Equivalent circuit of a spiral coil, its construction method, and impedance characteristic calculation.

Abstract

This invention provides an equivalent circuit of a helical coil, its construction method, and impedance characteristic calculation, belonging to the field of helical coil technology. The equivalent circuit includes multiple series-connected coil modules. Each coil module may include a coil resistance-inductance branch module, a coil-internal capacitance connected in parallel with the coil resistance-inductance branch module, and coil-to-ground capacitances connected between the two ends of the coil resistance-inductance branch module and ground. The coil resistance-inductance branch module may include an inductor and a resistor connected in series. Inter-turn capacitances are connected in parallel across the ends of two adjacent coil modules to form the equivalent circuit of the helical coil. The equivalent circuit structure of the helical coil provided by this invention provides an equivalent circuit for calculating the impedance characteristics of a helical coil based on the equivalent circuit method of impedance characteristics. The use of inter-turn capacitance and internal capacitance simplifies the equivalent circuit structure.

Description

Technical Field

[0001] This invention relates to the field of helical coil technology, specifically to an equivalent circuit of a helical coil and its construction method, as well as impedance characteristic calculation. Background Technology

[0002] A helical coil is formed by winding wire and is used as an inductor in a circuit. Helical coils function to pass direct current, block alternating current, filter harmonics, and store electrical energy. As a fundamental component, helical coils are widely used in electrical applications. Regarding the equivalent circuit of a helical coil, related technologies aim to improve its performance in practical applications through more refined modeling methods.

[0003] In related technologies, based on multiphysics coupling and loss analysis, finite element analysis is used to establish equivalent circuit simulation models and equivalent coil simulation models for electrothermal coupling simulation; an electromagnetic simulation model of coupling mechanics is established to improve prediction accuracy; and optimization algorithms are used for collaborative design. For impedance characteristics, different calculation methods are employed depending on the required accuracy and the complexity of the problem. For example, analytical methods, based on physical formulas and approximate empirical formulas, are suitable for rapid estimation, conceptual design, system simulation, and parameter variation trends. However, these methods are relatively complex and inefficient. Summary of the Invention

[0004] The purpose of this invention is to provide an equivalent circuit of a helical coil, its construction method, and impedance characteristic calculation, so as to solve the problem that the equivalent circuit structure of a helical coil is relatively complex and inefficient.

[0005] To achieve the above objectives, embodiments of the present invention provide an equivalent circuit for a helical coil. The equivalent circuit includes multiple series-connected coil modules. Each coil module includes a coil resistance-inductance branch module, an in-turn capacitance connected in parallel with the coil resistance-inductance branch module, and a coil-to-ground capacitance connected between both ends of the coil resistance-inductance branch module and ground. The coil resistance-inductance branch module includes an inductor and a resistor connected in series. Inter-turn capacitances are connected in parallel across the ends of two adjacent coil modules to form the equivalent circuit of the helical coil.

[0006] This invention also provides a method for calculating the impedance characteristics of a spiral coil. The method is based on the equivalent circuit described above. The method includes: merging the capacitance to ground at the same end of two adjacent coil modules into an equivalent capacitance to ground; merging the intra-turn capacitance and the corresponding inter-turn capacitance of each coil module into an equivalent capacitance; and connecting the equivalent capacitance in parallel with the coil resistance-inductance branch module of that coil module.

[0007] Optionally, for the i-th line-turn module, the i-th resistance of the i-th line-turn resistive-inductive branch module is represented by the following formula.R i : in, ρ Let be the resistivity of the conductor. l i Let be the length of the i-th turn. S Let be the cross-sectional area of ​​the coil.

[0008] Optionally, the i-th inductance of the i-th line-turn resistive inductor branch module can be represented by the following formula. L i : in, l i Let be the length of the i-th turn. μ 0 is the permeability of free space. r Let be the radius of the wire turn cross section. r 1 represents the inner radius of the helical coil. r 2 represents the outer radius of the helical coil.

[0009] Optionally, the capacitance to ground at the beginning of the equivalent circuit can be represented by the following formula. C g1 : in, l 1 represents the length of the first coil. ε 0 is the dielectric constant of vacuum. r Let be the radius of the wire turn cross section. r 1 represents the inner radius of the helical coil. r 2 represents the outer radius of the helical coil.

[0010] Optionally, the capacitance to ground at the end of the equivalent circuit can be represented by the following formula. C gn+1 : in, l n Let n be the length of the nth turn. ε 0 is the dielectric constant of vacuum. r Let be the radius of the wire turn cross section. r 1 represents the inner radius of the helical coil. r 2 represents the outer radius of the helical coil.

[0011] Optionally, the equivalent capacitance to ground can be expressed by the following formula. C gi : in, li Let be the length of the i-th turn. l i+1 Let i be the length of the (i+1)th turn. ε 0 is the dielectric constant of vacuum. r Let be the radius of the wire turn cross section. r 1 represents the inner radius of the spiral coil.

[0012] Optionally, the equivalent capacitance can be expressed by the following formula. C uk : in, l k Let k be the length of the k-th turn. ε 0 is the dielectric constant of vacuum. r Let be the radius of the wire turn cross section. r 1 represents the inner radius of the helical coil. r 2 represents the outer radius of the helical coil.

[0013] This invention also provides a method for constructing an equivalent circuit for a helical coil. The method includes: connecting an inductor and a resistor in series to construct a coil-to-turn resistive-inductance branch module; connecting an in-turn capacitor in parallel with the coil-to-turn resistive-inductance branch module; and connecting a coil-to-ground capacitor between the two ends of the coil-to-turn resistive-inductance branch module and ground to construct a coil module; and connecting multiple coil modules in series and connecting an inter-turn capacitor in parallel with the two ends of two adjacent coil modules to form an equivalent circuit for a helical coil.

[0014] The equivalent circuit of the helical coil provided by the above technical solution includes multiple series-connected coil modules. Each coil module may include a coil resistance-inductance branch module, a coil in-turn capacitor connected in parallel with the coil resistance-inductance branch module, and a coil-to-ground capacitor connected between the two ends of the coil resistance-inductance branch module and ground. The coil resistance-inductance branch module may include an inductor and a resistor connected in series. Inter-turn capacitors are connected in parallel at the ends of two adjacent coil modules to form the equivalent circuit of the helical coil. The equivalent circuit structure of the helical coil provided by the present invention can provide an equivalent circuit for calculating the impedance characteristics of the helical coil based on the equivalent circuit method of impedance characteristics. The use of inter-turn and in-turn capacitance representations simplifies the equivalent circuit structure.

[0015] Other features and advantages of the embodiments of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0016] The accompanying drawings are provided to further illustrate embodiments of the present invention and form part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation thereof. In the drawings: Figure 1 This is a schematic diagram of the equivalent circuit of the spiral coil provided in an embodiment of the present invention; Figure 2 This is a schematic flowchart of a method for calculating the impedance characteristics of a helical coil provided in an embodiment of the present invention; and Figure 3 This is a flowchart illustrating the method for constructing an equivalent circuit for a helical coil provided in an embodiment of the present invention. Detailed Implementation

[0017] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the scope of the present invention.

[0018] This invention provides an equivalent circuit for a helical coil. The equivalent circuit may include multiple series-connected coil modules. Each coil module may include a coil resistance-inductance branch module, an in-turn capacitance connected in parallel with the coil resistance-inductance branch module, and a coil-to-ground capacitance connected between both ends of the coil resistance-inductance branch module and ground. The coil resistance-inductance branch module may include an inductor and a resistor connected in series. Inter-turn capacitances are connected in parallel across the ends of two adjacent coil modules to form the equivalent circuit of the helical coil.

[0019] The equivalent circuit method uses lumped resistors, inductors, and capacitors (R, L, C) to represent the distributed parameters of the helical coil, making it suitable for circuit simulation, filter design, and analysis of wireless power transfer systems. Furthermore, the equivalent circuit method is more intuitive, requires no numerical calculations, and is more efficient. Therefore, the equivalent circuit structure of the helical coil provided in this embodiment of the invention is simpler.

[0020] Please refer to Figure 1 In this embodiment of the invention, the coiled inductance branch module is used to characterize the energy stored in the helical coil and the energy loss caused by DC resistance, hysteresis loss, etc. For example, the first resistor... R 1 and the first inductor L A series connection is formed to constitute a first-turn resistive-inductive branch module; a first-turn in-turn capacitor is connected in parallel across the two ends of the first-turn resistive-inductive branch module; and a first-turn-to-ground capacitor is connected between the two ends of the first-turn resistive-inductive branch module and ground, respectively, to form a first-turn module. In this embodiment of the invention, the ground capacitance and inter-turn capacitance of the turn module together determine the high-frequency response and voltage distribution of the helical coil. Similarly, the first... i resistanceR i With the i-th inductor L i Series connection forms the i-th line-turn resistive inductor branch module; parallel connection is made across the i-th line-turn internal capacitor; in the i-th line-turn... i The two ends of the line-turn resistive inductor branch module are respectively connected to ground. i The capacitance to ground of each wire turn constitutes the i-th wire turn module (i = 2, 3…N, where N is a natural number greater than 2). N wire turn modules are connected in series to form a coil. The inter-turn capacitance of the j-th wire turn is connected in parallel across the j-th and (j+1)-th wire turn modules to form the equivalent circuit of a spiral coil (j = 1, 2…N-1). Furthermore, the capacitance to ground at the same end of two adjacent wire turn modules is combined into a single capacitance to ground, denoted as [missing information]. C gi The capacitances to ground at both ends of the circuit are denoted as follows: C g1 and C gn+1 The capacitor connected in parallel within the turns of the k-th line and the inter-turn capacitor are combined into a single capacitor, denoted as C. uk k=1,2…N.

[0021] The equivalent circuit of the helical coil provided in this embodiment of the invention includes multiple series-connected coil modules. Each coil module may include a coil resistance-inductance branch module, a coil-internal capacitance connected in parallel with the coil resistance-inductance branch module, and a coil-to-ground capacitance connected between the two ends of the coil resistance-inductance branch module and ground. The coil resistance-inductance branch module may include an inductor and a resistor connected in series. Inter-turn capacitances are connected in parallel across the ends of two adjacent coil modules to form the equivalent circuit of the helical coil. The equivalent circuit structure of the helical coil provided in this embodiment of the invention can provide an equivalent circuit for calculating the impedance characteristics of the helical coil based on the equivalent circuit method of impedance characteristics. The use of inter-turn capacitance and internal capacitance simplifies the equivalent circuit structure.

[0022] Please refer to Figure 2 This invention also provides a method for calculating the impedance characteristics of a helical coil. This method is based on the equivalent circuit described above and may include the following steps: Step 210: Combine the capacitance to ground at the same end of two adjacent turn modules into an equivalent capacitance to ground.

[0023] Step 220: Combine the intra-turn capacitance of each wire-turn module with the corresponding inter-turn capacitance to form an equivalent capacitance, and connect the equivalent capacitance in parallel with the wire-turn resistance-inductance branch module of that wire-turn module.

[0024] In a preferred embodiment of the present invention, the i-th line-turn module can be represented by the following formula, which expresses the i-th resistance of the i-th line-turn resistive-inductive branch module.R i : (1) in, ρ Let be the resistivity of the conductor. l i Let be the length of the i-th turn. S Let be the cross-sectional area of ​​the coil.

[0025] In a preferred embodiment of the present invention, the i-th inductance of the i-th line-turn resistive inductor branch module can be represented by the following formula. L i : (2) in, μ 0 is the permeability of free space. r Let be the radius of the wire turn cross section. r 1 represents the inner radius of the helical coil. r 2 represents the outer radius of the helical coil.

[0026] In a preferred embodiment of the present invention, the capacitance to ground at the beginning of the equivalent circuit can be represented by the following formula. C g1 : (3) in, l 1 represents the length of the first coil. ε 0 is the dielectric constant of vacuum.

[0027] In a preferred embodiment of the present invention, the capacitance to ground at the end of the equivalent circuit can be represented by the following formula. C gn+1 : (4) in, l n Let be the length of the nth turn.

[0028] In a preferred embodiment of the present invention, the equivalent capacitance to ground can be expressed by the following formula. C gi : (5) in, l i+1 Let be the length of the (i+1)th line turn, where i∈[2,n].

[0029] In this embodiment of the invention, in step S220, the capacitors connected in parallel within the turns of the k-th line and the inter-turn capacitors are combined into an equivalent capacitor. C uk , and connected in parallel to the inductor branch module of the k-th line, k=1,2…N.

[0030] In a preferred embodiment of the present invention, the equivalent capacitance can be expressed by the following formula. C uk : (6) in, l k For the first k The length of the line turn, k∈[1,n].

[0031] Accordingly, this invention proposes an equivalent circuit and a method for calculating the impedance characteristics of a spiral coil based on the equivalent circuit method of impedance characteristics. The equivalent circuit structure is simplified by using the representation of inter-turn capacitance and intra-turn capacitance.

[0032] Please refer to Figure 3 The present invention also provides a method for constructing an equivalent circuit for a helical coil, the method comprising the following steps: Step 310: Connect the inductor and resistor in series to construct a wire-turn inductor branch module.

[0033] Please refer to Figure 1 For example, the first resistor R 1 and the first inductor L One coil is connected in series to form the first line-turn resistive inductor branch module. The line-turn resistive inductor branch module is used to characterize the energy stored in the helical coil and the energy loss caused by DC resistance, hysteresis loss, etc.

[0034] Step 320: Connect the in-turn capacitor in parallel to the in-turn resistive inductance branch module, and connect the in-turn to ground capacitor between the two ends of the in-turn resistive inductance branch module to the ground respectively, so as to construct the in-turn module.

[0035] Please refer to Figure 1 Following the example above, a first line-turn in-circuit capacitor is connected in parallel across the two ends of the first line-turn in-circuit module; and a first line-turn to-ground capacitor is connected between the two ends of the first line-turn in-circuit module and ground, respectively, to form the first line-turn module.

[0036] In this embodiment of the invention, the capacitance to ground and the inter-turn capacitance of the coil module together determine the high-frequency response and voltage distribution of the spiral coil.

[0037] Step 330: Connect multiple coil modules in series and connect inter-turn capacitors in parallel at both ends of two adjacent coil modules to form an equivalent circuit of a spiral coil.

[0038] Please refer to Figure 1 Following the example above, the first... i resistance R iWith the i-th inductor L i Series connection forms the i-th line-turn resistive inductor branch module; parallel connection is made across the i-th line-turn internal capacitor; in the i-th line-turn... i The two ends of the line-turn resistive inductor branch module are respectively connected to ground. i The capacitance of each coil turn to ground constitutes the i-th coil turn module (i=2, 3…N, where N is a natural number greater than 2). N coil turn modules are connected in series to form a coil. The inter-turn capacitance of the j-th coil turn is connected in parallel across the j-th and (j+1)-th coil turn modules to form the equivalent circuit of a spiral coil (j=1, 2…N-1).

[0039] Continuing with the example above, the capacitances to ground at the same end of the i-th and (i+1)-th line-turn modules are combined into an equivalent capacitance to ground C. gi , i=1,2…N. The equivalent capacitance to ground can be represented by equation (5). C gi。 The intra-turn and inter-turn capacitances connected in parallel on line k are combined into an equivalent capacitance. C uk The circuit is connected in parallel to the inductor branch module of the k-th turn, where k = 1, 2…N. The equivalent capacitance can be represented by equation (6). C uk .

[0040] Accordingly, this invention proposes an equivalent circuit for calculating the impedance characteristics of a spiral coil and a method for constructing the equivalent circuit of a spiral coil based on the equivalent circuit method of impedance characteristics. The equivalent circuit structure is simplified by using the representation of inter-turn capacitance and intra-turn capacitance.

[0041] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0042] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for calculating the impedance characteristics of a helical coil, characterized in that, The method is based on the equivalent circuit of a helical coil. The equivalent circuit includes multiple series-connected coil modules. Each coil module includes a coil resistance-inductance branch module, an in-turn capacitance connected in parallel with the coil resistance-inductance branch module, and coil-to-ground capacitances connected between the two ends of the coil resistance-inductance branch module and ground. Each coil resistance-inductance branch module includes an inductor and a resistor connected in series. An inter-turn capacitance is connected in parallel across the ends of two adjacent coil modules to form the equivalent circuit of the helical coil. The method includes: Combine the capacitance to ground at the same end of two adjacent line-turn modules into an equivalent capacitance to ground; and The in-turn capacitance of each wire-turn module and the corresponding inter-turn capacitance are combined into an equivalent capacitance, and the equivalent capacitance is connected in parallel with the wire-turn resistance-inductance branch module of the wire-turn module. The capacitance to ground at the beginning of the equivalent circuit is expressed by the following formula. C g1 : in, l 1 represents the length of the first coil. ε 0 is the dielectric constant of vacuum. r Let be the radius of the wire turn cross section. r 1 represents the inner radius of the helical coil. r 2 represents the outer radius of the helical coil.

2. The method according to claim 1, characterized in that, For the i-th line-turn module, the i-th resistance of the i-th line-turn resistive-inductive branch module is represented by the following formula. R i : in, ρ Let be the resistivity of the conductor. l i Let be the length of the i-th turn. S Let be the cross-sectional area of ​​the coil.

3. The method according to claim 1, characterized in that, The following formula represents the inductance of the i-th line-turn resistive inductor branch module. L i : in, l i Let be the length of the i-th turn. μ 0 is the permeability of free space. r Let be the radius of the wire turn cross section. r 1 represents the inner radius of the helical coil. r 2 represents the outer radius of the helical coil.

4. The method according to claim 1, characterized in that, The capacitance to ground at the end of the equivalent circuit is expressed by the following formula. C gn+1 : in, l n Let n be the length of the nth turn. ε 0 is the dielectric constant of vacuum. r Let be the radius of the wire turn cross section. r 1 represents the inner radius of the helical coil. r 2 represents the outer radius of the helical coil.

5. The method according to claim 1, characterized in that, The equivalent capacitance to ground is expressed by the following formula. C gi : in, l i Let be the length of the i-th turn. l i+1 Let i be the length of the (i+1)th turn. ε 0 is the dielectric constant of vacuum. r Let be the radius of the wire turn cross section. r 1 represents the inner radius of the spiral coil.

6. The method according to claim 1, characterized in that, The equivalent capacitance is expressed by the following formula. C uk : in, l k Let k be the length of the k-th turn. ε 0 is the dielectric constant of vacuum. r Let be the radius of the wire turn cross section. r 1 represents the inner radius of the helical coil. r 2 represents the outer radius of the helical coil.

7. The method according to claim 1, characterized in that, The equivalent circuit is constructed in the following manner: Connect the inductor and resistor in series to construct a wire-turn inductor branch module; A line-turn inductance branch module is connected in parallel with an inductance-resistance capacitor, and a line-turn-to-ground capacitor is connected between each end of the inductance-resistance branch module and ground to construct the line-turn module; and Multiple coil modules are connected in series, and inter-turn capacitors are connected in parallel at the two ends of adjacent coil modules to form the equivalent circuit of a spiral coil.

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