A long-distance parity-time symmetry wireless power transmission system with a multi-coil structure

Abstract

This invention discloses a long-distance parity-time symmetric wireless power transfer system with a multi-coil structure, belonging to the field of wireless power transfer technology. The invention includes a transmitting device, relay coil circuits, and a receiving device, with multiple sets of relay coil circuits arranged between the transmitting and receiving devices. Under the associated reference direction, the voltage and current flowing through the full-bridge inverter of the transmitting device are reversed, and together with the power supply, they are equivalent to a single negative resistance -R. N Resonant capacitor C 1s C 1p and resistance - R N The parallel connection, combined with inductor L1 in series, forms an SP structure. The resonant capacitor C of the receiving device... 5s C 5p and load R L The parallel connection, combined with inductor L5 in series, forms a PS structure. This invention not only enhances the energy transfer process but also reduces the critical coupling condition, allowing the system to operate more easily in the strong coupling region. Furthermore, the SP-PS topology further enhances the wide coupling characteristics of the PT system.

Description

Technical Field

[0001] This invention relates to the field of wireless power transmission technology, and in particular to a long-distance parity-time symmetric wireless power transmission system with a multi-coil structure. Background Technology

[0002] Wireless power transfer (WPT) has shown exciting and promising applications in a variety of fields where physical connections are not permitted. Driven by modern physics concepts and growing practical needs, the so-called magnetic resonance mechanism of non-radiative WPT technology has developed rapidly in recent years. However, conventional WPT systems are not robust when the transmitting and receiving coils are misaligned or there is relative motion, resulting in changes in mutual coupling.

[0003] Parity-time symmetry (PT-symmetric), rooted in quantum physics, has opened up a different perspective for studying non-Hermitian Hamiltonians. With the development of WPT devices, efficient, long-range, and robust PT-WPT is urgently needed. However, designing a robust long-distance PT-WPT system is extremely challenging. Currently, WPT schemes are inherently sensitive to transmission distance and structural perturbations, which is a fundamental challenge for various application scenarios.

[0004] Currently, research on magnetic resonance PT-WPT systems is relatively mature. PT-symmetric WPT systems possess a true spectrum and can automatically select the operating frequency corresponding to the highest efficiency, thus ensuring optimal power transfer over a wide transmission distance without any active tuning. Higher-order PT-symmetric systems hold promise for achieving robust WPT in a larger longitudinal frequency splitting range and a wider transversely precise PT-symmetric region.

[0005] In summary, constructing a high-order PT-WPT system, enabling further optimization of the system in terms of wide coupling range and wide coupling conditions, is of great significance to the development of this field. Summary of the Invention

[0006] 1. The technical problem that the invention aims to solve

[0007] This invention, based on non-Hermitian physics and parity-time symmetric wireless power transfer technology (PT-PWT), designs a long-distance parity-time symmetric wireless power transfer system with a multi-coil structure to solve or improve the following problems:

[0008] (1) Researchers have begun to move beyond traditional second-order PT systems and have started to attempt to construct higher-order PT systems to further explore and enhance the transmission advantages and inherent characteristics of the original PT systems. However, most current research focuses on low-order PT systems and lacks research on higher-order PT-WPT. That is, current research lacks a higher-order PT-WPT system that can meet the requirements of longer coupling distances and more stable transmission efficiency.

[0009] (2) The original PT-WPT with second-order coupled-mode equations is known for its wide coupling and transmission advantages that do not require active tuning. In current research, researchers are no longer satisfied with the transmission advantages of the original PT-WPT system, that is, the stability of the original PT-WPT no longer meets the current needs.

[0010] (3) In second-order PT-WPT systems, there is a high sensitivity to coupling strength. This requires the system to meet various parameter requirements to achieve wide coupling, and the system needs to eliminate various interferences, resulting in low effective stability of second-order PT-WPT.

[0011] (4) Most current PT systems use SS-type topology. However, SS-type PT-WPT systems are highly sensitive and have poor stability.

[0012] 2. Technical Solution

[0013] To achieve the above objectives, the technical solution provided by this invention is as follows:

[0014] The present invention discloses a long-distance parity-time symmetric wireless power transmission system with a multi-coil structure, comprising a transmitting device, a relay coil circuit, and a receiving device. The transmitting device and the receiving device are configured with an SP structure by two capacitors and a resistor connected in parallel and then in series with an inductor. Multiple sets of relay coil circuits are arranged between the transmitting device and the receiving device.

[0015] Furthermore, the transmitting device includes a power supply, a full-bridge inverter, and a resonant capacitor C. 1s C 1p And inductor L1; where, under the associated reference direction, the voltage and current flowing through the full-bridge inverter are in opposite directions, and together with the power supply, they are equivalent to a negative resistor -R. N Resonant capacitor C 1s C 1p and resistance -R N The parallel connection and series connection with inductor L1 form the SP structure.

[0016] Furthermore, the receiving device includes a receiving inductor L5 and a resonant capacitor C. 5s C 5p and load R L Among them, the resonant capacitor C5s C 5p and load R L The parallel connection and series connection with inductor L5 form a PS structure.

[0017] Furthermore, a total of three relay coil circuits are set between the transmitting and receiving devices.

[0018] Furthermore, in the first set of relay coil circuits, inductor L2 and capacitor C2 form a closed loop, and inductor L1 and inductor L2 are adjacent and have mutual inductance M. 12 In the second set of relay coil circuits, inductor L3 and capacitor C3 form a closed loop, and inductor L2 and inductor L3 are adjacent coils with mutual inductance M. 23 In the third group of relay coil circuits, inductor L4 and capacitor C4 form a closed loop. Inductor L3 and inductor L4 are adjacent coils and have mutual inductance M. 34 Meanwhile, inductors L4 and L5 are adjacent coils and have mutual inductance M. 45 .

[0019] Furthermore, the mutual inductance between non-adjacent coils in the transmitting device, relay coil circuit, and receiving device is 0.

[0020] Furthermore, the transmitting device, relay coil circuit, and receiving device contain coil internal resistance r. n For n = 1, 2, 3, 4, 5, the internal resistance of the coil is very small and can be ignored.

[0021] Furthermore, the number of turns of the inductor in the relay coil circuit is greater than the number of turns of the inductor in the transmitting and receiving devices.

[0022] Furthermore, the distances between the coils in the transmitting device, relay coil circuit, and receiving device are equal.

[0023] Furthermore, the coils in the transmitting device, relay coil circuit, and receiving device maintain the same resonant frequency, i.e., ω1=ω2=ω3=ω4=ω5=ω, and equal coupling coefficients, i.e., k. 12 =k 23 =k 34 =k 45 =k.

[0024] 3. Beneficial effects

[0025] Compared with existing known technologies, the technical solution provided by this invention has the following significant advantages:

[0026] (1) This invention designs a PT-WPT system with a multi-coil structure. By inserting a relay coil between the transmitting and receiving coils, the energy transmission process is enhanced, and the critical coupling condition is reduced, allowing the system to operate more easily in the strong coupling region. In addition, the SP-PS structure is adopted in the topology, which further enhances the wide coupling characteristics of the PT system.

[0027] (2) This invention extends the transmission distance of robust wireless power transmission by three times by designing a PT-WPT system with a multi-coil structure. In addition, the PT-WPT system exhibits stronger transmission stability under the multi-coil structure.

[0028] (3) Compared with the dual-coil PT-WPT system under the same conditions, the present invention has a larger spectrum and a wider frequency selection range in longitudinal frequency splitting. This indicates that the present invention has a larger longitudinal frequency splitting region, increases the wide coupling range, and expands the strong coupling region.

[0029] (4) The PT-WPT system of the present invention adopts an improved new SP-PS topology, which allows the relationship between the two capacitors on the receiving coil to dynamically adjust the transmission efficiency of the coil, making the transmission efficiency of the coil more flexible and controllable. Compared with the original PT-WPT system, the active tuning performance is better, and compared with the traditional PT-WPT system with SS and PP structures, the stability is better.

[0030] (5) The five-coil PT-WPT system in this invention has a real characteristic frequency that is independent of coupling. This means that compared with two-coil, four-coil, and six-coil PT-WPT systems, the five-coil PT-WPT system with PT symmetry can operate efficiently at different distances without frequency tracking. This can be explained by the fact that the characteristic frequency of the five-coil model used is less sensitive to coupling strength, giving the five-coil system a robust advantage. Attached Figure Description

[0031] Figure 1 (a) in the figure is a split diagram of the four-coil PT-WPT system in the strong coupling region; Figure 1 (b) is a comparison diagram of the splitting of a four-coil PT-WPT system in the strong coupling region and the splitting of a two-coil PT-WPT system in the strong coupling region.

[0032] Figure 2 (a) in the figure is a split diagram of the five-coil PT-WPT system in the strong coupling region; Figure 2 (b) is a comparison diagram of the splitting of a five-coil PT-WPT system in the strong coupling region and the splitting of a two-coil PT-WPT system in the strong coupling region.

[0033] Figure 3(a) in the diagram is a split diagram of the six-coil PT-WPT system in the strong coupling region; Figure 3 (b) is a comparison diagram of the splitting of a six-coil PT-WPT system in the strong coupling region and the splitting of a two-coil PT-WPT system in the strong coupling region.

[0034] Figure 4 This is a comparison diagram of the coupling coefficients between the coils in asymmetric and symmetric structures.

[0035] Figure 5 The circuit topology diagram for this invention is an improvement on the basic SS structure topology, resulting in an SP-PS structure topology diagram. It should be noted that, due to the inherent characteristics of the topology diagram, it cannot accurately represent the actual coil size; the number of turns in the relay coil is larger than that in the transmitting and receiving coils.

[0036] Figure 6 This is the equivalent topology diagram of the present invention. The receiving coil is equivalent to an equivalent circuit with a lower load, thereby reducing its intrinsic loss rate and expanding the accurate PT symmetry region. Detailed Implementation

[0037] To further understand the content of this invention, a detailed description of the invention will be provided in conjunction with the accompanying drawings and embodiments.

[0038] Example 1

[0039] Combination Figure 5 and Figure 6 This embodiment of a long-distance parity-time symmetric wireless power transmission system with a multi-coil structure includes a transmitting device, a relay coil, and a receiving device. Wherein:

[0040] In the aforementioned transmitting device, under the associated reference direction, the voltage and current flowing through the full-bridge inverter are reversed, equivalent to a negative resistor -R. N It is used as a power source to provide input voltage to the system. C 1s C 1p Let L1 be the resonant capacitor of the transmitting device, and r1 be the inductance of the transmitting device. The resonant capacitor C is... 1s One end is connected to the positive terminal of the power supply, and the other end splits into two branches, one of which is connected to the resonant capacitor C. 1p One end of the circuit is connected to one end of inductor L1, and the other end of inductor L1 is connected to resistor r1 and resonant capacitor C. 1p The other end is connected in parallel with the other end of resistor r1 and then connected to the negative terminal of the power supply.

[0041] The receiving device includes a receiving inductor L5 and a resonant capacitor C. 5s C 5p Resistor r5 and load R LOne end of the receiving inductor L5 is connected to the resonant capacitor C. 5s and resonant capacitor C 5p Resonant capacitor C 5s Series load R L Then, with the resonant capacitor C 5p The other end is connected in parallel, and then connected to the other end of the receiving inductor L5 via resistor r5.

[0042] Three sets of relay coil circuits are set between the transmitting and receiving devices. L2, L3, and L4 are relay coil inductors, C2, C3, and C4 are relay coil resonant capacitors, and r2, r3, and r4 are relay coil resistors. In the first set of relay coil circuits, inductor L2, capacitor C2, and resistor r2 form a closed loop. Inductors L1 and L2 are adjacent and have mutual inductance M. 12 In the second set of relay coil circuits, inductor L3, capacitor C3, and resistor r3 form a closed loop. Inductor L2 and inductor L3 are adjacent coils with mutual inductance M. 23 In the third group of relay coil circuits, inductor L4, capacitor C4, and resistor r4 form a closed loop. Inductor L3 and inductor L4 are adjacent coils and have mutual inductance M. 34 Meanwhile, inductors L4 and L5 are adjacent coils and have mutual inductance M. 45 Since the distance between non-adjacent coils is large, the magnetic field coupling between them can be ignored, meaning the mutual inductance between non-adjacent coils is zero.

[0043] It is worth noting that, Figure 5 The r shown n n = 1, 2, 3, 4, 5 represents the internal resistance of the coil, which is negligible in subsequent calculations due to its small size.

[0044] This embodiment is a five-coil PT-WPT system. A repeater coil is added during transmission, and the distance between each coil is defined as d (cm). The repeater coil is located between the transmitting and receiving devices. To ensure maximum system transmission efficiency and maintain PT phase symmetry, this embodiment sets the distance d (cm) between each coil to be equal, and the five coils to maintain the same resonant frequency, i.e., ω1=ω2=ω3=ω4=ω5=ω, and equal coupling coefficient, i.e., k. 12 =k 23 =k 34 =k 45 =k.

[0045] It is worth noting that, because adding relay coils leads to different critical coupling coefficients, the inventors continuously changed the distance between each coil to find the strong coupling region. Finally, they determined that when the distance between each coil was equal, and the system's operating frequency met the natural resonant frequency, the system's total gain equaled the total loss, achieving PT symmetry. When the system varied within the strong coupling region, it could achieve robust transmission over long distances.

[0046] Meanwhile, this embodiment further improves the structure of the transmitting and receiving devices. The parallel connection of two capacitors and a resistor, followed by the series connection of an inductor, constitutes the transmitting and receiving devices SP and PS. When the system load resistance R L At a given time, a smaller equivalent resistance R can be obtained by equivalent substitution of the receiving coil. Leq This makes the critical coupling coefficient of the SP-PS structure system much smaller than that of the SS structure. Therefore, the compensation network of the SP-PS structure can expand the PT symmetry area of ​​the PT-WPT system, giving the system better robust transmission characteristics, that is, more stable transmission efficiency within the lateral transmission distance.

[0047] With the increasingly widespread application of wireless power transfer, the even-odd time symmetry principle has been proven to significantly increase the degrees of freedom of WPT systems without increasing control complexity. Currently, supported by the theories of non-Hermitian physics, researchers have made considerable achievements in both extending wide coupling conditions and expanding the wide coupling range.

[0048] This invention also aims to achieve technological breakthroughs in two key areas: PT symmetry region, frequency splitting range, and transmission stability. The long-distance wireless power transmission system designed in this invention, featuring a multi-coil structure, utilizes the larger longitudinal frequency splitting range and real characteristic frequency of the multi-coil system to increase its stability. The original long-chain structure with an SS-type topology is improved into a PT-WPT system with a PS-SP structure to expand the system's lateral precise PT symmetry region. Over a larger axial transmission distance and within a wider lateral misalignment range, the transmission efficiency is more stable, achieving a three-fold increase in transmission distance compared to the traditional dual-coil PT-WPT system.

[0049] The following section will provide a detailed verification.

[0050] Since the research on dual-coil and triple-coil PT-WPT systems is relatively mature, and the results clearly show that PT-WPT systems with dual-coil and triple-coil structures are in the strong coupling region and exhibit robustness when the parameter conditions are met, the transmission characteristics of these two receiver groups will not be explained further. Here, we directly present the conditions under which they operate under ideal PT system conditions:

[0051] When g = γ, that is, when the gain equals the loss.

[0052]

[0053] However, in the derivation and calculation of higher-order coupled-mode equations, it was found that due to the complex conditions of various data, the condition g = γ could not be calculated. This means that the gain and loss cannot be balanced, that is, the wireless power transmission system of the PT system cannot be realized.

[0054] This invention utilizes Hamiltonians to represent coupled modes and establishes new equations. First, starting with a standard second-order demonstration, it shows the time evolution of the resonant amplitudes of the transmitting and receiving coils in a standard PT-symmetric system, expressed as a = [a1 a2]. T This indicates that it can evolve into

[0055] in, It is the Hamiltonian function, and in this way, fourth-, fifth-, and sixth-order Hamiltonian equations are constructed.

[0056] In calculations using the new Hamiltonian, we find that for the fourth-order equation when g = γ:

[0057]

[0058] Comparing the frequency splitting formulas for two-coil PT-WPT systems and four-coil PT-WPT systems reveals that the minimum longitudinal splitting range of the four-coil PT-WPT system is smaller than that of the two-coil PT-WPT system. Therefore, the following plots are drawn: Figure 1 .

[0059] An analysis is conducted on a long-distance PT-WPT system with a five-coil structure. A fifth-order Hamiltonian equation is constructed, yielding the formula for the equivalent system:

[0060]

[0061] in, Let γ represent the resonant angular frequency of the nth LC circuit, γ = γ⁵ + γ Leq , This represents the intrinsic loss rate of the nth LC circuit. The intrinsic loss rate of the load is represented by g = g A -γ1 is the gain of the transmitting coil. Represents the total gain of the system. This represents the coupling coefficient between two adjacent coils.

[0062] Set k 12 =k 23 =k 34 =k 45 =k, the five coils maintain the same resonant frequency ω1=ω2=ω3=ω4=ω5=ω.

[0063] By solving the characteristic equation, we can obtain:

[0064]

[0065] Simplifying Δω=ω-ω0, we can obtain the real and imaginary parts of the equation:

[0066]

[0067] From equation (5), we can further solve for:

[0068] When g = γ:

[0069]

[0070] Equation (6) shows that when the gain equals the loss, the system's resonant frequency exhibits wide coupling characteristics. Furthermore, a real characteristic frequency independent of γ can be obtained, indicating that it is unaffected by distance, thus enhancing the system's stability. Based on equation (6) and a comparison of the longitudinal frequency splitting ranges of the five-coil PT-WPT system and the two-coil PT-WPT system, the following diagram is drawn. Figure 2 Then, based on the real part equation, the critical coupling coefficient can be further solved:

[0071]

[0072] The critical coupling coefficient is called a singularity (EP) in non-Hermitian physics. When a singularity exists in a system, the topology exhibits topological protection properties. Based on equations (6) and (7), the PT-symmetric conditions of the system can be summarized as follows:

[0073]

[0074] Therefore, when the condition of equation (8) is satisfied, the system is in the PT-symmetric region. It is worth mentioning that the five-coil PT-WPT system splits multiple times at the singularity and has a wider coupling range, indicating that the five-coil system has a greater robustness advantage.

[0075] Furthermore, the sixth-order Hamiltonian equation is constructed and solved in the same way to obtain (for ease of writing and to make the expression more intuitive, ABCEFG is used instead of the expression):

[0076]

[0077] E = -g 4 +g 2 γ 2 -7γ 4

[0078]

[0079] G = g 4 -g 2 γ 2 +7γ 4

[0080]

[0081]

[0082] The frequency splitting range of the six-coil PT-WPT system was obtained from equation (9), and a comparison was made with the frequency splitting range of the two-coil PT-WPT system. Figure 3 .

[0083] Depend on Figure 2 Equation (6) shows that, compared to four-coil and six-coil systems, a real characteristic frequency independent of coupling exists when the fifth-order PT symmetry is maintained. This means that the frequency does not change when the distance changes, indicating that compared to two-coil, four-coil, or six-coil PT-WPT systems, the five-coil system with PT symmetry can operate efficiently at different distances without frequency tracking. This implies that stable and efficient power transmission can be achieved in the strongly coupled region by utilizing the coupling characteristics of nonlinear gain elements. Secondly, from... Figure 1 As can be seen from (b), the minimum longitudinal frequency splitting range of the four-coil PT-WPT system is smaller than that of the two-coil PT-WPT system, while Figure 2 (b) The minimum longitudinal frequency split range of the five-coil PT-WPT is larger than that of the two-coil PT-WPT system. This means that the five coils have a wider coupling range than the four coils. When the transmitting and receiving coils are misaligned or there is relative motion, the WPT system is still robust and can maintain stable transmission.

[0084] Depend on Figure 3 The results show that the longitudinal frequency splitting range and the transverse PT symmetry region of the six-coil PT-WPT system are larger than those of the two-coil PT-WPT system. However, the six-coil PT-WPT system inevitably suffers from increased frequency due to increased losses caused by the increase in the number of relay coils. Furthermore, the six-coil system has a lower active tuning capability due to the increased number of relay coils.

[0085] Furthermore, by changing the number of turns in the excitation coil and redesigning the relay coil, a long-distance PT-WPT system with an asymmetric structure was constructed. Simultaneously, the value of the resonant capacitor in the relay coil was changed to make the resonant frequencies between the coils equal, thus achieving the coupling condition. This design alters the symmetrical structure of the system, resulting in an asymmetric structure for the wireless power transmission system of this invention. The relay coil has a larger number of turns, unlike the traditional symmetrical structure, allowing for a higher coupling coefficient under the same conditions. Experiments were conducted, data was recorded, and the coupling coefficient was obtained through Ansys simulation, then plotted using Origin. Figure 4 A higher coupling coefficient means it's easier to reach the strong coupling region, i.e., it's easier to achieve stable wireless power transfer in the precisely symmetrical region of the PT. By improving the structure, the conditions for reaching the strong coupling region in the wireless power transfer system are reduced, allowing the system to more easily achieve robust power transfer. In conclusion, using a five-coil PT-WPT system is optimal for research.

[0086] However from Figure 2 Figure (b) shows that, compared to the original split, the fifth-order split has a higher k-value. c The larger (critical coupling condition) indicates that it will have the characteristic of delayed splitting compared to the original PT-WPT.

[0087] To address the delay hysteresis issue of the five-coil system, this invention designs a PT-WPT topology with PS-SP structural characteristics and equates the receiving coil, drawing the diagram. Figure 5 and Figure 6 .

[0088] The circuit structure of this invention generally exhibits an SP-PS structure. During energy transfer, energy is transmitted from the transmitting coil, which has negative resistance, and then transferred to the receiving coil, which has a PS structure, through relay coils. This enables long-distance energy transmission.

[0089] Will Figure 5 The equivalent of the receiving coil as a simple series topology of inductor and capacitor can be obtained by the following formula:

[0090]

[0091] Decomposing it into R+jX yields the equivalent capacitance and resistance as follows:

[0092]

[0093] ΘR L 2 ω 2 c 5p c 5s 2 ,RL 2 ω 2 c 5p 2 c 5s <<c 5p +c 5s Therefore, c = c 5p +c 5s (13)

[0094]

[0095] As can be seen from equation (14), the equivalent resistance R of the topology proposed in this invention is... Leq Compared to the original load R L It is much smaller, therefore its intrinsic loss rate γ Leq To reduce it, substituting into equation (7) gives k c The smaller size, meaning that its critical coupling condition is smaller, means that the present invention can expand the precise PT symmetry region under the same load resistance, thus making up for the inherent sensitivity of the original WPT and solving the problem of the small size of the fifth-order transverse PT region.

[0096] Next, a mathematical model is constructed to calculate the output power and transmission efficiency of the SP-PS structure.

[0097] Table 1 Performance Comparison of SP-PS and SS Structures

[0098]

[0099] Table 1 shows that the transmission efficiency and output power of the SP-PS system are related to α, and the derivation of formula (14) shows that α is related to the capacitance of the receiving coil, that is, the capacitance C on the receiving coil can be changed. 5p and C 5s The dynamic relationship between the input voltage and load resistance (α) changes the fifth-order transmission efficiency. This efficiency can be adapted to different product requirements by adjusting the capacitance distribution ratio of the receiving coil, allowing for a flexible balance between transmission distance and efficiency. With a fixed input voltage and load resistance, a smaller α can extend the system's transmission distance and increase output power, but it also reduces transmission efficiency. Therefore, in practice, we need to design appropriate α values ​​based on different application scenarios to maximize transmission efficiency while meeting product requirements for output power and transmission distance. Compared to the original PT-WPT system, the PS-SP system has a stronger advantage in active tuning.

[0100] As can be seen from the above, using the SP-PS compensation network significantly reduces the equivalent load resistance of the system, thereby effectively reducing the critical coupling coefficient k. cTherefore, this system exhibits an expanded transverse PT (potential contact) precision symmetry region, improving the system's inherent sensitivity and making it more stable during transmission. Furthermore, due to the parallel and series combination of capacitors and inductors, it is no longer limited to the limitations of current simple circuits; the SP-PS type wireless power transfer system can adjust according to the capacitance C. 5p C 5s The ability to dynamically adjust output power and transmission efficiency facilitates the design and modification of system parameters.

Claims

1. A long-range time-reversal symmetric wireless power transfer system with a multi-coil structure, characterized in that: The transmission device, the relay coil circuit and the receiving device, two capacitors and resistors are connected in parallel and then connected in series with an inductor to form a SP structure of the transmission device and a PS structure of the receiving device, and a plurality of groups of relay coil circuits are arranged between the transmission device and the receiving device; The transmitting device comprises a power supply, a full-bridge inverter, a resonance capacitor 、 and an inductor ; wherein, in the associated reference direction, the voltage across the full-bridge inverter and the current flowing through the full-bridge inverter are opposite, and the power supply is equivalent to a negative resistance , the resonance capacitor 、 and the resistance are connected in parallel, and the inductor is connected in series, thus forming an SP structure; The receiving device includes a receiving inductor , a resonant capacitor , and a load ; wherein the resonant capacitor , and the load are connected in parallel and the inductor is connected in series to form a PS structure; Three groups of relay coil circuits are arranged between the transmission device and the receiving device; In the first group of relay coil circuits, the inductance , the capacitance form a closed loop, the inductance and the inductance are adjacent, there is mutual inductance M 12 ; in the second group of relay coil circuits, the inductance , the capacitance form a closed loop, the inductance and the inductance are adjacent coils, there is mutual inductance M 23 ; in the third group of relay coil circuits, the inductance , the capacitance form a closed loop, the inductance and the inductance are adjacent coils, there is mutual inductance M 34 ; at the same time, the inductance and the inductance are adjacent coils, there is mutual inductance M 45 ; The number of turns of the inductor in the relay coil circuit is greater than the number of turns of the inductor in the transmission device and the receiving device; The distances between the coils in the transmission device, the relay coil circuit and the receiving device are equal; The coils in the transmitting device, the repeater coil circuit and the receiving device maintain the same resonance frequency, i.e. and the same coupling coefficient, i.e. .

2. The system according to claim 1, wherein the system is a multi-coil system. The mutual inductance between the non-adjacent coils in the transmission device, the relay coil circuit and the receiving device is 0.

3. The system according to claim 2, wherein the system is a multi-coil system. The coil internal resistance exists in the transmitting device, the relay coil circuit and the receiving device , n =1,2,3,4,5, the coil internal resistance is very small and can be ignored.

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