Memkapasitör ve Konformal Fraksiyonel Dereceli Kondansatörün Bir Araya Getirildiği İki Kapasitör Problemi

Öz

Kesirli mertebeli kondansatörler ve memkapasitörler son yıllarda önemli bir araştırma alanı haline geldi. Her iki devre elemanının analog uygulamaları giderek yaygınlaşmaktadır. Literatürde, uyumlu kesirli türev (UKT), kullanımı ve anlaşılması kolay olması nedeniyle çok ilgi görmektedir. Bazı süperkondansatörler zaten uyumlu kesirli türev ile modellenmiştir. İki kondansatör problemi fizikte önemli bir problemdir. Son zamanlarda, bir UKT kondansatörü ve bir lineer zamanla değişmeyen (LZD) kondansatörü ile bir iki kondansatör problemi incelenmiştir. Bildiğimiz kadarıyla, literatürde henüz bir UKT kondansatör ve bir memkapasitörden oluşan bir devre incelenmemiştir. Bu çalışmada, literatürde ilk kez simülasyonlar kullanılarak bir UKT kondansatörü ve bir memkapasitörden oluşan bir devre, bir - iki kondansatörlü bir problem incelenmiştir. Devrenin sürekli geçici rejimde olduğu görülmüştür.

Anahtar Kelimeler

• Memkapasitör
• Kesir Dereceli Kondansatör
• İki Kondansatör Problemi
• Devre Analizi
• Devre Teorisi.

A Two-capacitor Problem with a Memcapacitor and a Conformal Fractional-Order Capacitor Put Together

Öz

Fractional-order capacitors and memcapacitors have become a major research area in recent decades. Analog applications of both circuit elements are getting more common. In literature, the conformal fractional derivative (CFD) is getting lots of interest due to its easiness to use and to comprehend. Some supercapacitors have already been modeled with the conformal fractional derivative. Two-capacitor problem is an important problem in physics. Recently, a two-capacitor problem with a CFD capacitor and a linear time-invariant (LTI) capacitor has been examined. To the best of our knowledge, a circuit, which is made of a CFD capacitor and a memcapacitor, has not been analyzed in the literature yet. In this study, a two-capacitor problem, a circuit, which consists of a CFD capacitor and a memcapacitor, has been examined using simulations for the first time in literature. It is found that the circuit is in ever transient state.

Anahtar Kelimeler

• Memcapacitor
• Fractional Order Capacitor
• Two-capacitor Problem
• Circuit Analysis
• Circuit Theory

Kaynakça

1. I. Podlubny, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Elsevier, 1998.
2. X. J. Yang, General fractional derivatives: theory, methods, and applications, Chapman and Hall/CRC, 2019.
3. B. Ross, B, “The development of fractional calculus 1695– 1900”, Historia Mathematica, vol. 4, no.1, pp. 75-89, 1977.
4. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, 2006.
5. A. Babiarz, A. Czornik, J. Klamka, and M. Niezabitowski, “Theory and applications of non-integer order systems,” Lecture Notes Electrical Engineering, 407, 2017.
6. T. J. Freeborn, “A survey of fractional-order circuit models for biology and biomedicine,” IEEE Journal on emerging and selected topics in circuits and systems, vol. 3, no. 3, pp. 416-424, 2013.
7. R. Khalil, M. al Horani, A. Yousef, M. Sababheh, “A new definition of fractional derivative,” J. Comput. Appl. Math., vol. 264, pp. 65–70, 2014.
8. T. Abdeljawad, T, “On conformable fractional calculus,” Journal of computational and Applied Mathematics, vol. 279, pp. 57-66, 2015.

9. D. Zhao, M. Luo, “General conformable fractional derivative and its physical interpretation,” Calcolo, vol. 54, no. 3, pp. 903-917, 2017.
10. R. Sikora, “Fractional derivatives in electrical circuit theory–critical remarks,” Archives of Electrical Engineering, vol. 66, no. 1, pp. 155-163, 2017.
11. M. Lewandowski, M. Orzyłowski, “Fractional-order models: The case study of the supercapacitor capacitance measurement,” Bulletin of the Polish Academy of Sciences Technical Sciences, vol. 65, no. 4, pp. 449-457, 2017.
12. R. Kopka, “Estimation of supercapacitor energy storage based on fractional differential equations,” Nanoscale research letters, vol. 12, no. 1, pp. 636, 2017.
13. T. J. Freeborn, A. S. Elwakil, and A. Allagui, “Supercapacitor fractional-order model discharging from polynomial time-varying currents,” in 2018 IEEE International Symposium on Circuits and Systems (ISCAS), May 2018, pp. 1-5.
14. T. J. Freeborn, B. Maundy, A. S. Elwakil, “Measurement of supercapacitor fractional-order model parameters from voltage-excited step response,” IEEE Journal on Emerging and Selected Topics in Circuits and Systems, vol. 3, no. 3, pp. 367-376, 2013.
15. A. Kartci, A. Agambayev, N. Herencsar, K. N. Salama, “Series-, parallel-, and inter-connection of solid-state arbitrary fractional-order capacitors: theoretical study and experimental verification,” IEEE Access, vol. 6, pp. 10933- 10943, 2018.
16. E. Piotrowska, “Analysis the conformable fractional derivative and Caputo definitions in the action of an electric circuit containing a supercapacitor,” Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments, vol. 10808, p. 108081T, International Society for Optics and Photonics, 2018.
17. U. Palaz, R. Mutlu, “Analysis of a Capacitor Modelled with Conformable Fractional Derivative Under DC and Sinusoidal Signals,” Celal Bayar University Journal of Science, vol. 17, no. 2, pp. 193-198, 2021.
18. A. A. H. A. Mohammed, K. Kandemir, R. Mutlu, “Analysis of Parallel Resonance Circuit Consisting of a Capacitor Modelled Using Conformal Fractional Order Derivative Using Simulink,” European Journal of Engineering and Applied Sciences, vol. 3, no. 1, pp 13-18.
19. U. Palaz, R. Mutlu, “Two Capacitor Problem with an LTI Capacitor and a Capacitor Modelled Using Conformal Fractional Order Derivative,” European Journal of Engineering and Applied Sciences, vol. 4, no. 1, pp. 8-13, 2021.
20. L. O. Chua, “Memristor - The Missing Circuit Element,” IEEE Trans. Circuit Theory, vol. 18, pp. 507-519, 1971
21. L. O. Chua and S. M. Kang, “Memristive devices and systems,” Proc.IEEE, vol. 64, pp. 209-223, 1976.
22. D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, “The missing memristor found,” Nature (London), vol. 453, pp. 80-83, 2008.
23. M. Di Ventra, Yu. V. Pershin and L. O. Chua “Circuit Elements with Memory: Memristors, memcapacitors and meminductors” Proc. IEEE, vol. 97, pp. 1717–1724, 2009.
24. Y. V. Pershin, J. Martinez-Rincon, and M. Di Ventra, “Memory circuit elements: from systems to applications,” Journal of Computational and Theoretical Nanoscience, vol. 8, no. 3, pp. 441-448, 2011.
25. A. G. Radwan, and M. E. Fouda, On the mathematical modeling of memristor, memcapacitor, and meminductor, Berlin: Springer, 2015.
26. E. Karakulak, R. Mutlu, “Explanation of Hysteresis Curve of a Flux- dependent Memcapacitor (Memory-capacitor) Using Taylor Series and Parametric Functions,” in 6th International Advanced Technologies Symposium, 2011, pp. 419-422.
27. M. Madsar, Y. Babacan, K. K. Çiçek, “FCS Based Memcapacitor Emulator Circuit,” Journal of the Institute of Science and Technology, vol. 10, no. 1, pp. 112-117, 2020.
28. M. Konal, F. Kacar, and Y. Babacan, “Electronically controllable memcapacitor emulator employing VDCCs,” AEU-International Journal of Electronics and Communications, 140, 153932, 2021.
29. M. Konal, and F. Kacar, “Electronically tunable memcapacitor emulator based on operational transconductance amplifiers,” Journal of Circuits, Systems and Computers, vol. 30, no. 05, pp. 2150082, 2021.
30. A. G. Radwan, and M. E. Fouda. “Memcapacitor: Modeling, Analysis, and Emulators,” On the Mathematical Modeling of Memristor, Memcapacitor, and Meminductor, pp. 151-185, 2015, Springer, Cham.
31. D. Biolek, and V. Biolkova, “Mutator for transforming memristor into memcapacitor,” Electronics letters, vol. 46, no. 21, pp. 1428-1429, 2010.
32. F. J. Romero, A. Ohata, A. Toral-Lopez, A. Godoy, D. P. Morales, and N. Rodriguez, ”Memcapacitor and Meminductor Circuit Emulators: A Review,” Electronics, vol. 10, no. 11, pp. 1225, 2021.
33. Y. Babacan, “An Operational Transconductance Amplifier-based Memcapacitor and Meminductor.” Electrica vol. 18.1, pp. 36-38, 2018.
34. J. Martinez-Rincon, M. Di Ventra, and Y. V. Pershin, “Solid-state memcapacitive system with negative and diverging capacitance,” Physical Review B, vol. 81, no. 19, pp. 195430, 2010.
35. M. Krems, Y. V. Pershin and M. Di Ventra, “Ionic Memcapacitive Effects in Nanopores” Nano letters, vol. 10, no. 7, pp. 2674-2678, 2010.
36. Y. V. Pershin and M. Di Ventra, “Memory effects in complex materials and nanoscale systems”, Advances in Physics, vol. 60, pp. 145-227, 2011.
37. M. D. Goldflam, T. Driscoll, B. Chapler, O. Khatib, N. Marie Jokerst, S. Palit, and M. D. Ventra, “Reconfigurable gradient index using VO2 memory metamaterials,” Applied Physics Letters, vol. 99, no. 4, 044103, 2011.
38. R. K. Singh, and K. Mamta, “An account of spin memristive and memcapacitive systems: Next generation memory devices,” IOSR Journal of Applied Physics (IOSR-JAP) e-ISSN: 2278-4861, vol. 6, no. 3, pp. 07-23, 2014.
39. D. Park, P. Yang, H. J. Kim, K. Beom, H. H. Lee, C. J. Kang, and T. S. Yoon, “Analog reversible nonvolatile memcapacitance in metal-oxide-semiconductor memcapacitor with ITO/HfOx/Si structure,” Applied Physics Letters, vol. 113, no. 16, pp. 162102, 2018.
40. A. K. Khan, and B. H. Lee, “Monolayer MoS2 metal insulator transition based memcapacitor modeling with extension to a ternary device,” AIP Advances, vol. 6, no. 9, pp. 095022, 2016.
41. J. Flak, and J. K. Poikonen, “Solid-state memcapacitors and their applications," In: Memristor Networks, Springer, Cham, pp. 585-601, 2014.
42. Y. Shen, G. Wang, Y. Liang, S. Yu, and H. H. C. Iu, ”Parasitic memcapacitor effects on HP TiO2 memristor dynamics,” IEEE Access, vol. 7, pp. 59825-59831, 2019.
43. J. Sun, E. Lind, I. Maximov, H. Q. Xu, “Memristive and Memcapacitive Characteristics of a Au/Ti–HfO2-InP/InGaAs Diode,” Electron Device Letters, IEEE, vol.32, no.2, pp.131-133, Feb. 2011.
44. J. Martinez-Rincon, and Y. V. Pershin,” Bistable nonvolatile elastic-membrane memcapacitor exhibiting a chaotic behavior,” IEEE transactions on electron devices, vol. 58, no. 6, pp. 1809-1812, 2011.
45. Z. Hu, Y. Li, L. Jia, and J. Yu, “Chaotic oscillator based on voltage-controlled memcapacitor,” in International Conference on Communications, Circuits and Systems (ICCCAS), July 2010, pp. 824-827.
46. K. Rajagopal, A. Akgul, S. Jafari, and B. Aricioglu, “A chaotic memcapacitor oscillator with two unstable equilibriums and its fractional form with engineering applications,” Nonlinear Dynamics, vol. 91, no. 2, pp. 957-974, 2018.
47. F. Yuan, G. Wang, and X. Wang, “Chaotic oscillator containing memcapacitor and meminductor and its dimensionality reduction analysis,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 27, no. 3, pp. 033103, 2017.
48. M. E. Fouda, and A. G. Radwan, “Resistive‐less memcapacitor‐based relaxation oscillator,” International Journal of Circuit Theory and Applications, vol. 43, no. 7, pp. 959-965, 2015.
49. Ş. Ç. Yener, R. Mutlu, “Small signal model of memcapacitor-inductor oscillation circuit,” in Electric Electronics, Computer Science, Biomedical Engineerings’ Meeting (EBBT), 2017, pp. 1-4.
50. F. Tulumbacı, Ş. Ç. Yener, R. Mutlu, “Stored Energy and the Charging Energy Efficiency in a Memcapacitor Circuit,” in 6th International Conference on Electrical Engineering and Electronics, 2020.
51. K. U. Demasius, A. Kirschen, and S. Parkin, “Energy-efficient memcapacitor devices for neuromorphic computing,” Nature Electronics, vol.4, no.10, pp. 748-756 , 2021.
52. D. Halliday, R. Resnick, J. Walker, Fundamentals of physics, John Wiley & Sons, 2013.
53. RA. Powell, ”Two‐capacitor problem: A more realistic view,” American Journal of Physics, vol. 47, pp. 460-462, 1979.
54. S. M. Al-Jaber, S. K. Salih, “Energy consideration in the two-capacitor problem,” European Journal of Physics, vol. 21, pp. 341, 2000.
55. W. J. O'Connor, “The famous ' lost' energy when two capacitors are joined: a new law?” Physics Education, vol. 32, pp. 88, 1997.
56. A. M. Sommariva, “Solving the two-capacitor paradox through a new asymptotic approach,” IEE ProceedingsCircuits, Devices and Systems, vol. 150, pp. 227-231, 2003.
57. TC. Choy, “Capacitors can radiate: Further results for the two-capacitor problem,” American Journal of Physics, vol. 72: pp. 662-670, 2004.
58. R. Mutlu, O. Ç. Akın, “The memcapacitor-capacitor problem,” 2nd International Conference on Computing in Science and Engineering Proceedings, 2011.