Universal design method and system of memristor and its simplest memristor

Abstract

The present invention discloses a universal design method for memristors, including determining the type of memristors to be designed; selecting a memristor function of the memristor to be designed; differentiating the memristor function to obtain a derivative of the memristor function; integrating the derivative of the memristor function to obtain an integral equation; converting the integral equation into a volt-ampere relationship expression of the memristor; and completing the design of the memristor according to the volt-ampere relationship expression of the memristor. The present invention also discloses a system for implementing the universal design method for memristors, and a simplest memristor designed using the universal design method for memristors. The present invention is based on the differential form of the memristor function obtained by theoretical derivation, and integrates and converts the differential form to obtain the corresponding volt-ampere relationship of the memristor; therefore, the present invention can not only realize the universal design of memristors, but also provide a simplest memristor through the design scheme, and the present invention has higher reliability, better accuracy, and is universal and simple.

Description

Technical Field

[0001] The present invention belongs to the field of circuit design, and in particular relates to a universal design method and system of a memristor and a simplest memristor thereof. Background Art

[0002] Memristor is a device that expresses charge q and magnetic flux The fourth basic electronic component that has a relationship between can be divided into charge-controlled memristors and magnet-controlled memristors. The charge-controlled memristor is represented by In the formula is the charge-controlled memristor function; is the magnetic flux; q is the charge;

[0003] Similarly, the magnetically controlled memristor is expressed as In the formula is the magnetically controlled memristor function; is the charge; is the magnetic flux;

[0004] For the charge-controlled memristor, the volt-ampere relationship is ; For the magnetically controlled memristor, the volt-ampere relationship is ; Where v is the voltage across the memristor and i is the current flowing through the memristor.

[0005] The existing memristor design schemes are basically based on the design of the corresponding analog circuits based on the above two basic memristors. However, the memristor function of the existing memristors is relatively complex, and a large amount of circuit resources are required when designing analog circuits. In addition, the circuit design process is relatively complex, time-consuming and labor-intensive. Summary of the invention

[0006] One of the purposes of the present invention is to provide a universal design method for a memristor which is highly reliable, accurate, universal and simple.

[0007] A second objective of the present invention is to provide a system for implementing the universal memristor design method.

[0008] A third object of the present invention is to provide a simplest memristor designed using the universal memristor design method.

[0009] The universal memristor design method provided by the present invention comprises the following steps:

[0010] S1. Determine the type of memristor to be designed; the types of memristors to be designed include charge-controlled memristors and magneto-controlled memristors;

[0011] S2. According to the type of memristor to be designed determined in step S1, a memristor function is selected:

[0012] If it is determined that the memristor to be designed is a charge-controlled memristor, then a memristor function corresponding to the charge-controlled memristor is selected as the memristor function of the memristor to be designed;

[0013] If it is determined that the memristor to be designed is a magnetically controlled memristor, a memristor function corresponding to the magnetically controlled memristor is selected as the memristor function of the memristor to be designed;

[0014] S3. Deriving the memristor function selected in step S2 to obtain the derivative of the memristor function;

[0015] S4. Integrating the derivative of the memristor function obtained in step S3 to obtain an integral equation;

[0016] S5. The integral equation obtained in step S4 is converted into a volt-ampere relationship expression of the memristor;

[0017] S6. According to the volt-ampere relationship expression of the memristor obtained in step S5, the design of the memristor is completed.

[0018] The step S3 specifically includes the following steps:

[0019] For the load-controlled memristor, the memristor function of the memristor to be designed is ;

[0020] like Can be guided, then Directly derive and get like If it is not divisible, then Divide into several differentiable regions, and take the derivative of each differentiable region to obtain Where q is the charge; i is the current flowing through the memristor;

[0021] For the magnetically controlled memristor, the memristor function of the memristor to be designed is ;

[0022] like Can be guided, then Directly derive and get like If it is not divisible, then Divide into several differentiable regions, and take the derivative of each differentiable region to obtain In the formula is the magnetic flux; v is the voltage across the memristor.

[0023] The step S4 specifically comprises the following steps:

[0024] For the load-controlled memristor, Integrate and get Where a is time, and ; for The memristor value at for The memristor value at for The derivative value of the memristor function at ; is the starting time; is the end time;

[0025] For magnetically controlled memristors, Integrate and get In the formula for The memristor value at for The memristor value at for The derivative value of the memristor function at .

[0026] The step S5 specifically includes the following steps:

[0027] For the load-controlled memristor, Converted into the volt-ampere relationship expression of the memristor, we get In the formula for The voltage across the memristor at the moment

[0028] For magnetically controlled memristors, Converted into the volt-ampere relationship expression of the memristor, we get In the formula for The current flowing through the memristor at all times.

[0029] The present invention also provides a system for implementing the universal memristor design method, comprising a type determination module, a function selection module, a function derivation module, a function integration module, a volt-ampere expression module and a memristor design module; the type determination module, the function selection module, the function derivation module, the function integration module, the volt-ampere expression module and the memristor design module are connected in series in sequence; the type determination module is used to determine the type of the memristor to be designed, the type of the memristor to be designed includes a charge-controlled memristor and a magneto-controlled memristor, and upload data information to the function selection module; the function selection module is used to select a memristor function according to the received data information and the determined type of the memristor to be designed: if it is determined that the memristor to be designed is a charge-controlled memristor, then the memristor function corresponding to the charge-controlled memristor is selected as the memristor function of the memristor to be designed; if it is determined that the memristor to be designed is a charge-controlled memristor, then the memristor function corresponding to the charge-controlled memristor is selected as the memristor function of the memristor to be designed; For a magnetically controlled memristor, a memristor function corresponding to the magnetically controlled memristor is selected as the memristor function of the memristor to be designed, and the data information is uploaded to the function derivation module; the function derivation module is used to derive the selected memristor function according to the received data information to obtain the derivative of the memristor function, and upload the data information to the function integration module; the function integration module is used to integrate the obtained derivative of the memristor function according to the received data information to obtain the integral equation, and upload the data information to the volt-ampere expression module; the volt-ampere expression module is used to convert the obtained integral equation into the volt-ampere relationship expression of the memristor according to the received data information, and upload the data information to the memristor design module; the memristor design module is used to complete the design of the memristor according to the received data information and the obtained volt-ampere relationship expression of the memristor.

[0030] The present invention also provides a simplest memristor designed using the universal memristor design method, comprising an integrator circuit and a multiplier circuit; the integrator circuit and the multiplier circuit are connected in series; the integrator circuit integrates an input signal and uploads the integration result to the multiplier circuit; the multiplier circuit multiplies the received integration result with the input signal of the integrator circuit to obtain a final output signal.

[0031] The integrator circuit is an integrator composed of model AD711.

[0032] The multiplier circuit is a multiplier composed of model AD633.

[0033] The universal design method and system of memristor and the simplest memristor provided by the present invention are based on the differential form of the memristor function derived theoretically, and the differential form is integrated and converted to obtain the corresponding volt-ampere relationship of the memristor; therefore, the present invention can not only realize the universal design of the memristor, but also provide a simplest memristor through the design scheme, and the present invention has higher reliability, better accuracy, and is universal and simple. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 The figure is a schematic diagram of the method flow of the present invention.

[0035] Figure 2 Schematic diagram of the functional modules of the system of the present invention.

[0036] Figure 3 Schematic diagram of the analog circuit of the simplest memristor of the present invention; wherein, Figure 3 (a) is the schematic diagram of the analog circuit of the simplest passive memristor. Figure 3 (b) Schematic diagram of the analog circuit of the simplest active memristor.

[0037] Figure 4 This is a schematic diagram of the simulation results of the simplest passive memristor of the present invention when the input sine wave amplitude is 1V and the frequencies are 20Hz, 30Hz, and 300Hz respectively.

[0038] Figure 5 It is a schematic diagram of the simulation results of the simplest passive memristor of the present invention when the input sine wave frequency is 30 Hz and the amplitudes are 0.5 V, 1 V, and 1.5 V respectively.

[0039] Figure 6 This is a schematic diagram of the simulation results of the simplest active memristor of the present invention when the input sine wave amplitude is 1V and the frequencies are 20Hz, 30Hz, and 300Hz respectively.

[0040] Figure 7 It is a schematic diagram of the simulation results of the simplest active memristor of the present invention when the input sine wave frequency is 30 Hz and the amplitudes are 0.5 V, 1 V, and 1.5 V respectively.

[0041] Figure 8 It is a schematic diagram of the test results of the simplest memristor of the present invention when it is passive and the input amplitude is 1V, and the sine wave frequencies are 20Hz, 30Hz, and 300Hz respectively.

[0042] Fig. 9 It is a schematic diagram of the test results of the simplest memristor of the present invention when it is passive and the input frequency is 30 Hz and the amplitudes are 0.5 V, 1 V and 1.5 V respectively.

[0043] Fig.10 It is a schematic diagram of test results of the simplest memristor of the present invention when it is active and the input amplitude is 1V, and the sine wave frequencies are 20Hz, 30Hz, and 300Hz respectively.

[0044] Fig.11 It is a schematic diagram of the test results of the simplest memristor of the present invention when it is active and the input frequency is 30 Hz and the amplitudes are 0.5 V, 1 V and 1.5 V respectively. DETAILED DESCRIPTION

[0045] like Figure 1 The method flow chart of the method of the present invention is shown as follows: The universal memristor design method disclosed in the present invention comprises the following steps:

[0046] S1. Determine the type of memristor to be designed; the types of memristors to be designed include charge-controlled memristors and magneto-controlled memristors;

[0047] S2. According to the type of memristor to be designed determined in step S1, a memristor function is selected:

[0048] If it is determined that the memristor to be designed is a charge-controlled memristor, then a memristor function corresponding to the charge-controlled memristor is selected as the memristor function of the memristor to be designed;

[0049] If it is determined that the memristor to be designed is a magnetically controlled memristor, a memristor function corresponding to the magnetically controlled memristor is selected as the memristor function of the memristor to be designed;

[0050] In specific implementation, the memristor function of the memristor to be designed can be selected from existing public materials and papers according to the specific design needs of the device; for example, the memristor function can be selected from existing literature;

[0051] S3. Deriving the memristor function selected in step S2 to obtain a derivative of the memristor function; specifically comprising the following steps:

[0052] For the load-controlled memristor, the memristor function of the memristor to be designed is ;

[0053] like Can be guided, then Directly derive and obtain like If it is not divisible, then Divide into several differentiable regions, and take the derivative of each differentiable region to obtain Where q is the charge; i is the current flowing through the memristor;

[0054] For the magnetically controlled memristor, the memristor function of the memristor to be designed is ;

[0055] like Can be guided, then Directly derive and obtain like If it is not divisible, then Divide into several differentiable regions, and take the derivative of each differentiable region to obtain In the formula is the magnetic flux; v is the voltage across the memristor;

[0056] In specific implementation, it can be verified that the above formula is still valid when the memristor function is not differentiable;

[0057] S4. Integrating the derivative of the memristor function obtained in step S3 to obtain an integral equation; specifically comprising the following steps:

[0058] For the load-controlled memristor, Integrate and get Where a is time, and ; for The memristor value at for The memristor value at for The derivative value of the memristor function at ; is the starting time; is the termination time; for non-differentiable cases, non-differentiable points are removed;

[0059] For magnetically controlled memristors, Integrate and get In the formula for The memristor value at for The memristor value at for The derivative value of the memristor function at ; for the non-differentiable case, the non-differentiable point is removed;

[0060] S5. The integral equation obtained in step S4 is converted into a volt-ampere relationship expression of a memristor; specifically comprising the following steps:

[0061] For the load-controlled memristor, Converted into the volt-ampere relationship expression of the memristor, we get In the formula for The voltage across the memristor at the moment

[0062] For magnetically controlled memristors, Converted into the volt-ampere relationship expression of the memristor, we get In the formula for The current flowing through the memristor at all times;

[0063] From the obtained volt-ampere relationship expression, we can know that since the memristor's memristor function has been determined, , , and are all specific constant values ​​(which can be calculated based on the memristor function); therefore, the volt-ampere relationship of the memristor is only determined by the input signal and the integral of the input signal, that is, for a charge-controlled memristor, its volt-ampere relationship is only determined by the input current and the integral of the input current; for a magnetically controlled memristor, its volt-ampere relationship is only determined by the input voltage and the integral of the input voltage;

[0064] S6. According to the volt-ampere relationship expression of the memristor obtained in step S5, the design of the memristor is completed.

[0065] like Figure 2 The functional module schematic diagram of the system of the present invention is shown as follows: the system for realizing the universal design method of memristor disclosed in the present invention comprises a type determination module, a function selection module, a function derivation module, a function integration module, a volt-ampere expression module and a memristor design module; the type determination module, the function selection module, the function derivation module, the function integration module, the volt-ampere expression module and the memristor design module are connected in series in sequence; the type determination module is used to determine the type of the memristor to be designed, the type of the memristor to be designed includes a charge-controlled memristor and a magnetically controlled memristor, and upload data information to the function selection module; the function selection module is used to select a memristor function according to the received data information and the determined type of the memristor to be designed: if it is determined that the memristor to be designed is a charge-controlled memristor, then the memristor function corresponding to the charge-controlled memristor is selected as the memristor function of the memristor to be designed; if If it is determined that the memristor to be designed is a magnetically controlled memristor, the memristor function corresponding to the magnetically controlled memristor is selected as the memristor function of the memristor to be designed, and the data information is uploaded to the function derivation module; the function derivation module is used to derive the selected memristor function according to the received data information, obtain the derivative of the memristor function, and upload the data information to the function integration module; the function integration module is used to integrate the derivative of the obtained memristor function according to the received data information, obtain the integral equation, and upload the data information to the volt-ampere expression module; the volt-ampere expression module is used to convert the obtained integral equation into the volt-ampere relationship expression of the memristor according to the received data information, and upload the data information to the memristor design module; the memristor design module is used to complete the design of the memristor according to the received data information and the obtained volt-ampere relationship expression of the memristor.

[0066] In addition, the present invention also provides a simplest memristor designed using the universal memristor design method, including an integrator and a multiplier; the integrator and the multiplier are connected in series; the integrator integrates the input signal and uploads the integration result to the multiplier; the multiplier multiplies the received integration result with the input signal of the integrator to obtain a final output signal.

[0067] The integrator is an integrator of model AD711. The multiplier is a multiplier of model AD633.

[0068] For the simplest memristor above, the design process is as follows:

[0069] For the charge-controlled memristor, the volt-ampere relationship is Consider the simplest case, where the initial memristor is set to , for the derivative of the memristor function, the simplest derivative of the memristor function is a constant, that is, , is a dimensionless parameter; therefore, the simplest charge-controlled memristor simulator model is ;

[0070] Similarly, the simplest magnetically controlled memristor model is ;in, is a dimension parameter;

[0071] Therefore, the circuit design of the simplest memristor simulator is as follows: the circuit implementation only requires an integrator and a multiplier: the integrator integrates the input signal, and the multiplier multiplies the input signal with the integrator output result to obtain the final output signal. In addition, when the dimension parameter and When it is greater than 0, the resulting memristor is a passive memristor; when the dimension parameter and When it is less than 0, the resulting memristor is an active memristor.

[0072] The following is a simulation and experimental verification of the simplest memristor involved:

[0073] The design of the simplest memristor simulator uses an analog circuit. The analog circuit is designed according to the simplest memristor model and circuit simulation is performed. Figure 3 As shown, the circuit is mainly composed of two chips, an operational amplifier (the operational amplifier is used to implement the integration circuit) and a multiplier. The difference between the passive minimal memristor and the active minimal memristor is the integrated signal input. The integrated signal of the passive memristor is input to the negative input terminal of the multiplier, while the integrated signal of the active memristor is input to the positive input terminal of the multiplier.

[0074] For a passive memristor, the input-output voltage relationship is ;

[0075] For an active memristor, the input-output voltage relationship is ;

[0076] The circuit simulation of the simplest passive memristor is carried out, and the simulation results are as follows Figure 4The simplest memristor exhibits a tight hysteresis curve, and under the condition that the driving signal amplitude is fixed, the area of ​​the hysteresis curve decreases as the driving signal frequency increases. In addition, when the driving signal amplitude increases and the frequency remains unchanged, the hysteresis curve will be proportionally enlarged, as shown in Figure 5 As shown in the figure. The simplest memristor satisfies the three fingerprint characteristics of the memristor, verifying the correctness of the model. In addition, the circuit simulation of the simplest active memristor is carried out, and the simulation results are shown in the figure. Figure 6 As shown in Figure 2, the active memristor exhibits negative resistance characteristics and a tight hysteresis curve, and the increase in driving frequency leads to a decrease in the area of ​​the hysteresis curve. In addition, the area of ​​the hysteresis curve increases proportionally with the increase in the amplitude of the driving signal, as shown in Figure 2. Figure 7 Therefore, the simplest active memristor also satisfies the three-fingerprint characteristics of the memristor, verifying the correctness of the simplest active memristor model.

[0077] After the designed circuit is effectively simulated and verified, the circuit board is designed and manufactured. The resulting circuit board has a small size, 32 mm long and 18 mm wide, and consists of only two chips and two circuit elements. The operational amplifier chip is AD711, and the multiplier is AD633. The resistor and capacitor are used to form an integration circuit in combination with the operational amplifier, with a resistor value of 1kΩ and a capacitor of 2.2uF. The PCB circuit of the simplest memristor is experimentally verified. The experimental platform consists of a signal generator, a power supply and an oscilloscope. The power supply is used to power the chip on the PCB board, and the signal generator is used to generate a sinusoidal signal as the signal input of the memristor. The oscilloscope is used to observe the response curve of the memristor.

[0078] The circuit experiment of the simplest passive memristor PCB shows that the simplest passive memristor produces a tight hysteresis curve when driven by a sinusoidal signal. Under the same signal amplitude, the increase of signal frequency will reduce the area of ​​the hysteresis curve, such as Figure 8 In addition, when the amplitude of the driving signal is increased and the frequency is fixed, the area of ​​the hysteresis curve increases and the hysteresis curve is proportionally enlarged, as shown in Fig. 9 The simplest memristor simulator meets the three fingerprint characteristics of the memristor, which shows the correctness of the simplest memristor model and the practicality and feasibility of the memristor PCB.

[0079] The circuit experiment of the simplest active memristor PCB was carried out. Under the drive of the sinusoidal signal, the simplest passive memristor exhibited negative resistance characteristics and a tight hysteresis curve. Under the condition of fixed signal amplitude, the increase of the driving signal frequency will reduce the area of ​​the hysteresis curve. The experimental results are as follows: Fig.10 When the frequency of the driving signal is fixed and the amplitude of the driving signal is increased, the area of ​​the hysteresis curve is proportionally enlarged, as shown in Fig.11 As shown in the figure, the simplest active memristor satisfies the three-fingerprint characteristics of the memristor, indicating the correctness and feasibility of the simplest memristor model.

Claims

1. A universal design method for a memristor, characterized in that The steps include: S1. Determine the type of memristor to be designed; the types of memristors to be designed include charge-controlled memristors and magneto-controlled memristors; S2. According to the type of memristor to be designed determined in step S1, a memristor function is selected: If it is determined that the memristor to be designed is a charge-controlled memristor, then a memristor function corresponding to the charge-controlled memristor is selected as the memristor function of the memristor to be designed; If it is determined that the memristor to be designed is a magnetically controlled memristor, a memristor function corresponding to the magnetically controlled memristor is selected as the memristor function of the memristor to be designed; S3. Deriving the memristor function selected in step S2 to obtain a derivative of the memristor function; specifically comprising the following steps: For the load-controlled memristor, the memristor function of the memristor to be designed is ; like Can be guided, then Directly derive and get ; like If it is not divisible, then Divide into several differentiable regions, and take the derivative of each differentiable region to obtain Where q is the charge; i is the current flowing through the memristor; For the magnetically controlled memristor, the memristor function of the memristor to be designed is ; like Can be guided, then Directly derive and obtain ; like If it is not divisible, then Divide into several differentiable regions, and take the derivative of each differentiable region to obtain In the formula is the magnetic flux; v is the voltage across the memristor; S4. Integrating the derivative of the memristor function obtained in step S3 to obtain an integral equation; specifically comprising the following steps: For the load-controlled memristor, Integrate and get Where a is time, and ; for The memristor value at ; for The memristor value at for The derivative value of the memristor function at ; is the starting time; is the end time; For magnetically controlled memristors, Integrate and get In the formula for The memristor value at ; for The memristor value at for The derivative value of the memristor function at ; S5. The integral equation obtained in step S4 is converted into a volt-ampere relationship expression of a memristor; specifically comprising the following steps: For the load-controlled memristor, Converted into the volt-ampere relationship expression of the memristor, we get In the formula for The voltage across the memristor at the moment For magnetically controlled memristors, Converted into the volt-ampere relationship expression of the memristor, we get In the formula for The current flowing through the memristor at all times; S6. According to the volt-ampere relationship expression of the memristor obtained in step S5, the design of the memristor is completed.

2. A system for implementing the universal memristor design method according to claim 1, characterized in that It includes a type determination module, a function selection module, a function derivation module, a function integration module, a volt-ampere expression module and a memristor design module; the type determination module, the function selection module, the function derivation module, the function integration module, the volt-ampere expression module and the memristor design module are connected in series in sequence; the type determination module is used to determine the type of the memristor to be designed, the type of the memristor to be designed includes a charge-controlled memristor and a magnetically controlled memristor, and upload data information to the function selection module; The function selection module is used to select a memristor function according to the received data information and the determined type of the memristor to be designed: if the memristor to be designed is determined to be a charge-controlled memristor, the memristor function corresponding to the charge-controlled memristor is selected as the memristor function of the memristor to be designed; if the memristor to be designed is determined to be a magnetically controlled memristor, the memristor function corresponding to the magnetically controlled memristor is selected as the memristor function of the memristor to be designed, and the data information is uploaded to the function derivation module; The function derivation module is used to derive the selected memristor function according to the received data information, obtain the derivative of the memristor function, and upload the data information to the function integration module; The function integration module is used to integrate the derivative of the memristor function according to the received data information to obtain the integral equation, and upload the data information to the volt-ampere expression module; the volt-ampere expression module is used to convert the obtained integral equation into the volt-ampere relationship expression of the memristor according to the received data information, and upload the data information to the memristor design module; The memristor design module is used to complete the design of the memristor according to the received data information and the obtained volt-ampere relationship expression of the memristor.

3. A simplest memristor designed by the universal memristor design method according to claim 1, characterized in that It includes an integrator circuit and a multiplier circuit; the integrator circuit and the multiplier circuit are connected in series; the integrator circuit integrates the input model and uploads the integration result to the multiplier circuit; the multiplier circuit multiplies the received integration result with the input signal of the integrator circuit to obtain the final output signal.

4. The simplest memristor according to claim 3, characterized in that The integrator circuit is an integrator composed of a chip of model AD711.

5. The simplest memristor according to claim 3, characterized in that The multiplier circuit is a multiplier composed of a chip of model AD633.

Images