A method for direct measurement of band of periodic circuit

Abstract

The present application relates to a kind of novel periodic circuit energy band direct measurement method, comprising: the node circuit model of target circuit is constructed;The numerical value of translation term element is calculated, and translation term element is connected to node circuit model;For the target circuit model connected translation term element, printed circuit board experiment measurement is carried out, and the voltage amplitude and phase of each node are acquired;The voltage amplitude and phase of each node are Fourier transformed, and the coordinate points of two peak values in wave function Fourier transform image are acquired;The numerical value of different translation term element is replaced, and the repeated measurement of printed circuit board experiment is carried out, and the coordinate points of two peak values in different wave function Fourier transform image are acquired;The circuit energy band is reconstructed based on the coordinate points of all peak values.The present application has far-reaching significance for using circuit to realize various physical models in condensed matter physics.It can directly measure the energy band structure of system, and can directly observe its state topography and energy characteristics.

Description

Technical Field

[0001] This invention relates to the field of circuit band measurement technology, and in particular to a method for direct measurement of the band structure of a periodic circuit. Background Technology

[0002] The energy band diagram of a circuit is the admittance spectrum. Taking a one-dimensional Su-Schrieffer-Heeger (1D-SSH) circuit as an example, the desired value is... Figure 1 The image shown, Figure 1 The value of the k-coordinate in the middle is the first Brillouin zone, i.e. 'a' is the lattice constant, which corresponds to the spacing between adjacent lattice points in the tight-bound model. In circuit research, considering the spacing between adjacent nodes has no special physical meaning; generally, 'a' is taken as 1, in which case the value of the k-coordinate is... .

[0003] The most commonly used measurement methods are as follows: Figure 2 As shown, current I is fed in from node j. j Measure the voltage response V at node i i The mutual admittance between nodes can be obtained from the following formula, where G ij J is the impedance between nodes i and j. ij It is the admittance between nodes i and j. Thus, the admittance matrix is ​​reconstructed. After reconstructing the admittance matrix, it is equivalent to obtaining the Hamiltonian of the system. Then, the Hamiltonian in real space is transformed to k space by Fourier transform to obtain the Hamiltonian matrix in k space. Then, by solving the eigenvalues ​​of the Hamiltonian matrix in k space, the band structure can be solved.

[0004] However, this method essentially measures the admittance matrix, which is equivalent to measuring each term of the Hamiltonian one by one, and then obtaining the band structure by performing a Fourier transform on the Hamiltonian and solving its eigenvalue equations. It is not a measurement of the band structure itself. Therefore, the band structure is essentially calculated, not measured. Throughout the measurement process, there is no direct measurement of state morphology and energy characteristics, and this method cannot reveal the dispersion relation of the band structure during the measurement process.

[0005] In summary, existing methods for measuring band structure essentially measure the admittance matrix, which is equivalent to measuring each term of the Hamiltonian to obtain the system's Hamiltonian. Then, a Fourier transform is used to convert the real-space Hamiltonian to k-space, obtaining the k-space Hamiltonian matrix. Finally, the eigenvalues ​​of the k-space Hamiltonian matrix are solved to determine the band structure. Therefore, the band structure is essentially calculated, not measured. The entire measurement process does not involve direct measurement of state morphology and energy characteristics, and this method cannot reveal the dispersion relation of the band structure during the measurement process. Summary of the Invention

[0006] The purpose of this invention is to propose a direct measurement method for the energy band structure of a periodic circuit to solve the problems existing in the prior art. This method can directly measure the energy band diagram of the circuit, and it is expected that this method can reflect the characteristics such as state morphology and energy during the measurement process. This is different from the indirect measurement method that measures the Hamiltonian one by one, then performs Fourier transform on the Hamiltonian, and then calculates the eigenvalue equation to obtain the energy band structure.

[0007] To achieve the above objectives, the present invention provides the following solution: A method for direct band measurement of periodic circuits includes: Construct the node circuit model of the target circuit; Calculate the values ​​of the translation term elements and connect the translation term elements to the node circuit model; For the target circuit model connected to the translation term components, printed circuit board experiments were conducted to obtain the voltage amplitude and phase of each node. Perform a Fourier transform on the voltage amplitude and phase of each node to obtain the coordinates of the two peaks in the Fourier transform image of the wave function; By replacing the values ​​of different translation term components, repeated measurements were performed in the printed circuit board experiment to obtain the coordinates of two peaks in the Fourier transform images of different wave functions. The circuit band structure is reconstructed based on the coordinates of all peak values.

[0008] Optionally, the expression for the node circuit model is: Where I(ω) and V(ω) are vectors composed of the current and voltage of each node, and J(ω) is the admittance matrix.

[0009] Optionally, connecting translation term elements to the node circuit model includes: Add a capacitor between each node and ground.

[0010] Optionally, calculating the values ​​of the translation term elements includes: Where C is the value of the translation term element, and Y is the admittance. The input voltage is the angular frequency multiplied by the imaginary number i.

[0011] Optionally, experimental measurements of printed circuit boards include: After calculating the numerical values ​​of the translation term components, the printed circuit board is drawn for the target circuit model. Solder the components based on the drawn circuit board; Using an oscilloscope, the voltage of each node in the soldered circuit board was measured.

[0012] Optionally, performing a Fourier transform includes: in, This represents the Fourier transform image of the wave function, where N is the dimension of the nodal circuit model. Let 'a' be the spatial coordinates, and 'a' be the lattice constant in condensed matter physics. For the coefficients of the Fourier transform formula, n represents the lattice point number in condensed matter physics and the circuit node number in circuits.

[0013] The beneficial effects of this invention are as follows: This invention allows for direct measurement of the band structure of a circuit, unlike the indirect measurement method that involves measuring Hamiltonians one by one, performing Fourier transforms on the Hamiltonians, and then calculating the eigenvalue equations to obtain the band structure. Furthermore, this method is expected to reveal characteristics such as state morphology and energy during the measurement process.

[0014] This method has profound implications for realizing various physical models in condensed matter physics using circuits. It allows for direct measurement of the band structure of a system and direct observation of its state morphology and energy characteristics, deepening our understanding of topological physical models during experimental measurements. Furthermore, this method is widely applicable; it can be used to reconstruct the band structure for different topological circuits and even different dimensions. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 The admittance spectrum of the 1D-SSH circuit; Figure 2 This is a schematic diagram of the 1D-SSH circuit structure; Figure 3 This is a one-dimensional coupled chain model according to an embodiment of the present invention; Figure 4 This is the band structure of the 1D-SSH model in an embodiment of the present invention; Figure 5 This is a flowchart of the method for measuring the band structure of a periodic circuit according to an embodiment of the present invention; Figure 6 This is a schematic diagram of the 1D-SSH circuit structure according to an embodiment of the present invention; Figure 7 This is a schematic diagram of the 1D-SSH bandgap measurement circuit structure according to an embodiment of the present invention; Figure 8 This is a physical diagram of the 1D-SSH bandgap measurement circuit according to an embodiment of the present invention; Figure 9 This is a schematic diagram of voltage measurement using an oscilloscope according to an embodiment of the present invention; Figure 10 This is the translated admittance spectrum according to an embodiment of the present invention; Figure 11 This is the Fourier transform image of the wave function corresponding to C=2nF in an embodiment of the present invention; Figure 12 This is the Fourier transform image of the wave function corresponding to C=1nF in an embodiment of the present invention; Figure 13 This is the Fourier transform image of the wave function corresponding to C=1.5nF in an embodiment of the present invention; Figure 14 This is the Fourier transform image of the wave function corresponding to C=2.4nF in an embodiment of the present invention; Figure 15 This is the Fourier transform image of the wave function corresponding to C=2.7nF in an embodiment of the present invention; Figure 16 A comparison of band diagrams obtained from theoretical and experimental measurements in embodiments of the present invention. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] Explanation of the circuit energy bands appearing in this embodiment: like Figure 3 As shown, for example, for a one-dimensional chain with only nearest-neighbor coupling and coupling strength t, the Hamiltonian in k-space can be obtained through Fourier transform, and its eigenvalues ​​can be solved to obtain the relationship between energy and k, i.e., the energy band.

[0020] When using circuits to reproduce a topological model, it is actually based on , H is the circuit admittance matrix, and H is the real-space Hamiltonian. Therefore, for a circuit model, its band structure can also be theoretically obtained in the same way.

[0021] Explanation regarding why the frequency sweep method for measuring energy bands in condensed matter physics is not feasible in circuits: In condensed matter physics, the band structure of a model is typically obtained by frequency sweeping. This is because energy... It refers to frequency. By scanning the excitation frequency, the energy band can be scanned.

[0022] For example Figure 4 As shown, different states can be excited by adjusting the excitation frequency and shifting the black dashed line in the diagram up and down.

[0023] By measuring the wave function and performing a Fourier transform, the corresponding k-space coordinates can be obtained, thereby enabling the measurement of the band structure.

[0024] However, this method cannot be implemented in circuits for the following reasons: When using circuits to reproduce a topological model, it is actually based on , It is the circuit admittance matrix. By adjusting the circuit's admittance matrix, it can be made to correspond one-to-one with the real-space Hamiltonian at a specific frequency.

[0025] As can be seen, the admittance matrix is ​​a parameterized matrix. The variable matrix is ​​such that it's not feasible to measure the band structure using a frequency sweep method. This is because the admittance matrix changes with... The changes are equivalent to changes in the Hamiltonian, meaning the model itself has changed, making it impossible to measure the band structure.

[0026] The core idea of ​​the circuit band structure measurement method: So, if translation is not possible Figure 4 The black line shown can be used to translate the band structure, that is, to achieve measurement by changing the characteristic value of the Hamiltonian.

[0027] by Taking the k-space admittance matrix of a circuit as an example, as shown in the above equation, the value of the inductor L can be changed to achieve... The change in L only affects the diagonal terms, which is equivalent to a change in the eigenvalues. This allows for the vertical translation of the band structure diagram.

[0028] The vertical axis, i.e., the admittance value, can be obtained by the translation amount, i.e., the change in inductance. The coordinates in k-space can be obtained by the Fourier transform of the measured wave function. The wave function corresponds to the node voltage vector in the circuit. This method can be used to measure the energy band diagram.

[0029] Of course, different component parameters need to be changed for different models.

[0030] Theoretical principle of circuit band structure measurement method: Explanation of the voltage vector at the circuit node corresponding to the wave function: For a nodal circuit model, its circuit equations can be written as follows: Where I(ω) and V(ω) are vectors composed of the current and voltage at each node, and J(ω) is the admittance matrix.

[0031] If the externally injected current is 0, then V(ω) corresponds to the eigenmodes, i.e., the wave function, where the system admittance is 0.

[0032] Mathematical principles of circuit band structure measurement methods: In the tight-binding model, N is the total number of lattice points, n is the lattice point number, and a is the lattice constant. In circuit theory, N is the total number of nodes, n is the node number, and a is 1. The transformation result is a delta function, i.e.: A wave packet will appear at the corresponding k-coordinate.

[0033] This embodiment proposes a novel method for direct measurement of the energy band of periodic circuits, including: Construct the node circuit model of the target circuit; Calculate the values ​​of the translation term components and connect the translation term components to the nodal circuit model; For the target circuit model connected to the translation term components, printed circuit board experiments were conducted to obtain the voltage amplitude and phase of each node. Perform a Fourier transform on the voltage amplitude and phase of each node to obtain the coordinates of the two peaks in the Fourier transform image of the wave function; By replacing the values ​​of different translation term components, repeated measurements were performed in the printed circuit board experiment to obtain the coordinates of two peaks in the Fourier transform images of different wave functions. The circuit band structure is reconstructed based on the coordinates of all peak values.

[0034] Furthermore, the expression for the node circuit model is: Where I(ω) and V(ω) are vectors composed of the current and voltage of each node, and J(ω) is the admittance matrix.

[0035] Furthermore, the connection of translation term elements to the node circuit model includes: Add a capacitor between each node and ground. A node refers to the connection point between components.

[0036] Furthermore, experimental measurements on printed circuit boards include: After calculating the numerical values ​​of the translation term components, the printed circuit board is drawn for the target circuit model. Solder the components based on the drawn circuit board; Using an oscilloscope, the voltage of each node in the soldered circuit board was measured.

[0037] Specifically, in this embodiment, such as Figure 5 As shown, taking the 1D-SSH circuit as an example, the steps for measuring the band structure of the 1D-SSH circuit will be described in detail below; Step 1: Preliminary Preparations The above formula is The admittance matrix of a circuit is first introduced by the conventional 1D-SSH circuit structure, such as... Figure 6 As shown, the power supply is coupled through a node, i.e., a capacitor. The circuit is fed in from the first node, and each node is connected by a coupling capacitor. , Alternating connections, coupling term capacitance in the admittance matrix , This is mainly reflected in the off-diagonal terms. In addition to the coupling terms, each node is grounded through an inductor L as a grounding term. In the admittance matrix, the grounding inductor L is reflected in the diagonal terms.

[0038] The 1D-SSH bandgap measurement circuit used in this embodiment (such as...) Figure 7 As shown in the figure, unlike the conventional 1D-SSH circuit structure, a capacitor C is connected in parallel as a band shift term in addition to the original ground inductance L of each node.

[0039] Step 2: Calculate the value of the translation term capacitance C. First, it is necessary to calculate the specific values ​​of the translation term components required for the experiment. The calculation method is as follows: Taking the 1D-SSH circuit as an example, its admittance matrix is ​​written first: in .

[0040] According to the Fourier transform formula, transform it to k-space: according to The Hamiltonian is obtained as follows: Solving for the eigenvalues ​​of the Hamiltonian in k-space yields its band structure, such as... Figure 1 As shown.

[0041] Next, a translation element needs to be added to the circuit to shift the energy band, thereby exciting the desired state. The magnitude of the translation depends on the desired measurement accuracy. Figure 1 As shown, the vertical axis of the band structure diagram represents admittance. Since this band structure diagram is symmetrical, we will focus only on the upper half for now; its value is... If you want higher measurement accuracy, that is, to have more points in the final bandgap diagram, such as... Figure 16 As shown, we need to reduce the magnitude of each translation. For example, if only 5 translations are needed, then the interval between each translation would be... The change in capacitance value with each translation is: .

[0042] The specific value of the translation term can be calculated using the numerical value of the vertical axis admittance in the band structure diagram. In the band structure, the numerical value of the vertical axis admittance is: according to The calculated values ​​for the added translation term elements are: Where C is the value of the translation term element, and Y is the admittance. The input voltage is the angular frequency multiplied by the imaginary number i.

[0043] In this experiment, C=1nF, 1.5nF, 2nF, 2.4nF, and 2.7nF were used as terms for the translational band.

[0044] A grounding capacitor C is connected in parallel at each node, such as Figure 6 As shown, the Hamiltonian in k-space becomes: The band structure becomes as follows Figure 10 As shown.

[0045] Step 3: Layout design, PCB fabrication, and component soldering: The experiment here uses a printed circuit board (PCB), such as... Figure 8 As shown, the functional areas on the PCB can be divided into three parts: power input and ground, 1D-SSH circuit, and node voltage measurement probes. JLCPCB EDA was used to draw the PCB layout. After the board is fabricated, capacitors, inductors, and probes are soldered. Finally, experimental measurements are performed.

[0046] Step 4: Experimental Measurement Using a signal generator, a frequency of [frequency value] is fed in from the power input terminal. AC voltage signal.

[0047] Next, we will use an oscilloscope to measure the voltage at each node. The specific method is as follows: 1. By connecting the oscilloscope's CH1 to the first node, the voltage amplitude of the first node can be obtained. .

[0048] 2. By connecting the oscilloscope's CH2 circuit to the other nodes in turn, the voltage amplitude of the other nodes can be obtained. and the phase difference between the CH2 and CH1 measurement signals. That is, the phase difference between the voltages of the remaining nodes and the voltage of the first node. For example... Figure 9 The image shown is an oscilloscope image from the experiment. The waveform at the top of the image represents the voltage signal of CH1, and the waveform at the bottom represents the voltage signal of CH2. The amplitudes of the two voltage signals can be read directly, and the phase difference between the two signals can be measured using the cursor.

[0049] Step 5: Fourier Transform: Voltage vector The voltage is then transformed to k-space using Fourier transform. Measurements at all nodes are completed, yielding the voltage vector. .

[0050] That is, the wave function was obtained. Here, x is the spatial coordinate index of the node, i.e., 1, 2, 3... Then, according to the Discrete Fourier Transform formula: in, This represents the Fourier transform image of the wave function, where N is the dimension of the nodal circuit model. Here, represents spatial coordinates, corresponding to 1, 2, 3... in a circuit. 'a' is the lattice constant in condensed matter physics, but it has no physical meaning in circuits and is typically taken as 1. These are the coefficients of the Fourier transform formula. In condensed matter physics, n is the lattice point number; in circuits, it is the circuit node number.

[0051] To obtain the wave function in k-space, For example, Figure 11 As shown in the figure, there are two peaks, and their corresponding k-coordinates are... Figure 10 k1 and k2 in the figure. The values ​​corresponding to the vertical axis are: At this point, we can obtain the two coordinate points in the band structure diagram. , .

[0052] Step Six: Repeat the measurement by replacing the capacitor C with different translation terms: Replace the translation term capacitor C with other values ​​and repeat the above measurements. Each replacement of the translation term component corresponds to a different coordinate point in the energy band diagram, i.e., corresponds to... Figure 16 The point in the middle. Its x-coordinate is Figures 11-15 The transformed peak corresponds to the k-coordinate. The ordinate is the translation amount corresponding to the translation capacitance, i.e. .

[0053] Step 7: Reconstruct the energy bands: By replacing different translation term capacitors C, different coordinate points of the obtained band diagram can be measured. Plotting these points on a single graph reconstructs the band structure.

[0054] Step 8: Compare the theoretical and experimental band diagrams: By comparing the band structures obtained from theory and experiment, we can determine whether the experiment was successful.

[0055] Experimental results: Use this method for, for example Figure 2 shown Band measurements were performed on the circuit model (26 nodes in total). Compared to the original The circuit adds a grounding capacitor C as a term to shift the energy band, and its energy band structure (i.e., the energy band measurement result) also changes from: It has become: Using C=1nF, 1.5nF, 2nF, 2.4nF, and 2.7nF as terms for shifting the energy band, the voltage at each node was measured under a voltage input at a frequency of 505kHz. Then, a Fourier transform was performed to completely measure the energy band of the circuit.

[0056] The above experiment, using a 1D-SSH circuit as an example, introduces the complete method and steps for circuit bandgap measurement. This method is not just a special case; it can also be applied to other circuit models, even those of different dimensions.

[0057] Different circuit models correspond to different admittance matrices, i.e., Hamiltonians in real space. Theoretically, the method of transforming them to k-space and obtaining their band structure is the same.

[0058] All such circuit models can be divided into two parts: one is the connection element between nodes, and the other is the connection element between each node and ground.

[0059] For different circuit models, adding a capacitor between each node and ground can achieve the effect of shifting the energy band. The specific magnitude of the shift, i.e., the value of the capacitor, is determined as described in step two of the experimental procedure. For different circuits, it only requires considering the desired measurement accuracy and the specific value of the admittance on the vertical axis of the energy band diagram. Based on: Calculate the specific value of the translation capacitor and connect it to the ground connection point of each node.

[0060] For translation phase components, either capacitors or inductors can be used. The admittance of a capacitor is iwC, and that of an inductor is i / wL; they are essentially the same. The specific calculation methods for these values ​​have been provided. The selection criterion is to minimize parasitic resistance.

[0061] After translation, the voltage amplitude and phase of each node are measured using the same method. Then, based on the model's dimension N, an N-dimensional Fourier transform is performed to obtain the k-coordinate corresponding to the band structure. The admittance corresponding to this translation capacitor is then determined. The vertical axis represents the coordinates. By combining these coordinates, we can obtain different coordinate points in the band structure diagram. Then, by changing the translation capacitor with different values ​​and repeating the experiment, we can obtain the coordinate points in the band structure diagram. Finally, by plotting all the points on a single graph, we can complete the band structure measurement.

[0062] The band structure measured in this embodiment is as follows: Taking the k-space admittance matrix of a 1D-SSH circuit as an example, as shown in the above equation, a capacitor C can be added to the diagonal terms, or the value of the inductor L can be changed to achieve the desired result. The change in L only affects the diagonal terms, which is equivalent to a change in the eigenvalues. This allows for the vertical translation of the band structure diagram.

[0063] The vertical axis, i.e., the admittance value, can be obtained through translation, i.e., the change in inductance. The k-space coordinates can be obtained through the Fourier transform of the measured wavefunction. The wavefunction corresponds to the node voltage vector in the circuit. This method can be used to measure the band structure. Different component parameters need to be changed for different models. Furthermore, measuring the complete band structure requires changing multiple parameters.

[0064] For a circuit network model, existing methods for measuring the band structure essentially measure the admittance matrix, which is equivalent to measuring each term of the Hamiltonian to obtain the system's Hamiltonian. Then, a Fourier transform is used to convert the real-space Hamiltonian to k-space, obtaining the k-space Hamiltonian matrix. Finally, the eigenvalues ​​of the k-space Hamiltonian matrix are solved to obtain the band structure. Therefore, the band structure is essentially calculated, not measured. The entire measurement process does not involve direct measurement of state morphology and energy characteristics, and this method cannot reveal the dispersion relation of the band structure during the measurement process.

[0065] This method can be used if you do not want to use this indirect method of measuring band structure and instead want to directly measure the band diagram of a circuit. This method can reveal characteristics such as state morphology and energy during the measurement process, and it directly measures the band structure.

[0066] Existing methods for measuring band structure essentially measure the admittance matrix, which is equivalent to measuring each term of the Hamiltonian one by one to obtain the system's Hamiltonian. Then, a Fourier transform is used to convert the real-space Hamiltonian to k-space, obtaining the k-space Hamiltonian matrix. Finally, the eigenvalues ​​of the k-space Hamiltonian matrix are solved to determine the band structure. Therefore, the band structure is essentially calculated, not measured. The entire measurement process does not involve direct measurement of state morphology and energy characteristics, and this method cannot reveal the dispersion relation of the band structure during the measurement process.

[0067] The technical advantage and differentiation of the method in this embodiment is that it can directly measure the energy band diagram of the circuit, unlike the indirect measurement method that measures the Hamiltonian term by term, performs a Fourier transform on the Hamiltonian term, and then calculates the eigenvalue equation to obtain the energy band structure. Furthermore, it is expected that this method can reveal characteristics such as state morphology and energy during the measurement process.

[0068] In condensed matter physics, angle-resolved photoelectron spectroscopy (ARPS) is commonly used to measure band structure. Photons of different momentum are injected to excite electrons within the material, and the energy of the emitted electrons is measured to obtain the Ek relationship, i.e., the band structure. The method in this patent application, however, involves translating the band structure to excite different states, measuring the wavefunction, and then performing a Fourier transform to obtain the k-coordinates of the excited states, thus yielding the band structure. This method, consistent with the underlying principle of angle-resolved photoelectron spectroscopy for band structure measurement, directly measures the k-space band structure, rather than first measuring the Hamiltonian and then calculating the band structure using a Fourier transform.

[0069] The method described in this embodiment has profound implications for realizing various physical models in condensed matter physics using circuits. It allows for direct measurement of the band structure of a system and direct observation of its state morphology and energy characteristics, deepening the understanding of topological physical models during experimental measurements. Furthermore, this method has wide applicability; it can be used to reconstruct the band structure for different topological circuits and even different dimensions.

[0070] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for direct bandgap measurement of a periodic circuit, characterized in that, include: Construct the node circuit model of the target circuit; Calculate the values ​​of the translation term elements, and connect the translation term elements to the node circuit model, including connecting a capacitor in parallel as a translation term of the band in addition to the original ground term inductance of each node. The calculation of the translation term element includes: Where C is the value of the translation term element, and Y is the admittance. The angular frequency corresponding to the input voltage is multiplied by the imaginary number i; For the target circuit model connected to the translation term components, printed circuit board experiments were conducted to obtain the voltage amplitude and phase of each node. Perform a Fourier transform on the voltage amplitude and phase of each node to obtain the coordinates of the two peaks in the Fourier transform image of the wave function; By replacing the values ​​of different translation term components, repeated measurements were performed in the printed circuit board experiment to obtain the coordinates of two peaks in the Fourier transform images of different wave functions. The circuit energy band is reconstructed based on the coordinates of all peak values; where the k-coordinate corresponding to the peak value is used as the abscissa of the circuit energy band, and the admittance corresponding to the translation term element is used as the abscissa. C represents the ordinate of the circuit's energy band; The experimental measurements for printed circuit boards include: After calculating the numerical values ​​of the translation term components, the printed circuit board is drawn for the target circuit model. Solder the components based on the drawn circuit board; Using an oscilloscope, the voltage of each node in the soldered circuit board was measured; Performing a Fourier transform includes: in, This represents the Fourier transform image of the wave function, where N is the dimension of the nodal circuit model. Let 'a' be the spatial coordinates, and 'a' be the lattice constant in condensed matter physics. represents the coefficients of the Fourier transform formula, and n is the circuit node number.

2. The method for direct measurement of the energy band of a periodic circuit according to claim 1, characterized in that, The expression for the node circuit model is: Where I(ω) and V(ω) are vectors composed of the current and voltage of each node, and J(ω) is the admittance matrix.

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