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Boundary Dynamics of Memcapacitor in Voltage-Excited Circuits and Relaxation Oscillators

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Abstract

This paper discusses the boundary dynamics of the charge-controlled memcapacitor for Joglekar’s window function that describes the nonlinearities of the memcapacitor’s boundaries. A closed form solution for the memcapacitance is introduced for general doping factor \(p\). The derived formulas are used to predict the behavior of the memcapacitor under different voltage excitation sources showing a great matching with the circuit simulations. The effect of the doping factor \( p\) on the time domain response of the memcapacitor has been studied as compared to the linear model using the proposed formulas. Moreover, the generalized fundamentals such as the saturation time of the memcapacitor are introduced, which play an important role in many control applications. Then the boundary dynamics under sinusoidal excitation are used as a basis to analyze any periodic signal by Fourier series, and the results have been verified using PSPICE simulations showing a great matching. As an application, two configuration of resistive-less memcapacitor-based relaxation oscillators are proposed and closed form expressions for oscillation frequency and conditions for oscillation are derived in presence of nonlinear model. The proposed oscillator is verified using PSPICE simulation showing a perfect matching.

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Authors and Affiliations

  1. Engineering Mathematics and Physics Department, Cairo University, Giza, 12613, Egypt

    Mohammed E. Fouda & Ahmed G. Radwan

  2. Nanoelectronics Integrated Systems Center (NISC), Nile University, Cairo, Egypt

    Ahmed G. Radwan

Authors
  1. Mohammed E. Fouda
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  2. Ahmed G. Radwan
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Correspondence to Mohammed E. Fouda.

Appendix

Appendix

To prove that (11) will be reduced to its conventional linear dopant formula, (10) can be rewriten as

$$\begin{aligned} h(D(t),p)=y\Big (D_{s}-\frac{D_{d}}{2}y\Big )+ \sum ^{\infty }_{r=1}{y^{2pr+1}\left( \frac{(2pr+2)D_{s}-(2pr+1)D_{d}\ y}{(2pr+1)(2pr+2)}\right) }. \end{aligned}$$
(38)

Taking the limit \(p\rightarrow \infty \),

$$\begin{aligned} h(D(t),\infty )= D_{s} y-\frac{D_{d} y^{2}}{2}+ \sum ^{\infty }_{r=1} \lim _{p \rightarrow \infty }\left( {y^{2pr+1}\left( \frac{(2pr+2)D_{s}-(2pr+1)D_{d}\ y}{(2pr+1)(2pr+2)}\right) } \right) . \end{aligned}$$
(39)

Since \(y \in [-1,1]\), then \(y^{2p} \rightarrow 0\), the previous formula will be reduced to:

$$\begin{aligned} h(D(t),\infty )=\frac{D_{s}^{2}}{2D_{d}}-\frac{2D^{2}(t)}{D_{d}}. \end{aligned}$$
(40)

Consequently,

$$\begin{aligned} D^{2}(t)=D^{2}_\mathrm{in}+2\eta k \varphi (t) . \end{aligned}$$
(41)

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Fouda, M.E., Radwan, A.G. Boundary Dynamics of Memcapacitor in Voltage-Excited Circuits and Relaxation Oscillators. Circuits Syst Signal Process 34, 2765–2783 (2015). https://doi.org/10.1007/s00034-015-9995-6

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  • DOI: https://doi.org/10.1007/s00034-015-9995-6

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