This chapter is divided into three sections focusing on some memcapacitor-based applications. The first one discusses the mathematical analyses and design of resistive-less memcapacitor-based relaxation oscillators where different cases have been investigated and validated. Analytical expressions for the oscillation frequency, duty cycle, stored energy, and conditions of oscillation have been achieved with many numerical examples and circuit simulations. The second section discusses the boundary effect on the analysis and output behavior of memcapacitor-based oscillators compared to the previous case. The last section addresses the memcapacitor-bridge synapses with mathematical analysis, weight programming, and circuit simulations. © 2015, Springer International Publishing Switzerland.
Memcapacitor: Modeling, analysis, and emulators
This chapter reviews the memcapacitor, mathematical representations of time-invariant, physical realizations, and mathematical models. Moreover, the nonlinear boundary effect of the memcapacitor under step, sinusoidal, and general periodic excitation responses are discussed with analytical, numerical, and circuit simulations for different examples. The general analyses of series and parallel connections of memcapacitors are introduced with many examples and circuit simulations. Finally a charge-controlled, memristor-less memcapacitor is introduced and validated through different cases. © 2015, Springer International Publishing Switzerland.
Meminductor: Modeling, analysis, and emulators
This chapter introduces the basic definition of meminductor and its mathematical representation of time-invariant system (Ideal, Generic, and Extended) with some examples. The mathematical model of meminductor and its response under different current excitations (step, sinusoidal, and periodic) are discussed with analytical, numerical, and circuit simulations. Different meminductor emulators are introduced with their mathematical modeling and numerical simulation, and verified using PSPICE simulations. © 2015, Springer International Publishing Switzerland.
Memristor mathematical models and emulators
This chapter introduces different generalized mathematical classes of memristors which can be categorized as: continuous symmetrical models (current and voltage controlled emulators), continuous nonsymmetrical model, switched-memristor model, and fractional-order model with some experimental results. Different emulators with experimental results are discussed based on CCII, discrete components, and MOS realizations. Different analytical expressions, numerical analyses, circuit simulations results as well as experimental results are provided for most of the previous models. © 2015, Springer International Publishing Switzerland.
Memristor: Models, types, and applications
This chapter discusses the main properties of the memristor, a comparison between five recent memristor models, mathematical modeling of the HP memristor with analytical expressions for different excitations, mathematical representations of time-invariant memristor (ideal, generic, and extended), different memristor implementation types, and some memristor-based applications in digital and analog circuits. © 2015, Springer International Publishing Switzerland.
Memristor-based relaxation oscillator circuits
This chapter discusses the analysis and design of memristor-based oscillators which is considered one of the nonlinear analog block required for many applications such as chaotic memristor oscillators and artificial neuron network. The realizations of memristor-based oscillators have been discussed via replacing capacitors with memristors to construct relaxation reactance-less oscillators. The advantages of such oscillators are related to low frequency, nanoscale, and simple designs and can be used in neuromorphic systems. Different topologies of memristor-based relaxation oscillators have been discussed and either symmetric or asymmetric types with analytical formulas of oscillation frequency and condition for oscillations are derived. The analyses of these oscillators are introduced with their numerical simulations, and verified using PSPICE circuit simulations showing a great matching. Moreover, many fundamentals are also discussed such as the effect of boundary dynamics, series and parallel connections as well as power analysis in memristor-based circuits. © 2015, Springer International Publishing Switzerland.
Memristor-based multilevel digital systems
This chapter investigates the advantages of memristor-based digital applications using multi-level arithmetic concepts. Recently, there are huge concerns regarding the memristor in digital signal processing (DSP) circuits to enhance the performance and realize very high density, nonvolatile memories in neural networks. This can be achieved by mapping the high/low logic into the memristor high/low resistances. Recently, the potential to divide the memristance levels to build multilevel digital circuits such as the ternary and redundant circuits are discussed. The concepts have been initiated by designing a half ternary adder based on the memristor; then, the concept is generalized for redundant half adder, full adder, and N-bit adder circuits. The advantages of such circuits that the speed is independent on the operand and parallel processing can be handled efficiently. Moreover, a general approach to build digital functions using mixed memristor-transistor circuits are investigated such as multipliers. © 2015, Springer International Publishing Switzerland.
Fractional-order Memristor Response Under DC and Periodic Signals
Recently, there is an essential demand to extend the fundamentals of the conventional circuit theory to include the new generalized elements, fractional-order elements, and mem-elements due to their unique properties. This paper presents the relationships between seven different elements based on the four physical quantities and the fractional-order derivatives. One of them is the Fractional-order memristor, where the memristor dynamic is expressed by fractional-order derivative. This element merge the memristive and fractional-order concepts together where the conventional modeling becomes a special case. Moreover, the mathematical modeling of the fractional-order memristor is introduced. In addition, the response of applying DC, sinusoidal, and nonsinusoidal periodic signals is discussed. Finally, different numerical simulations are presented. © 2014, Springer Science+Business Media New York.
Boundary Dynamics of Memcapacitor in Voltage-Excited Circuits and Relaxation Oscillators
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 (Formula presented.)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 (Formula presented.) 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. © 2015, Springer Science+Business Media New York.
Resistive-less memcapacitor-based relaxation oscillator
Recently, the realization of the conventional relaxation oscillators was introduced based on memristors. This paper validates the concept using two series memcapacitors in general which is applicable for a capacitor and memcapacitor as well. Furthermore, the necessary conditions for oscillation are introduced, and a generalized closed-form expression for the oscillation frequency is derived. Two special cases are introduced and verified using PSPICE simulations showing a perfect matching. Copyright © 2014 John Wiley & Sons, Ltd.