A method for quickly detecting the open circuit position of an inductor based on non-destructive testing

Abstract

The application relates to the technical field of nondestructive testing, and discloses a method for quickly detecting a circuit breaking position of an inductor based on nondestructive testing, which comprises the following steps: obtaining the internal three-dimensional structure of the inductor by using a micro-focus X-ray computed tomography technology, extracting the winding conductive path and the insulation distance distribution, and calculating the capacitance distribution center according to the equivalent capacitance weight distributed along the path; performing wideband sweep frequency measurement on the inductor, positioning the first anti-resonance frequency point after the self-resonance frequency, fitting the local response near the frequency point by using an asymmetric resonance model, and extracting a resonance phase factor; constructing a phase propagation coefficient based on the measured low-frequency inductance and total parasitic capacitance, establishing the position correlation between the resonance phase factor and the capacitance distribution center, converting the resonance phase factor into an electric length offset relative to the capacitance distribution center, and then solving and mapping to obtain the three-dimensional geometric coordinates of the circuit breaking point along the winding conductive path.

Description

Technical Field

[0001] This invention relates to the field of nondestructive testing technology, and more specifically, to a method for rapid detection of open circuit location in an inductor based on nondestructive testing. Background Technology

[0002] Inductors, as fundamental components in electronic circuits, are widely used in power management, signal filtering, and energy storage modules. During manufacturing or long-term service, inductors are prone to open-circuit failures due to mechanical stress, thermal shock, or material defects. For high-reliability applications, failure analysis requires not only determining whether the device is damaged, but also precisely locating the specific location of the open circuit (such as at the pin, inner or outer layer of the winding) in order to analyze the failure mechanism and improve the process.

[0003] Current inductor open circuit detection technologies are mainly divided into two categories: destructive testing and non-destructive testing.

[0004] Destructive testing typically involves slicing and grinding or chemically decapsulating the device to expose its internal structure layer by layer in order to locate breakpoints. While this method is intuitive, it completely destroys the sample under test, making subsequent verification impossible. Furthermore, the process is extremely time-consuming, making it unsuitable for the needs of batch or rapid analysis.

[0005] Non-destructive inductive testing techniques currently mainly include X-ray fluoroscopy and electrical parameter measurement.

[0006] While conventional X-ray fluoroscopy or two-dimensional imaging can observe internal structures, it is often difficult to directly identify microcracks or breaks hidden deep within multilayer windings due to limitations in resolution and occlusion effects.

[0007] Traditional electrical parameter measurements (such as using an LCR meter) can only determine whether a device is open-circuited by measuring DC resistance or inductance, and cannot provide information on the location of the break. Time domain reflection (TDR) technology is often used to locate breaks in long cables, but the winding length of inductors is relatively short and there is a severe dispersion effect, resulting in insufficient spatial resolution of TDR technology, making it difficult to apply to internal location at the device level.

[0008] Existing methods based on frequency domain impedance analysis attempt to deduce the location of the breakpoint by observing the resonance peaks on the impedance spectrum. However, current techniques typically treat the inductor as a simple lumped parameter model, neglecting the non-uniformity of parasitic capacitance distribution along the path in multi-layered, interleaved winding structures. Furthermore, background parameters introduced by the test fixture and external environment often overwhelm the weak open-circuit response signal, leading to distortion of the extracted resonance parameters. Summary of the Invention

[0009] This invention provides a rapid detection method for the open circuit location of an inductor based on non-destructive testing, which solves the technical problems mentioned in the background art.

[0010] This invention provides a rapid method for detecting the open circuit location of an inductor based on non-destructive testing, comprising: The internal three-dimensional structure of the inductor under test is obtained by microfocus X-ray computed tomography, the winding conduction path and the insulation distance distribution of the winding to the reference substrate are extracted, and the capacitance distribution center is calculated based on the equivalent capacitance weight distributed along the winding conduction path. Broadband electrical measurements are performed on the inductor under test to obtain the complex impedance spectrum, the first anti-resonance frequency after the self-resonance frequency is located, and the local response within a preset range of the first anti-resonance frequency is fitted using an asymmetric resonance model to extract the resonance phase factor characterizing the asymmetry of the spectral waveform. Based on the measured low-frequency inductance, total parasitic capacitance, and total winding geometry, a phase propagation coefficient characterizing the propagation characteristics of high-frequency fluctuations is constructed. The positional relationship between the resonant phase factor and the center of the capacitance distribution is established. The resonant phase factor is converted into an electrical length offset relative to the center of the capacitance distribution, and then the geometric position of the break point along the conductive path of the winding is obtained.

[0011] The beneficial effects of this invention are as follows: By integrating microfocus X-ray computed tomography and broadband impedance spectroscopy, it overcomes the shortcomings of traditional destructive testing, which cannot preserve samples, and conventional electrical testing, which can only determine continuity but not location. This invention utilizes internal structural data to establish the capacitance distribution center, using it as the absolute reference for position calculation. Combined with the resonant phase factor in the frequency domain response, which is highly sensitive to structural changes, it eliminates the interference of the testing environment and device structural inhomogeneities on detection accuracy. This enables rapid and accurate quantification and location of the three-dimensional spatial position of the inductor's internal winding breakpoint without damaging the device's integrity, significantly improving the efficiency and accuracy of failure analysis. Attached Figure Description

[0012] Figure 1 This is a flowchart of a rapid detection method for the open circuit location of an inductor based on non-destructive testing according to the present invention; Figure 2 This is a schematic diagram illustrating a specific implementation of the present invention. Detailed Implementation

[0013] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, features described in some examples may be combined in other examples.

[0014] It should be noted that, unless otherwise defined, the technical or scientific terms used in one or more embodiments of the present invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in one or more embodiments of the present invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" indicate that the element or object preceding the term encompasses the elements or objects listed following the term and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0015] like Figure 1 As shown, a rapid detection method for the open circuit location of an inductor based on non-destructive testing includes: The internal three-dimensional structure of the inductor under test is obtained by microfocus X-ray computed tomography, the winding conduction path and the insulation distance distribution of the winding to the reference substrate are extracted, and the capacitance distribution center is calculated based on the equivalent capacitance weight distributed along the winding conduction path. Broadband electrical measurements are performed on the inductor under test to obtain the complex impedance spectrum, the first anti-resonance frequency after the self-resonance frequency is located, and the local response within a preset range of the first anti-resonance frequency is fitted using an asymmetric resonance model to extract the resonance phase factor characterizing the asymmetry of the spectral waveform. Based on the measured low-frequency inductance, total parasitic capacitance, and total winding geometry, a phase propagation coefficient characterizing the propagation characteristics of high-frequency fluctuations is constructed. The positional relationship between the resonant phase factor and the center of the capacitance distribution is established. The resonant phase factor is converted into an electrical length offset relative to the center of the capacitance distribution, and then the geometric position of the break point along the conductive path of the winding is obtained.

[0016] Preferably, the internal three-dimensional structure of the inductor under test is obtained using microfocus X-ray computed tomography (CT) technology, and the winding conductive path and the insulation distance distribution between the winding and the reference substrate are extracted, including: The inductor under test is scanned and reconstructed to obtain three-dimensional voxel grayscale data. Normalized grayscale data is obtained by performing normalization processing. : in, Represents three-dimensional spatial coordinates. and These are the minimum and maximum grayscale values ​​of the data, respectively. Based on a preset winding segmentation threshold and reference matrix segmentation threshold Identify the physical region of the winding and reference matrix region : right The centerline is extracted using a 3D skeleton refinement algorithm, resulting in an ordered sequence of points composed of discrete voxel nodes. As the conductive path of the winding, For node indexing; Calculate the first [number] on the conductive path of the winding. Each node to the reference matrix region Shortest Euclidean distance As the insulation distance distribution: in, To meet The set of all reference matrix voxel coordinates, This represents the Euclidean distance norm.

[0017] Three-dimensional voxel grayscale data is three-dimensional pixel-level grayscale information that reflects the density distribution of materials inside an inductor. It can be acquired by combining microfocus X-ray computed tomography with three-dimensional back projection reconstruction technology.

[0018] The minimum gray value is the minimum gray value of all pixels in the three-dimensional voxel gray data.

[0019] The maximum gray value is the maximum gray value of all pixels in the three-dimensional voxel gray data.

[0020] Normalized grayscale data is grayscale information obtained by linearly mapping three-dimensional voxel grayscale data to a specified range.

[0021] The winding segmentation threshold is a grayscale critical value used to distinguish the winding entity region from the normalized grayscale data. It is preferably 0.78 because the grayscale value of the copper winding material in the normalized grayscale domain is significantly higher than that of other materials. This value can effectively separate the copper winding from other regions.

[0022] The reference substrate segmentation threshold is a grayscale critical value used to distinguish the reference substrate region from the normalized grayscale data. It is preferably 0.45 because the grayscale values ​​of reference substrate materials such as magnetic core, magnetic resin, and external shielding layer in the normalized grayscale domain are between the winding and air. This value can accurately divide the reference substrate from other regions.

[0023] The winding entity region is a high-density region in the three-dimensional voxel grayscale data with a grayscale value not lower than the winding segmentation threshold, corresponding to the copper winding structure inside the inductor.

[0024] The reference substrate region is a medium-density region in the three-dimensional voxel grayscale data whose grayscale values ​​are between the reference substrate segmentation threshold and the winding segmentation threshold, and includes the magnetic core, magnetic resin and external shielding layer.

[0025] The winding conduction path voxel point array is an ordered set of voxel points that maintains the original connectivity and has the width of a single voxel after the three-dimensional skeleton of the winding solid region is refined.

[0026] The reference matrix voxel coordinate set is the set of spatial coordinates of all voxel points that satisfy the definition of the reference matrix region.

[0027] The insulation distance is the shortest spatial geometric distance from each voxel point on the winding conductive path to the boundary of the reference matrix region.

[0028] The node index is a sequence number used to identify the order of each voxel point on the winding conductive path.

[0029] To address the segmentation of inductor windings from the reference substrate, considering that the material density of the copper windings in the inductor is much higher than that of the magnetic core and magnetic resin reference substrate, resulting in significantly higher grayscale values ​​in CT scan grayscale data, this approach uses two different segmentation thresholds to identify the high-density copper windings and the medium-density reference substrate. This allows for precise separation of the two core structural regions, preventing confusion between different material regions that could lead to errors in subsequent path extraction and distance calculation. For example, in a power inductor, the copper windings typically have grayscale values ​​above 0.8 in normalized grayscale data, while the reference substrate's values ​​are between 0.4 and 0.7. Setting thresholds of 0.78 and 0.45 accurately distinguishes between the two regions.

[0030] The 3D skeleton refinement algorithm includes: employing a 3D skeleton extraction algorithm based on average outward flux, which iteratively calculates the average outward flux of each voxel in the winding entity region, gradually removing edge voxels while preserving the width curves of centrally connected voxels. During the iteration process, strict control is maintained to ensure that only non-critical edge voxels are removed each time, guaranteeing that the connectivity features of the winding, such as the helical structure and inter-layer connections, are not disrupted. For example, after refinement, a helical winding can still retain the complete connectivity of the helical path, accurately reflecting the actual conductive path.

[0031] The optimization of the 3D distance transformation algorithm includes: adopting the Euclidean distance transformation algorithm to directly calculate the straight-line distance from each voxel point on the winding's conductive path to all voxel points on the boundary of the reference substrate region, and taking the minimum value as the insulation distance. This algorithm avoids the path bending error that may be introduced by other distance calculation methods such as Manhattan distance, ensuring that the insulation distance can accurately reflect the coupling distance between the winding and the reference substrate. For example, if the straight-line distance from a voxel point to the reference substrate boundary is 20 micrometers, and the bending distance is 30 micrometers, the Euclidean distance transformation directly takes 20 micrometers as the insulation distance.

[0032] The sorting of the winding conduction path includes: first, identifying the metal pad areas at both ends of the inductor in the CT volume data; by calculating the geometric center coordinates of the pads, defining the endpoints closest to the center of the two pads as the first terminal and the last terminal respectively in the endpoints of the skeleton curve; and then sequentially numbering all voxel points along the skeleton curve from the first terminal to the last terminal to ensure that the obtained winding conduction path is completely consistent with the actual current flow path.

[0033] The target range for linear normalization of voxel data is between 0 and 1. Specifically, it involves subtracting the minimum gray value of the 3D voxel gray value from the original gray value of each voxel, and then dividing by the difference between the maximum and minimum gray values ​​to achieve a unified mapping of all gray values.

[0034] The three-dimensional skeleton refinement algorithm includes: adopting a skeleton extraction algorithm based on average outward flux, setting the number of iterations to 20, using a 3×3×3 voxel cube as the structuring element in each iteration, and terminating the iteration when the number of voxels in the skeleton curve no longer changes and connectivity is maintained.

[0035] The three-dimensional distance transformation includes: the search step size is set to 1 voxel, and the actual physical size is determined by the voxel size of the CT scan. For example, when the voxel size is 5 micrometers, the search step size is 5 micrometers; the accuracy is controlled within 1 micrometer. The voxel data is first filtered by 3×3×3 median to remove noise interference before the distance is calculated, so as to avoid distance errors caused by noise.

[0036] The determination of the winding start and end points includes: In the CT volume data, the metal pad areas at both ends of the device have high material density and grayscale values ​​close to the winding grayscale values. Through connectivity analysis, the metal areas connected to the winding solid area are found, which are the pad areas; the average coordinates of all voxel points in the pad area are calculated to obtain the geometric center of the pad; among the endpoints of the skeleton curve, the endpoints closest to the centers of the two pads are found respectively, and are designated as the start terminal and end point in turn.

[0037] Preferably, calculating the capacitance distribution center based on the equivalent capacitance weights distributed along the conductive path of the winding includes: For the first winding conductive path Individual points, extract their local traverse radius and path differential length And calculate the equivalent coupling surface area. : Determine the relative permittivity at this voxel point. ; Based on vacuum dielectric constant and the corresponding insulation distance in the insulation distance distribution Calculate the equivalent capacitance weight of the voxel point. : Determine the path arc length coordinates of the voxel point. ; Calculate the center of capacitance distribution : in, This represents the summation of all voxel points along the conductive path of the winding.

[0038] The local conductor radius is extracted from the internal distance field of the winding entity region and represents the thickness of the conductor at the corresponding voxel point on the winding conduction path.

[0039] The path differential length is the length of each segment after the winding conductive path is divided according to a preset rule.

[0040] The equivalent coupling surface area is calculated using the formula for the side area of ​​a cylinder, based on the local conductor radius and the differential length of the path. It is an area parameter that characterizes the capacitive coupling capability between the winding and the reference substrate.

[0041] The medium type is determined based on the gray value of the neighborhood around the voxel point, indicating the type of insulating medium at the location of the voxel point.

[0042] The relative permittivity is a physical quantity that characterizes the polarization properties of a dielectric. It is preferably 3.6 for resin, 4.2 for FR-4 substrate, and 10 for magnetic core, because the typical dielectric constant range of these materials in the inductor's operating frequency band can accurately reflect the influence of the dielectric on the capacitance.

[0043] The vacuum dielectric constant is the dielectric constant in a vacuum. It is a fixed physical constant with a value of approximately 8.85 × 10^-12 farads per meter.

[0044] The equivalent capacitance weight is a weight value that is calculated by combining the vacuum dielectric constant, relative dielectric constant, equivalent coupling surface area, and insulation distance, and characterizes the degree of contribution of parasitic capacitance at the corresponding voxel point.

[0045] The path arc length coordinate is the cumulative arc length value of a voxel point along the conductive path of the winding relative to the starting point of the path.

[0046] The center of capacitance distribution is obtained by weighting the corresponding path arc length coordinates using the equivalent capacitance weights of all voxel points, and it represents the path arc length position of the center of parasitic capacitance distribution of the winding.

[0047] The correlation model between the internal distance field and the local conductor radius includes: the internal distance field of the winding body region is calculated using the Euclidean distance field, and the distance field value of each voxel point represents the shortest distance from that point to the winding boundary. Since the winding cross-section is approximately circular, this distance field value is exactly equal to the local conductor radius at the corresponding location, realizing the mapping from structural data to electrical parameters. For example, if the distance field value of a voxel point is 20 micrometers, its corresponding local conductor radius is also 20 micrometers, without the need for additional conductor size measurement.

[0048] The medium type is determined based on neighborhood grayscale values. This involves selecting a 3×3×3 neighborhood around a voxel and statistically analyzing the grayscale distribution of all voxels within this range. If the grayscale values ​​within the neighborhood are concentrated between 0.3 and 0.5, it is identified as a resin medium; if concentrated between 0.5 and 0.7, it is identified as an FR-4 substrate; and if concentrated between 0.2 and 0.4, it is identified as a magnetic core medium. This logic distinguishes the medium type through local grayscale distribution characteristics, avoiding misjudgment based on a single grayscale value. For example, if a voxel has a grayscale value of 0.43, but most of its neighboring voxels have grayscale values ​​around 0.32, it is identified as a magnetic core medium.

[0049] The calculation model for equivalent capacitance weight is constructed as follows: the capacitance is directly proportional to the dielectric constant and the coupling area, and inversely proportional to the plate spacing. The winding and the reference substrate are considered as the two plates of a capacitor, the equivalent coupling surface area is the plate area, and the insulation distance is the plate spacing. Combining the vacuum dielectric constant and the relative dielectric constant, an equivalent capacitance weight calculation model is constructed so that the weight value accurately reflects the actual size of the parasitic capacitance at the voxel point. For example, for two voxel points with identical parameters, but with insulation distances of 10 micrometers and 20 micrometers respectively, the equivalent capacitance weight of the former is twice that of the latter.

[0050] The weighted average calculation of the capacitance distribution center takes into account the non-uniform distribution of parasitic capacitance along the winding, requiring the capacitance distribution center to reflect the differences in capacitance contribution at different locations. Using the equivalent capacitance weight as a weighting factor, the arc length coordinates of the path are weighted and averaged to ensure that locations with greater capacitance contribution have a higher proportion in the center calculation. For example, if the total equivalent capacitance weight for the first half of the winding is 100, with an average arc length of 50 mm; and the total weight for the second half is 200, with an average arc length of 100 mm, then the capacitance distribution center is (100×50+200×100)÷(100+200)=83.33 mm, which is closer to the densely populated capacitance area.

[0051] The calculation of the internal distance field includes: using the Euclidean distance transformation algorithm, taking the binary data of the winding entity region as input, traversing each voxel point, calculating the straight-line distance from the point to all voxel points of the winding boundary, taking the minimum value as the distance field value of the point, and controlling the calculation accuracy within 0.1 micrometers.

[0052] The preset material property table lists the relative permittivity of common dielectric materials in inductors, including epoxy resin 3.6, FR-4 substrate 4.2, ferrite core 10, air 1.0, and magnetic resin 5.0, covering the dielectric types of most inductors, and can be directly called up.

[0053] The path differential length is divided into the following methods: dividing at fixed length intervals, with the path differential length uniformly set to 5 micrometers. If the remaining length at the end of the winding conductive path is less than 5 micrometers, the actual length is used as the differential length of the last segment to ensure that the division rules are consistent and the calculation results are repeatable.

[0054] The starting point for accumulating the path arc length coordinates includes: being completely aligned with the first terminal of the winding conductive path, i.e., the path arc length coordinate of the voxel point corresponding to the first terminal is 0. The differential lengths of each segment are accumulated sequentially along the conductive path to obtain the arc length coordinates of subsequent voxel points.

[0055] The weighted average calculation includes: using 64-bit floating-point arithmetic to perform weighted summation and division operations, retaining four decimal places in the result, and using the rounding rule to avoid deviation in the calculation of the capacitance distribution center due to insufficient numerical precision.

[0056] Preferably, performing broadband electrical measurements on the inductor under test to obtain a complex impedance spectrum includes: The original scattering parameters were measured using a vector network analyzer and test fixture, and the intrinsic complex impedance spectrum of the inductor under test was obtained through de-embedding processing. ,in For testing frequency; Select the preset low-frequency detection frequency Calculate the low-frequency inductance. : in, This indicates taking the imaginary part of a complex number; The self-resonant frequency is determined by searching for the point of maximum impedance magnitude in the complex impedance spectrum. : in, This represents the value of the independent variable that maximizes the function value. This is the impedance magnitude; Calculate the total parasitic capacitance : The raw scattering parameters are obtained by the vector network analyzer through the test fixture to measure the inductor under test. These parameters reflect the electromagnetic energy scattering characteristics of the device port and can be acquired by the one-port sweep frequency measurement function of the vector network analyzer.

[0057] The test frequency is a series of continuous or discrete frequency values ​​covered in broadband sweep frequency measurement, which can be acquired through the frequency setting function of a vector network analyzer.

[0058] The intrinsic complex impedance spectrum is a curve that reflects the change of complex impedance with frequency, showing only the impedance characteristics of the inductor under test after removing the parasitic effects of the test fixture.

[0059] The low-frequency detection frequency is selected in the low-frequency range of the complex impedance spectrum and is a specific frequency used to calculate the low-frequency inductance. It is preferably 1 MHz because this frequency is much lower than the self-resonant frequency of most inductors, which can effectively avoid the interference of high-frequency parasitic parameters on the inductance measurement.

[0060] Low-frequency inductance is calculated based on the ratio of the imaginary part of the impedance to the angular frequency at the low-frequency detection frequency, and it reflects the inductance characteristics of the inductor in the low-frequency range.

[0061] The self-resonant frequency is the frequency at which the impedance magnitude in the complex impedance spectrum reaches its global maximum value.

[0062] Total parasitic capacitance is calculated based on the principle of LC parallel resonance using the self-resonant frequency and low-frequency inductance, reflecting the total parasitic capacitance inside the inductor.

[0063] The de-embedding algorithm for inductors includes a combined scheme of SOLT calibration and 2x-Thru de-embedding. First, a measurement baseline is established through short-circuit and open-circuit load calibration. Then, the 2x-Thru standard component (containing no inductor) is measured to extract the scattering parameter model of a single-sided fixture. Finally, fixture parasitics are removed from the total measurement data through inverse network parameter calculation. This design specifically addresses the additional inductive and capacitive interference introduced by the fixture in high-frequency inductor measurements. For example, a fixture may introduce a 1 picofarad parasitic capacitance at 10 MHz; de-embedding can remove this from the measurement results, ensuring the authenticity of the intrinsic complex impedance spectrum.

[0064] The selection of the low-frequency detection frequency includes: considering the common application frequency bands of inductors and the influence range of parasitic parameters, choosing 1 MHz as the default low-frequency detection frequency. At this frequency, the impedance characteristics of the inductor are mainly dominated by inductance, and the capacitive reactance of parasitic capacitance is much greater than that of inductive reactance, and will not significantly affect the inductance calculation. For example, if the self-resonant frequency of an inductor is 18 MHz, at 1 MHz the capacitive reactance is approximately 8.8 kΩ and the inductive reactance is approximately 29.5 Ω. The influence of capacitive reactance is negligible, and the measurement results are more accurate.

[0065] The calculation of low-frequency inductance involves considering that the imaginary part of the complex impedance in the low-frequency range is primarily contributed by inductance, with minimal influence from capacitance and resistance. By extracting the imaginary part of the impedance at this frequency and dividing it by the corresponding angular frequency (i.e., 2 multiplied by pi and the test frequency), the low-frequency inductance can be directly obtained. This logic eliminates the coupling effects of parasitic parameters at high frequencies. For example, an inductor with an imaginary impedance of 185 ohms at 1 MHz and an angular frequency of 6.28 × 10^6 radians per second calculates to an inductance of approximately 29.5 microhenries, consistent with actual low-frequency inductor characteristics.

[0066] Total parasitic capacitance includes the following: At the self-resonant frequency, the inductive reactance of the inductor and the capacitive reactance of the parasitic capacitance cancel each other out, and the impedance magnitude reaches its maximum, satisfying the LC parallel resonance condition. By working backward from this condition, the total parasitic capacitance equals 1 divided by 4, multiplied by the square of pi, multiplied by the square of the self-resonant frequency, and then multiplied by the low-frequency inductance. For example, if an inductor has a self-resonant frequency of 18 MHz and a low-frequency inductance of 4.7 μH, the calculated total parasitic capacitance is approximately 16.6 picofarads, which matches the actual total parasitic capacitance.

[0067] The three de-embedding algorithms include: a scheme using SOLT calibration plus 2x-Thru de-embedding. SOLT calibration uses standard short-circuit, open-circuit, and load components to calibrate at the test fixture port and establish a measurement reference surface; 2x-Thru de-embedding measures the scattering parameters of the fixture's through-structure, obtains a single-sided fixture model by symmetrical prior cutting, and then removes fixture parasites from the total measurement data through inverse operations of the network chain parameters, i.e., the ABCD parameters.

[0068] Wideband frequency sweep includes: the sweep range is set from 1 kHz to 100 MHz, covering the low-frequency operating range and self-resonant frequency range of most power inductors; the number of sampling points is 5000, which are evenly distributed logarithmically to ensure sufficient sampling density in both low-frequency and high-frequency bands and avoid missing key frequency points.

[0069] Noise suppression of the imaginary part of impedance includes: using the Savitzky-Golay smoothing filtering algorithm with a filter window length of 21 points and a polynomial order of 3 to smooth the collected imaginary part impedance data, removing fluctuations caused by random noise and ensuring the stability of inductance calculation. For example, if a set of original data fluctuates by ±5 ohms due to noise, the fluctuation amplitude is reduced to within ±0.5 ohms after filtering.

[0070] The threshold for determining the self-resonant frequency includes: setting a local extremum determination condition where the impedance magnitude at a certain frequency point is greater than the impedance magnitudes of the 10 adjacent frequency points before and after it, and the ratio of this magnitude to the average impedance magnitude over the entire frequency sweep range is greater than 5. This threshold can effectively distinguish between global maximum values ​​and local small peak values, avoiding misjudgment of the self-resonant frequency.

[0071] Preferably, the first anti-resonance frequency after the self-resonance frequency is located, and the local response within a preset range of the first anti-resonance frequency is fitted using an asymmetric resonance model to extract the resonance phase factor characterizing the asymmetry of the spectral waveform, including: The intrinsic complex impedance spectrum Searching for frequencies greater than the self-resonant frequency The first local minimum value is used to determine the first anti-resonant frequency. : Calculate complex admittance spectrum ,in At the angular frequency corresponding to the first anti-resonance frequency Within the preset frequency window centered on the data, fit the background channel admittance. And calculate the resonance residual admittance. : in, These are the fitting complex coefficients; Construct a complex Fano resonance model and determine the resonance residual admittance. Perform least-squares fitting to extract Fano asymmetric parameters. : in, For complex amplitude, For normalized detuning, For line width parameters, The imaginary unit; Calculate the resonance phase factor : in, This indicates taking the principal argument of a complex number.

[0072] The first anti-resonance frequency is the detection frequency corresponding to the first local minimum point of the impedance magnitude that appears after the self-resonance frequency in the intrinsic complex impedance spectrum.

[0073] Angular frequency is a frequency-related physical quantity obtained by multiplying the test frequency by twice pi.

[0074] The complex admittance spectrum is the reciprocal of the intrinsic complex impedance spectrum, and is a complex curve reflecting the change of inductor port admittance with angular frequency.

[0075] The anti-resonant angular frequency is a physical quantity obtained by multiplying the first anti-resonant frequency by twice the value of pi.

[0076] The preset frequency window range is the frequency range centered on the anti-resonance angular frequency, preferably with a relative bandwidth of 15%, because this bandwidth can completely cover the resonant response near the anti-resonance, while avoiding irrelevant frequency components from interfering with the fitting results.

[0077] The background channel admittance is the non-resonant admittance signal obtained by fitting a complex polynomial within a preset frequency window.

[0078] The fitting complex coefficients are complex coefficients obtained when fitting the background channel admittance using a complex polynomial, including constant, linear, and quadratic terms.

[0079] The resonant residual admittance is the admittance signal obtained by subtracting the background channel admittance from the complex admittance spectrum, and contains only the resonant component.

[0080] Complex amplitude is a complex parameter in the complex Fano resonance model that characterizes the intensity of the resonant signal.

[0081] Normalized detuning is a physical quantity that normalizes the difference between the angular frequency and the anti-resonant angular frequency, and is used to unify the degree of detuning at different frequencies.

[0082] The linewidth parameter is a parameter in the complex Fano resonance model that characterizes the width of the resonance peak, reflecting the sharpness and dissipation of the resonance.

[0083] The Fano asymmetry parameter is a complex parameter in the complex Fano resonance model that characterizes the degree of asymmetry of spectral lines.

[0084] The resonance phase factor is twice the argument of the complex function of the difference between the Fano asymmetry parameter and the imaginary unit, and it characterizes the phase feature of the asymmetry of the spectral waveform.

[0085] The determination of the first anti-resonant frequency includes: using local extremum search logic, a certain frequency point must satisfy the following condition: its impedance magnitude is less than the magnitudes of the preceding and following 10 frequency points, and the ratio of this magnitude to the impedance magnitude at the self-resonant frequency is less than 0.3. This standard can effectively distinguish between anti-resonance and small fluctuations caused by random noise. For example, if an inductor has a self-resonant frequency of 18 MHz, and its impedance magnitude at a subsequent frequency point is 0.25 of that at the self-resonant frequency, and is less than the magnitudes of the preceding and following points, it is determined to be the first anti-resonant frequency.

[0086] The model selection for complex polynomial fitting of background admittance is based on the following: the background admittance within the anti-resonant frequency window varies gradually with frequency, and a complex quadratic polynomial can accurately fit this smooth trend while avoiding overfitting by higher-order polynomials. During fitting, the real and imaginary parts of the admittance are treated separately, each using a quadratic polynomial to ensure the integrity of background stripping. For example, within a certain frequency window, the real part of the background admittance increases linearly with frequency, while the imaginary part exhibits a quadratic curve variation; fitting them separately allows for matching of these two types of variation characteristics.

[0087] The construction of the complex Fano resonance model includes: the resonant response of the inductor after circuit breaking is the result of interference between the continuous background channel and the discrete resonant channel, and the complex Fano model can precisely describe this asymmetric resonance characteristic. The normalized detuning quantity unifies the detuning at different frequencies, the Fano asymmetric parameter characterizes the relationship between interference intensity and phase, and the linewidth parameter reflects the resonance dissipation. The combination of these three parameters achieves accurate fitting of the resonance residual admittance. For example, if a certain resonance residual admittance exhibits an asymmetric curve that is steep on the left and gentle on the right, its shape can be completely reproduced through this model.

[0088] The mapping of the resonance phase factor includes: the Fano asymmetric parameter contains relative phase information between the resonance and the background; the argument of its difference from the imaginary unit can extract this phase relationship; multiplying by 2 can amplify the phase difference, facilitating subsequent position calculation. This mapping relationship is based on the intrinsic correlation between phase and asymmetric parameters in spectroscopy. For example, when the Fano asymmetric parameter is 0.35 plus 0.62 times the imaginary unit, the calculated resonance phase factor can accurately reflect the phase shift caused by the break point.

[0089] The preset frequency window includes: with the anti-resonance angular frequency as the center, the left frequency band is the anti-resonance angular frequency multiplied by 0.85, and the right frequency band is the anti-resonance angular frequency multiplied by 1.15, that is, a relative bandwidth of 15%, to ensure coverage of the complete resonance response before and after anti-resonance, while avoiding the introduction of too many irrelevant frequency components.

[0090] Complex polynomial fitting includes: fitting the real and imaginary parts of the background channel admittance separately, each using a quadratic polynomial model, and solving for the fitting coefficients using the least squares method. The fitting data is taken from the data on both sides of the frequency window, excluding the central 50% frequency band, to avoid resonance components interfering with the background fitting. For example, if the total width of the frequency window is 10 MHz, only the data within the 2.5 MHz range on both sides are used for fitting.

[0091] The parameters for least-squares iterative fitting include: a maximum number of iterations of 200, a convergence threshold of less than 1e-9 for the relative change in fitting error, and the stopping of fitting when the number of iterations reaches the upper limit or the error meets the convergence threshold. The initial values ​​of the fitting variables are set as follows: the complex amplitude is the value of the resonant residual admittance at the anti-resonant angular frequency; the Fano asymmetry parameter is 1 plus 0 times the imaginary unit; and the linewidth parameter is 8% of the anti-resonant angular frequency.

[0092] The initial values ​​of the Fano asymmetric parameters include: a fixed initial value of 1 plus 0 times the imaginary unit. This initial value is within the parameter distribution range of most real-world scenarios, which can accelerate the fitting convergence speed and avoid fitting divergence caused by improper initial values.

[0093] The preprocessing of the resonance residual admittance includes: before fitting, the resonance residual admittance is smoothed using the Savitzky-Golay filtering algorithm with a filter window length of 21 points and a polynomial order of 3 to remove signal fluctuations caused by random noise and ensure the stability of the fitting results.

[0094] Preferably, the phase propagation coefficient characterizing the high-frequency wave propagation properties is constructed based on the measured low-frequency inductance, total parasitic capacitance, and total winding geometry, including: The cumulative length of the conductive path along the winding is calculated as the total geometric length of the winding. : in, The first on the conductive path of the winding Individual node coordinates, Represents the Euclidean distance operation; The first anti-resonance frequency Converted to anti-resonant angular frequency : in, Pi; The phase propagation coefficient was calculated based on transmission line theory. : in, The low-frequency inductance, The total parasitic capacitance is... This represents the square root operation.

[0095] The total geometric length of the winding is obtained by summing the Euclidean distances between all adjacent voxel nodes on the winding's conductive path, and is a numerical value representing the total length of the winding's conductive path.

[0096] The anti-resonant angular frequency is the physical quantity of the angular frequency corresponding to the first anti-resonant frequency, obtained by multiplying the first anti-resonant frequency by twice pi.

[0097] The transmission line equivalent parameters are obtained by taking the square root of the product of the low-frequency inductance and the total parasitic capacitance. These parameters characterize the transmission line equivalent properties of an inductor.

[0098] The phase propagation coefficient is a parameter that characterizes the high-frequency wave propagation characteristics of an inductor. It is obtained by multiplying the anti-resonant angular frequency by the equivalent parameters of the transmission line and then dividing by the total geometric length of the winding.

[0099] The calculation of the total geometric length of the winding includes: using the method of accumulating the Euclidean distances between adjacent voxel nodes, rather than simply multiplying the number of voxels by the voxel size, which can effectively eliminate the path length error caused by voxel discretization. For example, if a winding's conductive path has 2000 voxel nodes, and the Euclidean distance between adjacent nodes fluctuates between 3 and 7 micrometers, the total length obtained by accumulating the distances pairwise is closer to the actual path length than the result obtained by multiplying an average of 5 micrometers by 1999 segments.

[0100] The correlation of transmission line equivalent parameters includes: Inductors at high frequencies can be equivalent to transmission line structures, and their distributed parameters and lumped parameters are inherently related. Taking the square root of the product of the low-frequency inductance and the total parasitic capacitance yields the transmission line equivalent parameters, which are essentially the reciprocal of the transmission line's characteristic impedance, thus bridging the gap between lumped and distributed parameters. For example, an inductor with a low-frequency inductance of 4.7 microhenries and a total parasitic capacitance of 16.6 picofarads, after taking the square root of their product, yields a transmission line equivalent parameter of approximately 8.8 × 10⁻⁸ henf², accurately reflecting its high-frequency transmission line characteristics.

[0101] The construction of the phase propagation coefficient involves: based on transmission line theory, the phase propagation coefficient is positively correlated with angular frequency and transmission line equivalent parameters, and negatively correlated with the total path length. This construction method organically integrates the inductor's structural parameters (total winding geometric length), electrical parameters (low-frequency inductance, total parasitic capacitance), and frequency domain parameters (anti-resonant angular frequency), providing a quantitative scale for the conversion between phase and electrical length. For example, with an anti-resonant angular frequency of 1.696 × 10⁸ radians per second, a transmission line equivalent parameter of 8.8 × 10⁻⁸ Henry's square root, and a total winding geometric length of 152 mm, the calculated phase propagation coefficient is approximately 0.097 radians per millimeter, which can be directly used for phase-to-length conversion.

[0102] The calculation of Euclidean distance includes: when calculating the Euclidean distance between adjacent voxel nodes, 64-bit floating-point arithmetic is used, four decimal places are retained, and the precision is controlled within 0.1 micrometers to avoid the cumulative numerical calculation error affecting the accuracy of the total length.

[0103] Outlier handling in the accumulation operation includes: setting an outlier threshold; if the Euclidean distance between a neighboring node is greater than 5 times the average of all neighboring distances, it is considered an outlier. The outlier is replaced with the average value before accumulation to avoid distortion of the total length caused by individual discrete points. For example, if the average of a group of neighboring distances is 5 micrometers and a certain distance is 30 micrometers, it is considered an outlier, replaced with 5 micrometers before accumulation.

[0104] The approximate conditions for the transmission line equivalent parameters include: the calculation of these parameters is based on a low-loss prior, which is applicable to the high-frequency operating range of inductors, where the effects of resistance and conductance losses are negligible. This prior holds true in the frequency range above the self-resonant frequency of most power inductors.

[0105] The numerical precision control of the phase propagation coefficient includes: using 64-bit floating-point operations throughout the calculation process, retaining four decimal places in the final result, and using the rounding rule to ensure that the coefficient precision meets the requirements of subsequent position calculations.

[0106] Preferably, establishing a positional association between the resonant phase factor and the center of the capacitance distribution, converting the resonant phase factor into an electrical length offset relative to the center of the capacitance distribution, and then solving for the geometric position of the break point along the winding conduction path, includes: Using the resonant phase factor The phase propagation coefficient and the capacitance distribution center Calculate the original calculation location of the circuit breaker point. : For the original calculation position Regarding the total geometric length of the winding Normalization and modulus processing are performed to obtain the effective arc length position of the circuit break point. : in, This indicates the floor function; Ordered voxel node array of the winding conductive path Search node index This makes the cumulative arc length of the node... satisfy ,in , ; The three-dimensional geometric location of the circuit breaker point is calculated using linear interpolation. : in, and The first winding on the conductive path of the winding, respectively The and the first Spatial coordinates of individual element nodes.

[0107] The offset distance is obtained by dividing the resonant phase factor by twice the phase propagation coefficient, and is the positional offset of the break point relative to the center of the capacitance distribution.

[0108] The original calculated position is obtained by adding the capacitance distribution center and the offset distance. The break point is not located at the initial arc length position of the range mapping.

[0109] The effective arc length position is the arc length position mapped to the winding conductive path length range after taking the original calculated position modulo the total geometric length of the winding.

[0110] The cumulative arc length is the cumulative length of each voxel point on the conductive path of the winding relative to the first terminal.

[0111] The node index is the sequence number that identifies the order of voxel nodes on the winding conductive path.

[0112] The interpolation coefficient is calculated based on the effective arc length position and the cumulative arc length at both ends of the point interval, and is used as a proportional coefficient for linear interpolation.

[0113] The three-dimensional geometric coordinates of the circuit breaker point are obtained by linear interpolation of the coordinates of the voxel nodes at both ends of the point interval, which indicates the specific location of the circuit breaker point in three-dimensional space.

[0114] The relationship between phase and position offset includes: the resonant phase factor essentially reflects the change in electrical length caused by the circuit breaker point, and the phase propagation coefficient is a conversion scale between electrical length and physical length. Dividing the resonant phase factor by twice the phase propagation coefficient directly converts the phase difference into a position offset in physical space. This logic is based on the proportional relationship between phase accumulation and path length in transmission line theory. For example, if a resonant phase factor is -1.654 radians and the phase propagation coefficient is 0.097 radians per millimeter, the calculated offset distance is approximately 8.6 millimeters, accurately reflecting the offset of the circuit breaker point relative to the center of capacitance distribution.

[0115] The rules for modulo operations include: the original calculated position may exceed the range of the total geometric length of the winding due to phase periodicity. The modulo operation maps the position to the effective range of 0 to the total geometric length of the winding by rounding down the ratio of the original calculated position to the total geometric length of the winding, and then subtracting the product of the integer and the total length from the original position. For example, if the total geometric length of the winding is 152 mm and the original calculated position is 160 mm, the effective arc length position after modulo operation is 8 mm, avoiding the position from exceeding the actual winding range.

[0116] An optimized algorithm for point interval search includes an algorithm combining sequential traversal and interval judgment. Starting from the voxel node corresponding to the first terminal, it sequentially compares the effective arc length position with the cumulative arc length of each node to find the point interval that satisfies the condition that the cumulative arc length of the preceding node ≤ the effective arc length position < the cumulative arc length of the following node. This algorithm does not require complex data structures and is adapted to the ordered characteristics of the winding's conductive path. For example, if the effective arc length position is 50 mm, it traverses to find adjacent nodes with cumulative arc lengths of 48 mm and 52 mm to determine the point interval.

[0117] The precise positioning model using linear interpolation includes: the cumulative arc length of the voxel nodes at both ends of a point interval is linearly related to the 3D coordinates. The effective arc length position is mapped to 3D space using interpolation coefficients. The interpolation coefficient is the difference between the effective arc length position and the cumulative arc length of the preceding node, divided by the difference between the cumulative arc lengths of the two nodes, ensuring a precise match between the 3D coordinates and the arc length position. For example, in a point interval, the cumulative arc length of the preceding node is 48 mm, coordinates (10, 20, 30), the cumulative arc length of the following node is 52 mm, coordinates (14, 24, 34), the effective arc length position is 50 mm, and the interpolation coefficient is 0.5, resulting in 3D coordinates (12, 22, 32).

[0118] The storage format of the cumulative arc length is matched with the index, including: the cumulative arc length is stored in 64-bit floating-point data type, retaining four decimal places, and each cumulative arc length value corresponds one-to-one with the three-dimensional coordinates of the corresponding voxel node. Fast lookup is achieved through node index, for example, the cumulative arc length corresponding to index j is bound to the coordinate.

[0119] The error evaluation criteria for linear interpolation include: setting the maximum allowable interpolation error to 0.1 micrometers, and ensuring that the three-dimensional coordinate error after interpolation does not exceed this range by controlling the calculation accuracy of the cumulative arc length and the number of floating-point operations, so as to meet the positioning accuracy requirements of failure analysis.

[0120] The output accuracy of the three-dimensional coordinates of the circuit breaker point includes: the final output three-dimensional coordinates are retained to three decimal places, in millimeters, for example (12.345, 22.567, 32.789), to ensure the consistency and usability of the output data.

[0121] The optimization of the traversal for point interval search includes: when there are a large number of voxel nodes in the winding conductive path, a segmented traversal strategy is adopted, dividing the nodes into 10 segments according to the cumulative arc length. First, the segment where the effective arc length is located is determined, and then the traversal is performed within the segment to reduce the number of traversals. For example, 20,000 nodes are divided into 10 segments, with 2,000 nodes in each segment, which can greatly improve the search efficiency.

[0122] like Figure 2 As shown, Figure 2 It includes key components of a microfocus X-ray computed tomography system (X-ray source, detector, rotating platform), the inductor under test and its internal windings and reference substrate, and also presents a vector network analyzer and test fixtures for broadband electrical measurement, as well as the technical connection of eliminating fixture parasitic effects through de-embedding processing. It demonstrates a combined detection scheme of structural 3D scanning and broadband electrical measurement, and clearly shows the coordination relationship between the equipment, the device under test and the core processing links.

[0123] It should be noted that the interval and threshold sizes are set for ease of comparison. The size of the threshold depends on the amount of sample data and the base number set by those skilled in the art for each set of sample data, as long as it does not affect the proportional relationship between the parameter and the quantized value. Furthermore, the above formulas are all dimensionless calculations, and the formulas are derived from software simulations using a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0124] The embodiments of this example have been described above. However, this example is not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms based on the guidance of this example, and all of them are within the protection scope of this example.

Claims

1. A rapid detection method for the open circuit location of an inductor based on non-destructive testing, characterized in that, include: The internal three-dimensional structure of the inductor under test is obtained by microfocus X-ray computed tomography, the winding conduction path and the insulation distance distribution of the winding to the reference substrate are extracted, and the capacitance distribution center is calculated based on the equivalent capacitance weight distributed along the winding conduction path. Broadband electrical measurements are performed on the inductor under test to obtain the complex impedance spectrum, the first anti-resonance frequency after the self-resonance frequency is located, and the local response within a preset range of the first anti-resonance frequency is fitted using an asymmetric resonance model to extract the resonance phase factor characterizing the asymmetry of the spectral waveform. Based on the measured low-frequency inductance, total parasitic capacitance, and total winding geometry, a phase propagation coefficient characterizing the propagation characteristics of high-frequency fluctuations is constructed. The positional relationship between the resonant phase factor and the center of the capacitance distribution is established. The resonant phase factor is converted into an electrical length offset relative to the center of the capacitance distribution, and then the geometric position of the break point along the conductive path of the winding is obtained.

2. The method for rapid detection of inductor open circuit location based on non-destructive testing according to claim 1, characterized in that, Microfocus X-ray computed tomography (XCT) was used to obtain the internal three-dimensional structure of the inductor under test, extracting the winding conduction path and the insulation distance distribution between the winding and the reference substrate, including: The inductor under test is subjected to tomographic scanning and three-dimensional back projection reconstruction to obtain three-dimensional voxel grayscale data reflecting the material density distribution, and the three-dimensional voxel grayscale data is linearly normalized. Based on a preset material density segmentation threshold, the high-density winding entity region and the medium-density reference substrate region are extracted from the normalized three-dimensional voxel grayscale data through binarization processing. The reference substrate region includes a magnetic core, magnetic resin and an external shielding layer. A three-dimensional skeleton thinning algorithm is used to perform topological thinning on the winding entity region to generate a three-dimensional center curve with the width of the voxel while maintaining the original connectivity. The voxel points on the curve are sorted in order from the first terminal to the last terminal to obtain the winding conductive path. For each voxel point on the conductive path of the winding, the shortest spatial geometric distance from the voxel point to the boundary of the reference substrate region is searched using a three-dimensional distance transformation algorithm, and the set of distances of all voxel points distributed along the path is taken as the insulation distance distribution.

3. The method for rapid detection of inductor open circuit location based on non-destructive testing according to claim 2, characterized in that, The capacitance distribution center is calculated based on the equivalent capacitance weights distributed along the conductive path of the winding, including: For each voxel point on the conductive path of the winding, the value of the voxel point is extracted using the internal distance field calculated for the solid region of the winding as the local conductor radius, and the equivalent coupling surface area is calculated by combining the differential length of the voxel point along the path. The type of medium at which the voxel point is located is determined based on the voxel gray value in the neighborhood around the voxel point, and the relative permittivity at the voxel point is determined according to the preset material property table. The equivalent capacitance weight of the voxel point is calculated based on the vacuum dielectric constant, the relative dielectric constant, the equivalent coupling surface area, and the insulation distance corresponding to the voxel point in the insulation distance distribution. The cumulative arc length of the voxel point along the conductive path of the winding relative to the starting point of the path is calculated as the path arc length coordinate. The center of capacitance distribution is obtained by performing a weighted average calculation on the corresponding path arc length coordinates using the equivalent capacitance weights of all voxel points.

4. The method for rapid detection of inductor open circuit location based on non-destructive testing according to claim 3, characterized in that, Broadband electrical measurements are performed on the inductor under test to obtain a complex impedance spectrum, including: The inductor under test is subjected to frequency sweep measurement using a vector network analyzer connected to a test fixture, and the parasitic effects of the test fixture are removed by a de-embedding algorithm to obtain the intrinsic complex impedance spectrum of the inductor under test. A preset detection frequency point is selected in the low-frequency band of the complex impedance spectrum, and the ratio of the imaginary part of the impedance to the angular frequency at the detection frequency point is extracted to obtain the low-frequency inductance. The self-resonant frequency is obtained by searching the detection frequency point corresponding to the global maximum value of the impedance modulus in the complex impedance spectrum. Based on the principle of LC parallel resonance, the total parasitic capacitance is calculated using the self-resonant frequency and the low-frequency inductance.

5. The method for rapid detection of inductor open circuit location based on non-destructive testing according to claim 4, characterized in that, The first anti-resonance frequency after the self-resonance frequency is located. An asymmetric resonance model is used to fit the local response within a preset range of the first anti-resonance frequency, and the resonance phase factor characterizing the asymmetry of the spectral waveform is extracted, including: Search for the first local minimum point of impedance magnitude that appears after the self-resonant frequency in the intrinsic complex impedance spectrum, and take the detection frequency corresponding to the minimum point as the first anti-resonant frequency; The intrinsic complex impedance spectrum is converted into a complex admittance spectrum, and within a preset frequency window centered on the first anti-resonance frequency, the non-resonant background channel admittance is fitted using a complex polynomial. The resonant residual admittance is obtained by subtracting the background channel admittance from the complex admittance spectrum. A complex Fano resonance model containing normalized detuning and Fano asymmetric parameters is constructed. The resonance residual admittance is iteratively fitted using the complex Fano resonance model by the least squares method to solve for the optimal Fano asymmetric parameters. Calculate the complex function argument of the difference between the Fano asymmetric parameter and the imaginary unit, and take twice the complex function argument as the resonance phase factor.

6. The method for rapid detection of inductor open circuit location based on non-destructive testing according to claim 5, characterized in that, The phase propagation coefficient, which characterizes the propagation properties of high-frequency waves, is constructed based on the measured low-frequency inductance, total parasitic capacitance, and total winding geometry. This includes: Calculate and sum the Euclidean distances between all adjacent voxel points on the conductive path of the winding to obtain the total geometric length of the winding. Multiplying the first anti-resonance frequency by twice pi yields the anti-resonance angular frequency. Calculate the product of the low-frequency inductance and the total parasitic capacitance, and then take the square root of the product to obtain the transmission line equivalent parameters; The phase propagation coefficient is obtained by multiplying the anti-resonance angular frequency by the equivalent parameters of the transmission line and then dividing by the total geometric length of the winding.

7. The method for rapid detection of inductor open circuit location based on non-destructive testing according to claim 6, characterized in that, Establishing a positional association between the resonant phase factor and the center of the capacitance distribution, converting the resonant phase factor into an electrical length offset relative to the center of the capacitance distribution, and then solving for the geometric position of the break point along the winding conduction path, including: The offset distance relative to the center of the capacitance distribution is calculated by dividing the resonant phase factor by twice the phase propagation coefficient. Add the capacitance distribution center to the offset distance to obtain the original calculated location of the circuit breaker point; The original calculated position is moduloed with respect to the total geometric length of the winding, and the calculation result is mapped to the length range of the conductive path of the winding to obtain the effective arc length position of the break point. Traverse all voxel points on the conductive path of the winding, and determine the point interval where the effective arc length of the break point is located based on the cumulative arc length of each voxel point relative to the first terminal. Using the three-dimensional spatial coordinates of the voxel points at both ends of the point interval and the cumulative arc length, the geometric position of the break point in three-dimensional space is calculated by linear interpolation.

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