A PT symmetry-based SP type wireless energy transmission system optimization method

Abstract

The application provides a PT symmetry-based SP type wireless energy transmission system optimization method. The optimization method constructs two PTs-WPT circuit systems with SP type receiving ends, namely, S-SP type and P-SP type circuits. The SP type impedance matching is used to transform the load to the optimal load, so that the system efficiency is always kept at the highest efficiency within a certain load range, and the system is always in the PT symmetry region. The impedance transformation method provided by the application uses the principle of parity time symmetry, has the frequency self-adaptive characteristics, and after entering the PT symmetry region, the output power and transmission efficiency of the system remain stable in the PT symmetry region, and has strong robustness. The traditional magnetic resonance WPT impedance transformation needs frequency tracking, real-time dynamic coupling coefficient identification and real-time adjustment of the impedance matching network, so that the design is simplified and the cost is saved.

Description

Technical Field

[0001] This invention belongs to the field of wireless power transmission, specifically referring to an optimization method for SP-type wireless power transmission systems based on PT symmetry. Background Technology

[0002] Parity-time symmetry (PTs) is a concept in quantum mechanics describing the fundamental theory of motion of microscopic objects. It refers to invariance under time and space reversal. When applied to wireless power transfer, this technology overcomes the shortcomings of traditional magnetic resonant coupling methods, which suffer from poor robustness due to short transmission distances. Specifically, strong coupling can lead to frequency splitting, resulting in decreased output power and transmission efficiency. In contrast, PTs-WPT systems, based on parity-time symmetry, possess frequency-adaptive characteristics, meaning their output power and transmission efficiency are independent of transmission distance. This improves the robustness, flexibility, and applicability of wireless power transfer systems.

[0003] In WPT systems, a series (S) receiver structure is more suitable for situations with low load resistance. However, in some wireless power transfer applications, such as implantable medical devices and wireless cars, where the load at the receiver has high resistance, a series and parallel (SP) receiver structure is required to transform the load resistance to a suitable load location.

[0004] Research has found that the coupling coefficient in the PTs-WPT system has a critical value. k C The corresponding critical point is called the symmetry breaking point. When the coupling coefficient is greater than this critical value, the system operates in the PT symmetry state, also known as the strong coupling region, where the system's output power and transmission efficiency remain stable. When the coupling coefficient is less than this critical value, the system operates in the PT symmetry breaking state, also known as the weak coupling region, where the system's output power and transmission efficiency cannot remain stable and will drop significantly.

[0005] This critical coupling coefficient corresponds to a critical load impedance ( R LC At this impedance, the efficiency extremum at the transition point between strong and weak coupling regions can be obtained. Since the transmission efficiency expression for the weak coupling region of the PTs-WPT system is consistent with that of the traditional WPT system, an efficiency extremum also exists in the traditional WPT method, corresponding to a load impedance of... R Lopt In different applications, the quality factors of the transmitting and receiving coils differ, leading to... R LC and R LoptThey are not necessarily equal. Therefore, depending on the quality factor of the transmitting and receiving coils and the size of the load in different applications, an SP-type impedance transformer can be used at the receiving end to transform the load impedance to the optimal load position in order to obtain the maximum transmission efficiency. Summary of the Invention

[0006] The purpose of this invention is to provide an optimization method for SP-type wireless power transmission system based on PT symmetry. This method is based on the PT symmetry principle and, according to the size of the load and the quality factors of the transmitting and receiving coils, uses SP-type impedance transformation at the receiving end to transform the original load to the optimal load position, so that the system can obtain the maximum transmission efficiency.

[0007] An optimization method for a PT-symmetric SP-type wireless power transfer system includes the following steps: Step 1: Construct the optimized wireless power transmission system. The optimized wireless power transmission system includes a transmitting circuit and a receiving circuit; the transmitting circuit includes a negative resistor structure connected in a closed loop and a transmitting-end LC resonant circuit. The receiving circuit includes a load RL connected in a closed loop and a receiving-end LC resonant circuit. The receiving-end LC resonant circuit includes a parallel resonant capacitor C2p, a series compensation capacitor C2s, and a receiving coil L2. The series compensation capacitor C2s, the receiving coil L2, and the load RL are connected in series to form a closed loop; the parallel resonant capacitor C2p is connected in parallel across the load RL.

[0008] Step 2: Set the inductance value of the receiving coil L2 L 2 and parasitic resistance R 2. Impedance of load RL R L The capacitance value of resonant capacitor C1 C 1 and coupling coefficient k .

[0009] Step 3: Obtain the capacitance value of the parallel resonant capacitor C2p. C 2P And the capacitance value of the series compensation capacitor C2s C 2S The specific process is as follows: 3-1. If the quality factor of transmitting coil L1 is... Q 1 and the quality factor of receiving coil L2 Q 2. Satisfy the relation Q 2> Q 1+2 / k Then the capacitance value of the parallel resonant capacitor C2p C 2P As shown in equation (1): Equation (1) in, It is the resonant angular frequency.

[0010] If the quality factor of transmitting coil L1 is Q 1 and the quality factor of receiving coil L2 Q 2. Satisfy the relation Q 2< Q 1+2 / k Then the capacitance value of the parallel resonant capacitor C2p C 2P As shown in equation (2): Equation (2) If the quality factor of transmitting coil L1 is Q 1 and the quality factor of receiving coil L2 Q 2. Satisfy the relation Q 2= Q 1+2 / k Then the capacitance value of the parallel resonant capacitor C2p C 2P The same equation can be calculated using either equation (1) or equation (2).

[0011] 3-2. Capacitance value of series compensation capacitor C2s C 2S As shown in equation (3): Equation (3) Among them, C 2P ' is the equivalent capacitance, and its expression is shown in equation (4): Equation (4) Step 4: Adjust the resistance value of the feedback resistor in the negative resistor structure of the transmitting circuit so that the transmitting circuit can oscillate, thus obtaining the optimized wireless power transmission system.

[0012] Preferably, the inductance, parasitic internal resistance, and resonant frequency of the transmitting coil L1 and the receiving coil L2 are the same.

[0013] Preferably, the transmitting end LC resonant circuit includes a resonant capacitor C1 and a transmitting coil L1. The transmitting end LC resonant circuit has either a series capacitor structure or a parallel capacitor structure; when the transmitting end LC resonant circuit adopts a series capacitor structure, the resonant capacitor C1 and the transmitting coil L1 are connected in series across the negative resistor structure; when the transmitting end LC resonant circuit adopts a parallel capacitor structure, the resonant capacitor C1 and the transmitting coil L1 are connected in parallel across the negative resistor structure.

[0014] Preferably, the negative resistance structure includes an operational amplifier and three feedback resistors. R t1 , R f1 and Rf2 When the LC resonant circuit at the transmitting end uses a capacitor series structure, the negative resistance structure adopts a CNIC negative resistance structure; when the LC resonant circuit at the transmitting end uses a capacitor parallel structure, the negative resistance structure adopts a VNIC negative resistance structure.

[0015] When the negative resistance structure adopts the CNIC negative resistance structure, the inverting input terminal of the operational amplifier is connected to one end of resistor Rf1; the output terminal of the operational amplifier is connected to the other end of resistor Rf1 and one end of resistor Rf2; the non-inverting input terminal of the operational amplifier is connected to the other end of resistor Rf2 and one end of resistor Rt1; the other end of resistor Rt1 and the inverting input terminal of the operational amplifier are the two terminals of the negative resistance structure.

[0016] When the negative resistance structure uses the VNIC negative resistance structure, the inverting input terminal of the operational amplifier is connected to one end of resistors Rf1 and Rf2; the output terminal of the operational amplifier is connected to the other end of resistor Rf1 and one end of resistor Rt1; the non-inverting input terminal of the operational amplifier is connected to the other end of resistor Rt1; the other end of resistor Rf2 and the non-inverting input terminal of the operational amplifier are the two terminals of the negative resistance structure.

[0017] Preferably, when the LC resonant circuit at the transmitting end adopts a capacitor series structure, the relationship shown in equation (5) is satisfied.

[0018] Equation (5) in, R f1 Let Rf1 be the resistance value. R f2 Let Rf2 be the resistance value. R t1 Let Rt1 be the resistance value. Let be the equivalent resistance of the load, and its expression is shown in equation (6). Equation (6) When the LC resonant circuit at the transmitting end adopts a capacitor parallel structure, the relationship shown in equation (7) is satisfied.

[0019] Equation (7) in, R f1 Let Rf1 be the resistance value. R f2 Let Rf2 be the resistance value. R t1 Let Rt1 be the resistance value. This refers to the load size.

[0020] The beneficial effects of this invention are as follows: 1. The S-SP type PTs-WPT wireless power transfer system provided by this invention, compared with the original SS and SP structure circuits, can maximize the impedance transformation and maintain efficiency when the load changes within a certain load range.

[0021] 2. The PTs-WPT system designed based on the parity-time symmetry principle of this invention has frequency adaptive characteristics. After the system enters the PT symmetry region, it can still maintain constant output power and transmission efficiency even after the coupling coefficient changes, and the spatial range of energy transmission is larger.

[0022] 3. This invention eliminates the need for frequency tracking, real-time dynamic coupling coefficient identification, and real-time adjustment of the impedance matching network required in traditional impedance transformation, simplifying the design and saving costs. Attached Figure Description

[0023] Figure 1a , 1b These are the circuit schematics of two PTs-WPT systems with SP-type receivers in this invention. Figure 1a Corresponding to S-SP type, Figure 1b (Corresponding to P-SP type).

[0024] Figure 2a , 2b 2c, 2d, and 2e are the coil quality factors, respectively. Q A comparison of the load efficiency of the traditional WPT system and the PTs-WPT system under five different values ​​( Figure 2a correspond" Q When the value is large, Q 2> Q 1+2 / k "Condition, Figure 2b correspond" Q When the value is large, Q 2< Q 1+2 / k "Condition, Figure 2c correspond" Q When the value is small, Q 2> Q 1+2 / k "Condition, Figure 2d correspond" Q When the value is small, Q 2< Q 1+2 / k "Condition, Figure 2e correspond" Q 2= Q 1+2 / k "Condition).

[0025] Figure 3The above is a simulation waveform diagram of the voltage at the transmitting and receiving ends of the S-SP type circuit provided in Embodiment 1 of the present invention.

[0026] Figure 4 This is a simulation waveform diagram of the voltage at the transmitting and receiving ends of the P-SP type circuit provided in Embodiment 2 of the present invention.

[0027] Figure 5 The diagram shows the relationship between the coupling coefficient and efficiency of S-SP and P-SP type circuit simulation and theory. Detailed Implementation

[0028] To make the objectives, functions, and advantages of this invention more readily understood, the invention will be further described below in conjunction with the accompanying drawings and specific embodiments. However, it should be understood that this invention can be implemented in various forms. The exemplary and non-limiting embodiments shown in the accompanying drawings and described below are not intended to limit the invention to the specific embodiments described.

[0029] Example 1 An optimization method for a PT-symmetric SP-type wireless power transfer system is presented, and the specific process is as follows: Based on the parity-time symmetry principle, an S-SP (series-parallel series) type PTs-WPT wireless power transfer system is constructed. For example... Figure 1a As shown, the wireless power transfer system includes a transmitting circuit and a receiving circuit. The transmitting circuit includes a negative resistance structure and a transmitting-end LC resonant circuit. The transmitting-end LC resonant circuit includes a resonant capacitor C1, a transmitting coil L1, and the parasitic resistance of the transmitting coil L1. R 1; The resonant capacitor C1 and the transmitting coil L1 are connected in parallel across the negative resistor structure.

[0030] The receiving circuit includes a load RL and a receiver LC resonant circuit. The receiver LC resonant circuit includes a parallel resonant capacitor C2p, a series compensation capacitor C2s, a receiving coil L2, and the parasitic resistance of the receiving coil L2. R 2. The transmitting coil L1 and the receiving coil L2 have the same inductance, parasitic internal resistance, and resonant frequency. The series compensation capacitor C2s, the receiving coil L2, and the load RL are connected in series to form a closed loop; the parallel resonant capacitor C2p is connected in parallel across the load RL.

[0031] The negative resistor structure adopts a CNIC (Current Inversion NIC) type negative resistor structure; the CNIC negative resistor structure consists of an operational amplifier and three feedback resistors. R t1 , R f1 and R f2Composition: The inverting input of the operational amplifier is connected to one end of resistor Rf1; the output of the operational amplifier is connected to the other end of resistor Rf1 and one end of resistor Rf2; the non-inverting input of the operational amplifier is connected to the other end of resistor Rf2 and one end of resistor Rt1; the other end of resistor Rt1 and the inverting input of the operational amplifier are the two terminals of a negative resistor structure. These two terminals are connected to the transmitting end LC resonant circuit; see [link to relevant documentation]. Figure 1a In the circuit diagram, the CNIC negative resistor structure can be equivalent to a negative resistor. R 0, whose absolute value is equal to the equivalent resistance of the load.

[0032] Compare the critical load based on the different quality factor values ​​of the transmitting and receiving coils. R LC Optimal load with weak coupling region R Lopt Based on the size of the load, find the optimal load corresponding to the maximum transmission efficiency, as follows: After circuit equivalent transformation, the S-SP type circuit is equivalent to a simple SS type circuit for circuit analysis.

[0033] The expression for the transmission efficiency of an SS-type PTs-WPT system is given. This is the ratio of the output power to the input power at the negative resistor terminal:

[0034] As can be seen from the formula, in the strongly coupled region, the transmission efficiency increases with the increase of the load, and at the critical coupling coefficient... k C Corresponding critical load R LC The efficiency reaches its peak at this point. After entering the weakly coupled region, the efficiency expression is consistent with the traditional WPT, and the efficiency has a non-linear relationship with the load. η S-S beg R L The derivative of the optimal load in a weakly coupled region. R Lopt This improves transmission efficiency. η S-S It has reached its maximum value.

[0035] Optimal load in weakly coupled region R Lopt The expression is as follows:

[0036] in, Q 1. Q 2 represents the quality factor of the transmitting coil and the receiving coil, respectively. Q 1= ω 1 L 1 / R 1, Q 2= ω 2 L 2 / R 2.

[0037] Based on the critical coupling coefficient under PT symmetry k C The expression for the corresponding critical load can be obtained. R LC The expression:

[0038] when k = k C At that time, it can be obtained R Lopt and R LC Different Q 1. Q The size relationship of the values ​​of 2 is as follows:

[0039] Selecting the same structural parameters and different Q Value, draw the load R L With transmission efficiency η Relationship diagram, such as Figures 2a-2e As shown in the figure. The coupling coefficients... k Set to 0.04, corresponding to 2 / k =50. In the figure, R Lopt The point corresponds to the vertex of the maximum value in the traditional WPT. R LC The point corresponds to the critical point of strong and weak coupling in the PTs-WPT system, from which the following conclusions can be drawn: when Q 2< Q 1+2 / k hour, R LC < R Lopt Maximum transmission efficiency at R Lopt Point, optimal load is R Lopt To achieve greater transmission efficiency for the PTs-WPT system, the load should be shifted to... R Lopt Place.

[0040] when Q 2=Q 1+2 / k hour, R LC = R Lopt At this point, the load can be arbitrarily changed to R LC Or R Lopt At any point, the system can achieve maximum transmission efficiency.

[0041] when Q 2> Q 1+2 / k hour, R LC > R Lopt Maximum transmission efficiency at R LC Point, optimal load is R LC At this point, the maximum transmission efficiency of the PTs-WPT system is... R LC The point should be chosen to transform the load to R LC Place.

[0042] Q When the value is large, R LC and R Lopt The efficiency difference between them is small, and the overall efficiency is large; Q When the value is small, R LC and R Lopt The efficiency difference between them is large, and the overall efficiency is small.

[0043] Similarly, the P-SP type structure circuit in Example 2 can produce the same results as the S-SP structure.

[0044] Further SP-type impedance transformation is performed on the load to obtain the optimal capacitance value of the parallel resonant capacitor C2p in the receiver's LC resonant circuit. C 2P And the capacitance value of the series compensation capacitor C2s C 2S as follows: (1) Determine circuit parameters: Determine the inductance value of transmitting coil L1. L 1 and parasitic resistance R 1. Inductance value of receiving coil L2 L 2 and parasitic resistance R 2. Impedance of load RL R LThe capacitance value of resonant capacitor C1 C 1. Resonant angular frequency ω 2= ω 1= ω 0.

[0045] (2) Set up the equation and solve it. C 2P and C 2S ①When Q 2> Q 1+2 / k The optimal load is R LC hour According to the PT symmetry condition, by k C The expression is obtained R LC expression:

[0046] The equivalent resistance is obtained from the formula for converting a parallel circuit into a series circuit. R L 'and equivalent capacitance C 2P 'expression:

[0047]

[0048] Equalizing the two equations above R L '= R LC The following equation is obtained:

[0049] In the above formula, the resonant angular frequency ω 0 is from the sending end L 1 C 1. The decision remains unchanged. The parallel compensation capacitor can then be calculated. C Optimal capacitor value for 2p as follows:

[0050] ②When Q 2< Q 1+2 / k The optimal load is R Lopt hour according to R Lopt The expression for the parallel equivalent resistance RL '

[0051]

[0052] Equalizing the two equations above R L '= R Lopt The following equation is obtained:

[0053] The parallel compensation capacitor can be solved. C 2P :

[0054] make C 2 represents the total capacitance at the receiving end, i.e.:

[0055] Substituting the two parallel compensation capacitors obtained above C 2P A series compensation capacitor can be obtained. C 2S :

[0056] Efficiency expression:

[0057] Scope of application of the method: According to the above formula, only when R LC ( R Lopt )≤ R L ≤ R LC + ω 0 2 L 2 2 / R LC ( R Lopt + ω 0 2 L 2 2 / R Lopt Only when the series capacitor is in series is the requirement met. C 2S ≥0 and parallel capacitors C 2P≥0 can form an S-SP impedance matching circuit. This means that the S-SP impedance matching circuit cannot meet the requirements of the entire load range (0≤ R L (≤+∞), the power transfer efficiency of the S-SP circuit can only be maximized within the aforementioned limited load range.

[0058] Initial critical coupling coefficient selection problem Parity-time symmetric WPT systems exhibit strong robustness in the PT-symmetric region. However, when the system is in the PT-symmetric broken region, its output power and transmission efficiency become highly sensitive to changes in the coupling coefficient, affecting its stability. Therefore, it is necessary to expand the PT-symmetric region to extend the distance of constant and efficient transmission. Reducing the critical coupling coefficient is also crucial. k C This can widen the symmetry region of pt, extend the distance between constant power and efficiency, and improve anti-alignment capability. However, as can be seen from the efficiency expression of the S-SP circuit listed above, reducing the critical coupling coefficient and improving efficiency are contradictory, making it difficult to reduce. k C This approach achieves high efficiency while simultaneously addressing the application context. Therefore, determining the initial critical coupling coefficient requires comprehensive consideration, taking into account whether a wider PT symmetry range or higher efficiency and a wider load range is preferred.

[0059] Technical effectiveness verification: To verify the effectiveness of the impedance matching of the S-SP type PTs-WPT system proposed in the above embodiments, a simulation circuit model of the system was built using the software Multisim.

[0060] In simulation and application, based on the frequency adaptive characteristics of the PT symmetry principle and the conditions for the amplifier circuit's self-excited oscillation, to enable oscillation at the negative resistor end, the equivalent resistance value— R 0 must satisfy:

[0061] Therefore, the system parameters are set as follows: R t1 =5kΩ, R f1 =5.5kΩ, R f2 =4.5kΩ, F =31.9kHz, L 1= L 2 = 2.325 mH C 1 = 10.675 nF, R 1= R 2 = 0.25Ω kC =0.02, R L =2kΩ. The simulation results are as follows: Figure 3 The waveform diagram shows the voltage simulation at the transmitting and receiving ends of the circuit. It can be seen that after entering the PT symmetrical state, the voltage amplitude at the receiving end is almost the same as that at the transmitting end. Figure 5 This is a comparison chart of the coupling coefficient and efficiency relationship between the S-SP circuit theory and simulation. It can be seen that the simulation and theory are almost consistent. After entering the strong coupling region, the efficiency is as high as 90% or more and remains stable, and the corresponding critical coupling coefficient is 0.02.

[0062] Example 2 An optimization method for a PT-symmetric SP-type wireless power transfer system is presented. The difference between this embodiment and Embodiment 1 is that this embodiment constructs a P-SP parallel-series parallel PTs-WPT system, as shown in the circuit diagram below. Figure 1b As shown; in this embodiment, the resonant capacitor C1 in the LC resonant circuit of the transmitting end is connected in series with the transmitting coil L1, and forms a closed loop with the two terminals of the negative resistor structure.

[0063] The negative resistor structure is transformed into a VNIC (Voltage Inversion NIC) type negative resistor structure. The VNIC type negative resistor structure consists of an operational amplifier and three feedback resistors. R t1 , R f1 and R f2 Composition: The inverting input of the operational amplifier is connected to one end of resistors Rf1 and Rf2; the output of the operational amplifier is connected to the other end of resistor Rf1 and one end of resistor Rt1; the non-inverting input of the operational amplifier is connected to the other end of resistor Rt1; the other end of resistor Rf2 and the non-inverting input of the operational amplifier are two terminals of a negative resistor structure. These two terminals are connected to the transmitting LC resonant circuit.

[0064] See Figure 1b The schematic diagram shows that the VNIC negative resistor structure can be equivalent to a resistor with a resistance value of R 0 negative resistance, R 0 is numerically the same as the equivalent load resistance of the receiving end. In simulation and application, similar to the negative resistance of the CNIC, for the circuit to oscillate, the equivalent resistance of the amplifier circuit— R 0 must satisfy:

[0065] When performing simulations using Example 2, the resistance values ​​of the three resistors in the negative resistance structure are also different from those in Example 1. The simulation parameters are as follows: Rt1 =5kΩ, R f1 =9.5kΩ, R f2 =0.5kΩ. All other transmitting and receiving end structural parameters are the same as those set in Example 1.

[0066] Apart from the above, the impedance transformation method at the receiving end in this embodiment is the same as that in Embodiment 1, and will not be described again here.

[0067] The simulation results are as follows: Figure 4 This is a simulation waveform diagram of the current-to-voltage conversion at the transmitting and receiving ends of a P-SP type circuit. It can be seen that after entering the PT symmetry region, the voltage amplitude at the receiving end is almost identical to that at the transmitting end. Figure 5 This is a comparison chart of the coupling coefficient and transmission efficiency between the theoretical and simulated P-SP circuits. It can be seen that the simulation and theory are almost identical. This is also consistent with the results obtained in Example 1.

[0068] It should be understood that the specific examples and embodiments described in this invention are non-limiting. Where technically feasible, different coil parameters and loads can achieve the effects of the claims, and corresponding modifications can be made to the above-described structure, steps, and sequence without departing from the protection scope of this invention.

Claims

1. An optimization method for a SP-type wireless power transfer system based on PT symmetry, characterized in that: Includes the following steps: Step 1: Construct the optimized wireless power transmission system. The optimized wireless power transmission system includes a transmitting circuit and a receiving circuit. The transmitting circuit includes a negative resistance structure connected in a closed loop and a transmitting-end LC resonant circuit. The receiving circuit includes a load RL connected in a closed loop and a receiving-end LC resonant circuit. The receiving-end LC resonant circuit includes a parallel resonant capacitor C2p, a series compensation capacitor C2s, and a receiving coil L2. The series compensation capacitor C2s, the receiving coil L2, and the load RL are connected in series to form a closed loop. The parallel resonant capacitor C2p is connected in parallel across the load RL. Step 2: Set the inductance value L2 and parasitic resistance R2 of the receiving coil L2, and the impedance R of the load RL. L The capacitance value of resonant capacitor C1 and the coupling coefficient k; Step 3: Obtain the capacitance value C of the parallel resonant capacitor C2p. 2P And the capacitance value C of the series compensation capacitor C2s 2S The specific process is as follows: 3-1. If the quality factor Q1 of the transmitting coil L1 and the quality factor Q2 of the receiving coil L2 satisfy the relationship Q2>Q1+2 / k, then the capacitance value C of the parallel resonant capacitor C2p is... 2P As shown in equation (1): Equation (1) in, It is the resonant angular frequency; If the quality factor Q1 of the transmitting coil L1 and the quality factor Q2 of the receiving coil L2 satisfy the relational expression Q2<Q1+2 / k, then the capacitance value C of the parallel resonant capacitor C2p 2P is as shown in Equation (2): Equation (2) If the quality factor Q1 of the transmitting coil L1 and the quality factor Q2 of the receiving coil L2 satisfy the relationship Q2=Q1+2 / k, then the capacitance value C of the parallel resonant capacitor C2p is... 2P The result is obtained by taking any one of equations (1) and (2); 3-2. The capacitance value C of the series compensation capacitor C2s 2S As shown in equation (3): Equation (3) Among them, C 2P ' is the equivalent capacitance, and its expression is shown in equation (4): Equation (4) Step 4: Adjust the resistance value of the feedback resistor in the negative resistor structure of the transmitting circuit so that the transmitting circuit can oscillate, thus obtaining the optimized wireless power transmission system.

2. The optimization method for a PT-symmetric SP-type wireless power transfer system according to claim 1, characterized in that: The transmitting coil L1 and the receiving coil L2 have the same inductance, parasitic internal resistance, and resonant frequency.

3. The optimization method for a PT-symmetric SP-type wireless power transfer system according to claim 1, characterized in that: The transmitting end LC resonant circuit includes a resonant capacitor C1 and a transmitting coil L1; the transmitting end LC resonant circuit has a capacitor series structure or a capacitor parallel structure; when the transmitting end LC resonant circuit adopts a capacitor series structure, the resonant capacitor C1 and the transmitting coil L1 are connected in series across the negative resistor structure. When the LC resonant circuit at the transmitting end adopts a parallel capacitor structure, the resonant capacitor C1 and the transmitting coil L1 are connected in parallel across the negative resistor structure.

4. The optimization method for a PT-symmetric SP-type wireless power transfer system according to claim 3, characterized in that: The negative resistance structure includes an operational amplifier and three feedback resistors R. t1 R f1 and R f2 The transmitting end LC resonant circuit adopts a capacitor series structure, and the negative resistance structure adopts a CNIC negative resistance structure. When the negative resistance structure adopts a CNIC negative resistance structure, the inverting input terminal of the operational amplifier is connected to one end of resistor Rf1; the output terminal of the operational amplifier is connected to the other end of resistor Rf1 and one end of resistor Rf2; the non-inverting input terminal of the operational amplifier is connected to the other end of resistor Rf2 and one end of resistor Rt1; the other end of resistor Rt1 and the inverting input terminal of the operational amplifier are the two terminals of the negative resistance structure.

5. The optimization method for a PT-symmetric SP-type wireless power transfer system according to claim 4, characterized in that: The resistance value R of resistor Rf1 f1 The resistance value R of resistor Rf2 f2 The resistance value R of resistor Rt1 t1 It satisfies the relationship shown in equation (5); Equation (5) in, Let be the equivalent resistance of the load, and its expression is shown in equation (6). Equation (6).

6. The optimization method for a PT-symmetric SP-type wireless power transfer system according to claim 4, characterized in that: The negative resistance structure includes an operational amplifier and three feedback resistors R. t1 R f1 and R f2 The transmitting end LC resonant circuit adopts a capacitor parallel structure, and the negative resistance structure adopts a VNIC negative resistance structure. When the negative resistance structure adopts a VNIC negative resistance structure, the inverting input terminal of the operational amplifier is connected to one end of resistor Rf1 and resistor Rf2; the output terminal of the operational amplifier is connected to the other end of resistor Rf1 and one end of resistor Rt1; the non-inverting input terminal of the operational amplifier is connected to the other end of resistor Rt1; the other end of resistor Rf2 and the non-inverting input terminal of the operational amplifier are the two terminals of the negative resistance structure.

7. The optimization method for a PT-symmetric SP-type wireless power transfer system according to claim 6, characterized in that: The resistance value R of resistor Rf1 f1 The resistance value R of resistor Rf2 f2 The resistance value R of resistor Rt1 t1 It satisfies the relationship shown in equation (7); Equation (7).

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