Wideband equivalent circuit of planar coil and its parameter extraction method

Abstract

The present application discloses a broadband equivalent circuit of a planar coil and a method for extracting its parameters, which relates to the field of equivalent circuits. The broadband equivalent circuit of the planar coil includes: multiple capacitors and N series-connected resistor-inductor composite branches; the resistor-inductor composite branch includes a resistor and an inductor connected in series with the resistor; a capacitor is connected in parallel to each resistor-inductor composite branch; a capacitor is connected in parallel to each resistor-inductor composite branch module; the kth resistor-inductor composite branch module includes the kth resistor-inductor composite branch and the (k + 1)th resistor-inductor composite branch; 1 ≤ k < N. The present application solves the problem that there is no broadband equivalent circuit of a planar coil in the prior art.

Description

Technical Field

[0001] This application relates to the field of equivalent circuits, and in particular to a broadband equivalent circuit of a planar coil and a method for extracting its parameters. Background Technology

[0002] Planar coils typically consist of a conductor layer and an insulating layer. Compared to other coil structures, planar coils offer higher integration and smaller size, making them suitable for applications with strict space constraints. Furthermore, planar coils boast advantages such as uniform current distribution, low loss, and high inductance, thus finding wide application in power electronics, communications, and automotive manufacturing. In power electronics, planar coils can serve as filtering elements, filtering high-frequency noise. Together with devices like thyristors, they enable AC-DC conversion of electrical energy, making them crucial components in power systems and applicable to flexible power transmission technologies. In communications, planar coils are used in the manufacture of smartphones and satellite communication antennas. In the automotive industry, planar coils convert low voltage supplied by the battery to high voltage, enabling spark plugs to ignite combustible gases. The applications of planar coils are extremely broad.

[0003] Establishing a broadband equivalent circuit for a coil can transform complex electromagnetic characteristics into a lumped element model that can be quantified and analyzed. This allows for the rapid prediction of key performance indicators of the coil at high frequencies, such as impedance and resonant frequency. Furthermore, establishing a broadband equivalent circuit for a coil can pre-calculate the transient voltage distribution of the coil under a certain voltage excitation, which helps improve the efficiency of coil design.

[0004] Wideband equivalent circuits can be divided into two types: white-box models and black-box models. Black-box models are mainly used to characterize the port characteristics of devices without requiring detailed internal parameters; while the construction of white-box models is closely related to the internal structure of devices and is often used to study the electromagnetic characteristics of devices. White-box models can be further divided into distributed parameter models and lumped parameter models. Existing wideband equivalent circuits mostly focus on the study of reactors and transformers, and do not address planar coils. Therefore, there is an urgent need for a wideband equivalent circuit for planar coils. Summary of the Invention

[0005] The purpose of this application is to provide a broadband equivalent circuit of a planar coil and a method for extracting its parameters.

[0006] To achieve the above objectives, this application provides the following solution:

[0007] In a first aspect, this application provides a broadband equivalent circuit for a planar coil, wherein the planar coil comprises N turns; N is an integer greater than or equal to 1; the broadband equivalent circuit of the planar coil comprises: multiple capacitors and N series-connected resistor-inductor composite branches; each resistor-inductor composite branch comprises a resistor and an inductor connected in series with the resistor; each resistor-inductor composite branch is connected in parallel with a capacitor; each resistor-inductor composite branch module is connected in parallel with a capacitor; the k-th resistor-inductor composite branch module comprises the k-th resistor-inductor composite branch and the (k+1)-th resistor-inductor composite branch; 1≤k <N。

[0008] Secondly, this application provides a method for extracting broadband equivalent circuit parameters of a planar coil, applied to the broadband equivalent circuit of the planar coil described above. The method for extracting broadband equivalent circuit parameters of the planar coil includes:

[0009] Calculate the resistance value of each turn in the coil domain to obtain the resistance value of each resistor in the broadband equivalent circuit of the planar coil; the coil domain is the coil obtained by connecting the end and beginning of the same turn in the planar coil.

[0010] Calculate the inductance value of each turn in the coil domain to obtain the inductance value of each inductor in the broadband equivalent circuit of the planar coil;

[0011] Calculate the capacitance value of the first terminal of the first coil in the coil domain to obtain the capacitance value of the first parallel resistor-inductor composite branch.

[0012] Calculate the capacitance value of the second terminal capacitor of the (N-1)th coil in the coil domain to obtain the capacitance value of the capacitor connected in parallel in the Nth resistive-inductor composite branch;

[0013] Calculate the sum of the capacitance value of the second terminal of the (k”-1)th turn and the capacitance value of the first terminal of the (k”)th turn in the coil domain to obtain the capacitance value of the parallel capacitor in the (k”)th resistive-inductor composite branch; 1 <k”<N:

[0014] Calculate the capacitance value of the third terminal of the k-th turn in the coil domain to obtain the capacitance value of the parallel capacitor of the resistive-inductor composite branch module composed of the k-th and (k+1)-th resistive-inductor composite branches; 1≤k <N。

[0015] According to the specific embodiments provided in this application, this application has the following technical effects:

[0016] This application provides a broadband equivalent circuit for a planar coil and a method for extracting its parameters. The broadband equivalent circuit for the planar coil includes: multiple capacitors and N series-connected resistor-inductor composite branches; each resistor-inductor composite branch includes a resistor and an inductor connected in series with the resistor; each resistor-inductor composite branch module has a capacitor connected in parallel; each k-th resistor-inductor composite branch module includes: the k-th resistor-inductor composite branch and the (k+1)-th resistor-inductor composite branch. This application solves the problem that existing technologies lack broadband equivalent circuits for planar coils. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a schematic diagram illustrating the idealized relationship between the racetrack-shaped coil domain and the coil turns, provided in another embodiment of this application.

[0019] Figure 2 This is a broadband equivalent circuit diagram of a coil provided in one embodiment of the present application, without considering the capacitive coupling of the coil;

[0020] Figure 3 This is a schematic diagram of a conductor element and a portion of a capacitor provided in an embodiment of this application;

[0021] Figure 4 This is an equivalent schematic diagram of the inter-turn capacitor network provided in one embodiment of this application;

[0022] Figure 5 This is a broadband equivalent circuit diagram of a planar coil provided in one embodiment of this application;

[0023] Figure 6 This is a broadband equivalent circuit diagram of a planar coil with only 3 turns provided in one embodiment of this application;

[0024] Figure 7 This is a flowchart illustrating the construction concept of a broadband equivalent circuit for a planar coil provided in one embodiment of this application;

[0025] Figure 8 This is a finite element model diagram of the magnetic field of the runway-shaped coil domain used in another embodiment of this application;

[0026] Figure 9 This is a schematic diagram of the structure of the kth and (k+1)th turns of the racetrack-shaped coil domain used in another embodiment of this application;

[0027] Figure 10 This is an impedance characteristic curve of the racetrack-shaped planar coil used in another embodiment of this application. Detailed Implementation

[0028] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0029] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0030] like Figure 7 As shown, the construction idea of ​​the broadband equivalent circuit of the planar coil provided in this application is as follows:

[0031] 1) Idealize the entire coil as a coil domain. An actual coil has input and output ends, while a coil domain is the coil formed by connecting the ends and beginnings of the same turn in a planar coil; it is an ideal shape determined by the coil's shape. Specifically, the outer ends of each turn in the planar coil are contracted inwards, causing the ends and beginnings of the turns to coincide. Each turn then forms a closed loop, and this planar coil is called a coil domain.

[0032] 2) Connect the combined resistance and inductance branches of each turn in the coil domain in series to form a broadband equivalent circuit that does not consider the capacitive coupling of the coil, such as... Figure 2 As shown in the figure, R tk L represents the resistance value of the k-th turn in the coil domain. tk This represents the inductance value of the k-th turn in the coil domain, where k represents the turn number, ranging from 1 to N.

[0033] 3) Divide each turn in the coil domain into a series of tiny conductor elements of equal size. The size of the conductor elements can be different for different turns. The capacitance between two turns is characterized by the partial capacitance between the conductor elements of two adjacent turns. For example... Figure 3 As shown, a small segment from each of the two turns is used to describe the concepts of a conductor element and partial capacitance.

[0034] 4) For the capacitance effect between turns in the coil domain, only adjacent turns are considered, while the capacitance effect of non-adjacent turns is ignored.

[0035] 5) Forming a partial capacitor network in the coil domain.

[0036] 6) According to the equivalent principle of terminal capacitance, use the four terminal capacitances C' tk1 , C' tk2 , C' tk3 and C' tk4 of the k-th turn in the coil domain to replace the partial capacitance network between two adjacent turns in the coil domain. As shown in Figure 4 , these 4 capacitances are called inter-turn capacitances, where C' tk4 is short-circuited. Among them, R′ tk represents the equivalent resistance of the k-th turn in the coil domain, and L′ tk represents the equivalent inductance of the k-th turn in the coil domain.

[0037] 7) Combine the terminal capacitance structure with the broadband equivalent circuit without considering the capacitive coupling of the coil to obtain the broadband equivalent circuit of the planar coil. As shown in Figure 5 , N in the figure represents the number of turns of the coil. When N is equal to 3, the broadband equivalent circuit of the planar coil is as shown in Figure 6 . Based on this, the present application provides an exemplary embodiment. As shown in Figure 5 , this embodiment provides a broadband equivalent circuit of a planar coil, and the planar coil includes N turns. The broadband equivalent circuit of the planar coil includes: multiple capacitances and N series-connected resistor-inductor composite branches. The resistor-inductor composite branch includes a resistor and an inductor connected in series with the resistor. A capacitance is connected in parallel to each resistor-inductor composite branch. A capacitance is connected in parallel to each resistor-inductor composite branch module; the k-th resistor-inductor composite branch module includes the k-th resistor-inductor composite branch and the (k + 1)-th resistor-inductor composite branch; 1 ≤ k < N; N is an integer greater than or equal to 1.

[0038] In another exemplary embodiment of the present application, the resistance value of the resistor in the k'-th resistor-inductor composite branch is the resistance value of the k'-th turn in the coil domain; the inductance value of the inductor in the k'-th resistor-inductor composite branch is the inductance value of the k'-th turn in the coil domain; 1 ≤ k' ≤ N. The coil domain is a coil obtained by connecting the end and the beginning of the same turn in the planar coil.

[0039] In another exemplary embodiment of the present application, the capacitance value of the capacitance connected in parallel to the first resistor-inductor composite branch is the capacitance value of the first terminal capacitance of the first turn in the coil domain;

[0040] The capacitance value of the capacitance connected in parallel to the N-th resistor-inductor composite branch is the capacitance value of the second terminal capacitance of the (N - 1)-th turn in the coil domain;

[0041] The capacitance value of the capacitance connected in parallel to the k''-th resistor-inductor composite branch is the sum of the capacitance value of the second terminal capacitance of the (k'' - 1)-th turn and the capacitance value of the first terminal capacitance of the k''-th turn in the coil domain; 1 < k'' < N:

[0042] The capacitance value of the capacitor connected in parallel in the resistive-inductor composite branch module, which consists of the kth resistive-inductor composite branch and the (k+1)th resistive-inductor composite branch, is the capacitance value of the third terminal capacitor of the kth coil in the coil domain.

[0043] This application also provides a method for extracting broadband equivalent circuit parameters of a planar coil, applied to the broadband equivalent circuit of the planar coil described above. The method for extracting broadband equivalent circuit parameters of the planar coil includes:

[0044] Calculate the resistance value of each turn in the coil domain to obtain the resistance value of each resistor in the broadband equivalent circuit of the planar coil.

[0045] Calculate the inductance value of each turn in the coil domain to obtain the inductance value of each inductor in the broadband equivalent circuit of the planar coil;

[0046] Calculate the capacitance value of the first terminal of the first coil in the coil domain to obtain the capacitance value of the first parallel resistor-inductor composite branch.

[0047] Calculate the capacitance value of the second terminal capacitor of the (N-1)th coil in the coil domain to obtain the capacitance value of the capacitor connected in parallel in the Nth resistive-inductor composite branch;

[0048] Calculate the sum of the capacitance value of the second terminal of the (k”-1)th turn and the capacitance value of the first terminal of the (k”)th turn in the coil domain to obtain the capacitance value of the parallel capacitor in the (k”)th resistive-inductor composite branch; 1 <k”<N:

[0049] Calculate the capacitance value of the third terminal of the k-th turn in the coil domain to obtain the capacitance value of the parallel capacitor of the resistive-inductor composite branch module composed of the k-th and (k+1)-th resistive-inductor composite branches; 1≤k <N。

[0050] In another exemplary embodiment of this application, the resistance value of each turn in the coil domain is calculated to obtain the resistance value of each resistor in the broadband equivalent circuit of the planar coil, specifically as follows:

[0051] The resistance values ​​of each coil in the coil domain are calculated based on the length of each coil turn, the total length of the coil domain, and the resistance value of the coil domain, thus obtaining the resistance values ​​of each resistor in the broadband equivalent circuit of the planar coil.

[0052] In practical applications, the resistance of a single turn in the coil domain and the resistance of the coil domain have the following relationship:

[0053]

[0054] In the formula, R is the resistance value of the coil domain, R tkIt is the resistance value of the k-th turn in the coil domain, l tk It is the length of the k-th turn in the coil domain. Figure 1 The length of the idealized coil turns. l is the total length of the coil domain.

[0055] The resistance R of the coil domain is calculated by equation (2):

[0056]

[0057] In the formula, ρ is the resistivity of the selected wire, l is the total length of the coil domain, and S is the cross-sectional area of ​​the coil turns.

[0058] A finite element model of the magnetic field in the coil domain can be established to extract the inductance of each turn, where the turns are idealized. In another exemplary embodiment of this application, the inductance value of each turn in the coil domain is calculated to obtain the inductance value of each inductor in the broadband equivalent circuit of the planar coil, specifically as follows:

[0059] The inductance values ​​of each turn in the coil domain are calculated based on the finite element model of the magnetic field in the coil domain, thus obtaining the inductance values ​​of each inductor in the broadband equivalent circuit of the planar coil.

[0060] In another exemplary embodiment of this application, calculating the capacitance values ​​of the first terminal capacitor, the second terminal capacitor, and the third terminal capacitor of the k-th turn in the coil domain specifically includes:

[0061] Each coil turn in the coil domain is divided into multiple conductor elements on an equal basis;

[0062] Based on the facing areas of each conductor element of the k-th turn and each conductor element of the (k+1)-th turn in the coil domain, and the distance between each conductor element of the k-th turn and each conductor element of the (k+1)-th turn in the coil domain, calculate the partial capacitance value between each conductor element of the k-th turn and each conductor element of the (k+1)-th turn in the coil domain; 1≤k <N;

[0063] Based on the capacitance values ​​of the partial capacitances between each conductor element of the k-th turn and each conductor element of the (k+1)-th turn in the coil domain, calculate the capacitance values ​​of the first terminal capacitor, the second terminal capacitor, and the third terminal capacitor of the k-th turn in the coil domain.

[0064] In another exemplary embodiment of this application, the capacitance value C of the first terminal capacitance of the k-th turn in the coil domain is calculated based on the capacitance value of the partial capacitance between each conductor element of the k-th turn and each conductor element of the (k+1)-th turn in the coil domain. tk1 The calculation formula is:

[0065]

[0066] Where n2 represents the number of conductor elements divided by the (k+1)th turn in the coil domain, n1 represents the number of conductor elements divided by the kth turn in the coil domain, and C ij This represents the capacitance value of the partial capacitance between the i-th wire element in the k-th turn of the coil domain and the j-th wire element in the (k+1)-th turn of the coil domain.

[0067] In another exemplary embodiment of this application, the capacitance value C of the second terminal capacitance of the k-th turn in the coil domain is calculated based on the capacitance value of the partial capacitance between each conductor element of the k-th turn and each conductor element of the (k+1)-th turn in the coil domain. tk2 The calculation formula is:

[0068]

[0069] Where n2 represents the number of conductor elements divided by the (k+1)th turn in the coil domain, n1 represents the number of conductor elements divided by the kth turn in the coil domain, and C ij This represents the capacitance value of the partial capacitance between the i-th wire element in the k-th turn of the coil domain and the j-th wire element in the (k+1)-th turn of the coil domain.

[0070] In another exemplary embodiment of this application, the capacitance value C of the third terminal capacitance of the k-th turn in the coil domain is calculated based on the capacitance value of the partial capacitance between each conductor element of the k-th turn and each conductor element of the (k+1)-th turn in the coil domain. tk3 The calculation formula is:

[0071]

[0072] Where n2 represents the number of conductor elements divided by the (k+1)th turn in the coil domain, n1 represents the number of conductor elements divided by the kth turn in the coil domain, and C ij This represents the capacitance value of the partial capacitance between the i-th wire element in the k-th turn of the coil domain and the j-th wire element in the (k+1)-th turn of the coil domain.

[0073] C ij Calculated by equation (6):

[0074]

[0075] In the formula, ε is the dielectric constant of the conductor insulation, S is the area of ​​the i-th conductor element in the k-th turn of the coil domain and the j-th conductor element in the (k+1)-th turn of the coil domain facing each other, and d is the distance between the i-th conductor element in the k-th turn of the coil domain and the j-th conductor element in the (k+1)-th turn of the coil domain.

[0076] By establishing a practical and refined broadband equivalent circuit for a planar coil and extracting various parameters from the circuit, key indicators such as the coil's impedance at different frequencies can be evaluated in advance, reducing the cost and time of repeated trials.

[0077] This application also provides an embodiment that constructs a broadband equivalent circuit of a racetrack-shaped planar coil and its parameter extraction method. The cross-section of the conductor is rectangular, and the detailed parameters are shown in Table 1. These parameters are manually selected before manufacturing the coil, which are the parameters of the coil domain corresponding to the racetrack-shaped planar coil.

[0078] Table 1. Detailed parameters of the coil domain corresponding to the runway-shaped planar coil.

[0079] Parameter name numerical values Parameter name numerical values Coil inner diameter 200mm Coil length 17.18m Length of the straight portion of the coil 200mm Number of wire turns 15 wire width 8mm Insulation thickness of wires 0.15mm conductor thickness 2mm conductor resistivity <![CDATA[2.85×10 -8 Ohm]]>

[0080] The broadband equivalent circuit of the racetrack-shaped planar coil is established according to the following steps:

[0081] 1) Idealize the entire coil as a coil domain. The relationship between the coil domain and the turns is as follows: Figure 1 As shown, a coil region is a coil obtained by connecting the ends and beginnings of the same turn in a planar coil. It is an ideal shape determined by the shape of the coil. The specific operation is as follows: the outer end of each turn of the planar coil is contracted inward so that the end and beginning of the turn coincide, and each turn forms a closed loop. The planar coil at this time is called a coil region, and the number of turns in the coil region is the same as the number of turns in the planar coil.

[0082] 2) Connect the combined resistance and inductance branches of each coil turn in the coil domain to form a wideband equivalent circuit without considering coil capacitance coupling.

[0083] 3) Divide each coil turn into a series of tiny wire elements of equal size. The size of the wire elements can be different for different coil turns. The capacitance effect between coil turns is characterized by the partial capacitance between the wire elements of two coil turns.

[0084] 4) For the capacitance effect between turns in the coil domain, only adjacent turns are considered, while the capacitance effect of non-adjacent turns is ignored.

[0085] 5) Forming a partial capacitor network in the coil domain.

[0086] 6) Based on the principle of equivalent terminal capacitance, use four terminal capacitors C' tk1 C' tk2 C' tk3 and C' tk4 It is used to replace part of the capacitance network between two adjacent turns in the coil domain.

[0087] 7) By combining the terminal capacitor structure with the broadband equivalent circuit when the capacitive coupling of the coil is not considered, a broadband equivalent circuit of the racetrack-shaped planar coil is obtained, such as... Figure 5 As shown, N is 15.

[0088] Furthermore, the resistance value of the broadband equivalent circuit of the racetrack-shaped planar coil is extracted:

[0089] 1) According to equation (2) and Table 1, the resistance value of the coil domain is R = 30.6mΩ.

[0090] In this embodiment, the ratio of the length of each coil turn to the length of the coil region is shown in Table 2.

[0091] Table 2 shows the ratio of each coil turn to the length of the coil region in this embodiment.

[0092] k <![CDATA[l tk / l]]> 1 0.0603 2 0.0613 3 0.0622 4 0.0631 5 0.0640 6 0.0649 7 0.0658 8 0.0667 9 0.0676 10 0.0685 11 0.0694 12 0.0703 13 0.0712 14 0.0721 15 0.0730

[0093] 2) Further, according to equation (1) and Table 2, the resistance value R of the k-th turn in the coil domain is obtained. tk .

[0094] Furthermore, the inductance value of the broadband equivalent circuit of the racetrack-shaped planar coil is extracted:

[0095] Using the finite element method, the finite element model of the magnetic field of the coil domain in this embodiment is constructed as follows: Figure 8 As shown in the figure, the inductance values ​​of each turn in the coil domain are obtained as shown in Table 3.

[0096] Table 3 shows the inductance values ​​of each turn in the coil region in this embodiment.

[0097]

[0098]

[0099] Furthermore, the capacitance value of the broadband equivalent circuit of the racetrack-shaped planar coil is extracted using the following steps:

[0100] 1) Construct and solve for the partial capacitance network in the semicircular region of the coil domain:

[0101] 1.1) A schematic diagram of the k-th and (k+1)-th turns of any two adjacent turns in the coil domain is shown below. Figure 9 As shown, the semicircular regions of both turns are uniformly divided into n conductor elements, where n is 18 × 10⁻⁶. 4 At this point, the conductor elements of the two turns remain paired.

[0102] 1.2) In the semicircular region, the average area of ​​the opposite sides of the conductor element is taken:

[0103]

[0104] In the formula, r1 and r2 represent the radii of the semicircular regions of the k-th and (k+1)-th turns in the coil domain, respectively; D is the width of the conductor; e is the thickness of the conductor insulation layer; and n is taken as 18 × 10⁻⁶. 4 .

[0105] 1.3) The spacing between the conductor elements is:

[0106] d=2e=3mm (8)1.4) According to Table 1 and Equations (6), (7) and (8), the partial capacitor network of the semicircular region of the coil domain can be solved.

[0107] 2) Construct and solve for the partial capacitance network in the straight region of the coil domain:

[0108] 2.1) In the straight-line regions of the k-th and (k+1)-th turns of the coil domain, the size of the conductor element is selected as the size of the conductor element in the semi-circular region of the k-th turn of the coil domain. At this time, the size of the conductor element in the straight-line region and the semi-circular region of the (k+1)-th turn of the coil domain is approximately equal, while ensuring that the conductor elements of the two turns in the straight-line region remain opposite to each other.

[0109] 2.2) The area of ​​the conductor elements facing each other and the spacing between the conductor elements are calculated using equations (7) and (8) respectively. The number of conductor elements in the straight-line region of the two turns is:

[0110]

[0111] In the formula, H is the length of the straight section of the coil.

[0112] 2.3) The capacitor network of the linear region of the coil domain can be solved according to Table 1 and Equations (6), (7), (8) and (9).

[0113] 3) Further, the value of the terminal capacitance can be obtained according to equations (10), (11), and (12), that is:

[0114] N = 2(m + n) (10)

[0115]

[0116]

[0117] In the formula, C ii C represents the capacitance value of the partial capacitance between the i-th conductor element in the k-th turn and the i-th conductor element in the (k+1)-th turn of the semicircular region of the coil domain. jj This represents the capacitance value of the partial capacitance between the j-th conductor element in the k-th turn and the j-th conductor element in the (k+1)-th turn of the coil domain in the straight line region.

[0118] The calculation results are shown in Table 4.

[0119] Table 4 shows the capacitance values ​​of the terminal capacitors in this embodiment.

[0120] k <![CDATA[C tk1 ]]> <![CDATA[C tk2 ]]> <![CDATA[C tk3 ]]> k <![CDATA[C tk1 ]]> <![CDATA[C tk2 ]]> <![CDATA[C tk3 ]]> 1 62.81pF 117.49pF 53.61pF 8 74.04pF 129.98pF 60.23pF 2 64.40pF 119.28pF 54.56pF 9 75.66pF 131.76pF 61.17pF 3 66.00pF 121.06pF 55.51pF 10 77.29pF 133.54pF 62.10pF 4 67.60pF 122.85pF 56.45pF 11 78.91pF 135.32pF 63.04pF 5 69.20pF 124.63pF 57.40pF 12 80.54pF 137.10pF 63.98pF 6 70.81pF 126.42pF 58.34pF 13 82.18pF 138.88pF 64.91pF 7 72.42pF 128.20pF 59.28pF 14 83.81pF 140.66pF 65.84pF

[0121] Using the planar coil broadband equivalent circuit of this embodiment and the circuit parameters described above, a simulated impedance analysis was performed on the racetrack-shaped planar coil of this embodiment. The racetrack-shaped coil with the parameters described in Table 1 was manufactured, and a measured impedance analysis was performed. The calculated values ​​and measured values ​​are shown below. Figure 10 As shown, the impedance characteristics before 2MHz are basically consistent, verifying the effectiveness of the broadband equivalent circuit and parameter extraction method proposed in this application.

[0122] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0123] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A broadband equivalent circuit for a planar coil, characterized in that, The planar coil includes N turns; N is an integer greater than or equal to 1; the broadband equivalent circuit of the planar coil includes: a plurality of capacitors and N series-connected resistor-inductor composite branches; the resistor-inductor composite branch includes: a resistor and an inductor connected in series with the resistor; a capacitor is connected in parallel to each resistor-inductor composite branch; a capacitor is connected in parallel to each resistor-inductor composite branch module; the k-th resistor-inductor composite branch module includes: the k-th resistor-inductor composite branch and the (k + 1)-th resistor-inductor composite branch; 1 ≤ k < N; the resistance value of the resistor in the k'-th resistor-inductor composite branch is the resistance value of the k'-th turn in the coil domain; the inductance value of the inductor in the k'-th resistor-inductor composite branch is the inductance value of the k'-th turn in the coil domain; 1 ≤ k' ≤ N; the coil domain is a coil obtained by connecting the end and the start of the same turn in the planar coil; the capacitance value of the capacitor connected in parallel to the first resistor-inductor composite branch is the capacitance value of the first terminal capacitor of the first turn in the coil domain; The capacitance value of the capacitor connected in parallel to the N-th resistor-inductor composite branch is the capacitance value of the second terminal capacitor of the (N - 1)-th turn in the coil domain; The capacitance value of the capacitor connected in parallel to the k''-th resistor-inductor composite branch is the sum of the capacitance value of the second terminal capacitor of the (k'' - 1)-th turn and the capacitance value of the first terminal capacitor of the k''-th turn in the coil domain; 1 < k'' < N; The capacitance value of the capacitor connected in parallel to the resistor-inductor composite branch module composed of the k-th resistor-inductor composite branch and the (k + 1)-th resistor-inductor composite branch is the capacitance value of the third terminal capacitor of the k-th turn in the coil domain.

2. A method for extracting broadband equivalent circuit parameters of a planar coil, characterized in that, Applied to the broadband equivalent circuit of the planar coil described in claim 1 above, the method for extracting the broadband equivalent circuit parameters of the planar coil includes: Calculating the resistance values of each turn in the coil domain to obtain the resistance values of each resistor in the broadband equivalent circuit of the planar coil; the coil domain is a coil obtained by connecting the end and the start of the same turn in the planar coil; Calculating the inductance values of each turn in the coil domain to obtain the inductance values of each inductor in the broadband equivalent circuit of the planar coil; Calculating the capacitance value of the first terminal capacitor of the first turn in the coil domain to obtain the capacitance value of the capacitor connected in parallel to the first resistor-inductor composite branch; Calculating the capacitance value of the second terminal capacitor of the (N - 1)-th turn in the coil domain to obtain the capacitance value of the capacitor connected in parallel to the N-th resistor-inductor composite branch; Calculating the sum of the capacitance value of the second terminal capacitor of the (k'' - 1)-th turn and the capacitance value of the first terminal capacitor of the k''-th turn in the coil domain to obtain the capacitance value of the capacitor connected in parallel to the k''-th resistor-inductor composite branch; 1 < k'' < N; Calculating the capacitance value of the third terminal capacitor of the k-th turn in the coil domain to obtain the capacitance value of the capacitor connected in parallel to the resistor-inductor composite branch module composed of the k-th resistor-inductor composite branch and the (k + 1)-th resistor-inductor composite branch; 1 ≤ k < N.

3. The method for extracting broadband equivalent circuit parameters of a planar coil according to claim 2, characterized in that, Calculating the resistance values of each turn in the coil domain to obtain the resistance values of each resistor in the broadband equivalent circuit of the planar coil, specifically: The resistance values ​​of each coil in the coil domain are calculated based on the length of each coil turn, the total length of the coil domain, and the resistance value of the coil domain, thus obtaining the resistance values ​​of each resistor in the broadband equivalent circuit of the planar coil.

4. The method for extracting broadband equivalent circuit parameters of a planar coil according to claim 2, characterized in that, Calculate the inductance value of each turn in the coil domain to obtain the inductance value of each inductor in the broadband equivalent circuit of the planar coil, specifically: The inductance values ​​of each turn in the coil domain are calculated based on the finite element model of the magnetic field in the coil domain, thus obtaining the inductance values ​​of each inductor in the broadband equivalent circuit of the planar coil.

5. The method for extracting broadband equivalent circuit parameters of a planar coil according to claim 2, characterized in that, The calculation of the capacitance values ​​of the first terminal, the second terminal, and the third terminal of the k-th turn in the coil domain specifically includes: Each coil turn in the coil domain is divided into multiple conductor elements on an equal basis; Based on the facing areas of each conductor element of the k-th turn and each conductor element of the (k+1)-th turn in the coil domain, and the distance between each conductor element of the k-th turn and each conductor element of the (k+1)-th turn in the coil domain, calculate the partial capacitance value between each conductor element of the k-th turn and each conductor element of the (k+1)-th turn in the coil domain; 1≤k <N; Based on the capacitance values ​​of the partial capacitances between each conductor element of the k-th turn and each conductor element of the (k+1)-th turn in the coil domain, calculate the capacitance values ​​of the first terminal capacitor, the second terminal capacitor, and the third terminal capacitor of the k-th turn in the coil domain.

6. The method for extracting broadband equivalent circuit parameters of a planar coil according to claim 5, characterized in that, Based on the capacitance values ​​of the partial capacitances between each conductor element of the k-th turn and each conductor element of the (k+1)-th turn in the coil domain, calculate the capacitance value of the first terminal capacitance of the k-th turn in the coil domain. The calculation formula is: ,in, This represents the number of conductor elements divided by the (k+1)th turn in the coil domain. This represents the number of conductor elements divided by the k-th turn in the coil domain. This represents the capacitance value of the partial capacitance between the i-th wire element in the k-th turn of the coil domain and the j-th wire element in the (k+1)-th turn of the coil domain.

7. The method for extracting broadband equivalent circuit parameters of a planar coil according to claim 5, characterized in that, Based on the capacitance values ​​of the partial capacitances between each conductor element of the k-th turn and each conductor element of the (k+1)-th turn in the coil domain, calculate the capacitance value of the second terminal capacitance of the k-th turn in the coil domain. The calculation formula is: ,in, This represents the number of conductor elements divided by the (k+1)th turn in the coil domain. This represents the number of conductor elements divided by the k-th turn in the coil domain. This represents the capacitance value of the partial capacitance between the i-th wire element in the k-th turn of the coil domain and the j-th wire element in the (k+1)-th turn of the coil domain.

8. The method for extracting broadband equivalent circuit parameters of a planar coil according to claim 5, characterized in that, Based on the capacitance values ​​of the partial capacitances between each conductor element of the k-th turn and each conductor element of the (k+1)-th turn in the coil domain, calculate the capacitance value of the third terminal capacitance of the k-th turn in the coil domain. The calculation formula is: ,in, This represents the number of conductor elements divided by the (k+1)th turn in the coil domain. This represents the number of conductor elements divided by the k-th turn in the coil domain. This represents the capacitance value of the partial capacitance between the i-th wire element in the k-th turn of the coil domain and the j-th wire element in the (k+1)-th turn of the coil domain.

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