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![Page 1: The fourth element: characteristics, modelling and electromagnetic theory of the memristor by O. Kavehei, A. Iqbal, Y. S. Kim, K. Eshraghian, S. F. Al-Sarawi,](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f0c5503460f94c20202/html5/thumbnails/1.jpg)
The fourth element: characteristics, modelling and electromagnetic theory of the memristor
by O. Kavehei, A. Iqbal, Y. S. Kim, K. Eshraghian, S. F. Al-Sarawi, and D. Abbott
Proceedings AVolume 466(2120):2175-2202
August 8, 2010
©2010 by The Royal Society
![Page 2: The fourth element: characteristics, modelling and electromagnetic theory of the memristor by O. Kavehei, A. Iqbal, Y. S. Kim, K. Eshraghian, S. F. Al-Sarawi,](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f0c5503460f94c20202/html5/thumbnails/2.jpg)
The four fundamental two-terminal circuit elements.
O. Kavehei et al. Proc. R. Soc. A 2010;466:2175-2202
©2010 by The Royal Society
![Page 3: The fourth element: characteristics, modelling and electromagnetic theory of the memristor by O. Kavehei, A. Iqbal, Y. S. Kim, K. Eshraghian, S. F. Al-Sarawi,](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f0c5503460f94c20202/html5/thumbnails/3.jpg)
Schematic of HP MR, where D is the device channel length and w is the length of the doped region.
O. Kavehei et al. Proc. R. Soc. A 2010;466:2175-2202
©2010 by The Royal Society
![Page 4: The fourth element: characteristics, modelling and electromagnetic theory of the memristor by O. Kavehei, A. Iqbal, Y. S. Kim, K. Eshraghian, S. F. Al-Sarawi,](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f0c5503460f94c20202/html5/thumbnails/4.jpg)
Two MRs in series: (a) with the same polarity, both η=−1 or both η=+1; (b) with opposite polarities, η=−1 and η=+1.
O. Kavehei et al. Proc. R. Soc. A 2010;466:2175-2202
©2010 by The Royal Society
![Page 5: The fourth element: characteristics, modelling and electromagnetic theory of the memristor by O. Kavehei, A. Iqbal, Y. S. Kim, K. Eshraghian, S. F. Al-Sarawi,](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f0c5503460f94c20202/html5/thumbnails/5.jpg)
The hysteresis of an MR based on equation (2.16).
O. Kavehei et al. Proc. R. Soc. A 2010;466:2175-2202
©2010 by The Royal Society
![Page 6: The fourth element: characteristics, modelling and electromagnetic theory of the memristor by O. Kavehei, A. Iqbal, Y. S. Kim, K. Eshraghian, S. F. Al-Sarawi,](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f0c5503460f94c20202/html5/thumbnails/6.jpg)
The hysteresis characteristics of the MR. It shows that the memristance value is varying from a very low to a very high resistance.
O. Kavehei et al. Proc. R. Soc. A 2010;466:2175-2202
©2010 by The Royal Society
![Page 7: The fourth element: characteristics, modelling and electromagnetic theory of the memristor by O. Kavehei, A. Iqbal, Y. S. Kim, K. Eshraghian, S. F. Al-Sarawi,](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f0c5503460f94c20202/html5/thumbnails/7.jpg)
The hysteresis characteristics using the nonlinear drift assumption.
O. Kavehei et al. Proc. R. Soc. A 2010;466:2175-2202
©2010 by The Royal Society
![Page 8: The fourth element: characteristics, modelling and electromagnetic theory of the memristor by O. Kavehei, A. Iqbal, Y. S. Kim, K. Eshraghian, S. F. Al-Sarawi,](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f0c5503460f94c20202/html5/thumbnails/8.jpg)
Nonlinear window functions, (a) F(x)=1−(2x−1)2p, (b) F(x)=1−(x− sgn(−i))2p.
O. Kavehei et al. Proc. R. Soc. A 2010;466:2175-2202
©2010 by The Royal Society
![Page 9: The fourth element: characteristics, modelling and electromagnetic theory of the memristor by O. Kavehei, A. Iqbal, Y. S. Kim, K. Eshraghian, S. F. Al-Sarawi,](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f0c5503460f94c20202/html5/thumbnails/9.jpg)
The SPICE macro-model of MR. Here, G, H and S are a VCCS, CCVS, and a switch (VON=−1.9 V and VOFF=−2 V), respectively.
O. Kavehei et al. Proc. R. Soc. A 2010;466:2175-2202
©2010 by The Royal Society
![Page 10: The fourth element: characteristics, modelling and electromagnetic theory of the memristor by O. Kavehei, A. Iqbal, Y. S. Kim, K. Eshraghian, S. F. Al-Sarawi,](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f0c5503460f94c20202/html5/thumbnails/10.jpg)
The MR characteristics.
O. Kavehei et al. Proc. R. Soc. A 2010;466:2175-2202
©2010 by The Royal Society
![Page 11: The fourth element: characteristics, modelling and electromagnetic theory of the memristor by O. Kavehei, A. Iqbal, Y. S. Kim, K. Eshraghian, S. F. Al-Sarawi,](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f0c5503460f94c20202/html5/thumbnails/11.jpg)
The MR characteristics when a step input voltage is applied.
O. Kavehei et al. Proc. R. Soc. A 2010;466:2175-2202
©2010 by The Royal Society
![Page 12: The fourth element: characteristics, modelling and electromagnetic theory of the memristor by O. Kavehei, A. Iqbal, Y. S. Kim, K. Eshraghian, S. F. Al-Sarawi,](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f0c5503460f94c20202/html5/thumbnails/12.jpg)
The MR characteristics when (i) a 1 kHz sinusoidal voltage is applied.
O. Kavehei et al. Proc. R. Soc. A 2010;466:2175-2202
©2010 by The Royal Society
![Page 13: The fourth element: characteristics, modelling and electromagnetic theory of the memristor by O. Kavehei, A. Iqbal, Y. S. Kim, K. Eshraghian, S. F. Al-Sarawi,](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f0c5503460f94c20202/html5/thumbnails/13.jpg)
The I–V curves for (a) two MRs in parallel, (b) two MRs in series and (c) a single MR. In all of the cases, there is no difference between an MR and equivalent resistor in the network.
O. Kavehei et al. Proc. R. Soc. A 2010;466:2175-2202
©2010 by The Royal Society
![Page 14: The fourth element: characteristics, modelling and electromagnetic theory of the memristor by O. Kavehei, A. Iqbal, Y. S. Kim, K. Eshraghian, S. F. Al-Sarawi,](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f0c5503460f94c20202/html5/thumbnails/14.jpg)
Step voltage response curves for (i) (R) resistor–memristor, (ii) (C) capacitor–memristor and (iii) (L) inductor–memristor.
O. Kavehei et al. Proc. R. Soc. A 2010;466:2175-2202
©2010 by The Royal Society
![Page 15: The fourth element: characteristics, modelling and electromagnetic theory of the memristor by O. Kavehei, A. Iqbal, Y. S. Kim, K. Eshraghian, S. F. Al-Sarawi,](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f0c5503460f94c20202/html5/thumbnails/15.jpg)
MR-op-amp integrator circuit and its response to the input step voltage.
O. Kavehei et al. Proc. R. Soc. A 2010;466:2175-2202
©2010 by The Royal Society