitor relaxation oscillator, Turkish Journal of Electrical Engineering and Computer Sciences, 23 (5), 1219–1229, 2015.
  • 24. Fouda M. E., Radwan A. G., Power dissipation of memristor-based relaxation oscillators, Radioengineering, 24 (4), 968-973, 2015.
  • 25. Talukdar A., Radwan A. G., Salama K. N., Generalized model for memristor-based Wien-family oscillators, Journal of Microelectronics, 42, 1032–1038, 2011.
  • 26. Itoh M., Chua L. O., Memristor Oscillators, International Journal of Bifurcation and Chaos, 18 (11), 3183–3206, 2011.
  • 27. Kaya, T., Memristor and Trivium-based true random number generator, Physica A: Statistical Mechanics and its Applications, 542, 124071, 2020.
  • 28. Kaya, T., Tuncer, T., Avaroğlu, E., True bit generation by using two different noise sources, Journal of Circuits, Systems and Computers, 30 (14), 2150261, 2021.
  • 29. Taskiran Z.G.C., Sedef H., Realization of memristor based chaotic rossler circuit, Journal of the Faculty of Engineering and Architecture of Gazi University, 35 (2), 765–774, 2019.
  • 30. Özgüvenç A., Mutlu R., Karakulak E., Sawtooth signal generator with a memristor, 1 st International Conference on Engineering Technology and Applied Sciences Afyon Kocatepe University, Turkey April 2016.
  • 31. Karakulak, E., Mutlu, R., Sawtooth Signal Generator Using a Carbon-Based Memristor, Gazi University Journal of Science, 1-1, 2024.
  • 32. Sabarathinam S., Volos C. K., Thamilmaran K., Implementation and study of the nonlinear dynamics of a memristor-based Duffing oscillator, Nonlinear Dyn, 87 (1), 37–49, 2017.
  • 33. Buscarino A., Fortuna L., Frasca M., Gambuzza L. V., A Gallery Of Chaotic Oscillators Based On Hp Memristor, International Journal of Bifurcation and Chaos, 23 (5), 2013.
  • 34. Bao B. C., Liu Z., Xu J. P., Steady periodic memristor oscillator with transient chaotic behaviours, Electronics Letters, 46(3), 228–230, 2010.
  • 35. Zidan M. A, Omran H., Smith C., Syed A., Radwan A. G., Salama K. N., A family of memristor-based reactance-less oscillators”, International Journal of Circuit Theory and Applications, 42 (11), 1103–1122, 2014.
  • 36. Selmy M. I., Mostafa H., Dessouki A. A. S., Hardware implementation of a low power memristor-based voltage controlled oscillator, Proceedings of the International Conference on Microelectronics, ICM, 258–261, 2019.
  • 37. Volos C. K., Pham V. T., Nistazakis H. E., Stouboulos I. N., A dream that has come true: Chaos from a nonlinear circuit with a real memristor, International Journal of Bifurcation and Chaos, 30 (13), 2030036, 2020.
  • 38. Van der Pol B., A theory of the amplitude of free and forced triode vibrations, Radio Review (London), 1, 701–710, 754–762, 1920.
  • 39. Van der Pol B., LXXXVIII. On relaxation-oscillations, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2 (11), 978-992, 1926.
  • 40. B. Van der Pol, J. Van Der Mark, “Frequency demultiplication”, Nature, 120 (3019), 363-364, 1927.
  • 41. B. Van der Pol, “The nonlinear theory of electric oscillations”, Proc. IRE, 22, 1051–1086, 1934.
  • 42. Liénard A., Etude des oscillations entretenues, Revue générale de l'électricité, 23, 901–912, 946–954, 1928.
  • 43. Slight T. J., Romeira B., Wang L., Figueiredo J. M., Wasige E., Ironside C. N., A Liénard oscillator resonant tunnelling diode-laser diode hybrid integrated circuit: model and experiment, IEEE journal of quantum electronics, 44 (12), 1158-1163, 2008.
  • 44. Wang L., Reliable design of tunnel diode and resonant tunnelling diode based microwave sources, Doctoral dissertation, University of Glasgow, 2012.
  • 45. 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, 11 (21), 81-91, 2021.
  • 46. Kingston S. L., Kapitaniak T., Rich dynamics of memristor based Liénard systems, Mem-elements for Neuromorphic Circuits with Artificial Intelligence Applications, 125–145, 2021.
  • 47. Knowm, Self Directed Channel Memristors, Rev. 3.2, October 6, 2019 https://knowm.org/downloads/Knowm_Memristors.pdf, Erişim tarihi: 2 Eylül 2022.
  • 48. InformationWeek, Memristor Developer, http://www.informationweek.com/desktop/hp-hynix-to-collaborate-on-memristormemory-technology/d/did/1092114, Erişim tarihi: Kasım 21, 2022.
  • 49. Biolek, Z., Biolek, D., Biolkova, V., SPICE model of memristor with nonlinear dopant drift, Radioengineering, 18 (2), 210–214, 2009.
  • 50. Dalmış C., Karbon ve Tungsten Tabanlı Memristör İçeren Kondansatör Devrelerinin Yön Bağımlı Dolması ve Boşalmasının İncelenmesi, Tekirdağ Namık Kemal Üniversitesi, Fen Bilimleri Enstitüsü, Yüksek Lisans Tezi, 2021.
  • 51. Biolek, Z., Biolek, D., Biolkova, V., Differential equations of ideal memristors, Radioengineering, 24 (2), 369-377, 2015.
  • 52. Yeşil A, Babacan Y, Kaçar F., A new DDCC based memristor emulator circuit and its applications, Microelectron J, 45 (3), 282–287, 2014.
  • 53. Zhang Z, Xu A, Ren HT, Liu G, Cheng X., Reconfigurable multivalued memristor FPGA model for digital recognition, Int J Circuit Theory Appl., 50 (11), 3846–3860, 2022.

A memristor-based Liénard Oscillator design

Yıl 2025, Cilt: 40 Sayı: 2, 1183 - 1196
https://doi.org/10.17341/gazimmfd.1273399

Öz

The new circuit element memristor can be used in the construction of sensors and in circuit applications such as cellular neural networks, chaotic systems, programmable analog circuits, and non-volatile memory devices. Liénard equations was proposed by Alfred-Marie Liénard in 1928 for modeling oscillating circuits. Semiconductor technology was not available when the first Liénard Oscillator was made, but, today, various semiconductor circuit elements are used in the construction of new types of Liénard oscillators. Nowadays, there are Carbon-based memristors sold on the market produced by Knowm company. According to the literature review done, there is not any Carbon Knowm memristor-based Liénard oscillators made yet. The purpose of this work is to present a new type of Liénard Oscillator to the literature by using two Carbon-based Knowm memristors. In this study, first, a memristor-based Liénard Oscillator circuit topology was proposed, the equations describing the circuit is given, then the circuit was built using a Carbon-based memristor integrated circuit, and the experiments were performed on the assembled oscillator to show that a Liénard oscillator can be made using two anti-parallel Carbon-based Knowm memristors for the first time in the literature.

Proje Numarası

NKUBAP.42.GA.19.206

Kaynakça

  • 1. Chua L.O, Memristor—The Missing Circuit Element, IEEE Transactions on Circuit Theory, 18 (5), 507–519, 1971.
  • 2. Chua L. O., Kang S. M., Memristive devices and systems, Proc. IEEE, 64, 209- 223, 1976.
  • 3. Strukov D. B., Snider G. S., Stewart D. R., Williams R. S., The missing memristor found, Nature (London), 453, 80-83, 2008.
  • 4. Chua L.O, If it’s pinched it’s a memristor, Semiconductor Science and Technology, 29, 104001, 2014.
  • 5. Pershin Y.V., Martinez-Rincon J., Di Ventra M., Memory circuit elements: from systems to applications, Journal of Computational and Theoretical Nanoscience, 8 (3), 441-448, 2011.
  • 6. Pershin Y. V., Di Ventra M., Memory effects in complex materials and nanoscale systems, Adv. Phys., 60, 145–227, 2011.
  • 7. Chua L.O., Resistance switching memories are memristors, Applied Physics A, 102, 765–783, 2011.
  • 8. Marani R., Gelao G., Perri A. G., A review on memristor applications, arXiv preprint arXiv:1506.06899 (2015).
  • 9. Karakulak E., Mutlu R., Erdem U., Reconstructive sensing circuit for complementary resistive switches-based crossbar memories, Turkish Journal of Electrical Engineering & Computer Sciences, 24 (3), 1371-1383, 2016.
  • 10. Rosezin R., Linn E., Nielen L., Kügeler C., Bruchhaus R., Waser R., Integrated Complementary Resistive Switches for Passive High-Density Nanocrossbar Arrays, Electron Device Letters, 32 (2), 191-193, 2011.
  • 11. Zheng J., Zeng Z., Zhu Y., Memristor-based nonvolatile synchronous flip-flop circuits, Seventh International Conference on Information Science and Technology (ICIST), 504-508, 2017.
  • 12. Sangho S., Kim K., Kang S. M., Memristor applications for programmable analog ICs, IEEE Transactions on Nanotechnology, 10 (2), 266-274, 2011.
  • 13. Prodromakis T., Toumazou C., A review on memristive devices and applications, 17th IEEE International Conference on Electronics, Circuits and Systems, 934-937, 2010.
  • 14. Yener Ş. Ç., Memristörün Analog Devre Tasarımına Katacağı Yeni Olanaklar, İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, Doktora Tezi, 2014.
  • 15. Pershin Y., Di Ventra M., Practical Approach to Programmable Analog Circuits With Memristors, IEEE Transactions on Circuits and Systems I: Regular Papers, 57, 1857 – 1864, 2010.
  • 16. Wey T. A., Jemison W.D, Variable gain amplifier circuit using titanium dioxide memristors, IET Circuits, Devices & Systems, 5, 59–65, 2011.
  • 17. Ascoli A., Tetzlaff R., Corinto F., Mirchev M., Gilli M., Memristor-based filtering applications, LATW 2013 - 14th IEEE Latin-American Test Workshop, 1-6, 2013.
  • 18. Yener Ş., Mutlu R., Kuntman H. H., Performance Analysis of a Memristor – Based Biquad Filter Using a Dynamic Model, Journal of Microelectronics, Electronic Components and Materials, 44, 109-118, 2014.
  • 19. Yener Ş.Ç., Mutlu R., Kuntman H.H., Memristor Based Sallen-Key Filters, Journal of the Faculty of Engineering and Architecture of Gazi University, 30 (2), 173–184, 2015.
  • 20. Wey T., Benderli S., Amplitude modulator circuit featuring TiO2 memristor with linear dopant drift, Electronics Letters, 45, 1103-1104, 2019.
  • 21. Mutlu R. Karakulak E., Memristor-Based Phase Shifter, ISMSIT 2018 - 2nd International Symposium on Multidisciplinary Studies and Innovative Technologies, Proceedings, Dec. 2018.
  • 22. Parlar İ., Almalı M.N., A new operational amplifier model using a memristor emulator circuit and application to a phase-shifted oscillator circuit, Journal of the Faculty of Engineering and Architecture of Gazi University, 39 (3), 1963–1972, 2024.
  • 23. Mutlu R., Solution of TiO2 memristor-capacitor series circuit excited by a constant voltage source and its application to calculate operation frequency of a programmable TiO2 memristor-capacitor relaxation oscillator, Turkish Journal of Electrical Engineering and Computer Sciences, 23 (5), 1219–1229, 2015.
  • 24. Fouda M. E., Radwan A. G., Power dissipation of memristor-based relaxation oscillators, Radioengineering, 24 (4), 968-973, 2015.
  • 25. Talukdar A., Radwan A. G., Salama K. N., Generalized model for memristor-based Wien-family oscillators, Journal of Microelectronics, 42, 1032–1038, 2011.
  • 26. Itoh M., Chua L. O., Memristor Oscillators, International Journal of Bifurcation and Chaos, 18 (11), 3183–3206, 2011.
  • 27. Kaya, T., Memristor and Trivium-based true random number generator, Physica A: Statistical Mechanics and its Applications, 542, 124071, 2020.
  • 28. Kaya, T., Tuncer, T., Avaroğlu, E., True bit generation by using two different noise sources, Journal of Circuits, Systems and Computers, 30 (14), 2150261, 2021.
  • 29. Taskiran Z.G.C., Sedef H., Realization of memristor based chaotic rossler circuit, Journal of the Faculty of Engineering and Architecture of Gazi University, 35 (2), 765–774, 2019.
  • 30. Özgüvenç A., Mutlu R., Karakulak E., Sawtooth signal generator with a memristor, 1 st International Conference on Engineering Technology and Applied Sciences Afyon Kocatepe University, Turkey April 2016.
  • 31. Karakulak, E., Mutlu, R., Sawtooth Signal Generator Using a Carbon-Based Memristor, Gazi University Journal of Science, 1-1, 2024.
  • 32. Sabarathinam S., Volos C. K., Thamilmaran K., Implementation and study of the nonlinear dynamics of a memristor-based Duffing oscillator, Nonlinear Dyn, 87 (1), 37–49, 2017.
  • 33. Buscarino A., Fortuna L., Frasca M., Gambuzza L. V., A Gallery Of Chaotic Oscillators Based On Hp Memristor, International Journal of Bifurcation and Chaos, 23 (5), 2013.
  • 34. Bao B. C., Liu Z., Xu J. P., Steady periodic memristor oscillator with transient chaotic behaviours, Electronics Letters, 46(3), 228–230, 2010.
  • 35. Zidan M. A, Omran H., Smith C., Syed A., Radwan A. G., Salama K. N., A family of memristor-based reactance-less oscillators”, International Journal of Circuit Theory and Applications, 42 (11), 1103–1122, 2014.
  • 36. Selmy M. I., Mostafa H., Dessouki A. A. S., Hardware implementation of a low power memristor-based voltage controlled oscillator, Proceedings of the International Conference on Microelectronics, ICM, 258–261, 2019.
  • 37. Volos C. K., Pham V. T., Nistazakis H. E., Stouboulos I. N., A dream that has come true: Chaos from a nonlinear circuit with a real memristor, International Journal of Bifurcation and Chaos, 30 (13), 2030036, 2020.
  • 38. Van der Pol B., A theory of the amplitude of free and forced triode vibrations, Radio Review (London), 1, 701–710, 754–762, 1920.
  • 39. Van der Pol B., LXXXVIII. On relaxation-oscillations, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2 (11), 978-992, 1926.
  • 40. B. Van der Pol, J. Van Der Mark, “Frequency demultiplication”, Nature, 120 (3019), 363-364, 1927.
  • 41. B. Van der Pol, “The nonlinear theory of electric oscillations”, Proc. IRE, 22, 1051–1086, 1934.
  • 42. Liénard A., Etude des oscillations entretenues, Revue générale de l'électricité, 23, 901–912, 946–954, 1928.
  • 43. Slight T. J., Romeira B., Wang L., Figueiredo J. M., Wasige E., Ironside C. N., A Liénard oscillator resonant tunnelling diode-laser diode hybrid integrated circuit: model and experiment, IEEE journal of quantum electronics, 44 (12), 1158-1163, 2008.
  • 44. Wang L., Reliable design of tunnel diode and resonant tunnelling diode based microwave sources, Doctoral dissertation, University of Glasgow, 2012.
  • 45. 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, 11 (21), 81-91, 2021.
  • 46. Kingston S. L., Kapitaniak T., Rich dynamics of memristor based Liénard systems, Mem-elements for Neuromorphic Circuits with Artificial Intelligence Applications, 125–145, 2021.
  • 47. Knowm, Self Directed Channel Memristors, Rev. 3.2, October 6, 2019 https://knowm.org/downloads/Knowm_Memristors.pdf, Erişim tarihi: 2 Eylül 2022.
  • 48. InformationWeek, Memristor Developer, http://www.informationweek.com/desktop/hp-hynix-to-collaborate-on-memristormemory-technology/d/did/1092114, Erişim tarihi: Kasım 21, 2022.
  • 49. Biolek, Z., Biolek, D., Biolkova, V., SPICE model of memristor with nonlinear dopant drift, Radioengineering, 18 (2), 210–214, 2009.
  • 50. Dalmış C., Karbon ve Tungsten Tabanlı Memristör İçeren Kondansatör Devrelerinin Yön Bağımlı Dolması ve Boşalmasının İncelenmesi, Tekirdağ Namık Kemal Üniversitesi, Fen Bilimleri Enstitüsü, Yüksek Lisans Tezi, 2021.
  • 51. Biolek, Z., Biolek, D., Biolkova, V., Differential equations of ideal memristors, Radioengineering, 24 (2), 369-377, 2015.
  • 52. Yeşil A, Babacan Y, Kaçar F., A new DDCC based memristor emulator circuit and its applications, Microelectron J, 45 (3), 282–287, 2014.
  • 53. Zhang Z, Xu A, Ren HT, Liu G, Cheng X., Reconfigurable multivalued memristor FPGA model for digital recognition, Int J Circuit Theory Appl., 50 (11), 3846–3860, 2022.
Toplam 53 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Kübra Çakır 0000-0003-4762-5780

Reşat Mutlu 0000-0003-0030-7136

Ertuğrul Karakulak 0000-0001-5937-2114

Proje Numarası NKUBAP.42.GA.19.206
Erken Görünüm Tarihi 30 Aralık 2024
Yayımlanma Tarihi
Gönderilme Tarihi 29 Mart 2023
Kabul Tarihi 7 Ekim 2024
Yayımlandığı Sayı Yıl 2025 Cilt: 40 Sayı: 2

Kaynak Göster

APA Çakır, K., Mutlu, R., & Karakulak, E. (2024). Memristör tabanlı bir Liénard Osilatörü tasarımı. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 40(2), 1183-1196. https://doi.org/10.17341/gazimmfd.1273399
AMA Çakır K, Mutlu R, Karakulak E. Memristör tabanlı bir Liénard Osilatörü tasarımı. GUMMFD. Aralık 2024;40(2):1183-1196. doi:10.17341/gazimmfd.1273399
Chicago Çakır, Kübra, Reşat Mutlu, ve Ertuğrul Karakulak. “Memristör Tabanlı Bir Liénard Osilatörü tasarımı”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 40, sy. 2 (Aralık 2024): 1183-96. https://doi.org/10.17341/gazimmfd.1273399.
EndNote Çakır K, Mutlu R, Karakulak E (01 Aralık 2024) Memristör tabanlı bir Liénard Osilatörü tasarımı. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 40 2 1183–1196.
IEEE K. Çakır, R. Mutlu, ve E. Karakulak, “Memristör tabanlı bir Liénard Osilatörü tasarımı”, GUMMFD, c. 40, sy. 2, ss. 1183–1196, 2024, doi: 10.17341/gazimmfd.1273399.
ISNAD Çakır, Kübra vd. “Memristör Tabanlı Bir Liénard Osilatörü tasarımı”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 40/2 (Aralık 2024), 1183-1196. https://doi.org/10.17341/gazimmfd.1273399.
JAMA Çakır K, Mutlu R, Karakulak E. Memristör tabanlı bir Liénard Osilatörü tasarımı. GUMMFD. 2024;40:1183–1196.
MLA Çakır, Kübra vd. “Memristör Tabanlı Bir Liénard Osilatörü tasarımı”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, c. 40, sy. 2, 2024, ss. 1183-96, doi:10.17341/gazimmfd.1273399.
Vancouver Çakır K, Mutlu R, Karakulak E. Memristör tabanlı bir Liénard Osilatörü tasarımı. GUMMFD. 2024;40(2):1183-96.