CN106709213A - Simplest memristor system and simulation circuit thereof - Google Patents

Abstract

The invention discloses a simplest memristor system and a simulation circuit thereof. The problems that an existing memristor system is complex in formula, many variables exist, accordingly real memristor components are difficult to manufacture, and mass production, application and popularization cannot be achieved are solved. According to the properties of memristor systems, the simplest memristor system is built. The properties of the simplest memristor system are proved by means of Matlab simulation and Multisim simulation. Finally, the circuit is built and debugged for property verification. The circuit based on a memristor has the advantages of being small in size, convenient to integrate, simple in structure, low in power consumption, long in service life and the like.

Description

A kind of most simple memristor system and its artificial circuit

Technical field

The present invention relates to the technical field of new electronic component, and in particular to a kind of most simple memristor system and its emulation electricity Road.

Background technology

Memristor has attracted the pass of Many researchers due to potential application since HP Lab successfully develops Note.Memristor is defined as the relation between circuit electric charge variable and magnetic flux.This definition extends to any both-end Memristor element, while extend to many memristor dynamical systems, or even can extend to and recall container and recall sensor dynamical system.Recall Three important features that resistance system is different from other dynamical systems are：I the hysteresis curve of () memristor system is one by original The Lissajou figure of point；(ii) if the frequency increase of input periodic signal, hysteresis curve shrinks；(iii) if frequency becomes When infinity, then the hysteresis curve of memristor system will tend to straight line.More New functions and new ideas on memristor system It is found and builds in different field, but most researchers pay close attention to the property of memristor system, little researcher's concern is recalled The simplification of resistance system, these memristor systems are too complicated to be difficult to produce real component.Thus, for the volume production of memristor system And popularization and application, the simplification of memristor system has certain Research Significance.

The content of the invention

The present invention proposes a kind of most simple memristor system and its artificial circuit, solves existing memristor system equations complexity, becomes Amount is too many so that it is difficult to produce real memristor component, and cannot volume production and popularization and application technical problem.

In order to solve the above-mentioned technical problem, the technical scheme is that：A kind of most simple memristor system, its modeling method It is：

Step one：Consider that u (t) is the input signal of dynamic system, y (t) is the output signal of dynamic system, state Variable x is the vector of n dimensions, then：

Wherein, f (x, u, t) and g (x, u, t) are two generalized functions containing state variable x and u, and t represents the time；

Step 2：Generalized function f (x, u, t) in step one is designated as u (t), generalized function g (x, u, t) and is designated as x (t), Then most simple memristor system is：

Y (t)=x (t) u (t), x (t)=u (t)

Method by the property of the most simple memristor system of Matlab simulating, verifyings is：

(1), input signal u (t) is sinusoidal signal：U (t)=Asin (ω t), wherein, A is the amplitude of input signal, ω It is the angular frequency of input signal；

(2), by input signal u (t) and most simple memristor system, obtain： Wherein, the original state of state variable x：

(3), by state variable x, input signal u (t) and most simple memristor system, output signal is：Then output signal y (t) is included Two parts and original state with state variable x, the amplitude of input signal and frequency are relevant；

(4) original state x, is drawn respectively using Matlab₀, angular frequency or amplitude A be when changing, input signal u (t) with The relation curve of output signal y (t), all of hysteresis curve is all shunk in origin, and with the angular frequency of input signal u (t) ω continuously shrinks from the increase of critical frequency, hysteresis curve, and the angular frequency of input signal u (t) tends to infinitely great, hysteresis curve Tend to straight line；

(5) area of input signal u (t) and output signal y (t) relation curve, the area and state of hysteresis curve are calculated The initial value of variable x is relevant, and the amplitude A with input signal increase, the area monotone increasing of hysteresis curve, with input The angular frequency of signal increases, the area monotone decreasing of hysteresis curve.

The original state x₀, angular frequency or amplitude A change include：As original state x₀When being fixed with angular frequency, width Value A changes；As original state x₀When being fixed with amplitude A, angular frequency change；When amplitude A and angular frequency are fixed, initial shape State x₀Three kinds of situations of change.

When integrator output state variable x (t) and output signal y (t) are respectively：

Y (t)=x (t) u (t)

When artificial circuit be：Including voltage follower U_m1, operational amplifier U_m2, operational amplifier U_m3With multiplier A₁, Voltage follower U_m1It is connected with input signal u (t), voltage follower U_m1In-phase input end and multiplier A₁It is connected, electricity Pressure follower U_m1Inverting input and voltage follower U_m1Output end be connected；Voltage follower U_m1Output end with electricity Resistance R_m1It is connected, resistance R_m1With operational amplifier U_m2Inverting input be connected, operational amplifier U_m2Inverting input and Resistance R is parallel between output end_m2With electric capacity C₀, operational amplifier U_m2In-phase input end ground connection, operational amplifier U_m2It is defeated Go out end and resistance R_m3It is connected, resistance R_m3With operational amplifier U_m3Inverting input be connected, operational amplifier U_m3Same phase Input end grounding, operational amplifier U_m3Inverting input and output end be provided with resistance R_m4, operational amplifier U_m3Output end electricity Resistance and multiplier A₁It is connected.

The present invention is built according to the representative property of memristor system, while being confirmed with Matlab and Multisim emulation It has the property of memristor system, finally builds artificial circuit and carries out debugging and verifies its property.The invention enables based on memristor Circuit there is small volume, be easy to that integrated, circuit structure is simple, low in energy consumption, long lifespan.

Brief description of the drawings

In order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing The accompanying drawing to be used needed for having technology description is briefly described, it should be apparent that, drawings in the following description are only this Some embodiments of invention, for those of ordinary skill in the art, on the premise of not paying creative work, can be with Other accompanying drawings are obtained according to these accompanying drawings.

Fig. 1 be original state of the present invention and angular frequency fix, the asynchronous input/output relation figure of amplitude.

Fig. 2 be original state of the present invention and amplitude fix, the asynchronous input/output relation figure of angular frequency.

Fig. 3 be amplitude of the present invention and angular frequency fix, the asynchronous input/output relation figure of original state.

Fig. 4 is artificial circuit of the invention.

Fig. 5 is the Multisim simulation curves of Fig. 4.

Fig. 6 is the input and output time domain beamformer of Fig. 4.

Fig. 7 is the input/output relation figure of Fig. 4.

Specific embodiment

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete Site preparation is described, it is clear that described embodiment is only a part of embodiment of the invention, rather than whole embodiments.It is based on Embodiment in the present invention, it is every other that those of ordinary skill in the art are obtained under the premise of creative work is not paid Embodiment, belongs to the scope of protection of the invention.

A kind of most simple memristor system, its modeling method is：

Step one：Consider that u (t) is the input signal of dynamic system, y (t) is the output signal of dynamic system, state Variable x is the vector of n dimensions, then：

Wherein, f (x, u, t) and g (x, u, t) are two generalized functions containing state variable x and u, and what t represents.Such as Fruit state variable u (t) and output signal y (t) represent voltage and current respectively, and dynamic system represents voltage-controlled memristor system respectively With magnetic flux control memristor system.

Step 2：Generalized function f (x, u, t) in step one is designated as u (t), generalized function g (x, u, t) and is designated as x (t), Then most simple memristor system is：

Y (t)=x (t) u (t), x (t)=u (t)

Method by the property of the most simple memristor system of Matlab simulating, verifyings is：

(1), input signal u (t) is sinusoidal signal：U (t)=Asin (ω t), wherein, A is the amplitude of input signal, ω It is the angular frequency of input signal.

(2), by input signal u (t) and most simple memristor system, obtain：

Wherein, the original state of state variable x：

(3), by state variable x, input signal u (t) and most simple memristor system, output signal is：Then output signal y (t) is included Two parts and original state with state variable x, the amplitude of input signal and frequency are relevant.

(4) original state x, is drawn respectively using Matlab₀, angular frequency or amplitude A be when changing, input signal u (t) with The relation curve of output signal y (t), all of hysteresis curve is all shunk in origin；Hysteresis curve is 8-shaped curve, and with The angular frequency of input signal u (t) is continuously shunk from the increase of critical frequency, hysteresis curve, the angular frequency of input signal u (t) ω tends to infinitely great, and hysteresis curve tends to straight line.

Input signal u (t) verifies the generation of most simple memristor system with the relation curve of output signal y (t) by Matlab Shrink the lag loop in origin.Original state x₀, angular frequency or amplitude A change include：As original state x₀And angular frequency When fixed, amplitude A changes；As original state x₀When being fixed with amplitude A, angular frequency change；When amplitude A and angular frequency are fixed When, original state x₀Three kinds of situations of change.Fig. 1 is original state x₀=1 and angular frequency=1, when amplitude A is respectively 1,2,3, The relation curve of input signal u (t) and output signal y (t).Fig. 2 represents original state x₀=1 and amplitude A=1, angular frequency When respectively 1,2,3, the relation curve of input signal u (t) and output signal y (t).Fig. 3 represents amplitude A=1 frequencies omega=1, Original state x₀When respectively 1,2,3, the relation curve of input signal u (t) and output signal y (t).

For the amplitude and frequency and different original states of any periodic signal, all of hysteresis curve is all receivable to be shunk in Origin, such as Fig. 1-3.As shown in Fig. 2 if the angular frequency of input signal u (t) increases from critical frequency, hysteresis curve is continuous Shrink.Meanwhile,If the angular frequency of input signal Tend to infinitely great, then the hysteresis curve of memristor system tends to straight line.If the angular frequency of input signal goes to zero, input Signal u (t) tends to 0.Specifically, if input signal is zero, then the value of memristor system is by the initial shape with memristor system State is relevant.

(5) area of input signal u (t) and output signal y (t) relation curve, the area and state of hysteresis curve are calculated The initial value of variable x is relevant, and the amplitude A with input signal increase, the area monotone increasing of hysteresis curve, with input The angular frequency of signal increases, the area monotone decreasing of hysteresis curve.

Two parts area S and S of input signal and output signal relation curve^*(S=S^*) be respectively：

By input signal u (t)=Asin (ω t) and output signal Bringing above formula into can obtain：

Can be obtained according to above formula, the area of hysteresis curve and the original state x of state variable₀It is relevant；With input signal Amplitude A increases, the area of hysteresis curve also monotone increasing；Angular frequency with input signal increases, the area of hysteresis curve Monotone decreasing.

Similarly, by the input signal and the relation of output signal in step (3) by Multisim simulating, verifyings, the present invention The generation of most simple memristor system shrink lag loop in origin.

When integrator output state variable x (t) and output signal y (t) are respectively：

Y (t)=x (t) u (t)

When artificial circuit include：Voltage follower U_m1, operational amplifier U_m2, operational amplifier U_m3With multiplier A₁, electricity Pressure follower U_m1It is connected with input signal u (t), voltage follower U_m1In-phase input end and multiplier A₁It is connected, voltage Follower U_m1Inverting input and voltage follower U_m1Output end be connected, voltage follower U_m1Play isolation rear class electricity Road is on the possible influence of input signal.Voltage follower U_m1Output end and resistance R_m1It is connected, resistance R_m1With operational amplifier U_m2Inverting input be connected, operational amplifier U_m2Inverting input and output end between be parallel with resistance R_m2And electric capacity C₀, operational amplifier U_m2In-phase input end ground connection, operational amplifier U_m2, resistance R_m2With electric capacity C₀Constitute an integrator.Fortune Calculate amplifier U_m2Output end and resistance R_m3It is connected, resistance R_m3With operational amplifier U_m3Inverting input be connected, computing Amplifier U_m3In-phase input end ground connection, operational amplifier U_m3With resistance R_m3Composition adjustable amplifying circuit.Operational amplifier U_m3Inverting input and output end be provided with resistance R_m4, operational amplifier U_m3Output end resistance and multiplier A₁It is connected, such as Shown in Fig. 4.

Using a piece of integrated four high guaily unit chip LM324N as main circuit, chip VCC pins access+15V direct currents to the present invention Electricity, GND pins access -15V direct current dual power supplies.Input signal u (t) is amplitude, the sinusoidal signal of frequency-adjustable, signal The voltage follower being made up of integrated transporting discharging is accessed first then accesses the integrating circuit being made up of integrated transporting discharging, integrating circuit again Middle integrating capacitor C₀Choose the ROHS of 1UF, integrating resistor R_m2From 10K adjustable potentiometers；Integration output access one is defeated Go out voltage follower and play isolation late-class circuit to the possible influence of integrator, then one anti-phase ratio of output access is adjustable puts Big circuit.Last scaling circuit output accesses AD633 four-quadrant analog multipliers A₁Y1 pins, sinusoidal input signal connects Enter the X1 pins of AD633, two X1 signals obtain memristor hysteresis curve after being multiplied by AD633 chips with Y1 signals.

Simulation Parameters electric capacity C in the present invention₀=100 μ F, resistance Multiplier A₁It is AD711KN multipliers.Voltage follower U_m1, operational amplifier U_m2, operational amplifier U_m3It is OP07CP computings Amplifier.Sinusoidal signal is Multisim simulation curves such as Fig. 5 institutes of input signal, input signal u (t) and output signal y (t) Show, it is consistent with Matlab simulation results in Fig. 1-3.According to artificial circuit, build circuit and carry out Multisim artificial debuggings and test Card, input and output time domain beamformer is as shown in fig. 6, input/output relation figure is as shown in Figure 7.From Fig. 6 and Fig. 7, the application Minimum memristor system can produce the lag loop shunk in origin.

Presently preferred embodiments of the present invention is the foregoing is only, is not intended to limit the invention, it is all in essence of the invention Within god and principle, any modification, equivalent substitution and improvements made etc. should be included within the scope of the present invention.

Claims (4)

1. a kind of most simple memristor system, it is characterised in that its modeling method is：

Step one：Consider that u (t) is the input signal of dynamic system, y (t) is the output signal of dynamic system, state variable X is the vector of n dimensions, then：

Y (t)=g (x, u, t) u (t),

Wherein, f (x, u, t) and g (x, u, t) are two generalized functions containing state variable x and u, and t represents the time；

Step 2：Generalized function f (x, u, t) in step one is designated as u (t), generalized function g (x, u, t) and is designated as x (t), then most Simple memristor system is：

$\left\{\begin{array}{c}y\left(t\right)=x\left(t\right)u\left(t\right)\\ x\left(t\right)=u\left(t\right)\end{array}\right..$

2. most simple memristor system according to claim 1, it is characterised in that by the most simple memristor system of Matlab simulating, verifyings The method of the property of system is：

(1), input signal u (t) is sinusoidal signal：U (t)=Asin (ω t), wherein, A is the amplitude of input signal, and ω is defeated Enter the angular frequency of signal；

(2), obtained by input signal u (t) and most simple memristor system：

$x\left(t\right)={\∫}_{-\mathrm{\∞}}^{t}u\left(\mathrm{\τ}\right)=x_0+{\∫}_0^{t}Asin\left(\mathrm{\ω}\mathrm{\τ}\right)=x_0+\frac{A}{\mathrm{\ω}}\[1-cos\left(\mathrm{\ω}t\right)\];$

Wherein, the original state of state variable x is：

(3), by state variable x, input signal u (t) and most simple memristor system, output signal is：

$y\left(t\right)=\{x_0+\frac{A}{\mathrm{\ω}}\[1-cos\left(\mathrm{\ω}t\right)\]\}Asin\left(\mathrm{\ω}t\right)=(x_0+\frac{A}{\mathrm{\ω}})Asin\left(\mathrm{\ω}t\right)-\frac{A^2}{2\mathrm{\ω}}sin\left(2\mathrm{\ω}t\right);$

Then output signal y (t) includes two parts, and output signal y (t) and state variable x original state, the width of input signal Value is relevant with frequency；

(4) original state x, is drawn respectively using Matlab₀, angular frequency or amplitude A be when changing, input signal u (t) and output The relation curve of signal y (t), all of hysteresis curve is all shunk in origin, and with input signal u (t) angular frequency from The increase of critical frequency, hysteresis curve continuously shrinks, and the angular frequency of input signal u (t) tends to infinitely great, and hysteresis curve tends to Straight line；

(5) area of input signal u (t) and output signal y (t) relation curve, the area and state variable of hysteresis curve, are calculated The initial value of x is relevant, and the amplitude A with input signal increase, the area monotone increasing of hysteresis curve, with input signal Angular frequency increase, the area monotone decreasing of hysteresis curve.

3. most simple memristor system according to claim 1, it is characterised in that the original state x₀, angular frequency or amplitude A changes include：As original state x₀When being fixed with angular frequency, amplitude A changes；As original state x₀When being fixed with amplitude A, angle Frequencies omega changes；When amplitude A and angular frequency are fixed, original state x₀Three kinds of situations of change.

4. most simple memristor system according to claim 1, it is characterised in that when integrator output state variable x (t) and defeated Go out signal y (t) to be respectively：

$x\left(t\right)=\frac{R_{m_4}}{R_{m_3}}\[-\frac{1}{R_{m_1}{C}_0}\∫u\left(t\right)dt\]=\∫u\left(t\right)$

Y (t)=x (t) u (t)

When artificial circuit be：Including voltage follower U_m1, operational amplifier U_m2, operational amplifier U_m3With multiplier A₁, voltage Follower U_m1It is connected with input signal u (t), voltage follower U_m1In-phase input end and multiplier A₁Be connected, voltage with With device U_m1Inverting input and voltage follower U_m1Output end be connected；Voltage follower U_m1Output end and resistance R_m1 It is connected, resistance R_m1With operational amplifier U_m2Inverting input be connected, operational amplifier U_m2Inverting input and output Resistance R is parallel between end_m2With electric capacity C₀, operational amplifier U_m2In-phase input end ground connection, operational amplifier U_m2Output end With resistance R_m3It is connected, resistance R_m3With operational amplifier U_m3Inverting input be connected, operational amplifier U_m3Homophase input End ground connection, operational amplifier U_m3Inverting input and output end be provided with resistance R_m4, operational amplifier U_m3Output end resistance with Multiplier A₁It is connected.