Vehicle capacitor structure with low inductance value

Abstract

The invention relates to a low-inductance automotive capacitor structure, which comprises a shell and a capacitor element arranged in the shell, and is characterized in that the capacitor element comprises a plurality of groups of copper bars, each group of copper bars comprises an input copper bar and an output copper bar which are stacked, the plurality of groups of copper bars are stacked in sequence, and the input copper bars and the output copper bars are stacked in sequence; an insulating diaphragm is arranged between every two adjacent copper bars; in the copper bars in the same group, the input copper bars and the output copper bars are provided with staggered structures, and the staggered structures can enable the input copper bars and the output copper bars to be arranged in a staggered mode in the thickness direction. The working inductance of the capacitor can be effectively reduced, and the capacitor is suitable for a high-frequency working condition and has higher stability and reliability.

Description

Technical Field

[0001] This application relates to the technical field of capacitors, and more specifically to a low-inductance automotive capacitor structure. Background Technology

[0002] With the continuous advancement of automotive technology, especially the development of electric vehicles (EVs) and intelligent vehicles, automotive electronic systems are becoming increasingly complex. The demand for capacitors is constantly increasing due to the numerous electronic components and electrical devices in modern automobiles (such as electric drive systems, in-vehicle communication systems, autonomous driving systems, and infotainment systems). Capacitors are commonly used in automobiles for functions such as power filtering, signal coupling, noise reduction, and providing instantaneous power.

[0003] Among these, power supply filtering and high-frequency signal suppression are particularly important. In modern automobiles, electronic devices operate at increasingly higher frequencies, especially in the complex electronic control systems of electric and intelligent vehicles, where high-frequency noise and electromagnetic interference (EMI) have a significant impact on system stability and accuracy. Therefore, capacitors with superior performance capable of operating under high-frequency conditions are needed.

[0004] Existing capacitor structures such as Figure 1 , Figure 2 As shown, the capacitor includes a housing and a capacitor assembly disposed inside the housing. The capacitor assembly includes multiple layers of copper busbars with terminals led out at fixed intervals. This structure generates superimposed inductance, which greatly increases the inductance generated when the capacitor is working. In addition, the copper busbars of existing capacitors are bolted to the circuit board, resulting in high contact resistance and unstable connection. Under high-frequency conditions, this generates a large parasitic inductance, which also increases the operating inductance of the capacitor. High operating inductance limits the performance of film capacitors in high-frequency applications, increases energy loss, causes parasitic resonance, affects stability, and may lead to electromagnetic interference and decreased reliability.

[0005] In summary, the problem of high operating inductance in existing capacitors urgently needs to be addressed. Summary of the Invention

[0006] To address the problems existing in the prior art, this application aims to provide a low-inductance automotive capacitor structure. This application effectively reduces the capacitor's operating inductance, making it suitable for high-frequency operating conditions and offering higher stability and reliability.

[0007] The low-inductance automotive capacitor structure described in this application includes a housing and a capacitor element disposed within the housing, the capacitor element comprising:

[0008] Multiple sets of copper busbars, each set of copper busbars including stacked input copper busbars and output copper busbars, the multiple sets of copper busbars are stacked sequentially, and an insulating diaphragm is provided between every two adjacent copper busbars; in the same set of copper busbars, the input copper busbars and the output copper busbars have a staggered structure, the staggered structure allows the input copper busbars and the output copper busbars to be staggered in the thickness direction.

[0009] Preferably, the misaligned structure includes a first comb tooth portion formed on an input copper busbar in the same group of copper busbars, and a second comb tooth portion formed on an output copper busbar in the same group as the first comb tooth portion. The first comb tooth portion and the second comb tooth portion are misaligned so that the solid area of ​​the first comb tooth portion and the hollow area of ​​the second comb tooth portion at least partially overlap in the thickness direction, and the hollow area of ​​the first comb tooth portion and the solid area of ​​the second comb tooth portion at least partially overlap in the thickness direction.

[0010] Preferably, the misaligned structure includes a first wave portion formed on an input copper busbar in the same group of copper busbars, and a second wave portion formed on an output copper busbar in the same group as the first wave portion. The first wave portion and the second wave portion are misaligned so that the solid area of ​​the first wave portion and the hollow area of ​​the second wave portion at least partially overlap in the thickness direction, and the hollow area of ​​the first wave portion and the solid area of ​​the second wave portion at least partially overlap in the thickness direction.

[0011] Preferably, the misaligned structure includes a first serrated portion formed on an input copper busbar in the same group of copper busbars, and a second serrated portion formed on an output copper busbar in the same group as the first serrated portion. The first serrated portion and the second serrated portion are misaligned so that the solid area of ​​the first serrated portion and the hollow area of ​​the second serrated portion at least partially overlap in the thickness direction, and the hollow area of ​​the first serrated portion and the solid area of ​​the second serrated portion at least partially overlap in the thickness direction.

[0012] Preferably, if the application current of the automotive capacitor is 100A to 200A, the thickness of the copper busbar is 0.8mm to 1.2mm; if the application current of the automotive capacitor is 200A to 400A, the thickness of the copper busbar is 1.2mm to 2.5mm.

[0013] Preferably, the insulating diaphragm is made of at least one of polypropylene, polyimide, or polytetrafluoroethylene.

[0014] Preferably, the capacitor assembly further includes a circuit board, which is laser-welded to the copper busbar.

[0015] Preferably, the capacitor assembly further includes connecting leads, which are electrically connected to the circuit board.

[0016] Preferably, the length of the connecting lead satisfies the inductance calculation formula:

[0017]

[0018] Where L represents inductance, μ0 represents free permeability, l represents the length of the connecting lead, and d represents the diameter of the connecting lead.

[0019] Preferably, the connecting lead is determined according to the following steps:

[0020] Based on the parameter requirements of automotive capacitors, a simulation model of the automotive capacitor is established, including the rated voltage, capacitance, and operating frequency.

[0021] The operating parameters of the automotive capacitor are input into the simulation model, including the input current and frequency.

[0022] The shortest lead length that satisfies electrical performance requirements is obtained through iterative calculations and is taken as the length of the connecting lead.

[0023] Specifically, the iterative calculation is as follows:

[0024] The diameter d of the connecting lead is determined based on the size of the circuit board pads and the current carrying requirements.

[0025] Set the target inductance value L according to the capacitor design requirements. max ;

[0026] Set inductance constraints:

[0027] L≤L max ,

[0028] Several values ​​for the length l of the connecting lead are preset. These values ​​are then substituted into the inductance calculation formula in ascending order of magnitude to obtain the inductance calculation result. When the inductance constraint condition is met, the corresponding connecting lead length is selected as the optional length.

[0029] The optional length is verified and corrected. The verification and correction includes: determining whether the optional length meets the wiring space and soldering process requirements. If so, the optional length is taken as the shortest lead length. Otherwise, the next value is substituted into the inductance calculation formula until the verification and correction are passed.

[0030] The low-inductance automotive capacitor structure described in this application has the advantage that, by stacking the input and output copper busbars and setting a partially overlapping staggered structure between adjacent input and output copper busbars, the capacitance and parasitic inductance generated by different layers of copper busbars can be mutually compensated by utilizing the electric field coupling effect between the copper busbar layers, thereby reducing the working inductance of the capacitor and making the capacitor suitable for high-frequency operating conditions, with higher stability and reliability.

[0031] In addition, this application also uses laser welding to effectively avoid the problems of high contact resistance and unstable connection of traditional bolted connections, which can generate large parasitic inductance under high frequency conditions, and further reduce the working inductance of the capacitor.

[0032] Furthermore, this application uses simulation models to rationally design the length of the connecting leads, enabling the connecting leads to achieve the shortest length under operating conditions, thereby reducing the problem of additional inductance caused by excessively long leads. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the external structure of a vehicle capacitor in the prior art;

[0034] Figure 2 This is a schematic diagram of the internal structure of a conventional automotive capacitor.

[0035] Figure 3 This is a schematic diagram of the external structure of the automotive capacitor structure of this application;

[0036] Figure 4 This is a schematic diagram of the internal structure of the automotive capacitor structure of this application;

[0037] Figure 5 This is a schematic diagram of the mating structure of the input copper busbar and the output copper busbar in Example 1;

[0038] Figure 6 This is a schematic diagram of the cooperative structure of the input copper busbar and the output copper busbar in Example 2;

[0039] Figure 7 This is a schematic diagram of the cooperative structure of the input copper busbar and the output copper busbar in Example 3.

[0040] Explanation of reference numerals in the attached drawings: 1-Housing, 2-Copper busbar, 21-Input copper busbar, 21a-First comb tooth section, 21b-First wave section, 21c-First sawtooth section, 22-Output copper busbar, 22a-Second comb tooth section, 22b-Second wave section, 22c-Second sawtooth section. Detailed Implementation

[0041] like Figure 3 , Figure 4As shown, the low inductance automotive capacitor structure described in this application includes a housing 1 and a capacitor element disposed within the housing 1. In a specific embodiment, the housing 1 has a square housing structure, is made of plastic material, and is hollow inside to accommodate the capacitor element.

[0042] The capacitor element includes multiple sets of copper busbars 2, which are plate-shaped structures. Each set of copper busbars 2 includes an input copper busbar 21 and an output copper busbar 22 stacked together. Multiple sets of copper busbars 2 are stacked sequentially to form a structure of input copper busbar 21-output copper busbar 22-input copper busbar 21-output copper busbar 22 stacked sequentially. In the same set of copper busbars 2, the input copper busbar 21 and the output copper busbar 22 have a staggered structure, which allows the input copper busbar 21 and the output copper busbar 22 to be staggered in the thickness direction.

[0043] This application optimizes the total capacitance and inductance of the capacitor without increasing the size of the device by adopting a multi-layer electrode copper busbar 2 stacked layout. The staggered electrode copper busbar 2 structure allows adjacent copper busbar 2 layers to perform current input and output functions respectively. The copper busbar 2 has complementary shapes and partial overlap, forming an interlayer coupling region. By utilizing the electric field coupling effect between the copper busbar 2 layers, the capacitance and parasitic inductance generated by different copper busbar 2 layers can compensate for each other, thereby reducing the working inductance of the capacitor.

[0044] Specifically, a copper busbar 2 with a staggered structure is formed by laser cutting, stamping and other processes. The layers are insulated and isolated by an insulating film. After multi-layer stacking, it is pressed and packaged. The interlayer capacitance and parasitic inductance can form a resonant circuit. In the operating frequency range of the capacitor, part of the inductance is canceled, thereby reducing the overall inductance. Compared with the single-layer or simply stacked copper busbar 2 structure in the prior art, the inductance can be reduced by 20% to 40% in high-frequency conditions, such as 10kHz and above.

[0045] Regarding the aforementioned misalignment structure, there are at least three implementation methods.

[0046] Example 1

[0047] like Figure 5 As shown, the misaligned structure includes a first comb tooth portion 21a formed on the input copper busbar 21 in the same group of copper busbars 2, and a second comb tooth portion 22a formed on the output copper busbar 22 in the same group as the first comb tooth portion 21a. The first comb tooth portion 21a and the second comb tooth portion 22a are misaligned so that the solid area of ​​the first comb tooth portion 21a and the hollow area of ​​the second comb tooth portion 22a overlap at least partially in the thickness direction, and the hollow area of ​​the first comb tooth portion 21a and the solid area of ​​the second comb tooth portion 22a overlap at least partially in the thickness direction.

[0048] Specifically, for the two copper busbars 2 in the same group, namely the input copper busbar 21 and the output copper busbar 22, a first comb tooth portion 21a is formed on one side edge of the input copper busbar 21. The first comb tooth portion 21a includes square protrusions and square recesses that are alternately arranged along the length direction of the copper busbar 2. The output copper busbar 22 is provided with a second comb tooth portion 22a at the position corresponding to the first comb tooth portion 21a. The second comb tooth portion 22a also includes square protrusions and square recesses that are alternately arranged. In a preferred embodiment, the square protrusions and square recesses have the same width. Each square protrusion of the first comb tooth portion 21a corresponds to each square recess of the second comb tooth portion 22a, thereby forming a structure in which the first comb tooth portion 21a and the second comb tooth portion 22a are staggered.

[0049] Example 2

[0050] like Figure 6 As shown, the misaligned structure includes a first wave portion 21b formed on the input copper busbar 21 in the same group of copper busbars 2, and a second wave portion 22b formed on the output copper busbar 22 in the same group as the first wave portion 21b. The first wave portion 21b and the second wave portion 22b are misaligned so that the solid area of ​​the first wave portion 21b and the hollow area of ​​the second wave portion 22b at least partially overlap in the thickness direction, and the hollow area of ​​the first wave portion 21b and the solid area of ​​the second wave portion 22b at least partially overlap in the thickness direction.

[0051] Specifically, for the two copper busbars 2 in the same group, namely the input copper busbar 21 and the output copper busbar 22, a first wave portion 21b is formed on one side edge of the input copper busbar 21. The first wave portion 21b includes arc-shaped protrusions and arc-shaped concave portions alternately arranged along the length direction of the copper busbar 2. The output copper busbar 22 is provided with a second wave portion 22b at the position corresponding to the first wave portion 21b. The second wave portion 22b also includes arc-shaped protrusions and arc-shaped concave portions alternately arranged. In a preferred embodiment, the diameters of the arc-shaped protrusions and arc-shaped concave portions are equal. Each arc-shaped protrusion of the first wave portion 21b corresponds to each arc-shaped concave portion of the second wave portion 22b, thereby forming a structure in which the first wave portion 21b and the second wave portion 22b are staggered.

[0052] Example 3

[0053] like Figure 7 As shown, the misaligned structure includes a first serrated portion 21c formed on the input copper busbar 21 in the same group of copper busbars 2, and a second serrated portion 22c formed on the output copper busbar 22 in the same group as the first serrated portion 21c. The first serrated portion 21c and the second serrated portion 22c are misaligned so that the solid area of ​​the first serrated portion 21c and the hollow area of ​​the second serrated portion 22c at least partially overlap in the thickness direction, and the hollow area of ​​the first serrated portion 21c and the solid area of ​​the second serrated portion 22c at least partially overlap in the thickness direction.

[0054] Specifically, for the two copper busbars 2 in the same group, namely the input copper busbar 21 and the output copper busbar 22, a first serrated portion 21c is formed on one side edge of the input copper busbar 21. The first serrated portion 21c includes angular protrusions and angular concave portions alternately arranged along the length direction of the copper busbar 2. The output copper busbar 22 is provided with a second serrated portion 22c at the corresponding position of the first serrated portion 21c. The second serrated portion 22c also includes angular protrusions and angular concave portions alternately arranged. In a preferred embodiment, the angular protrusions and angular concave portions are of equal size. Each angular protrusion of the first serrated portion 21c corresponds to each angular concave portion of the second serrated portion 22c, thereby forming a structure in which the first serrated portion 21c and the second serrated portion 22c are staggered.

[0055] Through the above three different implementation methods, the two copper busbars 2 in the same group can be staggered in the thickness direction to reduce the overall working inductance of the capacitor. It is easy to imagine that those skilled in the art can set the specific shape of the staggered structure according to processing requirements, material characteristics, etc. This application does not limit the specific shape of the staggered structure. Other conventional shapes designed based on the concept of this application should fall within the protection scope of this application.

[0056] Furthermore, in this embodiment, if the application current of the automotive capacitor is 100A to 200A, the thickness of the copper busbar 2 is 0.8mm to 1.2mm; if the application current of the automotive capacitor is 200A to 400A, the thickness of the copper busbar 2 is 1.2mm to 2.5mm. The thickness of the copper busbar 2 is designed according to the application current, making its size suitable for various working scenarios.

[0057] Furthermore, in this embodiment, the insulating diaphragm is made of at least one of polypropylene, polyimide, or polytetrafluoroethylene. The above-mentioned insulating materials have the characteristics of high insulation and low dielectric loss, and are suitable as insulating diaphragm materials.

[0058] Furthermore, in this embodiment, the capacitor assembly also includes a circuit board, which is laser-welded to the copper busbar 2. Laser welding can achieve high-quality metallurgical bonding between the copper busbar 2 and the circuit welding point, eliminating the contact gap and oxide layer effects of traditional connection methods, significantly reducing contact resistance by 70%-90%, significantly reducing losses during current transmission, and thus effectively reducing parasitic inductance. Compared with traditional connection methods, the inductance can be reduced to 1 / 5-1 / 3 of the original.

[0059] For example, the laser welding steps are as follows:

[0060] Surface treatment and positioning: Use a special cleaning agent to thoroughly clean the circuit busbars, load terminals, and welding areas of capacitor copper busbar 2 to remove oxide layers, oil stains, and other impurities, ensuring a clean and foreign object-free surface. Utilize a high-precision positioning fixture to precisely align the input and output copper busbars 22 of the multilayer electrode copper busbar 2 and the circuit welding points. Fixtures are used to ensure a tight fit between the copper busbar 2 and the welding points, with positioning errors controlled within ±0.05mm.

[0061] Laser welding process implementation: A high-power pulsed fiber laser is selected, and the laser parameters are precisely set according to the thickness and material (e.g., pure copper, copper alloy) of the copper busbar 2 and the welding requirements. Generally, the laser power is set to 1 to 3 kW, the pulse width is adjusted to 1 to 5 ms, the frequency is controlled between 10 and 50 Hz, and the defocusing amount is maintained at ±0.2 mm. Using continuous or lap welding methods, the laser scans along the edge of the welding point between the copper busbar 2 and the circuit, achieving a strong metallurgical bond between the copper busbar 2 and the circuit, forming a low-resistance, high-reliability connection path.

[0062] Welding quality inspection and debugging: After welding, non-destructive testing of the welded area is performed using laser ultrasonic testing technology to check for defects such as porosity and cracks; at the same time, the contact resistance of the weld point is measured using a micro-ohmmeter to ensure it is at an extremely low level. If the operating frequency, load, or other operating conditions of the circuit system change, copper busbar 2-layer modules with different interlayer coupling parameters (such as copper busbar shape, overlap area, and insulation dielectric thickness) can be replaced according to actual needs to optimize the capacitance-inductance compensation effect of the capacitors, thereby meeting the performance requirements of the circuit system.

[0063] Furthermore, in this embodiment, the capacitor assembly also includes connecting leads, which are electrically connected to the circuit board, and the length of the connecting leads satisfies the inductance calculation formula:

[0064]

[0065] Where L represents inductance, μ0 represents free permeability, l represents the length of the connecting lead, and d represents the diameter of the connecting lead.

[0066] The connection leads should be determined according to the following steps:

[0067] Based on the parameter requirements of the automotive capacitor, an electromagnetic simulation model of the automotive capacitor is established using electromagnetic simulation software, such as ANSYS. The parameter requirements include rated voltage, capacitance, and operating frequency.

[0068] The operating parameters of the automotive capacitor are input into the simulation model, including the input current and frequency.

[0069] The shortest lead length that satisfies electrical performance requirements is obtained through iterative calculations and is taken as the length of the connecting lead.

[0070] Specifically, the iterative calculation is as follows:

[0071] The diameter d of the connecting lead is determined based on the size of the circuit board pads and the current carrying requirements.

[0072] Set the target inductance value L according to the capacitor design requirements. max ;

[0073] Set inductance constraints:

[0074] L≤L max ,

[0075] Several values ​​for the length l of the connecting lead are preset. These values ​​are then substituted into the inductance calculation formula in ascending order of magnitude to obtain the inductance calculation result. When the inductance constraint condition is met, the corresponding connecting lead length is selected as the optional length.

[0076] The optional length is verified and corrected. The verification and correction includes: determining whether the optional length meets the wiring space and soldering process requirements. If so, the optional length is taken as the shortest lead length. Otherwise, the next value is substituted into the inductance calculation formula until the verification and correction are passed.

[0077] In this embodiment, electric field simulation analysis is used to optimize the electrode layout based on the principles of uniform current distribution and minimizing loop area, thereby reducing the problem of additional inductance caused by excessively long lead lengths.

[0078] In the description of this application, it should be understood that the orientation or positional relationship indicated by directional terms such as "front, back, up, down, left, right", "horizontal, vertical, horizontal" and "top, bottom" is usually based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing this application and simplifying the description. Unless otherwise stated, these directional terms do not indicate or imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on the scope of protection of this application.

[0079] For those skilled in the art, various other corresponding changes and modifications can be made based on the technical solutions and concepts described above, and all such changes and modifications should fall within the protection scope of the claims of this application.

Claims

1. A low-inductance automotive capacitor structure, comprising a housing and a capacitor element disposed within the housing, characterized in that, The capacitor element includes: Multiple sets of copper busbars, each set of copper busbars including stacked input copper busbars and output copper busbars, the multiple sets of copper busbars are stacked sequentially, and an insulating diaphragm is provided between every two adjacent copper busbars; in the same set of copper busbars, the input copper busbars and the output copper busbars have a staggered structure, the staggered structure allows the input copper busbars and the output copper busbars to be staggered in the thickness direction.

2. The low-inductance automotive capacitor structure according to claim 1, characterized in that, The misaligned structure includes a first comb tooth portion formed on an input copper busbar in the same group of copper busbars, and a second comb tooth portion formed on an output copper busbar in the same group as the first comb tooth portion. The first comb tooth portion and the second comb tooth portion are misaligned so that the solid area of ​​the first comb tooth portion and the hollow area of ​​the second comb tooth portion at least partially overlap in the thickness direction, and the hollow area of ​​the first comb tooth portion and the solid area of ​​the second comb tooth portion at least partially overlap in the thickness direction.

3. The low-inductance automotive capacitor structure according to claim 1, characterized in that, The misaligned structure includes a first wave portion formed on an input copper busbar in the same group of copper busbars, and a second wave portion formed on an output copper busbar in the same group as the first wave portion. The first wave portion and the second wave portion are misaligned so that the solid area of ​​the first wave portion and the hollow area of ​​the second wave portion at least partially overlap in the thickness direction, and the hollow area of ​​the first wave portion and the solid area of ​​the second wave portion at least partially overlap in the thickness direction.

4. The low-inductance automotive capacitor structure according to claim 1, characterized in that, The misaligned structure includes a first serrated portion formed on an input copper busbar in the same group of copper busbars, and a second serrated portion formed on an output copper busbar in the same group as the first serrated portion. The first serrated portion and the second serrated portion are misaligned so that the solid area of ​​the first serrated portion and the hollow area of ​​the second serrated portion at least partially overlap in the thickness direction, and the hollow area of ​​the first serrated portion and the solid area of ​​the second serrated portion at least partially overlap in the thickness direction.

5. The low-inductance automotive capacitor structure according to claim 1, characterized in that, If the application current of the automotive capacitor is 100A to 200A, the thickness of the copper busbar is 0.8mm to 1.2mm; if the application current of the automotive capacitor is 200A to 400A, the thickness of the copper busbar is 1.2mm to 2.5mm.

6. The low-inductance automotive capacitor structure according to claim 1, characterized in that, The insulating diaphragm is made of at least one of polypropylene, polyimide, or polytetrafluoroethylene.

7. The low-inductance automotive capacitor structure according to claim 1, characterized in that, The capacitor assembly also includes a circuit board, which is laser-welded to the copper busbar.

8. The low-inductance automotive capacitor structure according to claim 7, characterized in that, The capacitor assembly also includes connecting leads, which are electrically connected to the circuit board.

9. The low-inductance automotive capacitor structure according to claim 8, characterized in that, The length of the connecting lead satisfies the inductance calculation formula: Where L represents inductance, μ0 represents free permeability, l represents the length of the connecting lead, and d represents the diameter of the connecting lead.

10. The low-inductance automotive capacitor structure according to claim 9, characterized in that, The connecting leads are determined according to the following steps: Based on the parameter requirements of automotive capacitors, a simulation model of the automotive capacitor is established, wherein the parameter requirements include rated voltage, capacitance and operating frequency; The operating parameters of the automotive capacitor are input into the simulation model, including the input current and frequency. The shortest lead length that satisfies electrical performance requirements is obtained through iterative calculations and is taken as the length of the connecting lead. Specifically, the iterative calculation is as follows: The diameter d of the connecting lead is determined based on the size of the circuit board pads and the current carrying requirements. Set the target inductance value L according to the capacitor design requirements. max ; Set inductance constraints: L≤L max , Several values ​​for the length l of the connecting lead are preset. These values ​​are then substituted into the inductance calculation formula in ascending order of magnitude to obtain the inductance calculation result. When the inductance constraint condition is met, the corresponding connecting lead length is selected as the optional length. The optional length is verified and corrected. The verification and correction includes: determining whether the optional length meets the wiring space and soldering process requirements. If so, the optional length is taken as the shortest lead length. Otherwise, the next value is substituted into the inductance calculation formula until the verification and correction are passed.

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