Differential Equations of Ideal Memristors

Ideal memristor is a resistor with a memory, which adds dynamics to its behavior. The most usual characteristics describing this dynamics are the constitutive relation (i.e. the relation between flux and charge), or Parameter-vs-state- map (PSM), mostly represented by the memristance-to-charge dependence. One of the so far unheeded tools for memristor description is its differential equation (DEM), composed exclusively of instantaneous values of voltage, current, and their derivatives. The article derives a general form of DEM that holds for any ideal memristor and shows that it is always a nonlinear equation of the first order; the PSM forms are found for memristors which are governed by DEMs of the Bernoulli and the Riccati types; a classification of memristors according to the type of their dynamics with respect to voltage and current is carried out

Analytical Computation of the Area of Pinched Hysteresis Loops of Ideal Mem-Elements

The memory elements, memristor being the best known of them, driven by a periodical waveform exhibit the well-known pinched hysteresis loops. The hysteresis is caused by a memory effect which results in a nonzero area closed within the loop. This paper presents an analytical formula for the loop area. This formula is then applied to memory elements whose parameter-vs.-state maps are modeled in the polynomial form. The TiO2 memristor, a special subset of the above elements, is analyzed as a demonstration example

Reliable Modeling of Ideal Generic Memristors via State-Space Transformation

The paper refers to problems of modeling and computer simulation of generic memristors caused by the so-called window functions, namely the stick effect, nonconvergence, and finding fundamentally incorrect solutions. A profoundly different modeling approach is proposed, which is mathematically equivalent to window-based modeling. However, due to its numerical stability, it definitely smoothes the above problems away

Improved Model of TiO2 Memristor

Analysis of Pickett’s model of the HP TiO2 memristor presented in this paper reveals an ambiguity of its port equation, which may cause non-convergence, numerical errors, and non-physical solutions during time-domain simulation. As there is no easy fix of the original model a new behavioral approximation of static I-V characteristics has been proposed. The approximation matches well the original model and is unambiguous

Behavioral Modeling of Memcapacitor

Two behavioral models of memcapacitor are developed and implemented in SPICE-compatible simulators. Both models are related to the charge-controlled memcapacitor, the capacitance of which is controlled by the amount of electric charge conveyed through it. The first model starts from the state description of memcapacitor whereas the second one uses the memcapacitor constitutive relation as the only input data. Results of transient analyses clearly show the basic fingerprints of the memcapacitor

SPICE Model of Memristor with Nonlinear Dopant Drift

A mathematical model of the prototype of memristor, manufactured in 2008 in Hewlett-Packard Labs, is described in the paper. It is shown that the hitherto published approaches to the modeling of boundary conditions need not conform with the requirements for the behavior of a practical circuit element. The described SPICE model of the memristor is thus constructed as an open model, enabling additional modifications of non-linear boundary conditions. Its functionality is illustrated on computer simulations

Immediate Analysis of Periodic Steady States in Switched DC-DC Converters via SPICE

The method of immediate analysis of periodic steady states in switched DC-DC converters operating in the continuous current mode is described. The initial conditions, which correspond to the periodic steady state, are found in the first step. They are used consequently for the conventional transient analysis. A special SPICE model of the converter finds automatically these initial conditions, which are then available within the transient analysis. The method works both for the well-known behavioral models of switched converters and also for models which employ complex nonlinear SPICE models of semiconductor switches

Comments on Pinched Hysteresis Loops of Memristive Elements

The hysteresis loops pinched in the v-i origin belong to well-known fingerprints of memristive elements driven by bipolar periodical signals. Some element properties follow from the loop behavior in the close neighborhood of the origin. The paper analyzes this behavior of the memristive elements that produce steady-state hysteresis loops under harmonic excitation. It is shown that there is a connection between the frequency content of the state variable waveform and the type of the loop being pinched

High Input Impedance Voltage-Mode Biquad Filter Using VD-DIBAs

This paper deals with a single-input multiple-output biquadratic filter providing three functions (low-pass, high-pass and band-pass) based on voltage differencing differential input buffered amplifier (VD-DIBA). The quality factor and pole frequency can be electronically tuned via the bias current. The proposed circuit uses two VD-DIBAs and two grounded capacitors without any external resistors, which is suitable to further develop into an integrated circuit. Moreover, the circuit possesses high input impedance, providing easy voltage-mode cascading. It is shown that the filter structure can be easily extended to multi-input filter without any additional components, providing also all-pass and band-reject properties. The PSPICE simulation and experimental results are included, verifying the key characteristics of the proposed filter. The given results agree well with the theoretical presumptions