Constant Current Solution of a Memristor Modelled Using the Mutlu-Kumru Memristor Model and Two Possible Applications

Ertuğrul Karakulak; Reşat Mutlu

doi:10.59314/tujes.1736117

TR EN

Mutlu-Kumru Memristör Modeli Kullanılarak Modellenen Bir Memristörün Sabit Akım Çözümü ve İki Olası Uygulama

Öz

Memristör, yeni ve doğrusal olmayan bir devre elemanıdır. Doğrusal olmaması nedeniyle, içinde bulunduğu devrenin analitik çözümü her zaman mevcut olmayabilir. Ayrıca, yeni bir devre elemanı olması sebebiyle, memristör tabanlı devrelerin çözümlerinin incelenmesi gerekmektedir. Memristörler farklı yaklaşımlar kullanılarak modellenebilir. Memristör modellerinden bir grubu, doğrusal olmayan sürüklenme modelleri olarak adlandırılır ve bunlardan biri yakın zamanda önerilen Mutlu-Kumru modelidir. Bir memristör sabit bir akım kaynağı ile beslenebilir. Ancak, sabit akım kaynağı altında Mutlu-Kumru memristör modelinin çözümü henüz literatürde sunulmamıştır. Bu çalışmada, Mutlu-Kumru memristör modelinin sabit akım uyartımı altındaki analitik çözümü sunulmaktadır. Ayrıca, elde edilen çözümün rezistif belleklerin anahtarlanması ve memristör tabanlı testere dişi osilatörlerin modellenmesinde kullanılabileceği gösterilmektedir.

Anahtar Kelimeler

Memristör , Memristör modeli , Testere Dişi sinyal üreteci , Pencere fonksiyonu , Devre Analizi

Constant Current Solution of a Memristor Modelled Using the Mutlu-Kumru Memristor Model and Two Possible Applications

Abstract

The Memristor is a novel and nonlinear circuit element. An analytical solution for the circuit it is part of does not always exist due to its nonlinearity. Also, since it is a new circuit element, the solutions of the memristor-based circuits should be examined. Memristors can be modeled using different approaches. A set of memristor models is called the nonlinear drift models, one of which, the Mutlu-Kumru model is one of the recently proposed. A memristor can be fed with a constant current source. However, its solution under a constant current source for the Mutlu-Kumru memristor model has not been presented in the literature, yet. In this study, the analytical solution of the Mutlu-Kumru memristor model under constant current excitation is presented. It is also demonstrated that the obtained solution can be utilized in analyzing resistive switching of a resistive memory and the modeling of a memristor-based sawtooth oscillator.

Keywords

Memristor , Memristor model , Sawtooth signal generator , Window function , Circuit Analysis.

Kaynakça

Ascoli, A., Tetzlaff, R., Corinto, F., Mirchev, M., & Gilli, M. (2013). Memristor-based filtering applications. LATW 2013 - 14th IEEE Latin- American Test Workshop, 1, 1–6. https://doi.org/10.1109/LATW.2013.6562672
Bayır, Ö., & Mutlu, R. (2013). Investigation of Memristor-Inductor Series Circuit under DC Excitation Using a Piecewise Memristor Characteristic, 6. İleri Muhendislik Teknolojileri Sempozyumu, 25-26.
Berdan, R.; Prodromakis, T.; Toumazou, C. (2012). High precision analogue memristor state tuning. Electronics Letters, 48(18), 1105–1107.
Biolek, D., & Biolková, V. (2009). SPICE Model of Memristor with Nonlinear Dopant Drift. Radioengineering, 18(2), 210–214.
Biolek, Z., Biolek, D., & Biolkova, V. (2012). Analytical solution of circuits employing voltage-and current-excited memristors. IEEE Transactions on Circuits and Systems I: Regular Papers, 59(11), 2619-2628.
Chua, L. (2011). Resistance switching memories are memristors. Applied Physics A, 102(4), 765– 783. https://doi.org/10.1007/s00339-011-6264-9
Chua, L. O. (1971). Memristor—The Missing Circuit Element. IEEE Transactions on Circuit Theory, 18(5), 507–519. https://doi.org/10.1109/TCT.1971.1083337
Chua, L. O., & Kang, S. M. (1976). Memristive Devices and Systems. Proceedings of the IEEE, 64(2), 209–223. https://doi.org/10.1109/PROC.1976.10092
Çakır, K., Mutlu, R., & Karakulak, E. (2025). A memristor-based Liénard Oscillator design. Journal of the Faculty of Engineering and Architecture of Gazi University, 40(2), 1183- 1195.
Dautovic, S., Samardzic, N., Juhas, A., Ascoli, A., & Tetzlaff, R. (2024). Analytical Solutions for Charge and Flux in HP Ideal Generic Memristor Model with Joglekar and Prodromakis Window Functions. IEEE Access.

Eroğlu, Y. O. A. F. G. A. H. (2017). A new window function for memristor modeling. 8th International Adbanced Technologies Symposium, 3498–3502.
Fouda, Mohammed E.; RADWAN, Ahmed G. (2015). Power dissipation of memristor-based relaxation oscillators. Radioengineering, 24(4), 968-973. Itoh, M., & Chua, L. O. (2008). Memristor oscillators. International Journal of Bifurcation and Chaos, 18(11), 3183–3206. https://doi.org/10.1142/S0218127408022354
Joglekar, Y. N., & Wolf, S. J. (2009). The elusive memristor: Properties of basic electrical circuits. European Journal of Physics, 30(4), 661–675. https://doi.org/10.1088/0143-0807/30/4/001
Karakulak, E., & Mutlu, R. (2020). Spice model of current polarity-dependent piecewise linear window function for memristors. Gazi University Journal of Science, , 33(4), 766–777. https://doi.org/10.35378/gujs.605118
Karakulak, E., & Mutlu, R. (2024). SPICE Model of Mutlu-Kumru Memristor Model and Its Usage for Analysis, Modeling, And Simulation of a Memristor-Based Sawtooth Signal Generator. Trakya Üniversitesi Mühendislik Bilimleri Dergisi, 25(2), 91-100.
Khalid, M. (2019). Review on Various Memristor Models, Characteristics, Potential Applications, and Future Works. Transactions on Electrical and Electronic Materials, 20(4), 289–298. https://doi.org/10.1007/s42341-019-00116-8
Kurtdemir A.; Mutlu R. (2019). Modeling and Simulation of a Memristor-Based Sawtooth Signal Generator Using Nonlinear Dopant Drift Memristor Models. European Journal of Engineering and Applied Sciences, 2(1), 44–57.
Mosad, a. G., Fouda, M. E., Khatib, M. a., Salama, K. N., & Radwan, a. G. (2013). Improved memristor-based relaxation oscillator. Microelectronics Journal, 44(9), 814–820. https://doi.org/10.1016/j.mejo.2013.04.005
Muthuswamy, B. (2010). Implementing memristor based chaotic circuits. International Journal of Bifurcation and Chaos, 20(5), 1335–1350. https://doi.org/10.1142/S0218127410026514
Mutlu, R., Karakulak, E. (2018). Memristor-Based Phase Shifter. 2018 2nd International Symposium on Multidisciplinary Studies and Innovative Technologies (ISMSIT), 1–5.
Mutlu, R. (2015). Solution of TiO2 memristorcapacitor 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. https://doi.org/10.3906/elk-1108-38
Mutlu, R., & Kumru, T. D. (2023). A Zeno Paradox: Some Well-known Nonlinear Dopant Drift Memristor Models Have Infinite Resistive Switching Time. Radioengineering, 32(3), 312– 324. https://doi.org/10.13164/RE.2023.0312

Ayrıntılar

Birincil Dil

İngilizce

Konular

Mikroelektromekanik Sistemler (MEMS)

Bölüm

Araştırma Makalesi

Yazarlar

Ertuğrul Karakulak ^*
0000-0001-5937-2114
Türkiye

Reşat Mutlu
0000-0003-0030-7136
Türkiye

Yayımlanma Tarihi

31 Aralık 2025

Gönderilme Tarihi

6 Temmuz 2025

Kabul Tarihi

30 Aralık 2025

Yayımlandığı Sayı

Yıl 1970 Cilt: 26 Sayı: 2

DOI

https://doi.org/10.59314/tujes.1736117

IZ

https://izlik.org/JA42PC35UH

IEEE

[1]E. Karakulak ve R. Mutlu, “Constant Current Solution of a Memristor Modelled Using the Mutlu-Kumru Memristor Model and Two Possible Applications”, TUJES, c. 26, sy 2, ss. 77–90, Ara. 2025, doi: 10.59314/tujes.1736117.

Mutlu-Kumru Memristör Modeli Kullanılarak Modellenen Bir Memristörün Sabit Akım Çözümü ve İki Olası Uygulama

Öz

Anahtar Kelimeler

Constant Current Solution of a Memristor Modelled Using the Mutlu-Kumru Memristor Model and Two Possible Applications

Abstract

Keywords

Kaynakça

Ayrıntılar

Birincil Dil

Konular

Bölüm

Yazarlar

Yayımlanma Tarihi

Gönderilme Tarihi

Kabul Tarihi

Yayımlandığı Sayı

DOI

IZ

Kaynak Göster