Magnetic coupling mechanism optimization design method for fixed-point maximum power output of primary and secondary side heterogeneous wireless power transmission

Abstract

The invention provides a magnetic coupling mechanism optimization design method for fixed-point maximum power output of primary and secondary side heterogeneous wireless power transmission. An optimal receiving coil is designed in a limited space, the radius, the frequency and the load of a wire are determined firstly, then the self-inductance and the resistance of a transmitting coil are determined through a formula, 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 optimal mutual inductance is calculated to achieve the maximum power output of a fixed position. During static or quasi-static wireless charging, the output power of a receiving end is an important index for judging the performance of the receiving end. The magnetic coupling mechanism serves as an important component of wireless power transmission, and the electrical parameter characteristics of the magnetic coupling mechanism are directly related to the output characteristics.

Description

Technical Field

[0001] The present invention belongs to the field of wireless power transmission, and in particular relates to an optimization design method for a magnetic coupling mechanism for fixed-point maximum power output of primary-secondary heterogeneous wireless power transmission. Background Art

[0002] In recent years, the number of electric vehicles has increased dramatically. With a large number of electric vehicles put into use, the problem of electric vehicle charging must be properly solved. Charging piles are currently the most common EV power supplement equipment. The charging process requires manual operation. There are risks such as poor contact and electric shock on rainy days. Wireless power transmission technology provides a new idea for electric vehicle charging. The non-contact energy transmission method using electromagnetic fields as the medium avoids safety issues such as sparks and electric shock caused by physical contact. With intelligent recognition 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, both the wireless power transmission performance and the structural parameter optimization are based on the same primary and secondary coil structures. In practical applications, 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 terms of energy replenishment (electric vehicle charging and fuel vehicle refueling) compared to fuel vehicles requires maximizing the wireless power output power of EVs to shorten the charging time. Faced with the transmitter with unified parameter structure in public wireless charging facilities, the receiving end on different vehicles must be designed in a targeted manner to achieve the maximum system output power. The traditional maximum power output optimization method with the same primary and secondary coil structure is no longer applicable. Summary of the invention

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

[0005] To achieve the above object, the technical solution of the present invention is achieved as follows:

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

[0007] (1) Establish Kirchhoff's voltage law at the transmitter and receiver based on the equivalent circuit diagram of the SS compensation form of the wireless power transmission system;

[0008] (2) According to Kirchhoff's voltage equations, the current of the primary and secondary sides is obtained and

[0009] (3) The input power P of the wireless power transmission system is obtained based on the current of the primary and secondary sides. in , output power P out and transmission efficiency η;

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

[0011] (5) For a 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, the mutual inductance reactance X in step (4) is M The maximum output power is obtained by the impedance and mutual inductance of the receiving end.

[0012] (6) Formula X M The mutual inductances M and R influence and restrict each other. If the maximum power output state is to be achieved, in practical applications, the adjustment of R and M cannot be consistent with the theoretical values, and there will be a certain deviation. The coil needs to be corrected to make the deviation ΔP as small as possible.

[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 physical parameters of the optimal receiving coil to achieve maximum power output at a fixed point.

[0015] Furthermore, 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 l2 , X t =ωL1-1 / ωC1,X r =ωL2-1 / ωC2, X M =ωM;

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

[0019] Furthermore, in step (2), the current of the primary and secondary sides is and The values ​​are as follows:

[0020]

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

[0022] Furthermore, in step (3), the input power P in , output power P out The formula for the transmission efficiency η is as follows:

[0023]

[0024]

[0025]

[0026] Furthermore, when the output power in step (4) is the maximum, the formula satisfied by the mutual inductance reactance is as follows:

[0027]

[0028] in, and are the magnitudes of the primary and secondary impedances respectively;

[0029] The formula for maximum output power is:

[0030]

[0031] In step (4), when the primary and secondary sides of the wireless power transmission have the same resonant frequency and the same frequency as the excitation source, it is in an ideal resonant state, that is, f0 = f source When X t =X r =0, then the formula in step (4) can be simplified to:

[0032]

[0033] Furthermore, in the LC resonant circuit, the voltage across L and C and the current frequency f flowing through it are not affected by the LC ideal resonant frequency. The influence of the excitation source is always related to the frequency f0 = f source same;

[0034] Furthermore, the difference between the LC resonant frequency and the resonant frequency of the excitation source is Δf = |f0-f source |Equivalent reactance X that only affects LC resonance LC =2πf source L-1 / 2πf source C;

[0035] The mutual inductance and impedance adjustment in step (5) can satisfy the maximum power output in step (4). The parameter change of the transmitting coil does not affect the influence of the receiving coil parameters on the mutual inductance; therefore, when optimizing the design of a single-side coil, the other side is considered as a known parameter.

[0036] Furthermore, when the parameters of the transmitting coil and the magnetic coupling mechanism are known, the mutual inductance M of the magnetic coupling mechanism is mainly affected by the physical parameters of the single-side coil and can be expressed as:

[0037] M=x1(R r , N r , d r );

[0038] Furthermore, the coil self-inductance is only constrained by its own physical parameters and can be expressed as:

[0039] L=x2(R r , N r , d r );

[0040] Furthermore, the AC resistance R of the coil in the magnetic coupling mechanism AC The same is true for the single-sided coil radius R r 、Number of turns r and pitch d r The constraint can be expressed as:

[0041] R AC =x3(R r , N r , d r );

[0042] The physical parameters of the receiving coil in step (7) include four parts, which are as follows:

[0043] First, determine the wire radius, frequency, load, etc.; determine the self-inductance and resistance of the transmitting coil; determine the outer radius of the receiving coil based on the limited space;

[0044] Further, determining the optimal pitch range of the receiving coil, whether it includes the internal resistance of the coil, etc.; further, calculating the optimal mutual inductance (or mutual inductance) according to the mutual inductance reactance formula in step (4);

[0045] Furthermore, the optimal radius, number of turns and pitch are calculated, and the optimal coil structure is designed;

[0046] Compared with the prior art, the magnetic coupling mechanism optimization design method for fixed-point maximum power output of primary-secondary heterogeneous wireless power transmission described in the present invention has the following beneficial effects:

[0047] (1) The present invention can be optimized for the differences in chassis of different types of vehicles, and the maximum output power at a fixed point can be achieved by adjusting the mutual inductance between the receiving coil and the transmitting coil;

[0048] (2) The present invention only needs to optimize the physical parameters of the receiving coil and does not require the use of additional equipment, thereby reducing the design cost;

[0049] (3) Diverse batteries have differentiated load characteristics. The wireless charging process of different electric vehicles needs to combine the battery characteristics to determine the best receiving end. The present invention avoids the process of combining the battery characteristics during the charging process, saving the environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is the equivalent circuit diagram of wireless power transmission in the form of SS compensation used in the present invention;

[0051] Figure 2 It is a simplified equivalent circuit diagram obtained by coupling theory from the equivalent circuit diagram of SS compensation form;

[0052] Figure 3 It is the overall analysis and design process of the present invention;

[0053] Figure 4 is the effect of coil physical parameters on mutual inductance, (a) is the effect of coil inner diameter on mutual inductance, (b) is the effect of coil turns on mutual inductance, and (c) is the effect of coil pitch on mutual inductance;

[0054] Figure 5 is the effect of the physical parameters of the coil on the self-inductance, (a) is the effect of the inner diameter of the coil on the self-inductance, (b) is the effect of the number of turns of the coil on the self-inductance, and (c) is the effect of the pitch of the coil on the self-inductance;

[0055] Figure 6 is the effect of the physical parameters of the coil on the ohmic resistance, (a) is the effect of the inner diameter of the coil on the ohmic resistance, (b) is the effect of the number of turns of the coil on the ohmic resistance, and (c) is the effect of the pitch of the coil on the ohmic resistance;

[0056] Figure 7 Yes Figure 3 A detailed overview of the last step of the overall flow chart. DETAILED DESCRIPTION

[0057] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0058] The present invention will be described in detail below with reference to the accompanying drawings and in conjunction with embodiments.

[0059] See also Figure 1 As shown in the equivalent circuit diagram of the SS compensation form of the wireless power transmission system used in the present invention, the capacitor and the inductor form a resonant circuit, wherein R 11 is the internal resistance of the transmitting coil, R 12 is the internal resistance of the receiving coil, R S is the equivalent internal resistance of the transmitting end voltage, U S is the input voltage corresponding to the transmitter, I t is the current at the corresponding transmitting end, I r is the load current at the receiving end, R L is the load resistance, L1 and L2 are the inductors of the transmitting end and the receiving end respectively, and C1 and C2 are the resonant capacitors connected in series with the transmitting end and the receiving end respectively.

[0060] In the LC resonant circuit, the voltage across L and C and the current frequency f flowing through are not affected by the LC ideal resonant frequency. The influence of the excitation source is always related to the frequency f0 = f source Same. Figure 2 As shown, the difference between the LC resonant frequency and the resonant frequency of the excitation source is Δf = |f0-f source |Equivalent reactance X that only affects LC resonance LC =2πf source L-1 / 2πf source C. In this equivalent circuit, the LC resonance formed by the coil inductance (ignoring the small stray capacitance) and the compensation capacitor also has the same characteristics. Figure 1 In the typical SS compensation form of wireless power transmission shown in FIG. 1 , a simplified equivalent circuit based on coupling theory is obtained as follows: Figure 2 As shown. Among them, R t =R S +R l1 and R r =R L +R l2 is the total resistance of the primary and secondary sides, X t =ωL1-1 / ωC1 and X r =ωL2-1 / ωC2 is the total reactance of the primary and secondary sides, X M =ωM is the mutual inductance reactance.

[0061] Specifically, Figure 3 The figure shows the calculation steps of a method for optimizing the maximum power output of a primary-secondary heterogeneous magnetic coupling mechanism of the present invention:

[0062] Step 1: Establish Kirchhoff's voltage law at the transmitting and receiving ends according to the equivalent circuit diagram of the SS compensation form of the wireless power transmission system;

[0063] Step 2: Obtain the current of the primary and secondary sides according to Kirchhoff's voltage equations and

[0064] Step 3: Calculate the input power P of the wireless power transmission system based on the current of the primary and secondary sides in , output power P out and transmission efficiency η;

[0065] Step 4: The greater the mutual inductance of the system, the higher the transmission efficiency. For, when the mutual inductance is X M When a certain value is met, the system output power P out maximum.

[0066] Step 5: For 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, the mutual inductance reactance X in step 4 is M The maximum output power is obtained by the impedance and mutual inductance of the receiving end.

[0067] Step 6: Formula X M The mutual inductances M and R influence and restrict each other. If the maximum power output state is to be achieved, in practical applications, the adjustment of R and M cannot be consistent with the theoretical values, and there will be a certain deviation. The coil needs to be corrected to make the deviation ΔP as small as possible.

[0068] Step 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);

[0069] Step 8: Set the physical parameters of the optimal receiving coil to achieve maximum power output at a fixed position.

[0070] Preferably, in step 1, the Kirchhoff voltage law equations are as follows:

[0071]

[0072] Preferably, in step 2, the current of the primary and secondary sides is and The values ​​are as follows:

[0073]

[0074] in, B=R t X r +R rX t ;

[0075] Preferably, in step three, the input power P in , output power P out The formula for the transmission efficiency η is as follows:

[0076]

[0077]

[0078]

[0079] Preferably, when the output power in step 4 is maximum, the mutual inductance reactance satisfies the following formula:

[0080]

[0081] in, and are the magnitudes of the primary and secondary impedances respectively.

[0082] The formula for maximum output power is:

[0083]

[0084] Preferably, the mutual inductance and impedance adjustment in step 5 can satisfy the maximum power output in step 4. The parameter change of the transmitting coil does not affect the influence of the receiving coil parameters on the mutual inductance; therefore, when optimizing the design of a single-side coil, the other side is regarded as a known parameter.

[0085] Preferably, formula X M In the process, R and M influence and restrict each other, and it is difficult to reach an ideal value during the adjustment process. Therefore, the theoretical value of the maximum output power P out.max There is an error between the actual value P and the power error, which is denoted as 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 in the hope of reaching the maximum value.

[0086] Figure 4 The figure shows the influence of coil physical parameters on self-inductance. Curve change law, coil outer diameter R r and number of turns N r There is a positive correlation between the mutual inductance value M of the magnetic coupling mechanism, and the pitch d r The outer diameter of the coil is R. r , and pitch d r The slope of the corresponding curve is approximately constant, that is, the outer diameter R of the coil r , and pitch d r It is linearly related to the mutual inductance M of the magnetic coupling mechanism. rAs the coil outer diameter R increases, the rate of change of the mutual inductance M (the slope of the curve) decreases. This is because when the coil outer diameter R r and pitch d r Unchanged, number of turns N r As the coil radius R increases, the number of turns N decreases. r Influence on mutual inductance M.

[0087] Preferably, when the parameters of the transmitting coil and the magnetic coupling mechanism are known, the mutual inductance M of the magnetic coupling mechanism is mainly affected by the physical parameters of the single-side coil, which can be expressed as:

[0088] M=x1(R r , N r , d r )

[0089] Figure 5 The figure shows the influence of coil physical parameters on self-inductance. It has been verified that the overall change law of the curve is related to the outer diameter R of the coil. r and number of turns N r With coil self-inductance L r There is a positive correlation between them, and the pitch d r The outer diameter of the coil is R. r and pitch d r With coil self-inductance L r There is a linear relationship between them. However, the outer diameter of the coil R r and number of turns N r The corresponding curve has a larger slope, which means that 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 and can be expressed as:

[0090] L=x2(R r , N r , d r )

[0091] Figure 6 The physical parameters of the coil shown in the figure are related to the coil AC resistance R AC The influence of the coil outer diameter R r and number of turns N r With AC resistance R AC There is a linear positive correlation. Coil pitch d r With AC resistance R AC It is a linear negative correlation. The essence is the outer diameter R of the coil rThe increase in the number of turns N will lead to an increase in the total wire length l of the coil, while the increase in the pitch d will lead to a decrease in the total wire length l. Litz wire is usually used to wind the coil in wireless power transmission, which can effectively weaken the skin effect and proximity effect. Therefore, there is a linear relationship between the physical parameters of the coil and the AC resistance of the coil. Only when the pitch d is very small will there be an insignificant skin effect. That is, as the pitch increases, the normalized resistance decreases continuously and eventually stabilizes. The AC resistance R of the coil in the magnetic coupling mechanism AC The same is true for the single-sided coil radius R r 、Number of turns r and pitch d r The constraint can be expressed as: R AC =x3(R r , N r , d r )

[0092] Preferably, in step 7, based on the previous theory and analysis, the following is obtained: Figure 7 The coil optimization design process shown in the figure first determines the coil wire diameter, load impedance, resonant frequency and other parameters based on the load and charging performance requirements. In the unilateral restricted magnetic coupling mechanism, the physical parameters of the transmitting coil and the relative spatial position of the two coils in the magnetic coupling mechanism are known conditions. According to the above analysis, the self-inductance L of the transmitting coil is determined t and resistor R l1 The coefficient k(MCM, TX) is determined based on the structural parameters of the magnetic coupling mechanism. The magnetic coupling mechanism with the same or similar structure and parameters of the primary and secondary coils is the most favorable for wireless power transmission performance. In the confined space at the receiving end, the radius of the receiving coil R is also r As close as possible to the transmitting coil radius R t , to determine the receiving coil radius R r The best range. The resistance of the coil is generally very small, in the mΩ range. The resistance of the transmitting coil is generally higher than the power supply and compensation capacitor resistance, and is included in Z t As for the resistance of the receiving coil, it is necessary to calculate the load resistance R L , determine whether to include Z r In order to reduce coil loss, the skin effect should be weakened as much as possible when winding the coil. The optimal pitch d is determined by the resonant frequency determined by the system. r Then, based on the condition of maximum output power, the optimal impedance X is calculated. M Finally, the outer diameter R of the receiving coil that meets the requirements is calculated through the formula for the mutual inductance, self-inductance, and resistance characteristics of the AC coil. r 、Number of turns r , pitch d r . Construct a receiving coil that achieves maximum output power at a fixed point.

[0093] Those of ordinary skill in the art will appreciate that the units and method steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been generally described in terms of function in the above description. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0094] In the several embodiments provided in the present application, it should be understood that the disclosed methods and systems can be implemented in other ways. For example, the division of the units described above is only a logical function division, and there may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. The above-mentioned units may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the embodiments of the present invention.

[0095] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. 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 invention, and they should all be included in the scope of the claims and specification of the present invention.

[0096] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A magnetic coupling mechanism optimization design method for fixed-point maximum power output of primary-secondary heterogeneous wireless power transmission, characterized in that: The following steps are involved: (1) According to the equivalent circuit diagram of the SS compensation form of the wireless power transmission system, Kirchhoff's voltage law at the transmitting and receiving ends is established as follows: Among them: 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 t is the total resistance of the primary side, R r is the total resistance of the secondary side, X t is the total reactance on the primary side, X r is the total reactance on the secondary side, X M is the mutual inductive reactance; (2) According to Kirchhoff's voltage equations, the current of the primary and secondary sides is obtained and They are: in, (3) According to step (2), the input power P of the wireless power transmission system is obtained in , output power P out and the transmission efficiency η are: Among them, U s and I r for and Model; (4) From step (3), it can be concluded that the greater the mutual inductance of the system, the higher the transmission efficiency. For the output power P of the system out , when it is maximum, the mutual inductance reactance X M satisfy: in, and are the magnitudes of the primary and secondary impedances respectively; For wireless power transmission systems with determined physical structural parameters, there is a unique mutual inductance reactance that maximizes its output power. The formula is: (5) For a 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, the mutual inductance reactance X in step (4) is M The two formulas of maximum output power show that the impedance and mutual inductance at the receiving end restrict the maximum output power; (6) Formula X M The mutual inductances M and R affect and restrict each other. If the maximum power output state is to be achieved, in practical applications, there will be a certain deviation between the adjustment of R and M and the theoretical value. The coil needs to be corrected to make the deviation ΔP as small as possible. (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); (8) According to step (7), the physical parameters of the optimal receiving coil are set to achieve maximum power output at a fixed point.

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

3. The method for optimizing the design of a magnetic coupling mechanism for fixed-point maximum power output of primary-secondary heterogeneous wireless power transmission according to claim 2 is characterized in that: In the LC resonant circuit, the voltage across L and C and the current frequency f flowing through are not affected by the LC ideal resonant frequency. The influence of the excitation source is always related to the frequency f0 = f source same; The difference between the LC resonant frequency and the excitation source resonant frequency Δf=|f0-f source |Equivalent reactance X that only affects LC resonance LC =2πf source L-1 / 2πf source C.

4. The method for optimizing the design of a magnetic coupling mechanism for fixed-point maximum power output of primary-secondary heterogeneous wireless power transmission according to claim 1 is characterized in that: The mutual inductance and impedance adjustment in step (5) can satisfy the maximum power output in step (4); the parameter change of the transmitting coil does not affect the influence of the receiving coil parameters on the mutual inductance; therefore, when optimizing the design of the single-side coil, the other side is considered as a known parameter; 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-side coil, which can be expressed as: M=x1(R r ,N r ,d r ); The coil's self-inductance is only constrained by its own physical parameters and can be expressed as: L=x2(R r ,N r ,d r ); AC resistance R of the coil in the magnetic coupling mechanism AC The same is true for the single-sided coil radius R r 、Number of turns r and pitch d r The constraint can be expressed as: R AC =x3(R r ,N r ,d r ) It can be found that the outer diameter R r 、Number of turns r , pitch d r It has almost the same influence rules on the coil mutual inductance M, self-inductance L and resistance R.

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