Analysis of the HP Memristor and Capacitor (M-C) Series Circuit Using the Lambert W Function
Year 2020,
Volume: 3 Issue: 2, 27 - 32, 30.12.2020
Nurkut Nuray Urgan
,
Ceylan Dalmış
,
Reşat Mutlu
Abstract
Memristor is a new nonlinear circuit element. The HP memristor model is the first and the easiest model to understand memristor given in the literature. Examination of the usage of Memristor with other circuit elements is important for circuit analysis. There are publications in the literature that examine the use of memristor with various circuit elements and examine its usage areas. The circuits in which a capacitor and memristor are connected in series with and without a DC source have been studied in the literature. Lambert W function is a function encountered in system modeling in physics and engineering. In this study, it has been shown that the solution of the capacitor and memristor circuits connected in series with and without a DC source can be expressed using the Lambert W function.
References
- [1] Chua, L. O. (1971). Memristor - The Missing Circuit Element. IEEE Trans. Circuit Theory, vol. 18, pp. 507-519.
- [2] Strukov, D. B., Snider, G. S., Stewart, D. R. & Williams, R. S. (2008). The missing memristor Found. Nature (London), vol. 453, pp. 80-83.
- [3] Chua, L. O., Kang, S. M. (1976). Memrisive devices and systems. Proc. IEEE, vol. 64, pp. 209-223.
- [4] Prodromakis, T., Toumazou, C. (2010). A review on memristive devices and applications. 17th IEEE International Conference on Electronics, Circuits and Systems, 934-937.
- [5] Pershin, Y.V., Martinez-Rincon, J., Di Ventra, M. (2011). Memory circuit elements: from systems to applications. Journal of Computational and Theoretical Nanoscience, 8(3), 441-448.
- [6] Pershin, Y. V., Di Ventra, M. (2011). Memory effects in complex materials and nanoscale systems. Adv. Phys., 60, 145–227.
- [7] Chua, L. (2011). Resistance switching memories are memristors. Appl. Phys. A, 102, 765–783.
- [8] Marani, R., Gennaro, G., Perri, A. G. (2015). A Review on Memristor Applications. International Journal of Advances in Engineering & Technology, 8(3), 294.
- [9] Sangho, S., Kim, K., Kang, S-M. (2011). Memristor applications for programmable analog ICs. IEEE Transactions on Nanotechnology, 10(2), 266-274.
- [10] Adhikari, S. P., Sah, h. Kim, M. P. & Chua, L. O. (2013). Three Fingerprints of Memristor, IEEE Transactions Circuits ans Systems I: Regular Papers, pp. 60(11), 3008-3021.
- [11] Wang, F. Y. (2008). Memristor for introductory physics. arXiv preprint arXiv:0808.0286.
- [12] Joglekar, Y. N., & Wolf, S. J. (2009). The elusive memristor: properties of basic electrical circuits. European Journal of physics, 30(4), 661.
- [13] Bayır Ö., Mutlu R. (2013). Investigation of Memristor-Inductor Series Circuit under DC Excitation Using a Piecewise Memristor Characteristic, 6. İleri Muhendislik Teknolojileri Sempozyumu (25.04.2013-26.04.2013).
- [14] 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.
- [15] Lambert J. H. (1758). Observationes variae in mathesin puram. Acta Helveticae physico-mathematico-anatomico-botanico-medica, Band III, 128–168.
- [16] Euler, L. (1921). De serie Lambertina Plurimisque eius insignibus proprietatibus. Acta Acad. Scient. Petropol. 2, 29–51, 1783. Reprinted in Euler, L. Opera Omnia, Series Prima, Vol. 6, Commentationes Algebraicae. Leipzig, Germany: Teubner, pp. 350–369.
- [17] More, A. A. (2006). "Analytical solutions for the Colebrook and White equation and for pressure drop in ideal gas flow in pipes". Chemical Engineering Science. 61 (16): 5515–5519. doi:10.1016/j.ces.2006.04.003.
- [18] Sotero, Roberto C., Iturria-Medina, Yasser (2011). From Blood oxygenation level dependent (BOLD) signals to brain temperature maps". Bull Math Biol (Submitted manuscript). 73 (11): 2731–47. doi:10.1007/s11538-011-9645-5. PMID 21409512. S2CID 12080132.
- [19] Braun, A., Wokaun, A., Hermanns, H.G. (2003). Analytical Solution to a Growth Problem with Two Moving Boundaries. Appl Math Model. 27 (1): 47–52.
- [20] Braun, A., Baertsch, M., Schnyder, B. & Koetz, R. (2000). A Model for the film growth in samples with two moving boundaries – An Application and Extension of the Unreacted-Core Model. Chem Eng Sci. 55 (22): 5273–5282. doi:10.1016/S0009-2509(00)00143-3.
- [21] Scott, T.C., Babb, J.F., Dalgarno A. & Morgan, J. D. (1993). The Calculation of Exchange Forces: General Results and Specific Models. J. Chem. Phys., 99, pp. 2841-2854.
- [22] Banwell, T.C., Jayakumar, A. (2000). Exact analytical solution for current flow through diode with series resistance. Electronics Letters. 36 (4): 291. doi:10.1049/el:20000301
- [23] Gurleyen, H., Mese, E. (2017). Analytical modeling of magnetically saturated inductance by lambert W function. Journal of Magnetics, 22(3), 369-377.
- [24] Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jeffrey, D. J. & Knuth, D. E. (1996). On the Lambert W function, Advances in Computational Mathematics 5, 4, pp. 329–359.
- [25] Euler, L. (1921). De serie Lambertina plurimisque eius insignibus proprietatibus, Leonhardi Euleri Opera Omnia, Ser. 1, Opera Mathematica 6 [orig. date 1779] 350-369.
- [26] Yi, S., Nelson, P.W. & Ulsoy, A.G. (2010). Time-Delay Systems: Analysis and Control Using the Lambert W Function. Singapore: World Scientific.
- [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] Sozen, H., & Cam, U. (2014). First-order memristor–capacitor filter circuits employing hp memristor. Journal of Circuits, Systems, and Computers, 23(08), 1450116.
- [29] Yener, Ş. Ç., Mutlu, R., & Kuntman, H. H. (2015). Memristor Temelli Sallen-Key Süzgeçler. Gazi Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, 30(2): 173-184.
HP Memristör ve Kondansatör (M-C) Seri Devresinin Lambert W Fonksiyonu Kullanarak Analizi
Year 2020,
Volume: 3 Issue: 2, 27 - 32, 30.12.2020
Nurkut Nuray Urgan
,
Ceylan Dalmış
,
Reşat Mutlu
Abstract
Memristör yeni ve doğrusal olmayan devre elemanıdır. HP memristör model literatürde verilen ilk ve anlaması en kolay memristör modelidir. Memristörün diğer devre elemanları ile birlikte kullanımın incelenmesi Devre analizi açısından önemlidir. Literatürde memristörün türlü devre elemanları ile kullanımının incelendiği ve kullanım alanlarının incelendiği yayınlar mevcuttur. Bir kondansatör ile memristörün seri bağlı olduğu DC kaynaklı ve kaynaksız devreler literatürde incelenmiştir. Lambert W fonksiyonu fizikte ve mühendilikte system modellemede karşımıza çıkan bir fonksiyondur. Bu çalışmada bir kondansatör ile memristörün seri bağlı olduğu DC kaynaklı ve kaynaksız devrelerin çözümünün Lambert W fonksiyonu kullanarak ifade edilebileceği gösterilmiştir.
References
- [1] Chua, L. O. (1971). Memristor - The Missing Circuit Element. IEEE Trans. Circuit Theory, vol. 18, pp. 507-519.
- [2] Strukov, D. B., Snider, G. S., Stewart, D. R. & Williams, R. S. (2008). The missing memristor Found. Nature (London), vol. 453, pp. 80-83.
- [3] Chua, L. O., Kang, S. M. (1976). Memrisive devices and systems. Proc. IEEE, vol. 64, pp. 209-223.
- [4] Prodromakis, T., Toumazou, C. (2010). A review on memristive devices and applications. 17th IEEE International Conference on Electronics, Circuits and Systems, 934-937.
- [5] Pershin, Y.V., Martinez-Rincon, J., Di Ventra, M. (2011). Memory circuit elements: from systems to applications. Journal of Computational and Theoretical Nanoscience, 8(3), 441-448.
- [6] Pershin, Y. V., Di Ventra, M. (2011). Memory effects in complex materials and nanoscale systems. Adv. Phys., 60, 145–227.
- [7] Chua, L. (2011). Resistance switching memories are memristors. Appl. Phys. A, 102, 765–783.
- [8] Marani, R., Gennaro, G., Perri, A. G. (2015). A Review on Memristor Applications. International Journal of Advances in Engineering & Technology, 8(3), 294.
- [9] Sangho, S., Kim, K., Kang, S-M. (2011). Memristor applications for programmable analog ICs. IEEE Transactions on Nanotechnology, 10(2), 266-274.
- [10] Adhikari, S. P., Sah, h. Kim, M. P. & Chua, L. O. (2013). Three Fingerprints of Memristor, IEEE Transactions Circuits ans Systems I: Regular Papers, pp. 60(11), 3008-3021.
- [11] Wang, F. Y. (2008). Memristor for introductory physics. arXiv preprint arXiv:0808.0286.
- [12] Joglekar, Y. N., & Wolf, S. J. (2009). The elusive memristor: properties of basic electrical circuits. European Journal of physics, 30(4), 661.
- [13] Bayır Ö., Mutlu R. (2013). Investigation of Memristor-Inductor Series Circuit under DC Excitation Using a Piecewise Memristor Characteristic, 6. İleri Muhendislik Teknolojileri Sempozyumu (25.04.2013-26.04.2013).
- [14] 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.
- [15] Lambert J. H. (1758). Observationes variae in mathesin puram. Acta Helveticae physico-mathematico-anatomico-botanico-medica, Band III, 128–168.
- [16] Euler, L. (1921). De serie Lambertina Plurimisque eius insignibus proprietatibus. Acta Acad. Scient. Petropol. 2, 29–51, 1783. Reprinted in Euler, L. Opera Omnia, Series Prima, Vol. 6, Commentationes Algebraicae. Leipzig, Germany: Teubner, pp. 350–369.
- [17] More, A. A. (2006). "Analytical solutions for the Colebrook and White equation and for pressure drop in ideal gas flow in pipes". Chemical Engineering Science. 61 (16): 5515–5519. doi:10.1016/j.ces.2006.04.003.
- [18] Sotero, Roberto C., Iturria-Medina, Yasser (2011). From Blood oxygenation level dependent (BOLD) signals to brain temperature maps". Bull Math Biol (Submitted manuscript). 73 (11): 2731–47. doi:10.1007/s11538-011-9645-5. PMID 21409512. S2CID 12080132.
- [19] Braun, A., Wokaun, A., Hermanns, H.G. (2003). Analytical Solution to a Growth Problem with Two Moving Boundaries. Appl Math Model. 27 (1): 47–52.
- [20] Braun, A., Baertsch, M., Schnyder, B. & Koetz, R. (2000). A Model for the film growth in samples with two moving boundaries – An Application and Extension of the Unreacted-Core Model. Chem Eng Sci. 55 (22): 5273–5282. doi:10.1016/S0009-2509(00)00143-3.
- [21] Scott, T.C., Babb, J.F., Dalgarno A. & Morgan, J. D. (1993). The Calculation of Exchange Forces: General Results and Specific Models. J. Chem. Phys., 99, pp. 2841-2854.
- [22] Banwell, T.C., Jayakumar, A. (2000). Exact analytical solution for current flow through diode with series resistance. Electronics Letters. 36 (4): 291. doi:10.1049/el:20000301
- [23] Gurleyen, H., Mese, E. (2017). Analytical modeling of magnetically saturated inductance by lambert W function. Journal of Magnetics, 22(3), 369-377.
- [24] Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jeffrey, D. J. & Knuth, D. E. (1996). On the Lambert W function, Advances in Computational Mathematics 5, 4, pp. 329–359.
- [25] Euler, L. (1921). De serie Lambertina plurimisque eius insignibus proprietatibus, Leonhardi Euleri Opera Omnia, Ser. 1, Opera Mathematica 6 [orig. date 1779] 350-369.
- [26] Yi, S., Nelson, P.W. & Ulsoy, A.G. (2010). Time-Delay Systems: Analysis and Control Using the Lambert W Function. Singapore: World Scientific.
- [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] Sozen, H., & Cam, U. (2014). First-order memristor–capacitor filter circuits employing hp memristor. Journal of Circuits, Systems, and Computers, 23(08), 1450116.
- [29] Yener, Ş. Ç., Mutlu, R., & Kuntman, H. H. (2015). Memristor Temelli Sallen-Key Süzgeçler. Gazi Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, 30(2): 173-184.