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 A Volume 466(2120): August 8, 2010 ©2010 by The Royal Society

The four fundamental two-terminal circuit elements. O. Kavehei et al. Proc. R. Soc. A 2010;466: ©2010 by The Royal Society

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: ©2010 by The Royal Society

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: ©2010 by The Royal Society

The hysteresis of an MR based on equation (2.16). O. Kavehei et al. Proc. R. Soc. A 2010;466: ©2010 by The Royal Society

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: ©2010 by The Royal Society

The hysteresis characteristics using the nonlinear drift assumption. O. Kavehei et al. Proc. R. Soc. A 2010;466: ©2010 by The Royal Society

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: ©2010 by The Royal Society

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: ©2010 by The Royal Society

The MR characteristics. O. Kavehei et al. Proc. R. Soc. A 2010;466: ©2010 by The Royal Society

The MR characteristics when a step input voltage is applied. O. Kavehei et al. Proc. R. Soc. A 2010;466: ©2010 by The Royal Society

The MR characteristics when (i) a 1 kHz sinusoidal voltage is applied. O. Kavehei et al. Proc. R. Soc. A 2010;466: ©2010 by The Royal Society

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: ©2010 by The Royal Society

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: ©2010 by The Royal Society

MR-op-amp integrator circuit and its response to the input step voltage. O. Kavehei et al. Proc. R. Soc. A 2010;466: ©2010 by The Royal Society