An electrical equipment broadband impedance on-line measuring device and method based on frequency domain single-sensing probe configuration

Abstract

The application discloses a kind of based on frequency domain single inductive probe configuration electrical equipment broadband impedance online measurement device and method, comprising: main circuit and impedance measurement system;Wherein, main circuit is composed of power supply, cable and DUT;Power supply is connected with DUT by cable;Impedance measurement system is composed of VNA, inductive probe and signal processing unit;VNA is connected with inductive probe by radio frequency cable, for generating Chirp signal, then Chirp signal is input into inductive probe by radio frequency cable;Inductive probe, for Chirp signal is coupled into main circuit and excites disturbance, obtains the reflection coefficient of DUT;Signal processing unit is connected with VNA by miniUSB cable, for controlling VNA measurement reflection coefficient of DUT, measured data is grabbed and processed, extracts the impedance Z of DUT DUT .

Description

Technical Field

[0001] This invention belongs to the field of electrical equipment fault detection and condition monitoring, specifically relating to an online wideband impedance measurement device and method for electrical equipment based on a frequency domain single-inductive probe configuration. Background Technology

[0002] Wideband impedance is a crucial indicator characterizing the internal state of electrical equipment. Impedance measurement enables electromagnetic interference (EMI) design, battery state-of-charge (SOC) estimation, life science applications (such as virus detection and cell monitoring), and stability control of grid-connected inverter systems. In recent years, new energy power generation has been developing rapidly. A typical new energy system consists of a power generation unit, an energy storage unit, a grid-connected inverter unit, an inverter controller unit, and a grid unit. These units are interconnected via cables. The complexity of new energy systems poses challenges to their safe and stable operation; therefore, a consistent measure for effective system health management is impedance measurement of each unit.

[0003] Currently, impedance measurement techniques can be divided into passive measurement and active measurement. Passive measurement measures impedance by extracting harmonic disturbances in the circuit. Although it causes little interference to the main circuit operation, its accuracy is low and it is not suitable for measuring wideband impedance. Active methods inject disturbances into the main circuit and then extract impedance information from the disturbance response, which has higher accuracy, but it is still difficult to overcome the contradiction between measurement bandwidth and efficiency.

[0004] Furthermore, cables in electrical systems can range from tens to thousands of meters in length. At high frequencies, cables exhibit significant attenuation and phase shift characteristics. Additionally, cable mismatch can introduce multiple reflections, leading to ripple interference in impedance measurements. Therefore, broadband impedance measurements must also consider the impact of cable and line mismatch on the measurement process. Summary of the Invention

[0005] To address the problems of limited measurement bandwidth, inaccurate impedance measurement due to cable attenuation and phase shift at high frequencies, significant ripple, and noise interference in broadband impedance measurement of electrical equipment, the present invention provides a broadband online impedance measurement device and method for electrical equipment based on a frequency domain single-inductive probe configuration.

[0006] To achieve the above objectives, the present invention provides the following solution:

[0007] An online wideband impedance measurement device for electrical equipment based on a frequency domain single-inductive probe configuration, the device comprising: a main circuit and an impedance measurement system;

[0008] The main circuit consists of a power supply, cables, and a DUT (Device Under Test).

[0009] The power supply is connected to the DUT via a cable;

[0010] The impedance measurement system consists of a VNA, an inductive probe, and a signal processing unit, wherein the VNA is a vector network analyzer;

[0011] The VNA connects to the sensing probe via an RF cable to generate a Chirp signal, which is then input to the sensing probe via the RF cable.

[0012] The inductive probe is clamped onto the main circuit to maintain electrical isolation between the impedance measurement system and the main circuit, and to establish a signal coupling path between the impedance measurement system and the main circuit, so that the chirp signal is coupled into the main circuit through the inductive probe and excites disturbances to obtain the reflection coefficient of the DUT.

[0013] The signal processing unit connects to the VNA via a miniUSB cable to control the VNA to measure the reflection coefficient of the DUT, capture and process the measured data, and extract the impedance Z of the DUT. DUT .

[0014] This invention also provides a method for online measurement of broadband impedance of electrical equipment based on a frequency-domain single-inductive probe configuration, implemented using the aforementioned online measurement device for broadband impedance of electrical equipment based on a frequency-domain single-inductive probe configuration. The method includes:

[0015] S1: Measure the first reflection coefficient Γ1 using a calibrated vector network analyzer;

[0016] S2: Measure the S-matrix of the sensing probe. Based on the S-matrix and the port scattering principle, the influence of the sensing probe is embedded from the first reflection coefficient Γ1 to obtain the second reflection coefficient Γ2.

[0017] S3: Calculate the corresponding second impedance Z2 based on the second reflection coefficient Γ2;

[0018] S4: Using the known passive impedance Z Given Replace the cable and DUT, measure the second impedance Z2' in this configuration, and subtract Z from the second impedance Z2'. Given Obtain the internal resistance Z of the power supply s ;

[0019] S5: Subtract the obtained power supply internal resistance Z from the obtained second impedance Z2. s The impedance at the cable input end is obtained and denoted as the third impedance Z3.

[0020] S6: Based on the cable T matrix, the third impedance Z3, and transmission line theory, obtain the primary impedance of the device under test, denoted as the fourth impedance Z4;

[0021] S7: Take the real and imaginary parts of the fourth impedance Z4 to form a two-channel signal, and use the multivariate variational mode decomposition (MVMD) technique to decompose this two-channel signal into modes. Preserving signal modes

[0022] S8: For signal modes Continue performing MVMD decomposition until the error threshold is met, and output the signal mode obtained after the Nth decomposition. Using signal modes The impedance of the device under test after noise reduction.

[0023] Preferably, the method for measuring the S-matrix of the sensing probe includes:

[0024] Clamp the inductive probe onto the inner conductor of the calibration fixture. Label the probe port and the two ports on the right and left of the calibration fixture as P1, P2, and P3, respectively. Connect P1 to port 1 of the VNA, connect P2 to port 2 of the VNA, and connect P3 to a 50Ω terminal or a short-circuit terminal. Then, use the calibrated VNA to measure the scattering parameter matrix S of the inductive probe.

[0025] Preferably, the method for obtaining the second reflection coefficient Γ2 by removing the influence of the inductive probe from the first reflection coefficient Γ1 based on the S-matrix and the port scattering principle includes:

[0026] Based on scattering parameter S 11 S 12 S 21 and S 22 Based on the port scattering principle, the influence of the inductive probe is embedded from the first reflection coefficient Γ1 to obtain the second reflection coefficient Γ2, as shown below:

[0027]

[0028] Preferably, the method for calculating the corresponding second impedance Z2 based on the second reflection coefficient Γ2 includes:

[0029]

[0030] In the formula, Z0 represents the reference impedance.

[0031] Preferably, the cable T-matrix is:

[0032]

[0033] In the formula, γ and Z c l and l are the propagation constant, characteristic impedance, and length of the cable, respectively;

[0034] The methods for obtaining the primary impedance of the device under test, denoted as the fourth impedance Z4, based on the cable T-matrix, the third impedance Z3, and transmission line theory include:

[0035]

[0036] In the formula, Z3 is the third impedance.

[0037] Preferably, the real and imaginary parts of the fourth impedance Z4 are used to form a two-channel signal, and the two-channel signal is decomposed into modes using multivariate variational mode decomposition (MVMD) technology. Preserving signal modes The methods include:

[0038] The formulas for mode update and center frequency update in multivariate variational mode decomposition (MVMD) are as follows:

[0039]

[0040] In the formula, c = 1, 2 represents the channel number, k = 1, 2, ..., K represents the mode number, K represents the number of modes, i represents the mode number in each iteration, n represents the iteration number, λ represents the Lagrange multiplier, α represents the bandwidth balancing parameter, and s c (ω) represents a two-channel signal. U represents the k-th mode of the c-channel signal in the (n+1)th iteration. c,i (ω) represents the i-th mode of the c-channel signal in n iterations, λ c (ω) represents the Lagrange multiplier of the c-channel, and ω represents the angular frequency. This represents the center frequency of the k-th mode in the (n+1)th iteration;

[0041] Decomposition yields modes "1" indicates the first decomposition. The signal mode is represented by the main signal mode, while the other modes represent ripple and noise. The main signal mode is retained. And eliminate the remaining modes.

[0042] Preferably, for signal modes Continue performing MVMD decomposition until the error threshold is met. The error threshold is:

[0043]

[0044] In the formula, N u 1,1 Let be the mode of the first channel after the Nth decomposition, and represent the real part of the impedance; N u 2,1 Let be the mode of the second channel after the Nth decomposition, and represent the imaginary part of the impedance;

[0045] based onN u 1,1 and N u 2,1 The impedance Z of the device under test after synthesis and noise reduction DUT The expression is:

[0046] Z DUT = N u 1,1 +j N u 2,1 ;

[0047] In the formula, j represents the virtual unit.

[0048] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0049] First, the single-sensory probe configuration saves costs and reduces system size compared to the multi-probe configuration, and avoids mutual electromagnetic interference between multiple probes. Second, it can measure wideband impedance within tens or even hundreds of megahertz frequency bands. Third, it solves the problem of cable interference with measurement, broadens application scenarios, and this invention can measure impedance in some restricted access areas without interfering with system operation. Fourth, it integrates noise reduction methods, giving this invention good noise robustness. Attached Figure Description

[0050] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are 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.

[0051] Figure 1 This is a schematic diagram illustrating the principle of wideband impedance online measurement of electrical equipment according to an embodiment of the present invention.

[0052] Figure 2 This is a schematic diagram of the coupler scattering matrix measurement configuration structure according to an embodiment of the present invention;

[0053] Figure 3 This is a schematic diagram of the equivalent circuit model structure of the single coupler device according to an embodiment of the present invention;

[0054] Figure 4 This is a schematic flowchart of an online method for measuring the broadband impedance of electrical equipment based on a frequency-domain single-inductive probe according to an embodiment of the present invention.

[0055] Figure 5 This is a schematic diagram of the internal circuitry of the DUT simulated in an embodiment of the present invention;

[0056] Figure 6 This is a schematic diagram of the experimental results of an embodiment of the present invention. Detailed Implementation

[0057] 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.

[0058] 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.

[0059] Example 1

[0060] This invention provides a broadband impedance online measurement device for electrical equipment based on a frequency domain single-inductive probe configuration. Figure 1 The schematic diagram of impedance measurement is shown, consisting of a main circuit and an impedance measurement system. The main circuit comprises a power supply, cables, and a device under test (DUT), with the power supply connected to the DUT via cables. The impedance measurement system mainly consists of a signal processing unit, a vector network analyzer (VNA), and an inductive probe. The signal processing unit is connected to the VNA via a miniUSB cable, controls the VNA to measure the reflection coefficient, processes the data, and obtains the impedance Z of the DUT. DUT The VNA connects to the inductive probe via an RF cable. The VNA generates a chirp signal, which is then input to the inductive probe via the RF cable. The inductive probe is clamped to the main circuit, maintaining electrical isolation between the impedance measurement system and the main circuit, and establishing a signal coupling path between the impedance measurement system and the main circuit (equivalent to a transformer: the inductive probe is the primary side, and the cable is the secondary side. The coupling path refers to the coupling of the electrical signal from the primary side to the secondary side. The function of the coupling path is to couple the primary side signal to the secondary side. The signal coupled to the secondary side excites a disturbance in the main circuit). The chirp signal is coupled into the main circuit through the inductive probe and excites a disturbance. The disturbance response to the DUT contains information about the DUT's internal impedance; this disturbance response is called the reflection coefficient. The reflection coefficient is measured and the data is processed to obtain Z. DUT A two-port network is used to describe the inductive probe, and the following data is obtained: Figure 1 The equivalent circuit is as follows Figure 2 As shown.

[0061] Example 2

[0062] This invention also provides a method for online measurement of broadband impedance of electrical equipment based on a frequency-domain single-inductive probe configuration, comprising the following steps:

[0063] S1: Measure the first reflection coefficient Γ1. According to... Figure 1Connect the circuit and set the VNA's tracking source power, intermediate frequency bandwidth, frequency range, and number of sampling points. Then, connect the VNA's ports 1 and 2 sequentially to the Open, Short, Load, and Through calibration components to perform OSLT calibration on the VNA. Next, use the VNA to measure the overall system reflection coefficient, denoted as the first reflection coefficient Γ1, expressed as:

[0064]

[0065] In the above formula, V - and V + These represent the incident signal and the reflected signal at the inductive probe port, respectively. The overall system includes a main circuit and an inductive probe.

[0066] S2: Obtain Γ2 by de-embedding the sensing probe. Measure the scattering parameter matrix S of the sensing probe; the measurement principle is as follows... Figure 3 As shown. Clamp the inductive probe onto the inner conductor of the calibration fixture. Label the probe port and the two ports on the right and left of the calibration fixture as P1, P2, and P3, respectively. Connect P1 to port 1 of the VNA, P2 to port 2 of the VNA, and P3 to a 50Ω terminal or a short-circuit terminal. Then, use the calibrated VNA to measure the scattering parameter matrix S of the inductive probe. S is represented as follows:

[0067]

[0068] In the above formula, S 11 and S 22 To characterize the scattering parameters of return loss, S 12 and S 21 The scattering parameter is used to characterize the insertion loss. Based on the scattering parameter S 11 S 12 S 21 and S 22 The second reflection coefficient Γ2 is obtained by embedding the influence of the inductive probe into the first reflection coefficient Γ1 according to the port scattering principle. The method for obtaining the second reflection coefficient Γ2 is as follows:

[0069]

[0070] S3: Calculate the second impedance Z2. Calculate the corresponding second impedance Z2 based on the second scattering parameter Γ2. The corresponding calculation formula is:

[0071]

[0072] In the formula, Z0 represents the reference impedance, which is usually specified as 50Ω.

[0073] S4: Obtain the internal resistance Z of the power supply sChoose a known passive impedance, denoted as Z. Given Using Z Given Using the alternative cable and DUT, measure the second impedance under this configuration according to steps S1, S2, and S3, and denot it as Z2'. Then subtract Z from Z2'. Given Obtain the internal resistance Z of the power supply s as follows:

[0074] Z s =Z'2-Z Given (5)

[0075] S5: Obtain the third impedance Z3. Subtract the power supply internal resistance Z obtained in step S4 from the second impedance Z2 obtained in step S3. s The impedance at the cable input end is obtained and denoted as the third impedance Z3.

[0076] S6: Eliminate the influence of the cable on the measurement to obtain the fourth impedance Z4. The transmission parameter matrix T of the cable is given as follows:

[0077]

[0078] In the formula, γ and Z c Let l be the propagation constant, characteristic impedance, and length of the cable, respectively. Based on the transmission parameter matrix T, the third impedance Z3, and transmission line theory, the primary impedance of the device under test is derived, denoted as the fourth impedance Z4. The method for obtaining this impedance is as follows:

[0079]

[0080] S7: Primary noise reduction. A two-channel signal is formed by combining the real and imaginary parts of the fourth impedance Z4. This two-channel signal is then decomposed using multivariate variational mode decomposition (MVMD) technology. The mode update and center frequency update formulas for MVMD are as follows:

[0081]

[0082] In the above formula, c = 1, 2 represents the channel number, k = 1, 2, ... K represents the mode number, K represents the number of modes, i represents the mode number in each iteration, n represents the iteration number, α represents the bandwidth balancing parameter, and s c (ω) represents a two-channel signal. U represents the k-th mode of the c-channel signal in the (n+1)th iteration. c,i (ω) represents the i-th mode of the c-channel signal in n iterations, λ c (ω) represents the Lagrange multiplier of the c-channel, and ω represents the angular frequency. It represents the center frequency of the k-th mode in the (n+1)th iteration.

[0083] Initialize the mode as Initialize the center frequency as Then and Substituting into (8), we obtain the second iterative mode. Then Substituting into (9), we obtain the center frequency of the second iteration. Next, we will move on to the next iteration. and Substituting into (8), we obtain the mode of the third iteration. Will Substituting into (9), we obtain the center frequency of the third iteration. Repeat this iterative process until the threshold condition is met as follows:

[0084]

[0085] In the above formula, and These represent the k-th modes of the 1st and 2nd channel signals in the (n+1)th iteration, respectively. and This represents the k-th mode of the signals from channels 1 and 2 in n iterations. The mode is obtained after all iterations are completed. 1 u c,k Here, "1" indicates the first decomposition. Typically, the first mode of the channel, i.e. 1 u c,1 , represents the signal mode, and the other modes, i.e. 1 u c,k {k = 2, 3, ..., K} represents ripple and noise. Furthermore, the first mode of the first channel... 1 u 1,1 Represents the real part of the impedance, the first mode of the second channel. 1 u 2,1 Represents the imaginary part of the impedance. The first mode of the initial decomposition is retained. 1 u c,1 And eliminate the remaining modes 1 u c,k {k=2,3,…,K}, which can eliminate ripple and some noise.

[0086] S8: Advanced noise reduction. For the first mode of the first decomposition... 1 u c,1 Perform MVMD decomposition to obtain the first mode of the second decomposition. 2 u c,1 Then decompose 2 u c,1 Obtain the first mode of the third decomposition 3 u c,1Repeat this step until the error between the modes of two adjacent decompositions (N-1th and Nth) is less than the threshold ε, as shown in expression (11). Then, the first mode of the last decomposition (i.e., the Nth) is obtained as... N u c,1 .

[0087]

[0088] In the above formula N u 1,1 Let be the mode of the first channel after the Nth decomposition, and let it represent the real part of the impedance. N u 2,1 Let Z be the mode of the second channel after the Nth decomposition, representing the imaginary part of the impedance. The impedance Z of the device under test after noise reduction can be synthesized using the modes of these two channels. DUT The expression is as follows:

[0089] Z DUT = N u 1,1 +j N u 2,1 (12)

[0090] In the formula, j represents the virtual unit. The process of this invention is as follows: Figure 4 As shown.

[0091] Example 3

[0092] Experiments were conducted to verify the actual performance of the claimed invention. The internal circuitry of the DUT was simulated as follows: Figure 5 As shown, the circuit parameters are set as follows: R1 = 100Ω, R2 = 100Ω, C = 47pF. A SIGLENT SDG6052X-E arbitrary waveform generator is used to power the DUT, with parameters set to u. s =18Vpp,f s =50Hz, Z s =50Ω. The cable type is RG58, and the length is 100m. The inner diameter, outer diameter, and height of the clamp-type inductive probe are 26mm, 86mm, and 76mm, respectively, with an insertion loss of -3±1dB in the flat band. The VNA used is a Rohdeschwarz ZVH8, with a measurable frequency band of 100kHz-8 GHz. The signal processing unit is a personal computer with embedded signal processing algorithms. The measurable bandwidth depends on the VNA, the flat band of the IP, and the attenuation characteristics of the cable. Based on the above equipment specifications, the sweep frequency range of the chirp signal is determined to be 1MHz-100MHz.

[0093] Measurement results as follows Figure 6 As shown in the figure, Ref. represents the impedance measured by directly connecting the DUT to the impedance measuring instrument, which serves as the reference value for the impedance measurement in this invention. From Figure 6 As can be seen, although the overall frequency variation pattern of the impedance Z4 obtained through steps S1 to S6 matches the reference impedance, a large amount of noise and significant ripple obscure the true impedance of the DUT. The impedance Z4 after noise reduction... DUT Within the range of 1MHz to 100MHz, the amplitude and phase of the results are in good agreement with the reference values, and the experimental results verify the effectiveness of the present invention.

[0094] 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 online measurement of broadband impedance of electrical equipment based on a frequency-domain single-inductive probe configuration, characterized in that, The method employs an online wideband impedance measurement device for electrical equipment based on a frequency-domain single-inductive probe configuration. The device includes a main circuit and an impedance measurement system. The main circuit consists of a power supply, cables, and a DUT (Device Under Test). The power supply is connected to the DUT via a cable; The impedance measurement system consists of a VNA, an inductive probe, and a signal processing unit, wherein the VNA is a vector network analyzer; The VNA connects to the sensing probe via an RF cable to generate a Chirp signal, which is then input to the sensing probe via the RF cable. The inductive probe is clamped onto the main circuit to maintain electrical isolation between the impedance measurement system and the main circuit, and to establish a signal coupling path between the impedance measurement system and the main circuit, so that the chirp signal is coupled into the main circuit through the inductive probe and excites disturbances to obtain the reflection coefficient of the DUT. The signal processing unit connects to the VNA via a miniUSB cable to control the VNA to measure the reflection coefficient of the DUT, capture and process the measured data, and extract the impedance of the DUT. Z DUT ; A method for performing wideband impedance online measurement of electrical equipment using the aforementioned device includes: S1: Measure the first reflection coefficient Γ1 using a calibrated vector network analyzer; S2: Measure the S-matrix of the sensing probe. Based on the S-matrix and the port scattering principle, the influence of the sensing probe is embedded from the first reflection coefficient Γ1 to obtain the second reflection coefficient Γ2. S3: Calculate the corresponding second impedance Z2 based on the second reflection coefficient Γ2; S4: Using known passive impedance Z Given Replace the cable and DUT, measure the second impedance Z2' in this configuration, and subtract the second impedance Z2' from the DUT. Z Given Obtain the internal resistance of the power supply Z s ; S5: Subtract the obtained power supply internal resistance from the obtained second impedance Z2. Z s Obtain the impedance at the cable input end, denoted as the third impedance. Z 3; S6: Based on the cable T-matrix and the third impedance Z 3. Using transmission line theory, we obtain the primary impedance of the device under test, denoted as the fourth impedance. Z 4; S7: Take the fourth impedance Z The real and imaginary parts of 4 form a two-channel signal. This two-channel signal is decomposed into modes using multivariate variational mode decomposition (MVMD) technology. Preserve signal modes ; S8: For signal modes Continue performing MVMD decomposition until the error threshold is met, then output the first... N The signal modes obtained after the second decomposition Using signal modes The impedance of the device under test after noise reduction.

2. The method according to claim 1, characterized in that, Methods for measuring the S-matrix of an inductive probe include: Clamp the inductive probe onto the inner conductor of the calibration fixture. Label the probe port and the two ports on the right and left of the calibration fixture as P1, P2, and P3, respectively. Connect P1 to port 1 of the VNA, connect P2 to port 2 of the VNA, and connect P3 to a 50 Ω terminal or a short-circuit terminal. Then, use the calibrated VNA to measure the scattering parameter matrix S of the inductive probe.

3. The method according to claim 2, characterized in that, Based on the S-matrix and the port scattering principle, methods for obtaining the second reflection coefficient Γ2 by removing the influence of the inductive probe from the first reflection coefficient Γ1 include: Based on scattering parameters S 11 , S 12 , S 21 and S 22 Based on the port scattering principle, the influence of the inductive probe is embedded from the first reflection coefficient Γ1 to obtain the second reflection coefficient Γ2, as shown below: 。 4. The method according to claim 1, characterized in that, Methods for calculating the corresponding second impedance Z2 based on the second reflection coefficient Γ2 include: ； In the formula, Z 0 represents the reference impedance.

5. The method according to claim 1, characterized in that, The cable T matrix is: ； In the formula, γ , Z c and l These are the cable's propagation constant, characteristic impedance, and length, respectively. Based on the cable T-matrix and the third impedance Z 3. Using transmission line theory, we obtain the primary impedance of the device under test, denoted as the fourth impedance. Z Method 4 includes: ； In the formula, Z 3 represents the third impedance.

6. The method according to claim 1, characterized in that, Take the fourth impedance Z The real and imaginary parts of 4 form a two-channel signal. This two-channel signal is decomposed into modes using multivariate variational mode decomposition (MVMD) technology. Preserve signal modes The methods include: The formulas for mode update and center frequency update in multivariate variational mode decomposition (MVMD) are as follows: ； ； In the formula, c = 1, 2 represent channel numbers, k = 1, 2, ⋯ K Indicates the modal number. K Represents the number of modes. i This represents the modal index in each iteration. n Indicates the iteration number. λ Represents the Lagrange multipliers. α This represents the bandwidth balancing parameter. s c ( ω ) represents a two-channel signal. This indicates that in n + 1 iterations c The first channel signal k One modality, In n iterations c The first channel signal i One modality, λ c ( ω )express c The Lagrange multipliers of the channel, ω Represents angular frequency. This indicates the nth iteration in the (n+1)th iteration. k The center frequency of each mode; Decomposition yields modes "1" indicates the first decomposition. The signal mode is represented by the main signal mode, while the other modes represent ripple and noise. The main signal mode is retained. And eliminate the remaining modes.

7. The method according to claim 1, characterized in that, For signal modes Continue performing MVMD decomposition until the error threshold is met. The error threshold is: ； In the formula, For the first N The mode of the first channel after the decomposition represents the real part of the impedance; For the first N The mode of the second channel after the second decomposition represents the imaginary part of the impedance; based on and Impedance of the device under test after noise reduction Z DUT The expression is: ； In the formula, j Indicates a virtual unit.

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