A piecewise linear memristor model and design method

Abstract

The invention discloses a piecewise linear memristor model and a design method. The invention takes into account that the physical model of a local active memristor has strong nonlinearity and is not conducive to mathematical analysis, and the existence of an S-type negative differential conductance characteristic in its direct current V-I curve is the key and origin of generating oscillation behavior. The piecewise linear memristor model proposed in the invention can effectively simulate the overall passive, local active and S-type negative differential resistance characteristics of an S-type local active memristor physical device. The model determined by quasi-static testing and dynamic performance testing has the advantages of being simple, accurate, having few parameters, piecewise linearity, and the like, and is convenient for studying and analyzing the local active memristor and its application.

Description

Technical Field

[0001] The invention relates to a memristor model, in particular to a piecewise linear memristor model and a design method, and is applicable to the research field of local active memristors. Background Art

[0002] Locally active memristors refer to memristors with negative differential resistance or conductance. Nanoscale memristors have been found to exhibit local active properties, such as NbO x ,VO2 and TaO x Memristors are called S-type local active memristors because of their S-type negative differential conductance characteristics in the DC VI diagram. Their volt-ampere characteristic curves are distributed in the first and third quadrants, and they are a kind of overall passive and locally active device. Local active memristors have shown great application prospects in periodic oscillations, chaotic oscillations, digital logic devices, and brain-like neuromorphic computing. According to NbO x The model established based on the physical characteristics of the memristor can accurately simulate the S-type negative differential conductance characteristics of the memristor. However, since the negative differential conductance characteristics of the memristor are caused by Joule heating caused by the Poole effect, the physical models established based on this are mostly in exponential form or high-order polynomials, which have strong nonlinearity and are not conducive to the mathematical analysis of the locally active memristor. Therefore, designing a simple locally active memristor model is helpful to promote the research and development of locally active memristors. Summary of the invention

[0003] The purpose of the present invention is to propose a piecewise linear memristor model and a design method for the problems existing in the existing model. The model can accurately simulate an S-type local active memristor.

[0004] Considering that the physical model of the local active memristor has strong nonlinearity, which is not conducive to mathematical analysis, and the S-type negative differential conductance characteristic in its DC VI curve is the key and origin of the oscillation behavior, in order to achieve the above purpose, the present invention designs a piecewise linear memristor model, which can be used to simulate the negative differential conductance characteristics of the S-type local active memristor. The model is

[0005]

[0006] Among them, i, v, x are the current flowing through the memristor, the voltage across the memristor and the state variable of the memristor respectively, and n, β, m, k1, k2, I1, I2 are all constants. n, m, k1, k2, I1, I2 can be determined by the quasi-static test of the memristor. β determines the dynamic performance of the memristor and is determined by the dynamic characteristics of the memristor.

[0007] A design method for a piecewise linear memristor model, characterized by:

[0008] The local active memristor exhibits current control characteristics under the DC current I test; it is presented on the DC VI characteristic diagram, and two turning points are determined on the DC VI characteristic diagram. Let the origin be O, the first turning point be A, the second turning point be B, and the end be C; then the OA segment is the memristor working in the high impedance state, and the slope represents the high impedance state R off , the BC segment memristor works in the low resistance state, and the slope represents the low resistance state R on , the AB segment is the negative differential resistance area, which is the local active area, and the slope of the AB segment is the negative differential resistance R N ; The function expression of the DC VI characteristic curve is uniquely determined by the two turning points A (V1, I1), B (V2, I2) and the slope of the BC segment:

[0009]

[0010] The piecewise linearity is described by the absolute value function as follows:

[0011] V=g(I)=m+nI+k1|I-I1|+k2|I-I2| (2)

[0012] Among them, m, n, k1, k2 are the parameters to be determined, and I1, I2 are the currents at turning points A and B. According to the relationship between the three interval currents I and the turning point currents I1, I2, equation (2) is solved as follows:

[0013]

[0014] Combining equation (1) and equation (3), we can get:

[0015]

[0016] Solving equation (4) yields:

[0017]

[0018] According to Chua's expansion theorem, the general current-controlled memristor model is:

[0019]

[0020] Where i, v, and x are the current flowing through the memristor, the voltage across the memristor, and the state variable of the memristor, respectively. m (x) is the memristor function, and f is the differential function of the state variable x.

[0021] Since the memristor value R m (x) depends only on the state variable x, and a simple linear function is used to express the relationship between the two:

[0022] R m(x) = n + x (7)

[0023] According to Ohm's law, the DC resistance of the memristor can be expressed as:

[0024] V=g(I)=R m (X)I=(n+X)I (8)

[0025] In the formula, Satisfies the following relationship:

[0026] m+k1|I-I1|+k2|I-I2|-XI=0 (9)

[0027] For the DC test current I, the state equation satisfies:

[0028]

[0029] f(x,i) is a function of x and i. According to equations (9) and (10), the following state equation can be obtained:

[0030]

[0031] Where β is the dynamic characteristic parameter of the memristor, which reflects the rate of change of the state variable x.

[0032] Substituting equations (7) and (11) into equation (6), we get a simple and universal piecewise linear memristor model as follows:

[0033]

[0034] Beneficial effects: The piecewise linear memristor model proposed in the present invention can effectively simulate the overall passive, local active and S-type negative differential resistance characteristics of the S-type local active memristor physical device. The model determined by quasi-static testing and dynamic performance testing has the advantages of simplicity, accuracy, few parameters, and piecewise linearity, which facilitates the research and analysis of local active memristors and their applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is the DC VI characteristic diagram of the piecewise linear local active memristor. DETAILED DESCRIPTION

[0036] The following is combined with Figure 1 The present invention is further described as follows:

[0037] The present invention designs a simplified model based on the fact that the S-type local active memristor is overall passive, locally active, has S-type negative differential conductance and current control characteristics. The attached figure is a DC VI characteristic diagram of the piecewise linear local active memristor. Under the DC current I test, it shows the current control characteristics. The OA segment memristor works in the high impedance state, and the slope can represent the high impedance state R off , the BC segment memristor works in a low resistance state, and the slope can represent the low resistance state R on , the AB segment is the negative differential resistance area, which is the local active area, and the slope of the AB segment is the negative differential resistance R N From the attached figure, we can see that we only need to determine two turning points A (V1, I1), B (V2, I2) and the slope of the BC segment (low resistance R on ), we can uniquely determine the function expression of the DC VI characteristic curve in the attached figure:

[0038]

[0039] The piecewise linearity is described by the absolute value function as follows:

[0040] V=g(I)=m+nI+k1|I-I1|+k2|I-I2| (2)

[0041] Among them, m, n, k1, k2 are the parameters to be determined, and I1, I2 are the currents at turning points A and B. According to the relationship between the three interval currents I and the turning point currents I1, I2, equation (2) is solved as follows:

[0042]

[0043] Combining equation (1) and equation (3), we can get:

[0044]

[0045] Solving equation (4) yields:

[0046]

[0047] According to Chua's expansion theorem, the model of a general current-controlled memristor is:

[0048]

[0049] Where i, v, and x are the current flowing through the memristor, the voltage across the memristor, and the state variable of the memristor, respectively. m (x) is the memristor function, and f is the differential function of the state variable x.

[0050] Since the memristor value R m (x) depends only on the state variable x, and a simple linear function is used to express the relationship between the two:

[0051] R m (x) = n + x (7)

[0052] According to Ohm's law, the DC resistance of the memristor can be expressed as:

[0053] V=g(I)=R m (X)I=(n+X)I (8)

[0054] In the formula, Satisfies the following relationship:

[0055] m+k1|I-I1|+k2|I-I2|-XI=0 (9)

[0056] For the DC test current I, the state equation satisfies:

[0057]

[0058] f(x,i) is a function of x and i. According to equations (9) and (10), the following state equation can be obtained:

[0059]

[0060] Where β is the dynamic characteristic parameter of the memristor, which reflects the rate of change of the state variable x.

[0061] Substituting equations (7) and (11) into equation (6), we get a simple and universal piecewise linear memristor model as follows:

[0062]

Claims

1. A piecewise linear memristor, characterized in that: The model of the piecewise linear memristor is: Where i, v, x are the current flowing through the memristor, the voltage across the memristor and the state variable of the memristor respectively; n, β, m, k1, k2 are all constants; I1 and I2 represent the current values ​​at the first and second turning points on the DC VI characteristic diagram of the local active memristor under the DC current I test respectively; n, m, k1, k2, I1, I2 are determined by the quasi-static test of the memristor; β determines the dynamic performance of the memristor and is determined by the dynamic characteristics of the memristor.

2. The design method of a piecewise linear memristor according to claim 1, characterized in that: The local active memristor exhibits current control characteristics under the DC current I test; it is presented on the DC VI characteristic diagram, and two turning points are determined on the DC VI characteristic diagram. Let the origin be O, the first turning point be A, the second turning point be B, and the end be C; then the OA segment is the memristor working in the high impedance state, and the slope represents the high impedance state R off , the BC segment memristor works in the low resistance state, and the slope represents the low resistance state R on , the AB segment is the negative differential resistance area, which is the local active area, and the slope of the AB segment is the negative differential resistance R N ; The function expression of the DC VI characteristic curve is uniquely determined by the two turning points A (V1, I1), B (V2, I2) and the slope of the BC segment: The piecewise linearity is described by the absolute value function as follows: V=g(I)=m+nI+k1|I-I1|+k2|I-I2| (2) Where m, n, k1, k2 are the parameters to be determined, I1, I2 are the currents at turning points A and B; according to the relationship between the three interval currents I and the turning point currents I1, I2, equation (2) is solved as follows: Combining equation (1) and equation (3), we can get: Solving equation (4) yields: According to Chua's expansion theorem, the model of the current-controlled memristor is: Where i, v, and x are the current flowing through the memristor, the voltage across the memristor, and the state variable of the memristor, respectively. m (x) is the memristor function, f is the differential function of the state variable x; Since the memristor value R m (x) depends only on the state variable x, and a simple linear function is used to express the relationship between the two: R m (x)=n+x (7) According to Ohm's law, the DC resistance of the memristor can be expressed as: V=g(I)=R m (X)I=(n+X)I (8) In the formula, Satisfies the following relationship: m+k1|I-I1|+k2|I-I2|-XI=0 (9) For the DC test current I, the state equation satisfies: f(x,i) is a function of x and i. According to equations (9) and (10), the following state equation can be obtained: Where β is the dynamic characteristic parameter of the memristor, which reflects the rate of change of the state variable x; Substituting equations (7) and (11) into equation (6), we get a simple and universal piecewise linear memristor model as follows:

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