CN111931299B - Optimal design method of planar spiral coil in magnetic coupling resonance wireless power transmission application - Google Patents
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Abstract
The invention discloses an optimal design method of a planar spiral coil in magnetic coupling resonance wireless power transmission application, in particular to an optimal design method of a circular wire planar spiral coil, which comprises the following steps: determining the outer diameter and the self-resonance frequency of the circular wire planar spiral coil, selecting the wire type and the wire diameter, calculating the distance between each turn of the wire of the planar spiral coil, calculating the number of turns of the wire of the planar spiral coil to obtain a designed circular wire planar spiral coil, measuring the actual resonance frequency of the designed circular wire planar spiral coil, and then adjusting the number of turns of the wire until the actually measured resonance frequency meets the design requirement of the self-resonance frequency, thereby obtaining the finally optimized circular wire planar spiral coil. The optimal design method of the planar spiral coil in the magnetic coupling resonance wireless power transmission application has high design efficiency and optimizes the performance of the magnetic coupling resonance wireless power transmission system.
Description
Technical Field
The invention belongs to the technical field of wireless power transmission, and relates to an optimal design method of a planar spiral coil in magnetic coupling resonance wireless power transmission application.
Background
Wireless power transfer (Wireless Power Transfer, WPT) technology has become an increasingly attractive area of research as compared to wired power transfer technologies for its advantages such as convenience, safety, cleanliness and applicability. Among them, magnetic coupling resonance wireless power transmission (Magnetic Resonance Coupling WPT, MRC-WPT) has received increasing attention in the last decade and is increasingly being applied to more fields including electric automobiles, implantable medical devices, mobile device power supplies, and the like. The operating frequency of MRC-WPT systems is typically between a few hundred kilohertz and a few tens of megahertz and the transmission distance can be several times the diameter of the transmission coil using field-free shaping techniques. The MRC-WPT technology mainly comprises a two-coil structure and a four-coil structure, wherein the two-coil structure mainly comprises a single-turn driving ring, a multi-turn transmitting spiral coil, a multi-turn receiving spiral coil and a single-turn loading ring. In the four-coil structure MRC-WPT technology, the design of the multi-turn transmitting spiral coil and the multi-turn receiving spiral coil has a huge relation with the overall performance of the system. Therefore, how to design a multi-turn helical coil structure to improve the transmission performance of MRC-WPT systems is one of the hot spots of current research.
At present, multi-turn spiral coils applied to a magnetic coupling resonance wireless power transmission system are mainly divided into a three-dimensional spiral coil and a planar spiral coil. The three-dimensional spiral coil has good structural symmetry, and the radius of each coil is the same, so that the establishment and analysis of a coil physical model are facilitated, and meanwhile, the three-dimensional spiral coil has a longer transmission distance. But it is bulky, making space utilization low and not conducive to practical system design. Planar spiral coils, also known as archimedes spiral coils, have inferior structural symmetry, and have little difficulty in building and analyzing a physical model of the coil due to the different radii of each turn of the coil. But because the planar structure of the coil has smaller volume and high space utilization rate, the design of an actual system is facilitated.
Planar spiral coils can be divided into two different forms, flat wire planar spiral coils and round wire planar spiral coils. Flat wire coils are typically designed on printed circuit boards and are relatively small, often for low power applications at frequencies above hundred megahertz. The round wire coil is usually wound by an enameled wire or a litz wire, has a large volume and is often used for medium and high power application occasions with a few megahertz. These two structures differ greatly in terms of the derivation of the physical model. At present, the design schemes for flat wire spiral coils are more, but the design schemes for round wire flat spiral coils are not mature enough, and experiments are usually mainly used in design, so that the results of resource waste, lower design efficiency, poor system performance and the like are caused.
Disclosure of Invention
The invention aims to provide an optimal design method of a planar spiral coil in magnetic coupling resonance wireless power transmission application, which derives a mathematical expression of the self-resonance frequency of a circular wire planar spiral coil and the quality factor of the coil under the precondition that the outer diameter of the planar spiral coil and the self-resonance frequency of the coil are given, obtains an optimal coil quality factor and the corresponding number of turns of the coil and the distance between each turn of the coil, has high design efficiency, and optimizes the performance of a magnetic coupling resonance wireless power transmission system.
The technical scheme adopted by the invention is that the optimal design method of the planar spiral coil in the magnetic coupling resonance wireless power transmission application, in particular to the optimal design method of the planar spiral coil of the round wire, which is implemented according to the following steps:
step 1, determining the outer diameter D of a circular wire planar spiral coil o And a self-resonance frequency f;
step 2, selecting a wire type and determining a wire diameter w;
step 3, determining the outer diameter D of the circular wire planar spiral coil according to the steps 1 and 2 o Calculating the space s of each turn of the planar spiral coil wire from the resonance frequency f and the wire diameter w;
step 4, calculating the number of turns N of the planar spiral coil wire to obtain a designed circular wire planar spiral coil;
step 5, measuring the actual resonant frequency f of the round wire planar spiral coil designed in step 4 1 Then the number of turns N of the lead is adjusted until the actual measured resonant frequency f 1 The design requirement of the self-resonant frequency f is satisfied,and obtaining the final optimized round wire planar spiral coil.
The present invention is also characterized in that,
the step 1 specifically comprises the following steps: determining the outer diameter D of a circular wire planar spiral coil according to the required design size and the required working frequency of a specific magnetic coupling resonance wireless power transmission system o And a self-resonant frequency f.
The step 2 is specifically as follows: the wire type is selected to be enameled wire or litz wire according to actual conditions, and the wire diameter w is selected according to the actual conditions.
The step 3 is specifically as follows: calculating the pitch per turn s of the planar spiral coil wire according to equation (13):
wherein mu r Is relative permeability, mu 0 For vacuum permeability, epsilon r For relative conductivity, ε 0 For vacuum conductivity, D o For the outer diameter of a circular wire planar spiral coil, f is the self-resonant frequency, W is the wire diameter, Ω is the sign of the Lambert W function, which defines: Ω (x) =w [Im(x)/(2π)-1/2] (e x ) Wherein, the method comprises the steps of, wherein,
the step 4 is specifically as follows: calculating the number of turns N of the planar spiral coil wire according to the formula (14):
the beneficial effects of the invention are as follows: compared with the original design method mainly based on experiments, the method can obtain the optimal coil quality factor and the corresponding coil turns, coil turn-to-turn distance and round wire diameter by deducing the mathematical expression of the round wire planar spiral coil self-resonance frequency and the coil quality factor under the precondition that the planar spiral coil outer diameter and the coil self-resonance frequency are given. Compared with the original experimental trial-and-error method, the designed planar spiral coil saves design resources, improves design efficiency and optimizes the performance of the magnetic coupling resonance wireless power transmission system by utilizing the mathematical analysis method.
Drawings
FIG. 1 is a front view of the structural dimensions of a corresponding circular wire planar spiral coil of the present invention;
fig. 2 is a cross-sectional view of the corresponding circular wire planar spiral coil structure of the present invention.
Detailed Description
The invention will be described in detail below with reference to the drawings and the detailed description.
The invention relates to an optimal design method of a planar spiral coil in magnetic coupling resonance wireless power transmission application, in particular to an optimal design method of a circular wire planar spiral coil, which is shown in a front view of the structural dimension of the circular wire planar spiral coil corresponding to the invention as shown in figure 1, and is shown in a cross-sectional view of the structural dimension of the circular wire planar spiral coil corresponding to the invention as shown in figure 2, wherein the circular wire planar spiral coil takes O as a circle center, and D is shown as a circle center o For the outer diameter of a planar spiral coil, the total rotation angle of the inward rotation of the coil is defined as θ, the number of turns of the coil is defined as n=θ/(2pi), and when the coil is rotated Δθ, the radius of the coil is defined as r (Δθ) = (D) o +s)/2-s.delta.theta/(2pi), where s is the inter-turn pitch of the planar spiral coil and the inter-turn pitches are equal, and w is defined as the wire diameter of the round wire used.
The expression of the parasitic inductance of a circular wire planar spiral coil is shown in formula (1) and is a function of the planar spiral coil outer diameter Do, the number of turns N and the spacing s of each turn of the coil.
Wherein mu is r Is relative permeability, mu 0 Is vacuum magnetic permeability.
Skin depth delta of copper wire Cu The expression of (2) is shown as a function of the planar spiral coil operating frequency f.
In practice, litz wire or enameled wire is often used to wind planar spiral coils. Litz wire is stranded or braided from a plurality of independently insulated conductors, i.e. a single wire is replaced by a plurality of thin wires in parallel. Typically, the diameter of the individual thin wires is smaller than the skin depth, so the effect of the skin effect on the resistance is not considered when using litz wire. In contrast, when using the enamel wire, since the enamel wire is a single wire, the influence of the skin effect on the parasitic resistance of the coil must be considered in high frequency application.
The litz wire wound planar spiral parasitic resistance expression is shown in equation (3) and is a function of the planar spiral outer diameter Do, the number of turns N, the coil per turn spacing s, and the litz wire total diameter w.
The parasitic resistance expression of the planar spiral coil wound by the enameled wire is shown as a formula (4), and is a function of the outer diameter Do of the planar spiral coil, the number of turns N, the interval s of each turn of the coil, the diameter w of the wire and the working frequency f of the planar spiral coil.
In the formulas (3) and (4), ρ Cu Is the resistivity of copper.
The calculation of the distributed capacitance of the planar spiral coil of the circular wire is shown as (5), and is a function of the outer diameter Do of the planar spiral coil, the number of turns N, the spacing s of each turn of the coil and the diameter w of the wire.
Wherein ε r For relative conductivity, ε 0 Is vacuumConductivity.
The self-resonant frequency expression of the planar spiral coil is shown as a formula (6) and is the coil outer diameter D according to the parasitic inductance L expression of the planar spiral coil shown as a formula (1) and the distributed capacitance C expression shown as a formula (5) O A function of the number of turns N, the spacing s, and the line width w.
In planar spiral coil design, the planar spiral coil outer diameter Do and the ideal self-resonant frequency f are generally determined according to specific requirements. By varying the number of turns N, wire spacing s, and wire diameter w of the planar spiral coil, the performance of the coil can be varied. The wire diameter w is furthermore easily determined from other parameters, so that there are only two degrees of freedom for the three parameters of the number of turns N of the planar spiral, the wire spacing s and the wire diameter w. It is further obtained that the wire diameter w should satisfy the formula (7).
Wherein,
since the quality factor is related to the parasitic resistance of the coil, the calculated expression of the quality factor Q is different when the enamel wire and the litz wire are used.
The quality factor is represented by Q= (L/C) 0.5 R is calculated. When the enameled wire is used, according to a plane spiral coil parasitic inductance calculation formula (1), an enameled wire coil parasitic resistance calculation formula (4), a plane spiral coil distributed capacitance calculation formula (5), a skin depth expression (2) and a wire diameter expression (7), an expression of a quality factor Q of a coil wound by the enameled wire can be obtained as shown in an expression (8).
When litz wire is used, the expression of quality factor Q of the wound litz wire coil can be obtained as shown in expression (9) according to the planar spiral coil parasitic inductance calculation formula (1), the litz wire coil parasitic resistance calculation formula (3), the planar spiral coil distributed capacitance calculation formula (5), and the wire diameter expression (7).
The method is implemented according to the following steps:
step 1, determining the outer diameter D of a circular wire planar spiral coil o And a self-resonance frequency f; the method comprises the following steps: determining the outer diameter D of a circular wire planar spiral coil according to the required design size and the required working frequency of a specific magnetic coupling resonance wireless power transmission system o And a self-resonance frequency f;
step 2, selecting a wire type and determining a wire diameter w; the method comprises the following steps: the type of the wire is selected to be an enameled wire or a litz wire according to the actual situation, and the diameter w of the wire is selected according to the actual situation;
the quality factor of a circular wire planar spiral coil is a function of the parasitic inductance L, the parasitic capacitance C and the parasitic resistance R of the planar spiral coil, and according to the formulas (3) and (4), the wire type affects only the parasitic resistance R of the planar spiral coil, and the parasitic resistance is lower when litz wire is used, so that the quality factor of the planar spiral coil is higher. Litz wire is generally more costly than enameled wire, and therefore requires selection of wire types according to the design requirements and cost of a particular wireless power transmission system:
as can be obtained from the quality factor calculation formulas (8) and (9), increasing the wire diameter w increases the coil quality factor Q. This is because an increase in wire diameter reduces the planar spiral resistance with less impact on the planar spiral resistance and distributed capacitance. Taking a quality factor calculation formula of an enameled wire as an example, Q 2 The bias derivative for w can be given by formula (10):
in general, to ensure that the distributed capacitance of the coil is small, s/w >1.5 should be satisfied, where equation (10) is always positive, i.e., the larger the wire diameter w, the larger the quality factor Q. Similarly, it can be demonstrated that this conclusion holds for the figure of merit equation using litz wire;
therefore, when designing the round wire planar spiral coil, wires with wider wire diameters should be selected as much as possible according to the design requirements and cost of a specific wireless power transmission system;
step 3, determining the outer diameter D of the circular wire planar spiral coil according to the steps 1 and 2 o Calculating the space s of each turn of the planar spiral coil wire from the resonance frequency f and the wire diameter w; the method comprises the following steps: as can be obtained from the quality factor calculation formulas (8) and (9), increasing the number of turns N of the planar spiral coil increases the coil quality factor Q, but the relationship between the number of turns N of the coil and the quality factor Q is not linear, and there is an inflection point in the function, through which the quality factor Q is substantially unchanged, so that the coil parameter at the inflection point can be regarded as an optimal value,
the inflection point of the hidden function is obtained by using a quality factor equation of the enameled wire, and the hidden function can be obtained by the formula (9), wherein the number of turns N of the coil and the inter-turn distance s of the lead are required to meet, and the hidden function is shown as the formula (11):
the hidden function Q (N, s) has an inflection point, and ds/dN=0 is satisfied at the inflection point, so that the equation is satisfied at the inflection pointThus, it can be obtained that the number of coil turns N and the wire per turn spacing s should satisfy the formula (12):
to sum up, when the number of turns N of the wire is equal to the wireThe product of the spacing of turns s is about 0.376D 0 When the quality factor Q of the planar spiral coil is relatively optimal, the result is substituted into formula (6), and since the self-resonant frequency f is a known quantity and the turn-to-turn distance s is an unknown quantity, the expression of the turn-to-turn distance s of the coil can be obtained as shown in formula (13):
calculating the pitch per turn s of the planar spiral coil wire according to equation (13):
wherein mu r Is relative permeability, mu 0 For vacuum permeability, epsilon r For relative conductivity, ε 0 For vacuum conductivity, D o For the outer diameter of a circular wire planar spiral coil, f is the self-resonant frequency, W is the wire diameter, Ω is the sign of the Lambert W function, which defines: Ω (x) =w [Im(x)/(2π)-1/2] (e x ) Wherein, the method comprises the steps of, wherein,
although the figures of merit equations for the enameled wire and litz wire are different, the expression of the coil per turn spacing s under the optimal parameters can be obtained through calculation. Thus, the pitch per turn s of the planar spiral coil wire can be calculated according to equation (13);
step 4, calculating the number of turns N of the planar spiral coil wire to obtain the designed circular wire planar spiral coil, which is specifically as follows: calculating the number of turns N of the planar spiral coil wire according to the formula (14):
step 5, measuring the actual resonant frequency f of the round wire planar spiral coil designed in step 4 1 Then the number of turns N of the lead is adjusted until the actual measured resonant frequency f 1 The design requirement of the self-resonant frequency f is met, and the finally optimized circular wire planar spiral coil is obtained.
Claims (2)
1. The optimal design method of the planar spiral coil in the magnetic coupling resonance wireless power transmission application is characterized by comprising the following steps of:
step 1, determining the outer diameter of a circular wire planar spiral coilD o And self-resonant frequencyfThe method specifically comprises the following steps: determining the outer diameter of a circular wire planar spiral coil according to the required design size and the required working frequency of a specific magnetic coupling resonance wireless power transmission systemD o And self-resonant frequencyf；
Step 2, selecting the wire type and determining the wire diameterwThe method specifically comprises the following steps: the type of the wire is selected as an enameled wire or a litz wire according to the actual situation, and the diameter of the wire is selected according to the actual situationw；
Step 3, determining the outer diameter of the circular wire planar spiral coil according to the steps 1 and 2D o Self-resonant frequencyfAnd wire diameterwCalculating the inter-turn distance of the planar spiral coil wiresThe method comprises the steps of carrying out a first treatment on the surface of the The method comprises the following steps: calculating the inter-turn distance of the planar spiral coil wire according to (13)s：
（13）；
Wherein,μ r for the relative magnetic permeability to be high,μ 0 is the magnetic permeability of the vacuum and is equal to the magnetic permeability of the vacuum,ε r in order to be of relative electrical conductivity,ε 0 for the purpose of vacuum conductivity,D o is the outer diameter of a plane spiral coil of a round wire,fis a frequency of the self-resonance and,wfor the wire diameter,for the Lambert W function symbol,Lambert Wfunction definition: />Wherein->；
Step 4, calculating the number of turns of the planar spiral coil wireNObtaining a designed circular wire plane spiral coil;
step 5, measuring the actual resonant frequency of the round wire planar spiral coil designed in step 4f 1 Then the number of turns of the wire is adjustedN，Up to the actual measured resonant frequencyf 1 Satisfy the self-resonant frequencyfThe final optimized round wire planar spiral coil is obtained.
2. The method for optimizing design of planar spiral coils in magnetic coupling resonance wireless power transmission applications according to claim 1, wherein the step 4 is specifically: calculating the number of turns of the planar spiral coil wire according to formula (14)N：
（14）。
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