A method for optimizing design of a magnetic coupling mechanism for a primary-secondary heterogeneous wireless power transmission fixed-point maximum power output

Abstract

The application provides a magnetic coupling mechanism optimization design method for fixed-point maximum power output of primary and secondary side heterogeneous wireless power transmission. The optimal receiving coil is designed in a limited space. The self-inductance and resistance of the transmitting coil are determined through the formula after the wire radius, frequency and load are determined. Then, the outer radius of the receiving coil is determined according to the limited space, the optimal pitch range of the receiving coil is determined, and the optimal mutual inductance is calculated to realize the maximum power output at the fixed position. In static or quasi-static wireless charging, the output power of the receiving end is an important indicator to judge its performance. The magnetic coupling mechanism is an important part of wireless power transmission, and the electrical parameter characteristics and output characteristics are directly related.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of wireless power transmission, and particularly relates to a magnetic coupling mechanism optimization design method for fixed-point maximum power output of primary-secondary heterogeneous wireless power transmission. BACKGROUND

[0002] In recent years, the number of electric vehicles has increased dramatically, and a large number of electric vehicles have been put into use, so the charging problem of electric vehicles must be properly solved. The charging pile is the most common EV power supply device at present. The charging process needs manual operation. There are risks such as poor contact and electric shock in rainy days. The wireless power transmission technology provides a new idea for electric vehicle charging. The non-contact energy transmission mode with electromagnetic field as medium avoids the safety problems such as spark and electric shock caused by physical contact. With intelligent identification control, wireless power transmission can also eliminate manual operation of EV charging.

[0003] In the existing research on wireless power transmission technology in EV charging, whether it is wireless power transmission performance or structural parameter optimization, it is based on the same structure of primary and secondary coils. In actual application, wireless power transmission applied to electric vehicles will be affected by the characteristics of wireless power transmission itself and the application environment of electric vehicles. The disadvantage of electric vehicles in energy replenishment (electric vehicle charging and fuel vehicle refueling) in terms of time consumption requires the maximum output power of EV wireless power to shorten the charging time. In the face of the transmitting end with unified parameter structure in public wireless charging facilities, the receiving end on different vehicles needs to be designed to achieve the maximum system output power. The traditional maximum power output optimization method with the same structure of primary and secondary coils is no longer applicable. SUMMARY

[0004] Therefore, the present application comprehensively considers the size of the receiving coil, the transmission distance and the load difference, and proposes a magnetic coupling mechanism optimization design method for fixed-point maximum power output of primary-secondary heterogeneous wireless power transmission, in order to solve the above problems.

[0005] To achieve the above purpose, the technical scheme of the present application is as follows:

[0006] A magnetic coupling mechanism optimization design method for fixed-point maximum power output of primary-secondary heterogeneous wireless power transmission, comprising the following steps:

[0007] (1) According to the equivalent circuit diagram of the SS compensation form of the wireless power transmission system, the Kirchhoff voltage law of the transmitting end and the receiving end is established;

[0008] (2) According to the Kirchhoff voltage equation set, the currents of the primary and secondary sides are obtained and

[0009] (3) The input power P of the wireless power transfer system is derived from the current in the primary and secondary sides. in Output power P out and transmission efficiency η;

[0010] (4) The larger the mutual inductance of the system, the higher the transmission efficiency. For example, when the mutual inductance X M When a certain value is met, the system's output power P out maximum.

[0011] (5) In a magnetic coupling mechanism with heterogeneous primary and secondary sides and a limited transmitter (the structure of the transmitter coil is known), when the resonant frequency is constant, the mutual inductance X in step (4) is used. M The impedance and mutual inductance of the receiver are used to determine the maximum output power.

[0012] (6) Formula X M The mutual inductances M and R influence and restrict each other. In order to achieve the maximum power output, the adjustment of R and M in practical applications cannot match the theoretical values ​​and there will be a certain deviation. The coil needs to be corrected to minimize the deviation ΔP.

[0013] (7) According to steps (1) and (5), the impedance and mutual inductance of the receiving end are related to the electrical parameters of the coil (the relative spatial position of the two coils in the magnetic coupling mechanism and the physical parameters of the coil).

[0014] (8) Set the optimal physical parameters of the receiving coil to achieve maximum power output at a fixed location.

[0015] Further, in step (1), the Kirchhoff voltage law equations are as follows:

[0016]

[0017] Where: R t =R S +R l1 R r =R L +R 12 X t =ωL1-1 / ωC1,X r =ωL2-1 / ωC2,X M =ωM;

[0018] R t R is the total resistance on the primary side. r For the total resistance on the secondary side, X t X is the total reactance on the primary side. r For secondary side total reactance, X M For mutual inductance reactance;

[0019] Further, in step (2), the original secondary side current and The values are as follows:

[0020]

[0021] Where, B = R t X r + R r X t ;

[0022] Further, in step (3), the input power P in , output power P out and transmission efficiency η formula as follows:

[0023]

[0024] Further, for step (4) the output power maximum, mutual inductance reactance satisfy the formula as follows:

[0025]

[0026] Where, and are the amplitude of the primary and secondary side impedance;

[0027] The formula for the maximum output power is:

[0028]

[0029] The step (4) in wireless power transmission when the primary and secondary side have the same resonant frequency, and the same frequency as the excitation source, that is, in the ideal resonant state, that is, f0=f source , X t = X r = 0, then the formula in step (4) can be simplified as:

[0030]

[0031] Further, in the LC resonant circuit, the voltage across L and C and the current flowing through the frequency f will not be affected by the LC ideal resonant frequency , always the same as the frequency of the excitation source f0=f source ;

[0032] Further, the LC resonant frequency and the excitation source resonant frequency difference Δf=|f0-f source | only affects the equivalent reactance of LC resonance X LC = 2πf source L-1 / 2πfsource C;

[0033] The mutual inductance and impedance adjustment in the step (5) can meet the maximum power output in the step (4). The parameter change of the transmitting coil does not affect the influence law of the parameter of the receiving coil on the mutual inductance; therefore, when the unilateral coil is optimized and designed, the other side is regarded as a known parameter.

[0034] Further, when the parameter of the transmitting coil and the parameter of the magnetic coupling mechanism are known, the mutual inductance M of the magnetic coupling mechanism is mainly affected by the physical parameter of the unilateral coil, and can be expressed as:

[0035] M = x1 (R r , N r , d r ) ;

[0036] Further, the self-inductance of the coil is only constrained by the physical parameter of the coil, and can be expressed as:

[0037] L = x2 (R r , N r , d r ) ;

[0038] Further, the alternating current resistance R AC of the coil in the magnetic coupling mechanism is also constrained by the radius Rr, the number of turns N r and the pitch d r of the unilateral coil, and can be expressed as:

[0039] R AC = x3 (R r , N r , d r ) ;

[0040] The physical parameters of the receiving coil in the step (7) include four parts, which are as follows:

[0041] Firstly, the wire radius, frequency, load and the like are determined; the self-inductance and resistance of the transmitting coil are determined; and the outer radius of the receiving coil is determined according to the limited space;

[0042] Further, the optimal pitch range of the receiving coil is determined, whether the coil includes the internal resistance or not; further, the optimal mutual inductance (or mutual inductance) is calculated according to the mutual inductance reactance formula in the step (4);

[0043] Further, the optimal radius, number of turns and pitch are calculated, and the optimal coil structure is designed;

[0044] Compared with the prior art, the magnetic coupling mechanism optimization design method for the primary-secondary heterogeneous wireless power transmission fixed-point maximum power output has the following beneficial effects:

[0045] (1) The application can be optimized for different types of automobile chassis differences, and the mutual inductance between the receiving coil and the transmitting coil is adjusted to achieve the maximum output power at the fixed point.

[0046] (2) The application only needs to optimize the physical parameters of the receiving coil, without the need for additional equipment assistance, reducing the design cost.

[0047] (3) The diversity of the battery has different load characteristics. The wireless charging process of different electric vehicles needs to combine the battery characteristics to determine the best receiving end. The application avoids the process of combining the battery characteristics in the charging process, saving the environment. BRIEF DESCRIPTION OF DRAWINGS

[0048] Figure 1 is the equivalent circuit diagram of the wireless power transmission using the SS compensation form used in the application;

[0049] Figure 2 is the simplified equivalent circuit diagram obtained by coupling theory from the equivalent circuit diagram of the SS compensation form;

[0050] Figure 3 is the overall analysis and design process of the application;

[0051] Figure 4 is the influence of the coil physical parameters on the mutual inductance, (a) is the influence of the coil inner diameter on the mutual inductance, (b) is the influence of the coil turns on the mutual inductance, and (c) is the influence of the coil pitch on the mutual inductance;

[0052] Figure 5 is the influence of the coil physical parameters on the self-inductance, (a) is the influence of the coil inner diameter on the self-inductance, (b) is the influence of the coil turns on the self-inductance, and (c) is the influence of the coil pitch on the self-inductance;

[0053] Figure 6 is the influence of the coil physical parameters on the ohmic resistance, (a) is the influence of the coil inner diameter on the ohmic resistance, (b) is the influence of the coil turns on the ohmic resistance, and (c) is the influence of the coil pitch on the ohmic resistance;

[0054] Figure 7 is the influence of the coil physical parameters on the ohmic resistance, (a) is the influence of the coil inner diameter on the ohmic resistance, (b) is the influence of the coil turns on the ohmic resistance, and (c) is the influence of the coil pitch on the ohmic resistance; Figure 3 is the detailed summary diagram of the last step of the overall flowchart. DETAILED DESCRIPTION

[0055] It should be noted that the embodiments in the application and the features in the embodiments can be combined with each other without conflict.

[0056] The application will be described in detail below with reference to the accompanying drawings and embodiments.

[0057] Please refer to Figure 1As shown, the wireless power transmission system SS compensation form used by the application uses an equivalent circuit diagram, which is composed of a resonant circuit of capacitance and inductance, where R l1 is the internal resistance of the transmitting end coil, R 12 is the internal resistance of the receiving end coil, R S is the equivalent internal resistance of the transmitting end voltage, U S is the input voltage corresponding to the transmitting end, I t is the current corresponding to the transmitting end, I r is the load current of the receiving end, RL is the load resistance, L1 and L2 are the inductances of the transmitting end and the receiving end respectively, and C1 and C2 are the resonant capacitances connected in series with the transmitting end and the receiving end respectively.

[0058] In the LC resonant circuit, the voltage across L and C and the current flowing through them are not affected by the LC ideal resonant frequency , and are always the same as the frequency f0=f source of the excitation source. As shown, the difference Δf=|f0-f source | between the LC resonant frequency and the resonant frequency of the excitation source only affects the equivalent reactance X LC of the LC resonant circuit. source =2πf source L-1 / 2πf t C. In this equivalent circuit, the LC resonance formed by the coil inductance (ignoring the small stray capacitance) and the compensation capacitance also has the same characteristics. Therefore, in the typical SS compensation form wireless power transmission shown in Figure 1 , the simplified equivalent circuit based on the coupling theory is as shown in Figure 2 . Where R S =R l1 +R r and R L =R l2 +R t are the total resistances of the primary side and the secondary side, X r =ωL1-1 / ωC1 and X M =ωL2-1 / ωC2 are the total reactances of the primary side and the secondary side, and X in =ωM is the mutual inductance reactance.

[0059] Specifically, the calculation steps of the optimal design method of the maximum power output of the primary and secondary side heterogeneous magnetic coupling mechanism of the application are as shown in Figure 3 :

[0060] Step 1: Establish the Kirchhoff voltage law of the transmitting end and the receiving end according to the equivalent circuit diagram of the SS compensation form of the wireless power transmission system;

[0061] Step 2: Obtain the currents of the primary and secondary sides and

[0062] Step three: According to the current of the primary and secondary sides, the input power P in , the output power P out and the transmission efficiency η of the wireless power transmission system are obtained.

[0063] Step four: The transmission efficiency is higher when the mutual inductance reactance of the system is larger. For example, when the mutual inductance reactance X M satisfies a certain value, the output power P out of the system is maximum.

[0064] Step five: In the magnetic coupling mechanism with heterogeneous primary and secondary sides and limited transmitting end (the structure of the transmitting coil is known), when the resonant frequency is a constant value, the impedance and the mutual inductance of the receiving end are obtained from the mutual inductance X M and the maximum output power in step four, which restrict the maximum output power.

[0065] Step six: The mutual inductance M and R in the formula X M restrict each other. In order to achieve the maximum power output state, the adjustment of R and M in the actual application cannot be consistent with the theoretical value, and there will be a certain deviation. The coil needs to be corrected to make the deviation ΔP as small as possible.

[0066] Step seven: According to steps one and five, the impedance and the mutual inductance of the receiving end are related to the electrical parameters of the coil (the relative spatial position of the two coils in the magnetic coupling mechanism and the physical parameters of the coil).

[0067] Step eight: The physical parameters of the optimal receiving coil are set to achieve the maximum power output at a fixed point.

[0068] Preferably, in step one, the Kirchhoff voltage law equation group is as follows:

[0069]

[0070] Preferably, in step two, the currents of the primary and secondary sides are as follows: and

[0071]

[0072] wherein, B = R t X r + R r X t ;

[0073] Preferably, in step three, the formulas of the input power P in , the output power P out and the transmission efficiency η are as follows: ​

[0074]

[0075] Preferably, for the output power maximum in step four, the mutual inductance reactance satisfies the formula as follows:

[0076]

[0077] Wherein, and are the amplitude of the primary and secondary side impedance respectively.

[0078] The formula of the maximum output power is:

[0079]

[0080] Preferably, the mutual inductance and impedance adjustment in step five can satisfy the maximum power output in step four. The parameter change of the transmitting coil does not affect the influence law of the receiving coil parameter on the mutual inductance; therefore, when the single-sided coil is optimized and designed, the other side is regarded as a known parameter.

[0081] Preferably, the formula X M The mutual influence and mutual restraint between R and M are difficult to reach an ideal value in the adjustment process, so there is an error between the theoretical value P out.max of the maximum output power and the actual value P. The power error is ΔP. If the error between the actual power and the theoretical power is less than or greater than this range, the coil needs to be adjusted and corrected, and the maximum value is expected to be reached.

[0082] Figure 4 The influence of the coil physical parameters on the self-inductance is shown. The curve change law is that the coil outer diameter R r and the number of turns N r are positively correlated with the mutual inductance value M of the magnetic coupling mechanism, while the pitch d r is negatively correlated. The slopes of the curves corresponding to the coil outer diameter R r and the pitch d r are approximately constant, that is, the coil outer diameter R r and the pitch d r are linearly related to the mutual inductance M of the magnetic coupling mechanism. With the increase of the number of turns N r , the change rate (curve slope) of the mutual inductance M continuously decreases. This is because when the coil outer diameter R r and the pitch d r are constant, the increased coil radius R continuously decreases, and the number of turns N r continuously weakens the influence of the number of turns N r on the mutual inductance M.

[0083] Preferably, when the transmitting coil parameters and the magnetic coupling mechanism parameters are known, the mutual inductance M of the magnetic coupling mechanism is mainly affected by the physical parameters of the single-sided coil, which can be expressed as:

[0084] M = x1(R r , N r , d r )

[0085] Figure 5 The influence of the coil physical parameters on the self-inductance is shown in the figure. It is verified that the overall change rule of the curve is positively correlated between the coil outer diameter R r and the number of turns N r and the coil self-inductance L r , and the pitch d r is negatively correlated. The coil outer diameter R r and the pitch d r are linearly related to the coil self-inductance L r . But the curve slope corresponding to the coil outer diameter R r and the number of turns N r is larger, that is, the influence of these two coil parameters on the coil self-inductance is more obvious. The coil self-inductance is only constrained by its own physical parameters, which can be expressed as:

[0086] L = x2(R r , N r , d r )

[0087] Figure 6 The influence of the coil physical parameters on the coil ac resistance R AC is shown in the figure. The coil outer diameter R r and the number of turns N r are linearly and positively correlated with the ac resistance R AC . The coil pitch d r is linearly and negatively correlated with the ac resistance R AC . The essence is that the increase of the coil outer diameter R r and the number of turns N will lead to the increase of the total wire length l of the coil, and the increase of the pitch d will lead to the decrease of the total wire length l. In wireless power transmission, the coil is usually wound with Litz wire, which can effectively weaken the skin effect and proximity effect. Therefore, the coil physical parameters and the coil ac resistance are linearly related. Only when the pitch d is very small, the skin effect is not obvious. That is, as the pitch increases, the rate of decrease of the normalized resistance decreases continuously, and eventually stabilizes. The ac resistance R AC of the coil in the magnetic coupling mechanism is also constrained by the radius R r , the number of turns N r and the pitch d r of the single-sided coil, which can be expressed as:

[0088] R AC=x3(R) r N r d r )

[0089] Preferably, in step seven, based on the preceding theory and analysis, the following was obtained: Figure 7 The coil optimization design process shown first determines parameters such as coil wire diameter, load impedance, and resonant frequency based on load and charging performance requirements. In a single-sided confined magnetic coupling mechanism, the physical parameters of the transmitting coil and the relative spatial positions of the two coils in the magnetic coupling mechanism are known conditions. Based on the above analysis, the self-inductance L of the transmitting coil is determined. t and resistance R l1 Based on the structural parameter determination coefficient k(MCM,TX) of the magnetic coupling mechanism, a magnetic coupling mechanism with identical or similar primary and secondary coil structures and parameters is most favorable for wireless power transmission performance. Within the confined space at the receiving end, the radius R of the receiving coil is also kept constant. r As close as possible to the radius R of the transmitting coil t To determine the radius R of the receiving coil r Optimal range. The coil resistance is typically very small, in the mΩ range. The transmitting coil resistance is generally higher than that of the power supply and compensation capacitor, and this should be taken into account. t In the middle. As for the resistance of the receiving coil, it needs to be determined based on the load resistance R. L Determine whether to include Z r To reduce coil losses, the skin effect should be minimized during coil winding. The optimal pitch d is determined based on the resonant frequency determined by the system. r The range. Then, based on the condition of maximum output power, the optimal impedance X is calculated. M Finally, the required outer diameter R of the receiving coil is calculated using the formulas for the mutual inductance, self-inductance, and resistance characteristics of AC coils. r Number of turns N r Pitch d r Construct a receiving coil that maximizes output power at a fixed point.

[0090] Those skilled in the art will recognize that the units and method steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0091] In several embodiments provided in the present application, it should be understood that the disclosed method and system can be implemented in other manners. For example, the division of the above-mentioned units is only a logical function division, and there can be another division manner in actual implementation. For example, a plurality of units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the above-mentioned units can or can not be physical units, and can or can not be distributed on a network. Some or all of the units can be selected according to actual needs to achieve the purposes of the embodiments of the present application.

[0092] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application, and they should be covered in the scope of the claims and the specification of the present application.

[0093] The above only describes the preferred embodiments of the present application, and does not limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A method for optimizing the design of a magnetic coupling mechanism for a primary-secondary heterogeneous wireless power transfer with a fixed-point maximum power output, characterized in that, The method comprises the following steps: (1) The Kirchhoff voltage law of the transmitting end and the receiving end is established according to the equivalent circuit diagram of the wireless power transmission system SS compensation form, and has: where: R t = R S + R l1 , R r = R L + R l2 , X t = ωL1-1 / ωC1, X r = ωL2-1 / ωC2, X M = ωM; R l1 R is the internal resistance of the transmitting coil l2 R is the internal resistance of the receiving coil s R is the equivalent internal resistance of the transmitting voltage R is the input voltage corresponding to the transmitting end L R is the load resistance, L1, L2 are the inductances of the transmitting and receiving ends, respectively, C1, C2 are the resonance capacitances connected in series with the transmitting and receiving ends, respectively t R is the total resistance on the primary side, M is the mutual inductance r R is the total resistance on the secondary side, X t R is the total reactance on the primary side, X r R is the total reactance on the secondary side, X M R is the mutual reactance (2) The currents of the primary and secondary sides are obtained according to the Kirchhoff voltage equations and are respectively: wherein B = R t X r + R r X t ; (3) The input power P of the wireless power transfer system is derived from step (2) in , the output power P out and the transfer efficiency η are respectively: wherein U s and I r are and the modulus of; (4) From step (3), it can be concluded that the larger the mutual inductive reactance of the system, the higher the transmission efficiency. For the output power P out When it is maximum, the mutual inductive reactance X M satisfies: wherein, and are the magnitudes of the primary and secondary side impedances, respectively. For the wireless power transmission system with determined physical structure parameters, there is only one mutual inductance reactance to make the output power maximum, and the formula is: (5) For the magnetic coupling mechanism with original and secondary side heterostructure and limited transmitting end, when the resonant frequency is a constant, the impedance and mutual inductance reactance of the receiving end are obtained from the two formulas of step (4) mutual inductance reactance X M and maximum output power, which restrict the maximum output power. (6) Formula X M The mutual influence between mutual inductance M and R is mutual restraint. If the maximum power output state is to be reached, in actual application, there will be a certain deviation between the regulation of R and M and the theoretical value. The coil needs to be corrected so that the deviation ΔP is as small as possible. (7) According to steps (1) and (5), the impedance and mutual inductance reactance of the receiving end are related to the electrical parameters of the coil, i.e. the relative spatial position of the two coils in the magnetic coupling mechanism and the physical parameters of the coil; (8) According to step (7), the physical parameters of the optimal receiving coil are set to realize the maximum power output at the fixed point position.

2. The magnetic coupling mechanism optimization design method for the primary-secondary heterogeneous wireless power transmission fixed-point maximum power output according to claim 1, characterized in that: When the primary and secondary sides have the same resonant frequency and the same frequency as the excitation source in the wireless power transmission in step (4), that is, in the ideal resonant state, that is, f0=f source , X t =X r =0, the formula in step (4) can be simplified as:

3. The magnetic coupling mechanism optimization design method for the primary-secondary heterogeneous wireless power transmission fixed-point maximum power output according to claim 2, characterized in that: In an LC resonant circuit, the voltage across L and C and the current flowing through them at a frequency f is not influenced by the ideal resonant frequency of LC ; it is always the same as the frequency fo = f source 0 of the excitation source. LC resonance frequency difference from excitation source resonance frequency Δf = |f0-f source | equivalent reactance X that only affects LC resonance LC = 2πf source L-1 / 2πf source C.

4. The magnetic coupling mechanism optimization design method for the primary-secondary heterogeneous wireless power transmission fixed-point maximum power output according to claim 1, characterized in that: The mutual inductance and impedance adjustment in step (5) can meet the maximum power output in step (4); the parameter change of the transmitting coil does not affect the influence law of the receiving coil parameter on the mutual inductance; therefore, when optimizing the single-sided coil, the other side is regarded as a known parameter; when the transmitting coil parameter and the magnetic coupling mechanism parameter are known, the mutual inductance M of the magnetic coupling mechanism is mainly affected by the single-sided coil physical parameter, and can be represented as: M = x1(R r , N r , d r ) ; The self-inductance of the coil is only constrained by its own physical parameter, and can be represented as: L = x2(R r , N r , d r ); The AC resistance R of the coil in the magnetic coupling mechanism AC Similarly constrained by the unilateral coil radius R r , the number of turns N r and the pitch d r , can be expressed as: R AC = x3(R r , N r , d r ); It can be found that the outer diameter R r , the number of turns N r , the pitch d r have almost the same influence on the mutual inductance M, the self-inductance L and the resistance R.

5. The magnetic coupling mechanism optimization design method for the primary-secondary heterogeneous wireless power transmission fixed-point maximum power output according to claim 4, characterized in that: The optimization design of the receiving coil in step (8) includes four parts, which are as follows: 1) Determine the wire radius, frequency and load; determine the self-inductance and resistance of the transmitting coil according to the formula in step (5); determine the outer radius of the receiving coil according to the limited space; 2) Determine the optimal pitch range of the receiving coil, whether it includes the internal resistance of the coil; 3) Calculate the optimal mutual inductance according to the mutual inductance reactance formula in step (4); 4) Calculate the optimal radius, number of turns and pitch, and design the optimal coil structure.

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