Nonlinear resistance network voltage distribution measurement method

Abstract

The invention discloses a voltage distribution measurement method based on a nonlinear resistance network. According to the method, a physical grid model composed of a linear resistor and a nonlinear current source is constructed, and a node voltage model equation is established by taking a grid original point as a potential reference point. Two-dimensional measurement data are subjected to dimensionality reduction to form a univariate function by utilizing network physical symmetry, and efficient calculation is realized by combining an FPGA (Field Programmable Gate Array) pipeline architecture. And when the detected voltage value is lower than-15V, starting a cut-off protection mechanism to force the clamping voltage and closing the current source. And finally, a voltage change curve and a two-dimensional thermodynamic diagram are generated through a visualization module, and voltage distribution is visually reflected. The method solves the problems of large error, poor real-time performance and circuit oscillation of a traditional measurement method, is suitable for nonlinear resistance network voltage monitoring in the fields of condensed state physics, plasma control and the like, and has the advantages of high measurement precision, high response speed, reliable hardware protection and the like.

Description

Technical Field

[0001] The invention relates to a method for measuring the voltage of a resistance network. Background Art

[0002] In recent years, with the development of new electronic components, particularly nonlinear elements such as memristors, the demand for real-time voltage distribution measurement in nonlinear circuit networks has been growing. Resistor networks are interconnected systems composed of linear resistors, whose node voltages and branch currents follow Ohm's law and Kirchhoff's laws. They are widely used in physical computing to simulate Laplace operators and solve linear partial differential equations. Nonlinear resistor networks, on the other hand, incorporate nonlinear elements such as diodes and memristors. Their volt-ampere characteristics exhibit nonlinear relationships, such as exponential, piecewise, or hysteretic relationships. These networks can more realistically simulate nonlinear interactions in complex physical systems, such as particle self-coupling in quantum systems and collision effects in plasmas.

[0003] Current voltage measurement in nonlinear resistor networks relies primarily on two methods: Indirect calculation, which measures branch currents and then infers the voltage using an approximate mathematical model of the nonlinear element (such as the diode Shockley equation). This method has significant drawbacks. Simplifying the nonlinear model introduces theoretical errors, such as neglecting temperature effects and tunneling currents. Furthermore, iterative calculations result in latency, with typical response times exceeding 10ms, which cannot meet real-time control requirements. Direct sampling, which uses a high-precision ADC to directly sample node voltages, faces several bottlenecks: the chaotic nature of nonlinear networks can easily lead to transient voltage divergence, and traditional protection circuits can intercept the signal, resulting in data loss. Furthermore, existing solutions cannot distinguish between valid nonlinear responses (such as soliton waveforms) and parasitic oscillations (such as contact noise), resulting in a signal-to-noise ratio (SNR) below 40dB.

[0004] In the scenarios of artificial intelligence and the Internet of Things, the above defects seriously restrict the application of nonlinear resistor networks in the following fields: Condensed matter physics: In solving the Gross-Pitaevskii equation for Bose-Einstein condensates, the nonlinear term requires real-time voltage feedback, but the existing measurement error (>5%) will cause the quantum phase prediction to fail; Plasma control: The exponential nonlinear term of the bipolar diffusion equation requires μs-level voltage tracking, while the delay of traditional methods (ms-level) cannot suppress turbulent instabilities. Summary of the Invention

[0005] Purpose of the invention: In view of the above-mentioned existing technologies, a method for measuring the voltage distribution of a nonlinear resistor network is proposed to solve the problems of low efficiency and circuit oscillation in nonlinear resistor networks caused by traditional measurement methods.

[0006] Technical solution: A method for measuring voltage distribution in a nonlinear resistor network, comprising the following steps:

[0007] Step 1: Construct a physical grid model consisting of a planar network of linear resistors, with each node of the network connected to a nonlinear current source in parallel with the ground.

[0008] Step 2: Collect the ground potential of each node and use the physical symmetry requirement to reduce the dimensionality of the two-dimensional measurement data to a single variable function with equal voltage at points symmetrical about the network diagonal.

[0009] Step 3: Configure the control module and use a pipeline architecture to calculate the node voltage distribution. The architecture includes a Divider module, an ExpLUT module, and a Multiplier module. The Divider module is used to calculate the numerator of the voltage gradient of adjacent nodes. The ExpLUT module is used to implement hardware-accelerated calculation of nonlinear terms by looking up a pre-stored exponential function table. The Multiplier module is used to complete the voltage iterative calculation and perform the truncation protection judgment.

[0010] Step 4: When it is detected that the voltage value exceeds the preset threshold range, the cutoff protection mechanism is activated to turn off the nonlinear current output to achieve adaptive cutoff protection.

[0011] Step 5: Generate a voltage distribution heat map through the visualization output module for circuit status monitoring.

[0012] Furthermore, in step 1, the nonlinear current source is a memristor or a Schottky diode array, and the linear resistance value is 1Ω.

[0013] Furthermore, in the physical grid model, the grid origin (0,0) is the potential reference point, and the potential value u(0,0)=0, u m,n represents the voltage of node (m,n) to ground, then the voltage model equation of node (m,n) is:

[0014]

[0015] Among them, the nonlinear term Acts as a nonlinear current source from the node to ground.

[0016] Furthermore, in step 2, the voltages at points symmetrical about the network diagonal are equal, and the voltage model equation is simplified to an equation about a single variable function u(x). The simplified voltage model equation is:

[0017] 2u(x+1)+2u(x-1)-4u(x)+e 2u(x) =0

[0018] Where x=m+n, m and n are the horizontal and vertical coordinates of the node in the grid respectively.

[0019] Furthermore, in step 4, the truncation protection mechanism is specifically as follows: when the voltage value u(x) is lower than -15V, the FPGA is forced to write u(x) = -15V and trigger an interrupt signal, the interrupt signal is connected to the enable terminal of the current source, and the nonlinear current output is turned off.

[0020] Furthermore, in step 5, the voltage distribution heat map is generated by plotting the voltage u(x) versus x=m+n and mapping each node voltage u(m,n) into a color gradient map, which intuitively reflects the circuit potential distribution.

[0021] Beneficial effects: 1. The nonlinear resistor network voltage measurement method of the present invention directly solves the problem through the physical coupling of the resistor network and the nonlinear current source, avoiding the error of pure numerical calculation; and the discrete equation clearly reflects the physical characteristics of the nonlinear current source (such as Schottky diode), which is convenient for engineering application. 2. The present invention utilizes the physical symmetry of the resistor network to significantly reduce the number of measurement points, and the symmetry dimension reduction and hardware parallel system significantly improve efficiency, which is suitable for large-scale resistor networks. 3. It solves the problems of low efficiency and circuit oscillation in traditional measurement methods in nonlinear resistor networks. 4. The cutoff protection mechanism ensures that the circuit operates within a safe voltage range to avoid overload damage. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 This is a flow chart of a method for measuring voltage distribution in a nonlinear resistor network according to the present invention;

[0023] Figure 2 is a graph showing the attenuation characteristics of the nonlinear resistor network g(x) in an embodiment of the present invention;

[0024] Figure 3 The voltage distribution u in the embodiment of the present invention is m,n = Schematic diagram of the u(m+n) variation curve;

[0025] Figure 4 This is a two-dimensional voltage distribution heat map in an embodiment of the present invention;

[0026] Figure 5 This is a diagram of the FPGA pipeline architecture in an embodiment of the present invention. DETAILED DESCRIPTION

[0027] The present invention will be further explained below with reference to the accompanying drawings.

[0028] like Figure 1 As shown, a method for measuring voltage distribution based on a nonlinear resistor network includes the following steps:

[0029] Step 1: Create a 20×20 physical grid model consisting of linear resistors and nonlinear resistor units. The specific steps are as follows:

[0030] A 20×20 physical grid model is constructed. Adjacent nodes of the grid are connected by linear resistors. The linear resistance value between nodes is R0. Each node is connected in parallel with the ground with a nonlinear current source, such as a memristor or a Schottky diode array.

[0031] In this embodiment, the grid origin (0,0) is set as the potential reference point, and the potential value of the reference point u(0,0) = 0. For the network node (m,n), its current obeys Ohm's law:

[0032]

[0033] Since R0 = 1Ω, I 线性 =u 相邻 -u m,n Among them, I 线性 Represents the current through the linear resistor, u 相邻 represents the ground voltage of the node adjacent to the grid node (m,n), u m,n Represents the voltage of the grid node (m,n) to ground.

[0034] For node (m,n), the currents of the surrounding adjacent nodes (upper, lower, left, and right) are u m+1,n -u m,n 、u m-1,n -u m,n 、u m,n+1 -u m,n 、u m,n-1 -u m,n , the total current is the sum of the four, so the linear resistance can be simplified to:

[0035] Δu=u m+1,n +u m-1,n +u m,n+1 +u m,n-1 -4u m,n ;

[0036] Here, Δu represents the voltage gradient.

[0037] The nonlinear term As a nonlinear current source from the node to the ground, its physical model is:

[0038]

[0039] Among them, I 非线性项 Represents the current passing through the nonlinear current source, I0 represents the saturation current of the nonlinear current source, I0 is 1A, and normalization yields:

[0040]

[0041] The nonlinear current source and the linear resistance path together form the physical network model. Since R0 = 1Ω, the current = the voltage difference, which is balanced with the nonlinear current source. Combined with the voltage model equation, we get:

[0042]

[0043] Step 2: Collect the ground potential of each node and configure the control module to reduce the dimensionality of the two-dimensional measurement data according to the physical symmetry requirements.

[0044] Deploy a voltage sensor array to collect the ground potential u(m,n) of each node. Due to symmetry requirements, the voltages at points symmetrical to the network diagonal are equal, that is, u(m,n) = u(m+n). The network diagonal is a straight line with x = m+n = a constant. Therefore, a single-variable voltage function u(x) = u(m+n) is established, and the voltage model equation is simplified to:

[0045] u(x+1)+u(x-1)+u(x+1)+u(x-1)-4u(x)+e 2u(x) =0,

[0046] Right now:

[0047] 2u(x+1)+2u(x-1)-4u(x)+e 2u(x) =0.

[0048] The exponential auxiliary variable of the introduced voltage like Figure 2 As shown, the two-dimensional problem is transformed into a one-dimensional relationship, reflecting the exponential decay characteristics of the voltage.

[0049] Set the initial voltage value, where g(0) corresponds to the origin voltage reference value u(0) = u(0,0) = 0, and g(1) reflects the exponential decay characteristics of the adjacent node voltage. The initial physical quantity must be determined to ensure the stability of the recursion. In this embodiment, g(1) = e -1 .

[0050] The analog voltage signal collected by the voltage sensor is converted into a digital signal and input into the data processing module.

[0051] In this embodiment, a pipeline architecture is used to calculate the node voltage distribution. Specifically, the following is used: Figure 5 The three-stage pipeline architecture of the FPGA recursive module shown includes:

[0052] Divider module: used to calculate the numerator

[0053] ExpLUT module: hardware acceleration of nonlinear terms through table lookup;

[0054] Multiplier module: performs multiplication operations and implements truncation protection.

[0055] When the Divider module calculates the xth node When the ExpLUT module synchronously queries the e of the xth node -g(x) ; The Multiplier module is processing the multiplication and truncation judgment of the x-1th node, achieving full pipeline parallelism.

[0056] Step 3: When the voltage value is detected to be beyond the threshold range, the cutoff protection mechanism is activated. The specific steps are as follows:

[0057] Comparator real-time monitoring When the voltage value is detected to be beyond the threshold range, the cutoff protection mechanism is activated:

[0058] When u(x) is less than -15V, the FPGA forces u(x) to be written as -15V and triggers an interrupt signal. The interrupt signal is connected to the enable terminal of the current source, shutting down the nonlinear current output and implementing adaptive truncation protection (hardware protection).

[0059] Step 4: The visualization output module generates a voltage distribution heat map for circuit status monitoring. The specific steps are as follows:

[0060] Step 4.1: Plot the voltage u(x) versus x = m + n to verify the exponential decay of voltage with distance; and generate the attenuation characteristic curve of the nonlinear resistor network g(x) through MATLAB iterative code. Figure 3 , voltage attenuation characteristic curve Figure 4 .

[0061] Step 4.2: Map the voltage of each node u(m,n) into a color gradient map, and output a two-dimensional thermal map through the display device to intuitively reflect the circuit potential distribution. Figure 4 As shown in the figure, this heat map shows the voltage distribution relative to ground at each node in a 20×20 resistor network. Darker colors indicate lower voltages. In the figure, the horizontal and vertical axes represent the grid coordinates m and n, respectively, and the color scale indicates the voltage value in volts.

[0062] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A method for measuring voltage distribution in a nonlinear resistor network, characterized in that: The following steps are involved: Step 1: Construct a physical grid model consisting of a planar network of linear resistors, with each node of the network connected to a nonlinear current source in parallel with the ground. Step 2: Collect the ground potential of each node and use the physical symmetry requirement to reduce the dimensionality of the two-dimensional measurement data to a single variable function with equal voltage at points symmetrical about the network diagonal. Step 3: Configure the control module and use a pipeline architecture to calculate the node voltage distribution. The architecture includes a Divider module, an ExpLUT module, and a Multiplier module. The Divider module is used to calculate the numerator of the voltage gradient of adjacent nodes. The ExpLUT module is used to implement hardware-accelerated calculation of nonlinear terms by looking up a pre-stored exponential function table. The Multiplier module is used to complete the voltage iterative calculation and perform the truncation protection judgment. Step 4: When it is detected that the voltage value exceeds the preset threshold range, the cutoff protection mechanism is activated to turn off the nonlinear current output to achieve adaptive cutoff protection. Step 5: Generate a voltage distribution heat map through the visualization output module for circuit status monitoring.

2. The method for measuring voltage distribution of a nonlinear resistor network according to claim 1, wherein: In step 1, the nonlinear current source is a memristor or a Schottky diode array, and the linear resistance value is 1Ω.

3. The method for measuring voltage distribution of a nonlinear resistor network according to claim 2, wherein: In the physical grid model, the grid origin (0,0) is the potential reference point, and the potential value u(0,0)=0, u m,n represents the voltage of node (m,n) to ground, then the voltage model equation of node (m,n) is: Among them, the nonlinear term Acts as a nonlinear current source from the node to ground.

4. The method for measuring voltage distribution of a nonlinear resistor network according to claim 3, wherein: In step 2, the voltages at points symmetrical about the network diagonal are equal, and the voltage model equation is simplified to an equation about a single variable function u(x). The simplified voltage model equation is 2u(x+1)+2u(x-1)-4u(x)+e 2u(x) =0 Where x=m+n, m and n are the horizontal and vertical coordinates of the node in the grid respectively.

5. The method for measuring voltage distribution of a nonlinear resistor network according to any one of claims 1 to 4, characterized in that: In step 4, the truncation protection mechanism is specifically as follows: when the voltage value u(x) is lower than -15V, the FPGA is forced to write u(x) = -15V and trigger an interrupt signal, which is connected to the enable terminal of the current source to turn off the nonlinear current output.

6. The method for measuring voltage distribution of a nonlinear resistor network according to any one of claims 1 to 4, characterized in that: In step 5, the voltage distribution heat map is generated by plotting the voltage u(x) versus x=m+n and mapping each node voltage u(m,n) into a color gradient map, which intuitively reflects the circuit potential distribution.

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