PT symmetric MC-WPT system based on operational amplifier and parameter design method

Abstract

The present invention relates to wireless power transmission technology, specifically a PT-symmetrical MC-WPT system and parameter design method based on an operational amplifier, the system includes a primary circuit and a secondary circuit, the primary circuit includes a first negative resistance unit, a second negative resistance unit, a primary coil and a primary series resonant capacitor, and the secondary circuit includes a secondary coil, a secondary series resonant capacitor, a parallel resonant inductor, a series resonant inductor and an electrical load; the first negative resistance unit and the second negative resistance unit are constructed based on an operational amplifier, the secondary coil and the secondary series resonant capacitor constitute a first series branch of the secondary side connected in parallel to the front side of the parallel resonant inductor, the series resonant inductor and the electrical load constitute a second series branch of the secondary side connected in parallel to the rear side of the parallel resonant inductor, and the primary coil and the secondary coil are coupled to each other to realize wireless energy transmission. The effect is: the output power level can be flexibly adjusted according to demand within a large range, and the power and efficiency of the system are independent of mutual inductance and load.

Description

Technical Field

[0001] The present invention relates to the technical field of wireless power supply, and in particular to a PT-symmetric MC-WPT system based on an operational amplifier and a parameter design method. Background Art

[0002] Magnetic coupling wireless power transfer (MC-WPT) technology is one of the most mature and technically sound WPT technologies currently being studied, and has been widely used in the fields of robots, drones, household appliances, and electric vehicles. The traditional MC-WPT system itself has poor position robustness and can only achieve effective energy transmission within a limited distance. In order to maintain a reasonable level of energy efficiency when the transmission distance or transmission direction changes, external tuning methods such as frequency tracking control or impedance matching networks must be added.

[0003] In recent years, the introduction of a new working mechanism represented by the parity-time (PT) symmetric mechanism has provided a new idea for optimizing the energy efficiency characteristics of the MC-WPT system. There are two construction methods for the negative resistance in the PT symmetric MC-WPT system: inverter-based and operational amplifier-based. Among them, the inverter-based construction method has the constant power and constant efficiency output characteristics of the PT symmetric system, and can also achieve arbitrary power output by adjusting the size of the DC power supply connected to the primary inverter circuit. Due to the above advantages, the PT symmetric system using the inverter has received widespread attention, and related research has continued to deepen, and its application in high-power and high-spatial-degree-of-freedom occasions such as electric vehicles and drones has become more and more common. The PT symmetric MC-WPT system constructed based on the operational amplifier also has a high and constant transmission efficiency. At the same time, since the system itself has the property of self-selecting frequency, there is no need to add additional links such as detection, control, and regulation. Therefore, the PT symmetric system based on the operational amplifier has the advantages of simpler structure, low cost, and no additional loss caused by additional circuits.

[0004] However, in the prior art, there has been little research in recent years on the PT-symmetrical MC-WPT system built based on operational amplifiers. The main reason is that due to the limitations of the characteristics of the operational amplifier device itself, its input DC voltage is limited to a small range, which results in a small output voltage. The limitation of the output voltage leads to the limited output power of the system, which can only drive some loads with lower power levels, such as sensor networks, light bulbs, etc. Under the existing system parameter design criteria, if the output power level of the system is to be increased, the input power supply voltage of the operational amplifier can only be increased within the range allowed by the device, while reducing the coil internal resistance and load resistance. Therefore, the power boosting means of the PT-symmetrical MC-WPT system built based on operational amplifiers in the prior art are still relatively limited, and cannot meet some high-power wireless power transmission application scenarios, which greatly limits the application and promotion of this technology. Summary of the invention

[0005] In view of this, the present invention first provides a PT-symmetrical MC-WPT system constructed based on an operational amplifier, so that it can conveniently and flexibly adjust the output power level according to demand within a large range through parameter design, and the power and efficiency of the system are independent of mutual inductance.

[0006] In order to achieve the above object, the specific technical solutions adopted by the present invention are as follows:

[0007] A PT-symmetrical MC-WPT system constructed based on an operational amplifier comprises a primary circuit and a secondary circuit, wherein the primary circuit comprises a first negative resistance unit, a second negative resistance unit, a primary coil and a primary series resonant capacitor, and the secondary circuit comprises a secondary coil, a secondary series resonant capacitor, a parallel resonant inductor, a series resonant inductor and an electrical load; the first negative resistance unit and the second negative resistance unit are constructed based on an operational amplifier, wherein: one end of the first negative resistance unit is grounded, and the other end is used as a forward voltage output end; one end of the second negative resistance unit is grounded, and the other end is used as a reverse voltage output end, the primary coil and the primary series resonant capacitor are connected in series between the forward voltage output end and the reverse voltage output end, the secondary coil and the secondary series resonant capacitor constitute a secondary first series branch connected in parallel to the front side of the parallel resonant inductor, the series resonant inductor and the electrical load constitute a secondary second series branch connected in parallel to the rear side of the parallel resonant inductor, and the primary coil and the secondary coil are coupled to each other to realize wireless energy transmission.

[0008] Optionally, the first negative resistance unit and the second negative resistance unit have the same circuit structure and parameters, and respectively include an operational amplifier, a first resistor, a second resistor and a third resistor, the first resistor is connected between the positive input terminal and the output terminal of the operational amplifier, the second resistor is connected between the inverting input terminal and the output terminal of the operational amplifier, the third resistor is connected between the positive input terminal and the ground terminal of the operational amplifier, and the inverting input terminal of the operational amplifier is extended through a wire to form the forward voltage output terminal or the reverse voltage output terminal.

[0009] Optionally, the third resistor is formed by two sub-resistors connected in series, and two anti-parallel diodes are arranged on one of the sub-resistors.

[0010] Based on the above system, the present invention also provides a parameter design method for the PT symmetric MC-WPT system constructed based on an operational amplifier as described above, comprising the following steps:

[0011] S1: Determine the load resistance R according to the application scenario requirements L , power level P, negative resistance output voltage U in , primary coil inductance L1, primary coil internal resistance R p1 , secondary coil inductance L2, secondary coil internal resistance R p2 , the natural frequency level ω0 and the equivalent load resistance R that meets the target power level Leq ; The negative resistance output voltage U in is the effective voltage between the forward voltage output terminal and the reverse voltage output terminal;

[0012] S2: According to Determine the system parameters α and β that meet the target power level; where R s =R p2 +R Leq Represents the total resistance of the secondary side;

[0013] S3: According to L1 = α (L2 + L eq ) Determine the total secondary compensation inductance L eq The value of

[0014] S4: According to L a =L eq / (1-β) and L b =L eq / β determines the parallel resonant inductance L a and the series resonant inductor L b The self-inductance value;

[0015] S5: According to Determine the capacitance of the primary series compensation capacitor C1 and the secondary series compensation capacitor C2;

[0016] S6: Keep the primary coil and the secondary coil within the critical coupling range, and the system operates at any bifurcation frequency to achieve constant output power P and constant efficiency η.

[0017] Optionally, the critical coupling range in step S6 is k≥k0, where k is the coupling coefficient between the primary coil and the secondary coil, and the coupling coefficient critical value is is the quality factor of the secondary coil.

[0018] Optionally, the bifurcation frequency of the system in step S6 is:

[0019] Optionally, set parameters to ensure the quality factor of the secondary coil

[0020] Optionally, the structures and parameters of the primary coil and the secondary coil are set to be the same.

[0021] The system and method proposed in the present invention can flexibly adjust the output power level according to the demand within a large range. The power and efficiency of the system are independent of mutual inductance. At the same time, the reasonable adjustment of electrical parameters also has the characteristics of constant power and constant efficiency output when the load resistance changes. The present invention is competent for wireless charging in high energy efficiency requirements such as wearable electronic devices and human implantable medical electronic devices, and is also competent for wireless charging of high spatial freedom devices such as small robots and drones.

[0022] Compared with the traditional PT symmetrical MC-WPT system based on operational amplifier, the present invention has the following significant effects:

[0023] 1) The present invention designs the electrical parameters and circuit structure of the primary and secondary sides of the system so that the system works in a PT symmetrical state. The output power and efficiency of the system are not affected by the change of mutual inductance, and the output power level can be adjusted arbitrarily within a large range, and is suitable for a variety of different power levels;

[0024] 2) The operating frequency of the system corresponds to the transmission distance. The MC-WPT system can work in the PT symmetrical working mode without the need for additional setting links and primary and secondary side communication, and has strong position robustness and anti-drift capability;

[0025] 3) By adjusting the electrical parameters, it can achieve constant power and constant efficiency output when driving load resistances of different sizes. It is suitable for various types of electrical equipment, greatly expanding the application scope of this technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the specific implementation of the present invention or the technical solution in the prior art, the drawings required for use in the specific implementation or the description of the prior art are briefly introduced below.

[0027] Figure 1 A schematic diagram of a PT-symmetrical MC-WPT system based on an operational amplifier provided in an embodiment of the present invention;

[0028] Figure 2 for Figure 1 Analysis schematic diagram of the medium negative resistance module;

[0029] Figure 3 It is the circuit equivalent conversion diagram of the secondary side compensation topology;

[0030] Figure 4 for Figure 1 Simplified model diagram of

[0031] Figure 5 It is a parameter design flow chart in a specific embodiment of the present invention;

[0032] Figure 6 is the curve of system operating frequency changing with coupling system;

[0033] Figure 7 The curve of system output power changing with coupling system;

[0034] Figure 8 The curve of system transmission efficiency changing with coupling coefficient;

[0035] Fig. 9 The curve of system output power changing with the ratio of primary to secondary inductance;

[0036] Fig.10 Curve showing the change of system transmission efficiency with the ratio of primary to secondary inductance;

[0037] Fig.11 The curve of system output power changing with the primary-to-secondary inductance ratio under different topologies;

[0038] Fig.12 The curve of system output power changing with load resistance;

[0039] Fig.13 This is the curve of system compensation inductance changing with load resistance. DETAILED DESCRIPTION

[0040] The following specifically illustrates the implementation mode of the present invention in conjunction with the accompanying drawings. The embodiments are provided for illustrative purposes only and cannot be understood as limiting the present invention. The accompanying drawings are provided for reference and illustration only and do not constitute a limitation on the scope of patent protection of the present invention, because many changes can be made to the present invention without departing from the spirit and scope of the present invention.

[0041] like Figure 1As shown, the present embodiment provides a PT-symmetric MC-WPT system based on an operational amplifier, including a primary circuit and a secondary circuit, wherein the primary circuit includes a first negative resistance unit, a second negative resistance unit, a primary coil and a primary series resonant capacitor, and the secondary circuit includes a secondary coil, a secondary series resonant capacitor, a parallel resonant inductor, a series resonant inductor and an electrical load; the first negative resistance unit and the second negative resistance unit are constructed based on an operational amplifier, wherein: one end of the first negative resistance unit is grounded, and the other end is used as a forward voltage output end; one end of the second negative resistance unit is grounded, and the other end is used as a reverse voltage output end, the primary coil and the primary series resonant capacitor are connected in series between the forward voltage output end and the reverse voltage output end, the secondary coil and the secondary series resonant capacitor constitute a secondary first series branch connected in parallel on the front side of the parallel resonant inductor, the series resonant inductor and the electrical load constitute a secondary second series branch connected in parallel on the rear side of the parallel resonant inductor, and the primary coil and the secondary coil are coupled with each other to realize wireless energy transmission.

[0042] In this embodiment, the first negative resistance unit and the second negative resistance unit have the same circuit structure and parameters, and respectively include an operational amplifier, a first resistor, a second resistor and a third resistor. The first resistor is connected between the positive input terminal and the output terminal of the operational amplifier, the second resistor is connected between the inverting input terminal and the output terminal of the operational amplifier, the third resistor is connected between the positive input terminal and the ground terminal of the operational amplifier, and the inverting input terminal of the operational amplifier is extended through a wire to form the forward voltage output terminal or the reverse voltage output terminal. Figure 1 It can also be seen that, in a specific implementation, the third resistor is formed by two sub-resistors connected in series, and two anti-parallel diodes are arranged on one of the sub-resistors.

[0043] Figure 1 The first negative resistor - R g1 and the second negative resistor -R g2 The "ground" end of the two terminals is connected together, which is equivalent to reverse series connection. + and V - They represent the positive and negative DC power supplies for the operational amplifier, I1 represents the primary current, I2 represents the secondary current, and M represents the mutual inductance between the primary coil L1 and the secondary coil L2.

[0044] Figure 2 (a) is a schematic diagram of a traditional negative resistance structure based on an operational amplifier, where R eq represents the compensation topology of the WPT system, R1, R2, and R3 represent the peripheral resistors of the operational amplifier that form the negative resistance, and u i 、u f 、u oRepresent the voltage signals at the non-inverting input terminal, the inverting input terminal, and the output terminal of the op amp, respectively.

[0045] for Figure 2 The negative resistor shown in (a) has a resistance value and an output voltage effective value U1 as shown in formula (1):

[0046]

[0047] Among them U O Represents the effective value of the voltage signal at the output of the operational amplifier.

[0048] Figure 2 (b) shows the new negative resistor structure proposed in this patent, which consists of two traditional negative resistors with exactly the same parameters connected in reverse series, with the "ground" terminals of the two connected together, and the resistance value is -R g And the output voltage RMS U in for:

[0049]

[0050] From formula (2), it can be seen that the negative resistance structure proposed in this patent can increase the output voltage to twice the original value.

[0051] In addition, for Figure 1 The secondary compensation topology in Figure 3 The equivalent analysis is performed in the manner shown. Through impedance equivalent transformation, the equivalent resistance and equivalent inductance can be obtained as shown in formula (3):

[0052]

[0053] Since the resonant frequency of the PT-symmetric MC-WPT system can reach several hundred kHz, and in order to ensure a larger effective power transmission distance, the quality factor of the WPT system loop is usually set larger (i.e., the coil self-inductance is larger), it is easy to meet the simplified conditions shown in equation (4).

[0054]

[0055] The equivalent resistance and equivalent inductance of the secondary side high-order compensation topology can be simplified by equation (4):

[0056]

[0057] Define β = L a / (L a +L b ), so the electrical parameter relationship before and after the secondary side high-order compensation topology is equivalent:

[0058]

[0059] It can be seen from equations (5) and (6) that by selecting a suitable β, the compensation topology of the secondary side can be equivalent to a series connection of an inductor and a resistor, that is, a traditional SS compensation topology.

[0060] also, Figure 1 The PT symmetric MC-WPT system based on operational amplifier shown can also be simplified as follows Figure 4 The circuit shown, where -R g Represents the total negative resistance of the system, L eq Represents the total compensation inductance of the secondary side, R Leq is the equivalent load resistance.

[0061] When the system works in PT symmetric mode, the loop equation of the system can be obtained from Kirchhoff's voltage law (KVL) as shown in equation (7):

[0062]

[0063] Where g = R g -R p1 Represents the total negative resistance of the primary side, R S =R p2 +R Leq represents the total resistance of the secondary side, X1=ωL1-1 / ωC1 represents the primary side reactance, X2=ω(L2+L eq )-1 / ωC2 represents the secondary side reactance.

[0064] According to formula (7), the relationship between the secondary current and the primary current is:

[0065]

[0066] The relationship between the primary current and the secondary current amplitude ratio is as follows:

[0067]

[0068] make Substituting into equation (7), we can get the relationship that the primary and secondary electrical parameters should satisfy:

[0069]

[0070] Depend on The operating frequency of the system under the PT symmetric mode is obtained as shown in equation (11).

[0071]

[0072] in is the mutual inductance between the primary coil and the secondary coil of the system, is the natural resonant frequency of the secondary coil, is the quality factor of the secondary coil of the system. When the coupling coefficient is greater than k0, ω1 and ω2 can exist. k0 is the minimum coupling coefficient to ensure that the system works in the PT symmetric mode, and To ensure the minimum secondary quality factor of the system working in PT symmetric mode.

[0073] According to the law of conservation of energy, combined with the relationship between the primary and secondary current amplitudes shown in equation (9), the output power and transmission efficiency of the system can be obtained as follows:

[0074]

[0075] According to formula (12), it can be seen that once the structural parameters of the system are determined, its output power and transmission efficiency are independent of the mutual inductance M, that is, the power and efficiency are robust to changes in the transmission distance.

[0076] Based on the above analysis, this embodiment also provides a parameter design method for the PT symmetric MC-WPT system based on the operational amplifier described above. Figure 5 As shown, the following steps are included:

[0077] S1: Determine the load resistance R according to the application scenario requirements L , power level P, negative resistance output voltage U in , primary coil inductance L1, primary coil internal resistance R p1 , secondary coil inductance L2, secondary coil internal resistance R p2 , the natural frequency level ω0 and the equivalent load resistance R that meets the target power level Leq ; The negative resistance output voltage U in is the effective voltage between the forward voltage output terminal and the reverse voltage output terminal; in some application scenarios, the structure and parameters of the primary coil and the secondary coil may be set to be the same;

[0078] S2: According to Determine system parameters α and β that meet the target power level;

[0079] S3: According to L1 = α (L2 + L eq ) Determine the total secondary compensation inductance L eq The value of

[0080] S4: According to L a =L eq / (1-β) and L b =L eq / β determines the parallel resonant inductance L a and the series resonant inductor L bThe self-inductance value;

[0081] S5: According to Determine the capacitance of the primary series compensation capacitor C1 and the secondary series compensation capacitor C2;

[0082] S6: Keep the primary coil and the secondary coil within the critical coupling range, that is, satisfy k≥k0. The system works at any bifurcation frequency to achieve constant output power P and constant efficiency η.

[0083] In order to further verify the effectiveness of the above system and method, the working conditions and system characteristics are verified by MATLAB numerical simulation. The simulation parameters are shown in Table 1.

[0084] Table 1 Simulation parameter settings

[0085]

[0086] By changing the coupling coefficient of the system, the curves of system operating frequency, output power, and transmission efficiency changing with the coupling coefficient can be obtained as follows: Figure 6 , Figure 7 , Figure 8 shown.

[0087] according to Figure 6 It can be seen from the simulation results that in the range of k ≥ k0, any coupling coefficient corresponds to two operating frequencies that meet the conditions, namely frequency branch f1 and frequency branch f2.

[0088] according to Figure 7 and Figure 8 It can be seen from the simulation results in that within the range of k ≥ k0, regardless of the frequency branch f1 or f2, the output power and transmission efficiency of the system are constant and do not change with the change of the coupling coefficient.

[0089] also, Fig. 9 and Fig.10 The curves of output power and transmission efficiency changing with the ratio of primary to secondary inductance are given. Fig. 9 and Fig.10 It can be seen from the simulation results in that by adjusting the inductance ratio α between the primary and secondary sides, the system can flexibly adjust the output power within a larger range according to actual needs. When a smaller α is set, the system obtains a higher output power by sacrificing part of the transmission efficiency, effectively improving the application range of the PT symmetrical MC-WPT system built based on the operational amplifier.

[0090] Fig.11 The output power comparison curves under different system topologies are given. Fig.11It can be seen that when the primary-to-secondary inductance ratio α is maintained at the same level, the output power improvement effect of the dual negative resistor structure is significantly greater than that of the single negative resistor structure, and the power improvement effect of adding a high-order compensation structure to the secondary side is also significant compared to the power improvement effect of adding a high-order compensation structure to the secondary side without compensation. Therefore, the system and method proposed in this patent have a good effect on improving the output power on both the primary side and the secondary side.

[0091] Fig.12 The curve of system output power changing with load resistance; Fig.13 The curve of system compensation inductance changing with load resistance. Fig.12 and Fig.13 It can be seen that by adjusting the parameter β, constant power output can be achieved when driving load resistances of different sizes, and the adjustment of the parameter β is achieved by changing the compensation inductance L a and L b The value of Fig.13 As shown in the figure, different load resistances correspond to a set of compensation inductors L that can achieve constant power output. a and L b .

[0092] It can be seen that the simulation results are consistent with the theoretical derivation conclusions. The present invention adopts a dual negative resistance structure and adjusts the primary-to-secondary inductance ratio coefficient α and the secondary-side compensation topology parameter β according to the proposed parameter design criteria. The system based on the operational amplifier can realize the PT symmetrical working mode, and has the characteristics of arbitrarily adjusting the output power in a large range, maintaining constant power output and constant efficiency when the coupling coefficient and load resistance change.

[0093] In summary, the PT symmetric MC-WPT system and parameter design method based on an operational amplifier provided by the present invention have the following advantages:

[0094] (1) Without any additional detection, control, adjustment or other additional links, the system can automatically select the appropriate operating frequency and operate in the PT symmetric mode. Its output power and transmission efficiency have good position robustness and are not affected by changes in mutual inductance.

[0095] (2) Two negative resistors are connected in reverse series to provide gain for the system, doubling the output voltage of the primary negative resistor and effectively increasing the output power from the power supply side.

[0096] (3) Under the premise of a smaller negative resistance output voltage, by adjusting the primary-to-secondary inductance ratio α, the equivalent resistance reflected from the secondary side to the primary side can be reduced, thereby effectively improving the output power of the system from the WPT compensation topology side.

[0097] (4) By adjusting the L in the secondary side high-order compensation topology a and L bThe value of the two inductors can adjust β in the range of 0 to 1, and thus adjust the load resistance R L When the secondary side high-order compensation topology has the same equivalent resistance R Leq , thus achieving the goal of driving load resistances of different sizes R L It can achieve constant power output, which greatly expands the application scenarios of the PT-symmetrical MC-WPT system built based on operational amplifiers.

[0098] Finally, it should be noted that the above embodiments are preferred implementations of the present invention, but the implementations of the present invention are not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A PT-symmetrical MC-WPT system based on an operational amplifier, comprising a primary circuit and a secondary circuit, characterized in that: The primary circuit includes a first negative resistance unit, a second negative resistance unit, a primary coil and a primary series resonant capacitor, and the secondary circuit includes a secondary coil, a secondary series resonant capacitor, a parallel resonant inductor, a series resonant inductor and an electrical load; the first negative resistance unit and the second negative resistance unit are constructed based on an operational amplifier, wherein: one end of the first negative resistance unit is grounded, and the other end is used as a forward voltage output end; one end of the second negative resistance unit is grounded, and the other end is used as a reverse voltage output end, the primary coil and the primary series resonant capacitor are connected in series between the forward voltage output end and the reverse voltage output end, the secondary coil and the secondary series resonant capacitor constitute a first series branch of the secondary side connected in parallel on the front side of the parallel resonant inductor, the series resonant inductor and the electrical load constitute a second series branch of the secondary side connected in parallel on the rear side of the parallel resonant inductor, and the primary coil and the secondary coil are coupled with each other to realize wireless energy transmission.

2. The PT-symmetric MC-WPT system based on an operational amplifier according to claim 1, characterized in that: The first negative resistance unit and the second negative resistance unit have the same circuit structure and parameters, and respectively include an operational amplifier, a first resistor, a second resistor and a third resistor. The first resistor is connected between the positive input terminal and the output terminal of the operational amplifier, the second resistor is connected between the inverting input terminal and the output terminal of the operational amplifier, the third resistor is connected between the positive input terminal and the ground terminal of the operational amplifier, and the inverting input terminal of the operational amplifier is extended through a wire to form the forward voltage output terminal or the reverse voltage output terminal.

3. The PT-symmetric MC-WPT system based on an operational amplifier according to claim 2, characterized in that: The third resistor is formed by two sub-resistors connected in series, and two anti-parallel diodes are arranged on one of the sub-resistors.

4. A parameter design method for a PT-symmetric MC-WPT system based on an operational amplifier as described in any one of claims 1 to 3, characterized in that: The following steps are involved: S1: Determine the load resistance R according to the application scenario requirements L , power level P, negative resistance output voltage U in , primary coil inductance L1, primary coil internal resistance R p1 , secondary coil inductance L2, secondary coil internal resistance R p2 , the natural frequency level ω0 and the equivalent load resistance R that meets the target power level Leq ; The negative resistance output voltage U in is the effective voltage between the forward voltage output terminal and the reverse voltage output terminal; S2: According to Determine the system parameters α and β that meet the target power level; where R s =R p2 +R Leq Represents the total resistance of the secondary side; S3: According to L1=α(L2+L eq ) Determine the total secondary compensation inductance L eq The value of S4: According to L a =L eq / (1-β) and L b =L eq / β determines the parallel resonant inductance L a and the series resonant inductor L b The self-inductance value; S5: According to Determine the capacitance of the primary series compensation capacitor C1 and the secondary series compensation capacitor C2; S6: Keep the primary coil and the secondary coil within the critical coupling range, and the system works at any bifurcation frequency to achieve constant output power P and constant efficiency η; The critical coupling range is k ≥ k0, where k is the coupling coefficient between the primary coil and the secondary coil, and the critical value of the coupling coefficient is is the quality factor of the secondary coil; the bifurcation frequency is:

5. The parameter design method according to claim 4, characterized in that: Set parameters to ensure the quality factor of the secondary coil 6. The parameter design method according to claim 4, characterized in that: Set the structure and parameters of the primary coil and the secondary coil to be the same.

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