Zdenek Biolek

SPICE modeling of memristive, memcapacitative and meminductive systems

A methodology of SPICE modeling of general memristive, memcapacitative, and meminductive systems is proposed and their special cases such as memristors (MR), memcapacitors (MC), and meminductors (ML) are given. These elements are included alongside the conventional R, C, and L elements in a proposed constellation, which generalizes the hitherto approach when the memristor is regarded as a fourth missing passive element. It is shown that the memristor, designed in HP laboratories, can be modeled as a first-order memristive system with nonlinear dependence of the time derivative of the state variable on this variable and on the current flowing through. The outputs of SPICE analyses are consistent with the hitherto published results.

Specification of one classical fingerprint of ideal memristor

It is well known that the memristor hysteresis vanishes if the frequency of its sinusoidal excitation increases. Such a regularity is frequently interpreted as one of the most widely known fingerprints of the memristor. Specifying this fingerprint, the paper yields a new piece of knowledge about the frequency dependence of hysteresis for a constant amplitude of the excitation. Display Omitted Ideal memristors defined by memristance vs. charge maps are studied.The areas of v-i pinched hysteresis loops for low and high frequencies are analyzed.The asymptotic curves for area vs. frequency dependences are found.

Fourth Fundamental Circuit Element: SPICE Modeling and Simulation

This chapter deals with two possible stages of exploring the memristor as the fourth fundamental circuit element: (1) generation of the model and (2) simulation of the element behavior with the aid of the model. The initial stage, i.e. modeling of the two-terminal device, belonging to the family of memristors, should be based on the basic rules of a “correct modeling” as proposed by L. Chua. These rules are brought up in the introductory part of the chapter. The characteristics, defining the memristor, in particular the port and state equations, the constitutive relation, and the parameter-vs.-state-map, are the starting points of such a “correct modeling.” Several memristor fingerprints (FPs), which can be deduced from the above characteristics, are summarized. Their knowledge can be useful for determining whether the memristor model, irrespective of its nature (mathematical, software- or hardware-implemented) behaves correctly. Some methods for the implementation of memristor models in the SPICE-family programs are also described.

Memristor models for SPICE simulation of extremely large memristive networks

In order to avoid non-convergence and other numerical problems associated with the simulation of extremely large memristive networks, suitable models of the individual memristors need to be developed. A circuit containing thousands of memristors for finding the shortest path in a complicated maze is a typical example of a numerically challenging simulation. A benchmark circuit for testing the applications of various complexities is used for the transient analysis. It is shown that various commonly used models, from simple behavioral to Pickett models, require special modifications for minimizing the simulation time and improving the convergence issue.

Modeling of TiO2 memristor: from analytic to numerical analyses

This paper points out that some hitherto published models of ideal memristors can generate serious numerical errors in the environment of SPICE-family programs. The reasons for these errors are analyzed on one model of the TiO2 memristor. From the character of these reasons one can deduce the rules for identifying other potentially problematic memristor models and also the starting points for designing models which are more robust and reliable.

Computing Areas of Pinched Hysteresis Loops of Mem-Systems in OrCAD PSPICE

The pinched hysteresis loop belongs to the fingerprints of the so-called mem-systems, their well-known special cases being memristors. The memory effect of the system is determined by the area of the curve lobes which gradually decrease with increasing repeating frequency of the excitation signal. The paper describes a method for automated computation of the above areas via the commonly utilized OrCAD PSpice simulation software with the help of special measuring functions of the PROBE postprocessor. The usefulness of the method is illustrated on an example of the analysis of a TiO2 memristor.

Modeling and simulation of large memristive networks.

Summary The paper deals with the modeling of memristors operating in extremely large memristive networks such as crossbar structures for memory and computational circuits, memristor-based neural networks or circuits for massively parallel analog computations. Because the non-convergence and other numerical problems increase with increasing complexity of the simulated circuit, suitable models of the individual memristors need to be choicely developed and optimized. Three different models are considered, each representing a specific trade-off between speed and accuracy. Benchmark circuits for testing the applications of various complexities are used for the transient analysis in HSPICE. It is shown how the models can be modified to minimize the simulation time and improve the convergence. Copyright

Generalized rule of homothety of ideal memristors and their siblings

The pinched hysteresis loop area increasing with the square of the frequency of driving harmonic signal on the assumption of constant charge delivered within the half-period belongs to the less known fingerprints of ideal memristor. The paper proves that this fingerprint holds not only for the harmonic excitation: the v-i characteristic of a memristor driven by n-times accelerated and simultaneously n-times amplified signal of arbitrary waveform is a homothetic entity with respect to the original characteristic, with the homothetic center at the v-i origin and with the homothety ratio n. This rule holds for an arbitrary ideal memristor but not for an arbitrary general memristive element. Breaking this rule indicates reliably that the element analyzed is not an ideal memristor.

The simplest memristor in the world

It is well known that thermally dependent resistive two-terminal devices formally conform to the definition of memristive systems. They can be studied as generic memristors on the assumption that their temperature is regarded as a state variable. It is shown in the paper that, due to the Joule dissipation, the parasitic memristance accompanies an arbitrary resistive two-terminal device, which is manifested via the v-i pinched hysteresis loop. Under the common conditions, such hysteresis is not easy to observe. However, this feature can be evident if the varying current induces large temperature variations. The paper analyses the properties of the simplest memristor — a piece of wire. The measurements on a fast current fuse just be fore its blowing clearly demonstrate the typical non-crossing type pinched hysteresis loop.

Evaluation of memristor models for large crossbar structures

This paper is focused on comparing selected SPICE models of TiO2 memristors with respect to time- and memory requirements in the simulation of very large artificial neural networks, which are most likely the first real-world applications of memristors as analog memories. All models were implemented as HSPICE macros and simulated in a Multilayer Perceptron artificial neural network with variable configuration. The results show that after applying modifications to the models in order to prevent numerical overflows it is possible to simulate networks with tens of thousands of memristors.