Pinched Hysteresis Loops of Two Memristor SPICE ModelsAkzharkyn Izbassarova and Daulet Kengesbek

Department of Electrical and Electronics Engineering Nazarbayev University Astana, Kazakhstan

aizbassarova@nu.edu.kz, dkengesbek@nu.edu.kz

Abstract— This paper compares two different SPICE models for memristor device by analyzing pinched hysteresis loops. A sinusoidal voltage source is applied in order to obtain i-v characteristics for both models. Then different set of simulations are done with distinct frequency and initial state values.

I. INTRODUCTION

The fourth passive element, named memristor, was firstly proposed 44 years ago by circuit theorist Leon Chua. The main feature of this two-terminal element is that it behaves like a nonlinear resistance and has nonvolatile memory. [1]. The first solid-state prototype of the memristor device was designed at Hewlett-Packard (HP) Laboratories in 2008. [2].

In this paper two memristor models, which were designed in order to observe application of memristor in microwave devices, are considered. [3] The scope of this paper is to compare these two models and identify whether they follow the same basic characteristics as a memristor in terms of pinched-hysteresis loop.

II. MEMRISTOR SPICE MODELS

A. Model A

Fig. 1. Represents the first proposed model that consists of a voltage-dependent voltage source (VSDS), a low pass filter (LPF), and buffer. [3]. Operational amplifier (Op-AMP) is used as an integrator to solve the differential equation (1). In general, Model A is characterize by the following equation:

𝜐 𝑜𝑢𝑡( )𝑡 =−(1/𝑅1𝐶1)∫ ( ) +𝑖𝑛 𝑡 𝑑𝑡 𝑉0 (1)

where 𝑉0 is the initial applied voltage. For the simulation in SPICE the following parameters are used:𝑅𝑂𝑁=100 Ω,

𝑅𝑂𝐹𝐹=10 ∙Ω, k=1*1012, 𝑘 𝑅𝐿𝑂𝐴𝐷=106 Ω.

B. Model B

Model B, shown on Fig.2, is designed by using an integrator, consisting of the following components: a capacitor, a resistor, a current dependent source and a VDVS. [3]. The same values for parameters, as given in Model A, are used. The formula for output voltage is given as

𝜐𝑜𝑢𝑡( )𝑡 =(1/𝑅𝐶)∫𝜐𝑖𝑛( ) +𝑡 𝑑𝑡 𝑉0 (2)

III. SIMULATION RESULTS

A. Comparison of Model A and Model B

The results obtained show that two models are identical in terms of frequency response for initial state values between (0)=0.2 and (0)=0.8. In case of initial state (0)=1 , 𝑥 𝑥 𝑥 i-v characteristics of two models are different. Model A does not give any results and simulation shows error at frequencies higher than 10 MHz. However, at small frequency f=100 kHz the pinched hysteresis loop for Model A becomes a straight line. Model B also has a linear relation but at higher frequencies, up to 20 MHz. There is also error at frequency value 100 MHz.

When (0)=1, the memristor is fully doped and acts as a resistor. The difference between 𝑥two models when (0)=1 can be explained by the different threshold values for frequency 𝑥under which they do not change the main characteristics of the linear resistor.

B. Dependance of i-v cuve on initial state

For the same frequency values but for an arbitrary value of the initial state, i-v curves of two memristor models obtain different shapes. As shown on Figs. 3-4, the area of pinched hysteresis loop expands when x(0) is changed from 0.2 to 0.8. It can be explained that by increasing the width of doped region we also increase the difference between the 𝑅𝑂𝐹𝐹 and 𝑅𝑂𝑁 states.

C. Dependance of i-v curve on frequency

When both memristor models are simulated by applying different frequencies of sinusoidal signal, pinched hysteresis loops shrinks or expands depending on frequency. At very low frequency f=100 kHz there is no hysteresis because the resistance has enough time to settle to certain value for each of the instantaneous values of voltage feeded. For high frequency f=100 MHz the conductivity of memristor is also relatively high. Moreover, the slight vibration during transient time can be observed in the figures for high frequencies.

The conductive region of the memristor refers to RON (LOW) state. The resistive region, acting as an insulator, is known as ROFF (HIGH) state. The hysteresis loops, obtained before, can be divided into two sections. The first part includes two straight lines, corresponding to RON and ROFF states, whereas two bending parts refer to transition region between these two states. Fig. 5. Shows how fast it takes to switch between these two states when x(0) = 0.2 and f = 100MHz.

IV. CONCLUSION In this paper two SPICE models are simulated using LTSpice. Similarities and differences are identified and analyzed. Both models satisfy three main properties corresponding to the memristor. Further work can be conducted on identifying threshold frequency value for which the model of memristor behaves as a resistor.

REFERENCES

[1] L.O. Chua, “Memristor-the missing circuit element” IEEE Trans. Circuit Theory, vol. 18, no. 5, pp. 507–519, 1971. [2] J. M. Tour and T. He, The fourth clement, Nature 453, pp. 42-43 , May 2008 [3] K. D. Xu, Y. H. Zhang, L. Wang, M.Q. Yuan, Y.Fan and W. T. Joines, “Two Memristor SPICE Models and Their Applications in Microwave Devices” IEEE Trans. on Nanotechnology, vol. 13, no. 3, May 2014

Fig. 1. Proposed memristor Model A

Fig. 2. Proposed memristor Model B

Fig. 3. Simulated transient i-v characteristics of the Model A, where initial state x=0.2

Fig. 4. Simulated transient i-v characteristics of the Model A, where initial state x=0.8

Fig. 5. High and Low level state