Finite-Difference Time-Domain Solution of a Memristor Fed by a Transmission Line

Öz

Memristor is a new nonlinear circuit element. Examination of its use with other circuit elements is important from Circuit analysis point of view. A memristor connected at the end of a transmission line will exhibit a different behavior than a resistor does. It is difficult or impossible to solve such a problem since the memristor is a nonlinear circuit element. In this study, the equation of the electromagnetic wave propagating over the transmission line with a memristor load is solved using the finite-difference time-domain (FDTM) method. Memristor current and voltage are calculated depending on time. The simulations are made with the MATLAB program.

Anahtar Kelimeler

• FDTD
• memristor
• transmission line
• reflection analysis.

Bir İletim Hattından Beslenen Bir Memristörün Zamanda Sonlu Farklar Yöntemi İle Çözümü

Öz

Memristör yeni bir doğrusal olmayan devre elemanıdır. Diğer devre elemanları ile birlikte kullanımın incelenmesi Devre analizi açısından önemlidir. Bir iletim hattının sonuna bağlanan memristör elemanı bir dirence göre daha farklı bir davranış sergileyecektir. Memristor nonlineer bir devre elemanı olduğu için, böyle bir problemin çözümünün yapılması zor ya da imkansızdır. Bu çalışmada, bir memristor ile yüklü bir iletim hattının üzerinde yayılan elektromanyetik dalganın denklemi Zaman Domeninde Sonlu Farklar (ZDSF) yöntemi kullanılarak çözülmüştür. Memristör akımı ve gerilimi zamana bağlı olarak hesaplanmıştır. Simülasyonlar MATLAB programı ile yapılmıştır.

Anahtar Kelimeler

• FDTD
• memristör
• iletim hattı
• yansıma analizi

Kaynakça

1. [1] Taflove, A., & Hagness, S. C. (2005). Computational electrodynamics: the finite-difference time-domain method. Artech house.
2. [2] Shlager, K. L., & Schneider, J. B. (1995). A selective survey of the finite-difference time-domain literature. IEEE Antennas and Propagation Magazine, 37(4), 39-57.
3. [3] Sadiku, M. N. (2018). Numerical techniques in electromagnetics with MATLAB. CRC press.
4. [4] Yee, K. (1966). Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Transactions on antennas and propagation, 14(3), 302-307.
5. [5] Komisarek, K. S., Chamerberlin, K. A., & Sivaprasad, K. (1993). A method of moment analysis of a twisted-pair transmission line. In Proceedings of IEEE Antennas and Propagation Society International Symposium 1993 (pp. 64-67). IEEE.
6. [6] Roden, J. A., Gedney, S. D., & Paul, C. R. (1996). A rigorous analysis of twisted pair transmission lines using non-orthogonal FDTD and the PML absorbing boundary condition. In Proceedings of Symposium on Electromagnetic Compatibility (pp. 254-258). IEEE.
7. [7] Poltz, J., Gleich, D., Josefsson, M., & Lindstrom, M. (2000). Electromagnetic modeling of twisted pair cables. In Proceedings of the 49th International Wire and Cable symposium. International Wire and Cable Symposium, 2000.
8. [8] Kirawanich, P., Islam, N. E., & Yakura, S. J. (2006). An electromagnetic topology approach: Crosstalk characterizations of the unshielded twisted-pair cable. Progress In Electromagnetics Research, 58, 285-299.

9. [9] Liu, X. (2006). Low pressure partial discharge investigation with FEM modeling for a twisted pair of insulated conductors. In 2006 IEEE Conference on Electrical Insulation and Dielectric Phenomena (pp. 611-614). IEEE.
10. [10] Tatematsu, A., Rachidi, F., & Rubinstein, M. (2016). A technique for calculating voltages induced on twisted-wire pairs using the FDTD method. IEEE Transactions on Electromagnetic Compatibility, 59(1), 301-304.
11. [11] Pozar, D. M. (1998). Microwave engineering, John Wiley & Sons. Inc.
12. [12] Heaviside, O. (1876). XIX. On the extra current. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2(9), 135-145.
13. [13] Miano, G., & Maffucci, A. (2001). Transmission lines and lumped circuits: fundamentals and applications. Elsevier.
14. [14] Reçber Kablo Datasheet (2021, 19 December), retrieved from, https://www.recber.com.tr/pdf/urun-katalog.pdf
15. [15] Öztürk, P., ALİSOY, H., & Mutlu, R. (2019)Yapay Sinir Ağları Kullanarak İkili ve Üçlü Büküm Makinaların Ürettiği CAT 6A U/FTP Kabloların Parametrelerinin Tahmini ve Tahmin Edilen Sonuçların Karşılaştırılması. European Journal of Engineering and Applied Sciences, 2(2), 41-51.
16. [16] Chua, L. (1971). Memristor-the missing circuit element. IEEE Transactions on circuit theory, 18(5), 507- 519.
17. [17] Chua, L. O., & Kang, S. M. (1976). Memristive devices and systems. Proceedings of the IEEE, 64(2), 209-223.
18. [18] Strukov, D. B., Snider, G. S., Stewart, D. R., & Williams, R. S. (2008). The missing memristor found. nature, 453(7191), 80-83.
19. [19] Williams, R. S. (2008). How We Found The Missing Memristor IEEE Spectrum, 45(12), 28-35.
20. [20] Kavehei, O., Iqbal, A., Kim, Y. S., Eshraghian, K., Al- Sarawi, S. F., & Abbott, D. (2010). The fourth element: characteristics, modelling and electromagnetic theory of the memristor. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 466(2120), 2175-2202.
21. [21] Mazumder, P., Kang, S. M., & Waser, R. (2012). Memristors: devices, models, and applications. Proceedings of the IEEE, 100(6), 1911-1919.
22. [22] Wang, F. Y. (2008). Memristor for introductory physics. arXiv preprint arXiv:0808.0286.
23. [23] Joglekar, Y. N., & Wolf, S. J. (2009). The elusive memristor: properties of basic electrical circuits. European Journal of physics, 30(4), 661.
24. [24] Mutlu, R. (2015). 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 & Computer Sciences, 23(5), 1219-1229.
25. [25] Bayır Ö., & Mutlu R. (2013). Investigation of Memristor-Inductor Series Circuit under DC Excitation Using a Piecewise Memristor Characteristic, 6. İleri Muhendislik Teknolojileri Sempozyumu 2013. Çankaya Üniversitesi
26. [26] Yener, S. C., Mutlu, R., & Kuntman, H. H. (2015). A new memristor-based low-pass filter topology and its small- signal solution using MacLaurin series. SAT, 1(1), 2.
27. [27]Yener, S. C., Mutlu, R., & Kuntman, H. H. (2018). Small signal analysis of memristor-based low-pass and high-pass filters using the perturbation theory. Optoelectronics and Advanced Materials-Rapid Communications, 12(January-February 2018), 55-62.
28. [28] Mutlu, R. (2018). AC Power Formula for Unsaturated TiO2 Memristors with Linear Dopant Drift, Small Signal AC Power Formula for All Memristors, and Some Applications for These Formulas. European Journal of Engineering and Applied Sciences, 1(2), 1-8.
29. [29] Mutlu R. (2010). Taylor Serisi ve Kutupsal Fonksiyonlar Kullanarak Memristorün (Hafızalı Direncin) Histeresis Eğrisinin Açıklanması. 3. Ileri Muhendislik Teknolojileri Sempozyumu 2010 (pp. 401–408). Çankaya University.
30. [30] Urgan, N. N., Dalmış, C., & Mutlu, R. (2021). Analysis of the HP Memristor and Capacitor (MC) Series Circuit Using the Lambert W Function. European Journal of Engineering and Applied Sciences, 3(2), 27-32.
31. [31] Kvatinsky, S., Friedman, E. G., Kolodny, A., & Weiser, U. C. (2013). The desired memristor for circuit designers. IEEE Circuits and Systems Magazine, 13(2), 17-22.
32. [32] Potrebić, M., Tošić, D., & Biolek, D. (2017). Rf/microwave applications of memristors. In Advances in Memristors, Memristive Devices and Systems (pp. 159- 185). Springer, Cham.
33. [33] Potrebic, M., & Tosic, D. (2015). Application of memristors in microwave passive circuits. Radioengineering, 24(2), 408-419.
34. [34] Yang, Z., & Tan, E. L. (2015). Two finite-difference time-domain methods incorporated with memristor. Progress In Electromagnetics Research, 42, 153-158.
35. [35] Yang, J. J., Pickett, M. D., Li, X., Ohlberg, D. A., Stewart, D. R., & Williams, R. S. (2008). Memristive switching mechanism for metal/oxide/metal nanodevices. Nature nanotechnology, 3(7), 429-433.
36. [36] Biolek, Z., Biolek, D., & Biolkova, V. (2009). SPICE Model of Memristor with Nonlinear Dopant Drift. Radioengineering, 18(2), 210-214.
37. [37] Prodromakis, T., Peh, B. P., Papavassiliou, C., & Toumazou, C. (2011). A versatile memristor model with nonlinear dopant kinetics. IEEE transactions on electron devices, 58(9), 3099-3105.
38. [38] Zha, J., Huang, H., & Liu, Y. (2015). A novel window function for memristor model with application in programming analog circuits. IEEE Transactions on Circuits and Systems II: Express Briefs, 63(5), 423-427.
39. [39] Oğuz, Y., Gül, F., & Eroğlu, H. (2017). A New Window Function for Memristor Modeling. In 8th International Advanced Technologies Symposium (IATS17). (pp. 3498- 3502). Elazığ.
40. [40] Karakulak, E., & Mutlu, R. (2020). SPICE Model of Current Polarity-Dependent Piecewise Linear Window Function for Memristors. Gazi University Journal of Science, 33(4), 776-777.