A frequency response characteristic calculation method suitable for a PCB coil with an arbitrary shape

Abstract

The application discloses a kind of structural arbitrary PCB coil frequency response characteristic calculation method, belong to electrical and electronic equipment component and sensor measurement technical field, comprising: the point inside PCB coil is set as the origin of three-dimensional rectangular coordinate system, according to the flow direction of current inside coil to the intersection of each section of coil turn of the turn of coil turn that constitutes PCB coil and the end point of coil is numbered in turn, obtain the intersection coordinates of the PCB coil with symmetrical structure;And all coil turn intersection numbering and coordinates are stored in matrix, obtain the space parameter equation of each section of coil turn, obtain the mutual inductance between any coil turn section;The self-induction coefficient of coil turn section, the capacitance between coil section;The electrical relationship between the end points of adjacent two coil turn sections is written into matrix form and the matrix equation is simplified, obtain the port frequency response characteristic of coil.The application has strong universality, is convenient to calculate, is easy to program and is calculated, saves design time;There is no experience formula in the calculation process, and the calculation precision is high.

Description

Technical Field

[0001] The present invention belongs to the technical field of designing PCB coil components of arbitrary structures in electrical equipment and the technical field of measuring PCB coil sensors, and in particular relates to a method for quickly calculating frequency response characteristics of PCB coils of arbitrary shapes. Background Art

[0002] PCB coils are widely used in the electrical and measurement fields due to their inherent flexibility, flexibility in shape and size, lack of magnetic saturation, ease of production, and low cost. They overcome the drawbacks of traditional wire winding processes, such as the monotonous structure that hinders the production of complex and diverse structures. Furthermore, they can produce coils with uniformly distributed turns without the need for expensive winding machines. For example, they are used in transmitting and receiving PCB coils in wireless power transmission (IPT) systems, current sensors for measuring high currents, PCB coils for inspecting the condition and appearance of metal materials, and for generating or measuring electromagnetic environments. The structure and internal parasitic parameters of PCB coils determine their port frequency response characteristics. The port frequency response characteristics of PCB coils as components, in turn, affect the parameters of electrical equipment. The port frequency response characteristics of PCB coils as sensors, in turn, influence the structure and matching parameters of external circuits. Therefore, a fast method for calculating the port frequency response characteristics of PCB coils is of great significance.

[0003] Although PCB coils have been widely used as components and sensors in electrical equipment and measurement applications, current design and parameter calculation methods are only applicable to specific situations and are not suitable for PCB coils with arbitrary structures. Two common calculation methods are currently used. One is to use theoretically derived formulas to calculate the port characteristics of PCB coils, but these formulas are only applicable to ideal structures with regular shapes. The other is to use finite element electromagnetic simulation software to calculate the port frequency response characteristics of PCB coils. However, finite element electromagnetic simulation software is only suitable for PCB coils with sparse and thick turns. To increase the coil inductance and reduce the coil volume, the turns of PCB coils are often very thin and dense. Therefore, it is difficult to use finite element electromagnetic simulation software to mesh and perform calculations. This greatly increases the designer's workload. Therefore, it is important to propose a fast calculation method for the frequency response characteristics of PCB coils with arbitrary shapes. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to address the defects in the prior art and provide a method for quickly calculating the frequency response characteristics of a PCB coil port of any structure with convenient calculation, high calculation accuracy and short calculation cycle.

[0005] To achieve the above object, according to one aspect of the present application, a frequency response characteristic calculation method suitable for a PCB coil with an arbitrary shape is provided, comprising:

[0006] A point inside the PCB coil is set as the origin of a three-dimensional rectangular coordinate system, and the intersection points of the turns of the coil and the two end points of the coil are numbered in sequence from one end point of the coil according to the flow direction of the current inside the coil, wherein the starting end of the coil is the reference potential and the reference point, and if the turns are M, the total number of the turn point numbers is M+1;

[0007] The intersection point coordinates of each turn are obtained, and the intersection point numbers of the turns, the two end point numbers of the coil, and the intersection point coordinates and the two end point coordinates of each turn are stored in a matrix with M+1 rows and 4 columns;

[0008] The spatial parameter equation of each turn of the turns is obtained according to the matrix, and then the mutual inductance M ij between the i th turn and the j th turn is obtained;

[0009] The end point coordinates and the serial numbers stored in the matrix, the mutual inductance M ij between the i th turn and the j th turn, the self-inductance coefficient of the m th turn, the inter-turn capacitance, and the parallel impedance of the coil port are used to obtain the electrical relationship between the adjacent two points, and the electrical relationship is converted into a matrix form;

[0010] The converted matrix is combined into a relationship formula of the port voltage and the port current, and the frequency response characteristic of the coil is calculated through the relationship formula of the port voltage and the port current.

[0011] In some optional embodiments, the obtaining of the intersection point coordinates of each turn, the storing of the intersection point numbers of the turns, the two end point numbers of the coil, and the intersection point coordinates and the two end point coordinates of each turn in a matrix with M+1 rows and 4 columns comprises:

[0012] If the coil has no same or symmetric geometric shape, the coordinates of each turn end point are written in sequence, and the number of each turn end point and the coordinates of each turn end point are stored in a matrix with M+1 rows and 4 columns;

[0013] For a PCB coil composed of a plurality of symmetric and structurally identical small PCBs, the geometric center line of one of the small PCBs constituting the PCB coil is coincided with the x-axis of the coordinate system, and the small PCB coil is regarded as a reference PCB skeleton unit, wherein each layer of the turn of the reference PCB skeleton unit is parallel to the x-axis;

[0014] Number the small PCBs that make up the PCB coil, starting from the reference PCB skeleton unit and numbering them counterclockwise. Starting from one end of the wire turn on the reference PCB skeleton unit, number the end points of the wire turn segments in the direction of the coil current.

[0015] If it is a multi-layer PCB, obtain the coordinates of the endpoints of the outermost turn of the coil on the first layer of the reference PCB skeleton unit and the coordinates of the endpoints of the innermost turn of the coil on the second layer of the reference PCB skeleton unit. The distance between the turns on each layer is b, the distance between the turns on each layer of the small PCB is b1, there are two trace segments on the small PCB connecting the coils of other small PCBs, that is, there are two trace segment endpoints, the number of trace segment endpoints on each turn is i1, the number of turns on each layer is i2, and the number of layers per PCB is i3; the coordinates of the intersection point s of the i-th turn end of the j-th layer on the reference PCB skeleton unit (x ji ,y ji , z ji ):

[0016] (j is an odd number), (j is an even number), where x k1 ,y k1 and z k1 is the coordinate of the k1th endpoint of the outermost turn segment of the coil on the first layer of the reference PCB skeleton unit, x k2 ,y k2 and z k2 is the coordinate of the k2th endpoint of the innermost turn of the coil on the second layer of the reference PCB skeleton unit, s = (j-1)*i1*i2+1+i; when k1 and k2 are zero, k1 and k2 are both equal to i1;

[0017] The coordinate expression of the intersection point of the wire turns of the i-th wire turn unit of the j1-th wire turn unit is obtained according to the endpoint coordinates on the reference PCB skeleton unit and the mathematical expression of the symmetrical structure of the skeleton unit;

[0018] Depend on Get the coordinates (x s1+s ,y s1+s , z s1+s ), where (x s ,y s , z s) represents the coordinates of the endpoint of the sth wire turn of the j1th skeleton unit, θ' is the angle between the x-axis and the line connecting the coordinate origin and the geometric center of the j1th skeleton unit on the xOy plane, the subscript s1 = (j1-1)*N1, s1+s, s∈(1,2,3,…,N1), represents the serial number of point s1 in the entire PCB coil, the total number of wire turn endpoints of each reference PCB skeleton unit is N1 = i1*i2*i3+2, the number of skeleton units of each coil is N2, and the number of all intersections of the wire turn segments of the PCB coil is N2*N1;

[0019] The turn segment intersection serial numbers and the x, y, z coordinates of N2*N1 points are stored in a matrix with N2*N1 rows and 4 columns. The turn segment intersections are calculated and numbered according to the order of current flow inside the PCB Rogowski coil.

[0020] In some optional embodiments, The mutual inductance between the i-th turn segment and the j-th turn segment is obtained, where A(x A ,y A ,z A ),B(x B ,y B ,z B ),C(x C ,y C ,z C ) and D(x D ,y D ,z D ) are the coordinates of any two line segments AB and CD in space. Line segments AB and CD are divided into N3 and N4 equal parts respectively. u0 represents the magnetic permeability of vacuum.

[0021] In some optional embodiments, Get the self-inductance of the i-th turn, where l i is the length of the i-th line segment, r l is the length of the wire turn cross section.

[0022] In some optional embodiments, The capacitance between any two turns is obtained, where ε is the dielectric constant and s k is the area between the two turns, h k is the shortest distance between turns, parameter l k is the length of the shortest of the two parallel turn segments, and w1 is the width of the turn.

[0023] In some optional embodiments, Get the electrical relationship between the endpoints of two adjacent wire turns, where R i is the resistance of the ith turn, I i is the branch current at the end of the i-th turn, N is the total number of turns, I i-1 is the branch current at the end of the i-1th turn, U i is the terminal voltage at the end of the i-th turn, U i-1 is the port voltage at the end of the i-1th turn, I S is the input current of the coil, ω=2πf, f is the frequency, C i-1,j is the capacitance between the i-1th turn and the jth turn, C S is the parasitic capacitance of the impedance analyzer probe.

[0024] In some optional embodiments, the matrix form of the electrical relationship is: and in,

[0025]

[0026] Among them, A, B, C, and Z represent the intermediate matrices of the calculation process, and Z i is the impedance of the i-th turn segment.

[0027] In some optional embodiments, The electrical relationship matrix is ​​transformed into an upper triangular matrix form, where (A-ZB -1 C) into the form of an upper triangle, that is (A-ZB -1 C)=DE, E is an upper triangular matrix.

[0028] In some optional implementations, according to the upper triangular coefficient matrix form, Get the ratio of port voltage and port current, matrix F=D -1 ZB -1 ;

[0029] Depend on The frequency response characteristics of the coil are obtained, where Z I (f), R(f) and L(f) are the frequency-dependent port input impedance, equivalent resistance and equivalent inductance of the coil, respectively.

[0030] 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.

[0031] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0032] This invention provides a rapid calculation method for the frequency response characteristics of PCB coils of arbitrary shapes. It is highly versatile and applicable to calculating the frequency characteristics of PCB coil ports with high-density turns and arbitrary wiring structures, as well as to the rapid design of PCB coils of arbitrary structures. The calculation is convenient, requiring no finite element analysis or other calculation software; it is easy to program, saving design time; and the calculation process requires no empirical formulas, resulting in high accuracy. Finally, the theoretical research is validated through experiments.

[0033] It can solve the following problems: 1. Existing common electromagnetic simulation software cannot perform meshing calculations on Rogowski coils with high-density and fine traces; 2. Existing theoretical calculation methods are only applicable to PCB coils with circular and square turns and sparse turns, and are not suitable for PCB coils with high-density and fine traces of arbitrary trace structures.

[0034] The fast calculation method proposed in the present invention is of great significance for the rapid design of PCB coil components and PCB coil sensors and their external circuit parameter matching. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 A PCB coil with high turn density provided by an embodiment of the present invention;

[0036] Figure 2 This embodiment of the present invention provides a Figure 1 A simplified diagram of the PCB coil;

[0037] Figure 3 This is an equivalent circuit of a PCB coil provided by an embodiment of the present invention;

[0038] Figure 4 The following are the calculation and experimental results (10kHz to 2MHz) of the input impedance of a PCB coil provided in an embodiment of the present invention, where (a) is the equivalent inductance and (b) is the equivalent resistance. DETAILED DESCRIPTION

[0039] 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.

[0040] The present invention provides a fast calculation method for the frequency response characteristics of a PCB coil with any structure, comprising the following steps:

[0041] Step 1. Set a point inside the PCB coil as the origin of the 3D rectangular coordinate system. If the PCB coil is geometrically symmetrical, set the geometric center of the PCB coil as the origin of the 3D rectangular coordinate system, and the geometric symmetry axis of the PCB coil as the z-axis of the coordinate system.

[0042] Step 2: The PCB coil's wire turns are generally straight segments. Starting from one end point of the PCB coil, number the intersections of the PCB coil's wire turns and the two end points of the coil in sequence according to the direction of the current flowing inside the coil. The starting end of the coil serves as the reference potential and reference point. If there are M wire turn segments, the total number of wire turn points is M+1.

[0043] Step 3: Obtain the coordinates of the intersection of each turn segment, store the intersection number of the turn segment, the number of the two end points of the coil, and the coordinates of the intersection of each turn segment and the coordinates of the two end points of the coil in a matrix with M+1 rows and 4 columns;

[0044] Step 4: Obtain the spatial parameter equation of each turn of the wire according to the matrix, and then obtain the mutual inductance M between the i-th turn segment and the j-th turn segment. ij ;

[0045] Step 5. Since the PCB coil's wire turns are very thin and their cross-section is generally rectangular, calculate the self-inductance of the mth wire turn segment.

[0046] Step 6: Consider the capacitance between adjacent parallel turn segments and calculate the inter-turn capacitance.

[0047] Step 7: Based on the endpoint coordinates and serial numbers stored in the matrix, the mutual inductance M between the i-th turn segment and the j-th turn segment is calculated. ij , the self-inductance coefficient of the m-th turn segment, the capacitance between turns, and the parallel impedance of the coil port, write the electrical relationship between two adjacent points;

[0048] Step 8: Write the electrical relationship in step 7 into matrix form;

[0049] Step 9: The matrix obtained in step 8 is combined into an equation representing the relationship between the port voltage and the port current through a series of operations, and the frequency response characteristics of the coil are calculated through the equation.

[0050] Furthermore, the method in step 2 specifically includes:

[0051] If the coils do not have identical or symmetrical geometric shapes, write the coordinates of the endpoints of each turn in turn;

[0052] For a PCB coil composed of multiple symmetrical and identically structured small PCBs, the calculation can be performed using the following steps: 1) Align the geometric centerline of one of the small PCBs that make up the coil with the x-axis of the coordinate system. This small PCB coil is considered a reference PCB skeleton unit, and the traces on each layer of this reference skeleton unit are parallel to the x-axis. 2) Number the small PCBs that make up the coil, starting from the reference skeleton and numbering them counterclockwise. Starting from one end of the turns on the reference PCB skeleton, the endpoints of the turn trace segments are numbered in sequence according to the direction of the coil current. 3) If it is a multi-layer PCB board, write down the coordinates of the endpoints of the outermost turn trace segment of the coil on the first layer of the reference small PCB skeleton unit and the coordinates of the endpoints of the innermost turn trace segment of the coil on the second layer of the reference PCB skeleton unit. The distance between the turns on each layer is b, and the distance between the turns on each layer of the small PCB is b1. There are two trace segments on a small PCB connecting coils to other small PCBs, meaning there are two trace segment endpoints. Each turn has i1 trace segment endpoints, each layer has i2 turns, and each PCB has i3 layers. The coordinates of the intersection point s of the i-th turn end on the j-th layer of the reference PCB skeleton (i.e., the trace segment endpoint of the s-th turn on the reference PCB) are calculated as follows:

[0053] (j is an odd number)

[0054] (j is an even number)

[0055] Among them, x k1 ,y k1 and z k1 It is the coordinate of the k1th endpoint of the outermost turn of the coil on the first layer of the reference PCB skeleton unit. k2 ,y k2 and z k2 It is the coordinate of the k2th endpoint of the innermost turn of the coil on the second layer of the reference PCB skeleton unit. s and z s The "±" of is determined by the odd or even number of i, and the formula y s The "±" in the equation is determined by the positive or negative y-coordinate of the first layer of the reference PCB. s=(j-1)*i1*i2+1+i. When k1 and k2 are zero, let k1 and k2 be equal to i1. Finally, based on the endpoint coordinates on the reference PCB skeleton unit obtained in step 2) and the mathematical expression of the symmetrical structure of the skeleton unit, write the coordinate expression of the intersection of the wire turns of the i-th wire turn unit of the j-th skeleton unit; the total number of wire turn segment endpoints of each reference PCB skeleton unit is N1=i1*i2*i3+2, and the number of skeleton units for each coil is N2; the coordinate expression of the s1-th wire turn routing endpoint of the j1-th skeleton unit is:

[0056]

[0057] Where θ' is the angle between the x-axis and the line connecting the origin and the geometric center of the jth skeleton unit on the xOy plane. Subscript s1 = (j1-1)*N1, s1+s, s∈(1,2,3,…,N1) is the serial number of point s1 within the entire PCB coil. The total number of intersections of the PCB coil turns is N2*N1. The turn intersection serial numbers and the x, y, and z coordinates of these N2*N1 points are stored in a matrix with N2*N1 rows and 4 columns. The turn intersections are calculated and numbered according to the order of current flow within the PCB Rogowski coil.

[0058] Furthermore, the mutual inductance M between any two turns in step 4 is calculated as follows: Among them, A(x A ,y A ,z A ),B(x B ,y B ,z B ),C(x C ,y C ,z C ) and D(x D ,y D ,z D ) are the coordinates of any two line segments AB and CD in space. Divide line segments AB and CD into N3 and N4 equal parts, respectively. u0 represents the magnetic permeability of vacuum.

[0059] Furthermore, the method for calculating the self-inductance of the i-th turn in step 5 is: Among them, l i is the length of the i-th line segment, r l is the length of the wire turn cross section.

[0060] Furthermore, the formula for calculating the capacitance in step 6 is: The calculation expression for the capacitance between any two wire turn segments is: Where ε is the dielectric constant, S k is the area between the two turns, h k is the shortest distance between turns, parameter l k is the length of the shortest of the two parallel turn segments, and w1 is the width of the turn.

[0061] Furthermore, the electrical relationship between the endpoints of two adjacent turn segments in step 7 is: Among them, R i is the resistance of the ith turn. iis the branch current at the end of the i-th turn, N is the total number of turns, U i is the port voltage at the end of the i-th turn, I S is the input current of the coil, ω=2πf, f is the frequency. i,j is the capacitance between the end of the i-th wire turn and the end of the j-th wire turn. C S is the parasitic capacitance of the impedance analyzer probe.

[0062] Furthermore, the matrix form of the electrical relationship in step 7 is: and in,

[0063]

[0064] Z i =(jωL i +R i )

[0065] Among them, A, B, C, and Z represent the intermediate matrices of the calculation process, and Z i is the impedance of the i-th turn segment.

[0066] Furthermore, the method for converting the matrix in step 8 into an upper triangular matrix form is:

[0067]

[0068] (A-ZB -1 C) into the form of an upper triangle, that is (A-ZB -1 C)=DE, E is an upper triangular matrix.

[0069] Furthermore, the method for calculating the frequency response characteristics of the coil in step 9 is: based on the upper triangular coefficient matrix obtained in step 8, the steps for obtaining the ratio of the port voltage to the port current are:

[0070]

[0071] Among them, the matrix F = D -1 ZB -1 .

[0072] The frequency response characteristics of the coil are:

[0073]

[0074] Among them, Z I (f), R(f) and L(f) are the frequency-dependent port input impedance, equivalent resistance and equivalent inductance of the coil, respectively.

[0075] The following uses a common PCB coil with thin wire turns and a complex structure and high wire turn density to illustrate this method.

[0076] like Figure 1 As shown in the example, the PCB coil consists of eighteen 40-turn coils on two small PCBs and two circular PCB bases. The bases secure the eighteen PCBs and electrically connect them, forming a circuit path. To prevent electromagnetic interference at right angles in the PCB traces, the commonly used method of creating obtuse angles at the turns is employed. The trace thickness and width are 1 oz and 0.254 mm, respectively.

[0077] Step 1 Figure 2 yes Figure 1 The geometric center of the PCB coil is set as the origin of the three-dimensional rectangular coordinate system, and the geometric symmetry axis of the PCB coil is the z-axis of the coordinate system;

[0078] Step 2: To better illustrate the calculation method of the embodiment, Figure 2 Shown Figure 1 The following diagram illustrates the circuit diagram. The solid and dashed lines represent the traces on the upper and lower PCB chassis, respectively. Points o1, o2, o3, o4, o5, o6, o7, c1, c2, c3, c4, c5, c6, c7, and c8 are located on the outermost turns. b is the distance between adjacent turns.

[0079] The distance between turns on each layer of the small PCB is b1. There are two trace segments connecting each small PCB coil on the small PCB, meaning there are two trace segment endpoints. Each turn has i1 trace segment endpoints, the number of turns per layer is i2, and the number of layers per PCB is i3. The coordinates of the intersection point s of the i-th turn end on the j-th layer of the reference PCB skeleton (i.e., the trace segment endpoint of the s-th turn on the reference PCB) are calculated as follows:

[0080] (j is an odd number)

[0081] (j is an even number)

[0082] Among them, x k1 ,y k1 and z k1 It is the coordinate of the k1th endpoint of the outermost turn of the coil on the first layer of the reference PCB skeleton unit. k2 ,y k2 and z k2 It is the coordinate of the k2th endpoint of the innermost turn of the coil on the second layer of the reference PCB skeleton unit. s and z sThe "±" of is determined by the odd or even number of i, and the formula y s The "±" in this equation is determined by the sign of the y-coordinate of the first layer of the reference PCB. s = (j-1)*i1*i2+1+i. When k1 and k2 are zero, set k1 and k2 equal to i1.

[0083] The total number of turn endpoints of each reference PCB skeleton unit is N1 = i1 * i2 * i3 + 2, and the number of skeleton units per coil is N2. The coordinate expression of the s1th turn endpoint of the j1th skeleton unit is: Where θ' is the angle between the x-axis and the line connecting the origin and the geometric center of the j1th skeleton unit on the xOy plane. The subscript s1 = (j1-1)*N1, s1+s, s∈(1,2,3,…,N1) is the serial number of point s1 within the entire PCB coil. The total number of intersections of the PCB coil's turns is N2*N1. The serial numbers and the x, y, and z coordinates of these N2*N1 points are stored in a matrix with N2*N1 rows and 4 columns. The intersections of the turns are calculated and numbered according to the order of current flow within the PCB Rogowski coil.

[0084] Step 4. Calculate the mutual inductance M between any two turns: Among them, A(x A ,y A ,z A ),B(x B ,y B ,z B ),C(x C ,y C ,z C ) and D(x D ,y D ,z D ) are the coordinates of any two line segments AB and CD in space. Divide line segments AB and CD into N3 and N4 equal parts, respectively. u0 represents the magnetic permeability of vacuum.

[0085] Step 5. Calculate the self-inductance of the i-th turn according to the following formula: Among them, l i is the length of the i-th line segment, r l is the length of the wire turn cross section.

[0086] Step 6. Calculate the parasitic capacitance using the following formula: The capacitance between turn segment AB and turn segment CD is calculated as: Where ε is the dielectric constant, S k is the relative area between the two turns, h kis the shortest distance between turns, parameter l k is the length of the shortest of the two parallel turn segments, and w1 is the width of the turn.

[0087] Step 7: According to Figure 3 Write the electrical relationship between the endpoints of two adjacent turn segments as: Among them, R i is the resistance of the ith turn. i is the branch current at the end of the i-th turn, U i is the port voltage at the end of the i-th turn, I S is the input current of the coil, ω=2πf, f is the frequency. i,j is the capacitance between the end of the i-th wire turn and the end of the j-th wire turn. C S is the parasitic capacitance of the impedance analyzer probe.

[0088] Step 8. Convert the electrical relationship in step 7 into matrix form:

[0089] and in,

[0090] Z i =(jωL i +R i )

[0091] Among them, B, C, and Z represent the intermediate matrices of the calculation process.

[0092] Step 9. Convert the matrix in step 8 into an upper triangular matrix:

[0093]

[0094] (A-ZB -1 C) into the form of an upper triangle, that is (A-ZB -1 C)=DE, E is an upper triangular matrix.

[0095] According to the obtained upper triangular coefficient matrix form, the steps to obtain the ratio of port voltage and port current are:

[0096]

[0097] The frequency response characteristics of the coil are:

[0098]

[0099] Among them, Z I(f), R(f) and L(f) are the frequency-dependent port input impedance, equivalent resistance and equivalent inductance of the coil, respectively.

[0100] When the current frequency is high, the internal parameters of the PCB Rogowski coil begin to affect the output voltage of the Rogowski coil. Figure 4 As shown in the figure, when the frequency is in the range of 10kHz to 2MHz, the comparison between the data based on the fast calculation method and the experimental data shows that the experimental data is basically consistent with the theoretical calculation data, where (a) is the equivalent inductance and (b) is the equivalent resistance.

[0101] 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 (e.g., 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 store, etc., on which a computer program is stored. When the program is executed by a processor, the method for calculating the frequency response characteristics of a PCB coil of any shape in the method embodiment is implemented.

[0102] 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.

[0103] 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 PCB coils of arbitrary shapes, characterized in that: include: Set a point inside the PCB coil as the origin of the three-dimensional rectangular coordinate system. Using one end point of the PCB coil as the starting point, number the intersections of the PCB coil segments and the two end points of the coil in sequence according to the direction of current flow inside the coil. The starting end of the coil serves as the reference potential and reference point. If there are M segments, the total number of the segments is M+1. Obtain the coordinates of the intersection of each turn segment, and store the intersection number of the turn segment, the number of the two end points of the coil, and the coordinates of the intersection of each turn segment and the coordinates of the two end points of the coil in a matrix with M+1 rows and 4 columns; According to the matrix, the spatial parameter equation of each turn of the wire is obtained, and then the mutual inductance M between the i-th turn segment and the j-th turn segment is obtained. ij ; According to the endpoint coordinates and serial numbers stored in the matrix, the mutual inductance M between the i-th wire turn segment and the j-th wire turn segment ij , the self-inductance coefficient of the m-th turn segment, the capacitance between turns, and the parallel impedance of the coil port, to obtain the electrical relationship between two adjacent points, and convert the electrical relationship into a matrix form; The converted matrices are combined into a relationship between the port voltage and the port current, and the frequency response characteristics of the coil are calculated through the relationship between the port voltage and the port current; The method of obtaining the coordinates of the intersection of each turn segment and storing the intersection number of the turn segment, the number of the two end points of the coil, and the coordinates of the intersection of each turn segment and the coordinates of the two end points of the coil in a matrix with M+1 rows and 4 columns includes: If the coils do not have the same or symmetrical geometric shape, write the coordinates of each turn endpoint in turn, and store each turn endpoint number and each turn endpoint coordinate in a matrix with M+1 rows and 4 columns; For a PCB coil composed of multiple symmetrical and identically structured small PCBs, the geometric centerline of one of the small PCBs forming the PCB coil is aligned with the x-axis of the coordinate system, and this small PCB coil is considered the reference PCB skeleton unit. Each layer of the reference PCB skeleton unit has its traces parallel to the x-axis. Number the small PCBs that make up the PCB coil, starting from the reference PCB skeleton unit and numbering them counterclockwise. Starting from one end of the wire turn on the reference PCB skeleton unit, number the end points of the wire turn segments in the direction of the coil current. If it is a multi-layer PCB, obtain the coordinates of the endpoints of the outermost turn of the coil on the first layer of the reference PCB skeleton unit and the coordinates of the endpoints of the innermost turn of the coil on the second layer of the reference PCB skeleton unit. The distance between the turns on each layer is b, the distance between the turns on each layer of the small PCB is b1, there are two trace segments on the small PCB connecting the coils of other small PCBs, that is, there are two trace segment endpoints, the number of trace segment endpoints on each turn is i1, the number of turns on each layer is i2, and the number of layers per PCB is i3; the coordinates of the intersection point s of the i-th turn end of the j-th layer on the reference PCB skeleton unit (x ji ,y ji , z ji ): Among them, x k1 ,y k1 and z k1 is the coordinate of the k1th endpoint of the outermost turn segment of the coil on the first layer of the reference PCB skeleton unit, x k2 ,y k2 and z k2 is the coordinate of the k2th endpoint of the innermost turn of the coil on the second layer of the reference PCB skeleton unit, s = (j-1)*i1*i2+1+i; when k1 and k2 are zero, k1 and k2 are both equal to i1; The coordinate expression of the intersection point of the wire turns of the i-th wire turn unit of the j1-th wire turn unit is obtained according to the endpoint coordinates on the reference PCB skeleton unit and the mathematical expression of the symmetrical structure of the skeleton unit; Depend on Get the coordinates (x s1+s ,y s1+s , z s1+s ), where (x s ,y s , z s ) represents the coordinates of the endpoint of the sth wire turn of the j1th skeleton unit, θ′ is the angle between the x-axis and the line connecting the coordinate origin and the projection of the geometric center of the j1th skeleton unit on the xOy plane, subscript s1 = (j1-1)*N1, s1+s, s∈(1,2,3,…,N1), subscript s1 represents the serial number of point s1 in the entire PCB coil, the total number of wire turn endpoints of each reference PCB skeleton unit is N1 = i1*i2*i3+2, the number of skeleton units of each coil is N2, and the number of all intersections of the wire turn segments of the PCB coil is N2*N1; The turn segment intersection serial numbers and the x, y, z coordinates of N2*N1 points are stored in a matrix with N2*N1 rows and 4 columns. The turn segment intersections are calculated and numbered according to the order of current flow inside the PCB Rogowski coil.

2. The method according to claim 1, characterized in that Depend on The mutual inductance between the i-th turn segment and the j-th turn segment is obtained, where A(x A ,y A ,z A ),B(x B ,y B ,z B ),C(x C ,y C ,z C ) and D(x D ,y D ,z D ) are the coordinates of any two line segments AB and CD in space. Line segments AB and CD are divided into N3 and N4 equal parts respectively. u0 represents the magnetic permeability of vacuum.

3. The method according to claim 2, characterized in that Depend on Get the self-inductance of the i-th turn, where l i is the length of the i-th line segment, r l is the length of the wire turn cross section.

4. The method according to claim 3, characterized in that Depend on The capacitance between any two turns is obtained, where ε is the dielectric constant and s k is the area between the two turns, h k is the shortest distance between turns, parameter l k is the length of the shortest of the two parallel turn segments, and w1 is the width of the turn.

5. The method according to claim 4, characterized in that Depend on Get the electrical relationship between the endpoints of two adjacent wire turns, where R i is the resistance of the ith turn, I i is the branch current at the end of the i-th turn, N is the total number of turns, I i-1 is the branch current at the end of the i-1th turn, U i is the terminal voltage at the end of the i-th turn, U i-1 is the port voltage at the end of the i-1th turn, I S is the input current of the coil, ω=2πf, f is the frequency, C i-1,j is the capacitance between the i-1th turn and the jth turn, C S is the parasitic capacitance of the impedance analyzer probe.

6. The method according to claim 5, characterized in that The matrix form of the electrical relationship is: and in, Among them, A, B, C, and Z represent the intermediate matrices of the calculation process, and Z i is the impedance of the i-th turn segment.

7. The method according to claim 6, characterized in that Depend on The electrical relationship matrix is ​​transformed into an upper triangular matrix form, where (A-ZB -1 C) into the form of an upper triangle, that is (A-ZB -1 C)=DE, E is an upper triangular matrix.

8. The method according to claim 7, characterized in that According to the upper triangular coefficient matrix form, Get the ratio of port voltage and port current, matrix F=D -1 ZB -1 ; Depend on The frequency response characteristics of the coil are obtained, where Z I (f), R(f) and L(f) are the frequency-dependent port input impedance, equivalent resistance and equivalent inductance of the coil, respectively.

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.

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