A method for calculating the frequency response characteristics of hollow coupled coils of arbitrary shape

Abstract

The present invention discloses a method for quickly calculating the port frequency response characteristics of coupled hollow coils of arbitrary structures, which belongs to the field of electrical and electronic equipment components and sensor measurement design. The method comprises: establishing a three-dimensional rectangular coordinate system with a certain point in the coupled coil as the coordinate origin, discretizing the coupled coil into a number of wire turn units, and obtaining the spatial parameter equation of each wire turn of the coupled coil; calculating the mutual inductance and capacitance between any wire turns of two coupled coils, and the self-inductance and resistance of any wire turn unit. The electrical relationship between the voltage and branch current of each wire turn unit in the mutually coupled coils and the other wire turn units of coil one and coil two is obtained, and the electrical relationship is converted into a matrix. According to the port conditions of the coupled coil, based on the boundary conditions of the matrix and substituted into the matrix equation, the matrix equation is simplified to a relationship that can express the ratio of the port voltage and the port current, and the port frequency response characteristics of the coupled coil are obtained. The present invention has strong versatility, is easy to calculate, does not require empirical formulas, and has high calculation accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical field of rapid design methods for coupled hollow coils of arbitrary shapes in electrical and electronic equipment, and in particular relates to a rapid calculation method for frequency response characteristics of hollow coupled coils of arbitrary shapes. Background Art

[0002] Coupled coils play a vital role in electrical equipment and have been widely used in recent years. A coupled coil is an electromagnetic device that uses the principle of electromagnetic induction to transfer electrical energy from one circuit to another. In AC circuits, coupled coils perform various functions, including electrical isolation, power transmission, and voltage conversion. For example, they connect two circuits for signal transmission, transmitting the signal from the preceding circuit to the subsequent circuit. They form a series or parallel resonant circuit with a capacitor, and are used in frequency selection circuits. Applying a high-frequency voltage to the transmitting coil generates a varying magnetic field, which is then received by the receiving coil, where the resonant network selectively amplifies the signal of the corresponding frequency. The voltage conversion ratio between the transmitting and receiving coils is equal to the turns ratio of their windings. In some specialized circuits, coupled coils can act as protectors for electronic equipment, preventing damage caused by excessively high or low voltages. They can also isolate two interfering circuits, ensuring proper operation. Common applications include power supply systems, radio communication systems, and electronic equipment. Therefore, coupled coils are important electronic components with a wide range of applications in electromagnetic energy transmission and conversion, signal transmission and isolation, and electronic equipment protection. Understanding and skillfully applying the rapid design method of coupling coils with arbitrary structures is of great significance to practitioners and enthusiasts in the fields of electrical and electronics.

[0003] However, there is currently no fast calculation and design method for coupling coils of arbitrary structure. Most coils currently have small cross-sectional dimensions (wire diameter is usually less than 0.1mm), large coil bobbins (thousands of times larger than the winding wire diameter), and hundreds or even thousands of turns. In this case, it is difficult to calculate the various electromagnetic parameters of the coil using electromagnetic simulation software and a general computer. The calculation formula based on theoretical derivation is only applicable to coils with cylindrical or annular bobbins, and is not applicable to coupling coils of arbitrary structure, resulting in poor versatility. Therefore, a fast calculation method for coupling coils of arbitrary structure is of great significance to practitioners and enthusiasts in the fields of electronics and electrical engineering. Summary of the Invention

[0004] In response to the above defects or improvement needs of the prior art, the present invention proposes a fast calculation method for the frequency response characteristics of hollow coupled coils of arbitrary shapes, which has convenient calculation, high calculation accuracy and short calculation cycle.

[0005] To achieve the above objectives, according to one aspect of the present invention, a method for calculating the frequency response characteristics of an air-core coupled coil of arbitrary shape is provided, comprising:

[0006] A three-dimensional rectangular coordinate system is established with a point near the coupled coil as the origin. The coupled coils are divided into several turn units. Each turn unit is numbered in sequence according to the direction of current flow in the coil. One end of one of the coupled coils is used as the reference potential to obtain the spatial parameter equation of each turn unit.

[0007] Based on the spatial parameter equation and geometric shape of each wire turn unit, the self-inductance and frequency-dependent resistance of each wire turn unit considering skin effect and proximity effect are calculated, and the mutual inductance and capacitance between any two wire turn units are calculated;

[0008] Based on the self-inductance of each wire turn unit and the resistance affected by frequency taking into account the skin effect and the proximity effect, and the mutual inductance and capacitance between any two wire turn units, a first electrical relationship between the voltage and branch current of each wire turn unit of the coupled coil 1 in the two mutually coupled coils and the other wire turn units of the coil 1 and the coil 2 is obtained, where the coil 2 represents the other coil of the two mutually coupled coils;

[0009] Based on the self-inductance of each wire turn unit and the resistance affected by frequency taking into account the skin effect and proximity effect, and the mutual inductance and capacitance between any two wire turn units, a second electrical relationship between the voltage and branch current of each wire turn unit of the coupled coil 2 in the two mutually coupled coils and the other wire turn units of the coil 1 and the coil 2 is obtained;

[0010] Converting the first electrical relationship of the coupling coil 1 and the second electrical relationship of the coupling coil 2 into a matrix equation form;

[0011] Based on the port conditions of the two mutually coupled coils, the boundary conditions of the matrix equation are obtained;

[0012] The matrix equation is transformed and simplified into an equation representing the relationship between the coil port voltage and the port current. The port frequency response characteristics of the mutually coupled coils are obtained based on the equation representing the relationship between the coil port voltage and the port current.

[0013] In some optional embodiments, the electrical relationship between the voltage and branch current of each turn unit in the coupled coil 1 and the other turn units of the coil 1 and the coil 2 is:

[0014] pi(i≥2):

[0015]

[0016] Where p1 represents the first turn unit of the coupling coil 1, the subscript pi represents the i-th turn unit of the coupling coil 1, the subscript sj represents the j-th turn unit of the coupling coil 2, and I pi and V pi (i≠0) respectively represent the branch current of the i-th winding unit and the terminal voltage of the i-th winding unit, I si and V si (i≠0) respectively represent the branch current of the i-th winding unit in the coupling coil 2 and the terminal voltage of the i-th winding unit, M pi，pj is the mutual inductance between the i-th and j-th turn units of the coupling coil, C pi，pj is the capacitance between the i-th and j-th winding units of the coupling coil, C pi，sj is the capacitance between the i-th winding unit of the coupling coil 1 and the j-th winding unit of the coupling coil 2, Z pi is the impedance of the i-th turn unit of the coupling coil, Z pi =R pi +jωL pi , R pi and L pi They are the resistance and self-inductance of the i-th winding unit of the coupling coil 1, N represents the number of winding units of the coupling coil 1, M represents the number of winding units of the coupling coil 2, and I p is the input current of coupled coil 1.

[0017] In some optional implementation schemes, the second electrical relationship between the voltage and branch current of each turn unit in the coupled coil 2 and the other turn units of the coil 1 and the coil 2 is:

[0018]

[0019] si(i≥2):

[0020]

[0021] Among them, M si，sj is the mutual inductance between the jth and ith turn units of coil 2, M si，pj is the mutual inductance between the i-th turn unit of the coupling coil 2 and the j-th turn unit of the coupling coil 1, C si，sj is the capacitance between the i-th and j-th winding units of the coupling coil 2, C s(i-1)，pj is the capacitance between the i-1th turn unit of the coupling coil 2 and the jth turn unit of the coupling coil 1, Z si is the impedance of the i-th turn unit of the coupling coil 2, Z si =R si +jωL si , R siand L si are the resistance and self-inductance of the i-th turn unit of the coupling coil 2, I s is the input current of coupling coil 2.

[0022] In some optional embodiments, converting the first electrical relationship of the coupled coil 1 and the second electrical relationship of the coupled coil 2 into a matrix equation includes: in,

[0023]

[0024]

[0025]

[0026]

[0027]

[0028]

[0029] In some optional embodiments, The first electrical relationship of the coupling coil 1 and the second electrical relationship of the coupling coil 2 are converted into the form of matrix equations.

[0030] In some optional implementation schemes, according to the port conditions of the coil, if the coupling coil 1 is connected to the impedance analyzer and the coupling coil 2 is short-circuited, the boundary condition is I s =0, Z pp =V pN / I p , Z pp is the input impedance of coupled coil 1, V pN and I p are the port voltage and input current of coupling coil 1 respectively.

[0031] In some optional embodiments, The matrix equation is transformed into an equation that represents the relationship between the coil port voltage and port current, where D[(N+M), 1] = (Q (N+M)×(N+M) ) -1 A (N+M)×1 .

[0032] In some optional embodiments, Obtain the port frequency response characteristics of coupled coil one.

[0033] According to another aspect of the present invention, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps of any one of the above methods are implemented.

[0034] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0035] This invention provides a rapid calculation method for the port frequency response characteristics of coupled air-core coils of arbitrary structure. The method is highly versatile and can be used to calculate the port frequency response characteristics of coupled coils of arbitrary structure with any distribution of dense and fine windings. The calculation is convenient, requiring no finite element method or other calculation software. The calculation is easy to program, saving design time. The calculation process does not require empirical formulas, resulting in high accuracy.

[0036] It can solve the problem that existing common electromagnetic simulation software cannot perform grid division calculations on coils with dense windings (the number of turns is often several thousand, and the diameter of the enameled wire is often less than 0.1mm), and the problem that existing theoretical calculation methods are only applicable to ideal specific situations and are not applicable to coupled coils with arbitrary shapes. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 A coupling coil is provided in an embodiment of the present invention;

[0038] Figure 2 This is a coupled coil equivalent circuit provided by an embodiment of the present invention;

[0039] Figure 3 This is a comparison chart of experimental and theoretical calculation data of the frequency response characteristics of coil 1 when coupling coil 2 is open-circuited, provided by an embodiment of the present invention, (a) equivalent inductance, (b) equivalent resistance;

[0040] Figure 4 This is a comparison diagram of experimental and theoretical calculation data of the frequency response characteristics of coil 1 when coupling coil 2 is short-circuited, provided by an embodiment of the present invention, (a) equivalent inductance, (b) equivalent resistance. DETAILED DESCRIPTION

[0041] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0042] In the examples of the present invention, “first”, “second”, etc. are used to distinguish different objects rather than to describe a specific order or sequence.

[0043] The present invention provides a method for quickly calculating the port frequency response characteristics of a coupled air-core coil of any structure, characterized in that the method comprises the following steps:

[0044] Step 1: Establish a three-dimensional rectangular coordinate system with a point near the coupled coil as the origin. Divide the coupled coils into N and M turn units, respectively. Number each turn unit in sequence according to the direction of current flow in the coil. Use one end of one coupled coil, where the current starts in the coil, as the reference potential. Write the spatial parameter equation for each turn unit.

[0045] Step 2: Based on the spatial parameter equation and geometric shape of each wire turn unit, calculate the self-inductance and frequency-dependent resistance of each wire turn unit taking into account skin effect and proximity effect, and calculate the mutual inductance and capacitance between any two wire turn units;

[0046] Step 3: Based on the self-inductance of each wire turn unit and the frequency-dependent resistance taking into account the skin effect and proximity effect, as well as the mutual inductance and capacitance between any two wire turn units, obtain the electrical relationship between the voltage and branch current of each wire turn unit of the coupled coil 1 in the two mutually coupled coils and the other wire turn units of the coil 1 and coil 2;

[0047] Step 4: Based on the self-inductance of each wire turn unit and the frequency-dependent resistance taking into account the skin effect and proximity effect, as well as the mutual inductance and capacitance between any two wire turn units, obtain the electrical relationship between the voltage and branch current of each wire turn unit of the coupled coil 2 in the two mutually coupled coils and the other wire turn units of the coils 1 and 2.

[0048] Step 5: Convert the electrical relationship between the coupling coil 1 and the coupling coil 2 into a matrix equation.

[0049] Step 6: Based on the port conditions of the two mutually coupled coils, the boundary conditions of the matrix equation are obtained;

[0050] Step 7: The matrix equation is transformed and simplified into an equation representing the relationship between the coil port voltage and the port current. The port frequency response characteristics of the mutually coupled coils are obtained based on the equation representing the relationship between the coil port voltage and the port current.

[0051] Furthermore, the electrical relationship between the voltage and branch current of each turn unit in the coupled coil 1 in step 3 and the other turn units of the coil 1 and the coil 2 is:

[0052]

[0053]

[0054] Here, ω is the angular frequency. p1 represents the first turn unit of the coupling coil 1, and the subscript pi represents the i-th turn unit of the coupling coil 1. The subscript sj represents the j-th turn unit of the coupling coil 2. pi and V pi (i≠0) is the branch current of the i-th winding unit in coil 1 and the voltage at the end of the i-th winding unit. si and V si (i≠0) is the branch current of the i-th winding unit in coil 2 and the terminal voltage at the end of the i-th winding unit. pi，pj is the mutual inductance between the i-th and j-th coil turn units, M pi，sj is the mutual inductance between the i-th coil turn unit and the j-th coil turn unit. pi，pj is the capacitance between the i-th and j-th coil turn units; Z pi is the impedance of the i-th turn unit of the coupling coil, where Z pi =R pi +jωL pi , R pi and L pi are the resistance and self-inductance of the i-th turn unit of coil 1 respectively.

[0055] Furthermore, the electrical relationship between the voltage and branch current of each turn unit in the coupled coil 2 in step 4 and the other turn units of coil 1 and coil 2 is:

[0056]

[0057]

[0058] Among them, M si，pj is the mutual inductance between the i-th turn unit of coil 2 and the j-th turn unit of coil 1. si,sj is the capacitance between the i-th and j-th turn units of coil 2; Z si is the impedance of the i-th turn unit of the coupling coil 2, where Z si =R si +jωL si , R si and L si are the resistance and self-inductance of the i-th turn unit of coil 2 respectively.

[0059] Furthermore, in step 5, the method for converting the electrical relationship between the coupling coil 1 and the coupling coil 2 into a matrix equation is:

[0060]

[0061] here

[0062]

[0063]

[0064]

[0065] Furthermore, the method for simplifying the matrix equation in step 7 into an equation that can express the relationship between the coil port voltage and the port current is:

[0066] In step 5, the equation

[0067]

[0068] Multiply both sides by E2 on the left -1 Transformed into the following form

[0069]

[0070] Substitute the above formula into

[0071]

[0072] Later you can get

[0073]

[0074] According to the port conditions of the coil, write the boundary conditions in matrix form and substitute them into the above equation. For example, if coil 1 is connected to the impedance analyzer and coil 2 is short-circuited, the boundary conditions are (I s =0), Z pp =V pN / I p . Z pp is the input impedance of coil 1. V pN and I p are the port voltage and input current of coil 1 respectively. Substituting the boundary conditions into the above formula, we can get

[0075]

[0076] Here, A (N+M)×1 =Z(E2 -1 ), B (N+M)×(N+M) =(Z(E2 -1 jωC)+E1).

[0077] Use calculation software to transform matrix B (N+M)×(N+M) Transformed into upper triangular form B (N+M)×(N+M) =Q (N+M)×(N+M) U (N+M)×(N+M) , here U (N+M)×(N+M) are the three matrices above. Then the above formula can be transformed into:

[0078]

[0079] The calculation method of the port frequency response characteristics of the coupling coil is:

[0080]

[0081] The above formula is also the relationship between the coupling coil port voltage and port current.

[0082] The embodiment of the present invention uses two common double-layer PCB coupling coils for wireless power transmission for illustration, such as Figure 1 As shown, the number of turns per layer is 20.

[0083] Step 1: Establish a three-dimensional rectangular coordinate system with a point near the coil as the origin. Divide the coupled coils into N and M turn units respectively. Number each turn unit in sequence according to the direction of current flow in the coil. Use one end of the coil, where the current starts, as the reference potential. Write the spatial parameter equation for each unit.

[0084] Step 2: Based on the spatial parameter equation and geometric shape of each wire turn unit, calculate the self-inductance of each wire turn unit and the resistance affected by frequency considering the skin effect and proximity effect, and calculate the mutual inductance and capacitance between any two wire turn units, such as Figure 2 As shown;

[0085] Step 3. Write down the electrical relationship between the voltage and branch current of each turn unit in the coupled coil 1 and the other turn units in coil 1 and coil 2:

[0086]

[0087] Here p1 represents the first turn unit of the coupling coil 1, the subscript pi represents the i-th turn unit of the coupling coil 1, and the subscript sj represents the j-th turn unit of the coupling coil 2. pi and V pi (i≠0) is the branch current of the i-th winding unit in coil 1 and the voltage at the end of the i-th winding unit. si and V si (i≠0) is the branch current of the i-th winding unit in coil 2 and the terminal voltage at the end of the i-th winding unit. pi，pj is the mutual inductance between the i-th and j-th coil turn units. p(i-1)，pj is the capacitance between the i-th and j-th coil turn units; Z pi is the impedance of the i-th turn unit of the coupling coil, where Z pi =R pi +jωL pi, R pi and L pi are the resistance and self-inductance of the i-th turn unit of coil 1 respectively.

[0088] Step 4: The electrical relationship between the voltage and branch current of each wire turn unit in the coupling coil 2 and the other wire turn units in the coupling coil 1 and coil 2 is:

[0089]

[0090] Among them, M si，pj is the mutual inductance between the i-th turn unit of coil 2 and the j-th turn unit of coil 1. si，sj is the capacitance between the i-th and j-th turn units of coil 2; Z si is the impedance of the i-th turn unit of the coupling coil 2, where Z si =R si +jωL si , R si and L si are the resistance and self-inductance of the i-th turn unit of coil 2 respectively.

[0091] Step 5: The method for converting the electrical relationship between the coupling coil 1 and the coupling coil 2 into a matrix equation is as follows:

[0092]

[0093] here

[0094]

[0095]

[0096] Step 6: An impedance analyzer is used to measure the frequency response characteristics of the two coupling coils in the frequency range of 0 to 2 MHz. The port of coupling coil one is connected to the impedance analyzer. When the port of coupling coil two is short-circuited, Vs = 0; when coupling coil two is open, Is = 0.

[0097] Step 7: The matrix equation is transformed into an equation that can express the relationship between the coil port voltage and the port current:

[0098] In step 5, the equation

[0099]

[0100] Multiply both sides by E2 on the left -1 Transformed into the following form

[0101]

[0102] Substitute the above formula into

[0103]

[0104] Later you can get

[0105]

[0106] According to the port conditions of the coil, the boundary conditions are written in matrix form and substituted into the above equation. For example, the coupling coil 1 is connected to the impedance analyzer and the coil 2 is short-circuited. The boundary conditions are (I s =0), Z pp =V pN / I p . Z pp is the input impedance of coil 1. V pN and I p are the port voltage and input current of coil 1 respectively. Substituting the boundary conditions into the above equation, we can obtain:

[0107]

[0108] Use calculation software to transform matrix B (N+M)×(N+M) Transformed into upper triangular form B (N+M)×(N+M) =Q (N+M)×(N+M) U (N+M)×(N+M) , here U (N+M)×(N+M) For the three matrices above. Then the above formula can be transformed into

[0109]

[0110] The calculation method of the port frequency response characteristics of the coupling coil is:

[0111]

[0112] The above formula is also the relationship between the coupling coil port voltage and port current.

[0113] Figure 3 This is a comparison diagram between the experimental and theoretical frequency response characteristics of the coupling coil 1 port within 0~2MHz when the coupling coil 2 is open. Figure 4 This is a comparison diagram between the experimental and theoretical frequency response characteristics of the port of coupling coil one within 0 to 2 MHz when coupling coil two is short-circuited. Figure 3 and Figure 4 The correctness of this method was verified.

[0114] The present application also provides a computer-readable storage medium, such as a flash memory, a hard disk, a multimedia card, a card-type memory (for example, an SD or DX memory), a random access memory (RAM), a static random access memory (SRAM), a read-only memory (ROM), an electrically erasable programmable read-only memory (EEPROM), a programmable read-only memory (PROM), a magnetic memory, a disk, an optical disk, a server, an App application store, etc., on which a computer program is stored. When the program is executed by a processor, a method for calculating the frequency response characteristics of a hollow coupled coil of arbitrary shape in a method embodiment is implemented.

[0115] It should be pointed out that, according to the needs of implementation, the various steps / components described in this application can be split into more steps / components, or two or more steps / components or partial operations of steps / components can be combined into new steps / components to achieve the purpose of the present invention.

[0116] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for calculating the frequency response characteristics of a hollow coupling coil of arbitrary shape, characterized in that: include: A three-dimensional rectangular coordinate system is established with a point near the coupled coil as the origin. The coupled coils are divided into several turn units. Each turn unit is numbered in sequence according to the direction of current flow in the coil. One end of one of the coupled coils is used as the reference potential to obtain the spatial parameter equation of each turn unit. Based on the spatial parameter equation and geometric shape of each wire turn unit, the self-inductance and frequency-dependent resistance of each wire turn unit considering skin effect and proximity effect are calculated, and the mutual inductance and capacitance between any two wire turn units are calculated; Based on the self-inductance of each wire turn unit and the resistance affected by frequency taking into account the skin effect and the proximity effect, and the mutual inductance and capacitance between any two wire turn units, a first electrical relationship between the voltage and branch current of each wire turn unit of the coupled coil 1 in the two mutually coupled coils and the other wire turn units of the coil 1 and the coil 2 is obtained, where the coil 2 represents the other coil of the two mutually coupled coils; Based on the self-inductance of each wire turn unit and the resistance affected by frequency taking into account the skin effect and proximity effect, and the mutual inductance and capacitance between any two wire turn units, a second electrical relationship between the voltage and branch current of each wire turn unit of the coupled coil 2 in the two mutually coupled coils and the other wire turn units of the coil 1 and the coil 2 is obtained; Converting the first electrical relationship of the coupling coil 1 and the second electrical relationship of the coupling coil 2 into a matrix equation form; Based on the port conditions of the two mutually coupled coils, the boundary conditions of the matrix equation are obtained; The matrix equation is transformed and simplified into an equation representing the relationship between the coil port voltage and the port current. The port frequency response characteristics of the mutually coupled coils are obtained based on the equation representing the relationship between the coil port voltage and the port current.

2. The method according to claim 1, characterized in that The first electrical relationship between the voltage and branch current of each turn unit in the coupled coil 1 and the other turn units in the coil 1 and coil 2 is: p1: pi, i≥2: Where ω is the angular frequency, p1 represents the first turn unit of the coupling coil 1, the subscript pi represents the i-th turn unit of the coupling coil 1, the subscript sj represents the j-th turn unit of the coupling coil 2, and I pi and V pi , i≠0 represent the branch current of the i-th winding unit in coil 1 and the voltage at the end of the i-th winding unit, I si and V si , i≠0 respectively represent the branch current of the i-th winding unit in the coupling coil 2 and the terminal voltage of the i-th winding unit at the end, M pi,pj is the mutual inductance between the i-th and j-th turn units of the coupling coil, C pi,pj is the capacitance between the i-th and j-th winding turn units of the coupling coil, M pi,sj is the mutual inductance between the i-th turn unit of coil 1 and the j-th turn unit of coil 2, C pi,sj is the capacitance between the i-th winding unit of the coupling coil 1 and the j-th winding unit of the coupling coil 2, Z pi is the impedance of the i-th turn unit of the coupling coil, Z pi =R pi +jωL pi , R pi and L pi They are the resistance and self-inductance of the i-th winding unit of the coupling coil 1, N represents the number of winding units of the coupling coil 1, M represents the number of winding units of the coupling coil 2, and I p is the input current of coupled coil 1.

3. The method according to claim 2, characterized in that The second electrical relationship between the voltage and branch current of each turn unit in the coupling coil 2 and the other turn units of coils 1 and 2 is: s1: si, i≥2: Among them, M si,pj is the mutual inductance between the i-th turn unit of coil 2 and the j-th turn unit of coil 1, M si,sj is the mutual inductance between the jth and ith turn units of coil 2, M si,pj is the mutual inductance between the i-th turn unit of the coupling coil 2 and the j-th turn unit of the coupling coil 1, C si,sj is the capacitance between the i-th and j-th winding turn units of the coupling coil 2, C s(i-1),pj is the capacitance between the i-1th turn unit of the coupling coil 2 and the jth turn unit of the coupling coil 1, Z si is the impedance of the i-th turn unit of the coupling coil 2, Z si =R si +jωL si , r si and L si are the resistance and self-inductance of the i-th turn unit of the coupling coil 2, I s is the input current of coupling coil 2.

4. The method according to claim 3, characterized in that The step of converting the first electrical relationship of the coupling coil 1 and the second electrical relationship of the coupling coil 2 into a matrix equation includes: in, 5. The method according to claim 4, characterized in that Depend on The first electrical relationship of the coupling coil 1 and the second electrical relationship of the coupling coil 2 are converted into the form of matrix equations.

6. The method according to claim 5, characterized in that According to the port conditions of the coil, if the coupling coil 1 is connected to the impedance analyzer and the coupling coil 2 is short-circuited, the boundary condition is I s =0, Z pp =V pN / I p , Z pp is the input impedance of coupled coil 1, V pN and I p are the port voltage and input current of coupling coil 1 respectively.

7. The method according to claim 6, characterized in that Depend on The matrix equation is transformed into an equation that represents the relationship between the coil port voltage and port current, where D[(N+M),1]=(Q (N+M)×(N+M) ) -1 A (N+M)×1 .

8. The method according to claim 7, characterized in that Depend on Obtain the port frequency response characteristics of coupled coil one.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

Images