Adaptive resonant wireless power transfer system

Abstract

The application relates to an adaptive resonant type wireless power transmission system, wherein the system comprises: a transmitting end for exciting a transmitting coil to generate an alternating electromagnetic field through high-frequency alternating current generated after inverting an accessed direct-current power supply; a receiving end for picking up energy from the alternating electromagnetic field generated by the transmitting coil through a receiving coil by utilizing magnetic field coupling, and converting the energy into direct-current power to supply a load; wherein the transmitting end further comprises: an adaptive reactive compensation circuit comprising at least an auxiliary inverter and an energy storage capacitor, the auxiliary inverter being electrically connected with the transmitting coil, and the energy storage capacitor being connected with the auxiliary inverter, the capacitor and the auxiliary inverter forming an alternating voltage source, and the voltage and current of the transmitting coil are always operated in a resonant state by restricting the phase angle of the alternating voltage source to be +90 DEG. Through the application, the resonant deviation caused by impedance mismatch is solved, and the energy density and robustness of the wireless power transmission system are effectively improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless charging, in particular to an adaptive resonant wireless power transmission system. BACKGROUND

[0002] Wireless power transmission technology can achieve non-contact energy transmission through high-frequency alternating electromagnetic field, and is increasingly favored due to its excellent sealing, flexibility and convenience. However, due to the change of the relative position between the load or the coil, impedance mismatching is easily caused, which will lead to uncertain output power, increase the difficulty of power control and system state monitoring, and affect the robustness of the wireless power transmission system.

[0003] The traditional passive impedance matching network realizes continuous voltage and current output by adjusting inductance and capacitance, but such a topology network lacks gain adjustment capability. In order to obtain gain adjustment capability, the prior art method is to additionally connect a DC-DC converter in the wireless power transmission system, but this will generate additional conduction loss, increase the system cost and volume, and is not friendly to energy density.

[0004] In addition, the prior art method also needs to add a communication module for communication between the transmitting end and the receiving end, and the communication module of the receiving end will cause a non-monotonic relationship between the voltage gain and the duty cycle, making the parameter design process more difficult. In the prior art, a dynamic rectifier using an active switch is also used to realize rectification and power regulation functions at the same time with fewer components, but the corresponding control strategy will generate additional reactance and cause the input voltage and current to deviate from the resonance state, further weakening the energy injection capability of the input voltage source. SUMMARY

[0005] The embodiment of the present application provides an adaptive resonant wireless power transmission system to work in a resonant state by compensating impedance adjustment, effectively improving the energy density and robustness of the wireless power transmission system.

[0006] In order to achieve the above purpose, the embodiment of the present application provides an adaptive resonant wireless power transmission system, comprising:

[0007] a transmitting end for exciting a transmitting coil to generate an alternating electromagnetic field by high-frequency alternating current generated after inverting an accessed direct-current power supply;

[0008] a receiving end for picking up energy from the alternating electromagnetic field generated by the transmitting coil through a receiving coil by magnetic field coupling effect, and converting the energy into direct-current power for a load through rectification;

[0009] wherein the transmitting end further comprises:

[0010] The adaptive reactive compensation circuit comprises at least an auxiliary inverter and a storage capacitor C i2 The auxiliary inverter is electrically connected to the transmitting coil, and the storage capacitor is connected to the auxiliary inverter. i2 An auxiliary DC voltage V i2 The capacitor and the auxiliary inverter form an AC voltage source, and by restricting the phase angle of the AC voltage source to ±90°, the voltage and current of the transmitting coil are always operated in a resonant state.

[0011] Based on the adaptive reactive compensation circuit, the phase angle of the AC voltage source is restricted to ensure that the voltage and current of the transmitting end are always operated in a fully resonant state, maintain the power transmission capability, and effectively improve the energy density of the wireless power transmission system.

[0012] In some embodiments, the phase angle of the AC voltage source is restricted by the following parameter configuration:

[0013] and |c i | and |d r have the same order of magnitude.

[0014] wherein a r , d r are real numbers, b i , c i are imaginary numbers, and R eq is the equivalent load of the receiving end.

[0015] In some embodiments, the phase angle of the AC voltage source is represented by the following calculation model:

[0016]

[0017] In some embodiments, the transmitting end further comprises a DC power supply, an inverter, a transmitting coil L1, and a resonant capacitor C1, which are electrically connected in series.

[0018] In some embodiments, the adaptive reactive compensation circuit further comprises:

[0019] a capacitor C2 electrically connected to the resonant capacitor C1;

[0020] a capacitor C3 connected to the capacitor C2; and

[0021] an inductor L3 connected to the capacitor C3 and the auxiliary inverter.

[0022] In some embodiments, the inverter and the auxiliary inverter are half-bridge inverters, each comprising two series-connected switching tubes, for generating high-frequency square-wave voltages v1 and v2, respectively.

[0023] In some embodiments, the real number a r , d r , the imaginary number b i , c i are calculated by the following calculation model, respectively:

[0024]

[0025] wherein Z1' represents the total reactance of Z1 and Z eq , Z eq is the equivalent impedance from the receiving end to the transmitting end, Z1 is the impedance of the transmitting coil L1 and the corresponding branch of the resonance capacitor C1, Z2 is the impedance of the capacitor C2 corresponding branch, and Z3 is the impedance of the inductor L3 and the capacitor C3 corresponding branch.

[0026] In some embodiments, the Z1, Z2, and Z3 are calculated by the following calculation model:

[0027]

[0028] In some embodiments, the receiving end further comprises, in sequence: a receiving coil L s , a capacitor C s , and a class-E rectifier.

[0029] In some embodiments, the class-E rectifier further comprises:

[0030] an inductor L e , and the capacitor C s ;

[0031] a capacitor C e , and the capacitor C s ;

[0032] a diode D e , connected across the capacitor C e ;

[0033] a capacitor C o , and the capacitor C e ;

[0034] an equivalent load R o , and the capacitor C o , and the capacitor C e , further connected across a switching tube S a and a capacitor C a .

[0035] Compared with the related art, the adaptive resonant wireless power transmission system provided by the embodiments of the present application adjusts an AC voltage source by using an auxiliary inverter and a capacitor of a topology structure, the AC voltage source can adjust the transmitting coil and the current to return to a complete resonance state, the present application does not need a complex element matrix, a detection and control circuit, simplifies the circuit, and compared with the existing impedance adjustment method, can eliminate inductive reactance or capacitive reactance in a wide range, effectively improves the energy density and robustness of the system.

[0036] The details of one or more embodiments of the present application are presented in the following drawings and description to make other features, objects and advantages of the present application more clear and simple. BRIEF DESCRIPTION OF DRAWINGS

[0037] The drawings described herein are used to provide further understanding of the present application, constitute a part of the present application, the schematic embodiments of the present application and the description thereof are used to explain the present application, and do not constitute an improper limitation on the present application. In the drawings:

[0038] Figure 1 is a schematic diagram of a series-series type wireless power transmission system according to the related art;

[0039] Figure 2 is a structural schematic diagram of a wireless power transmission system according to an embodiment of the present application;

[0040] Figure 3 is a schematic diagram of a transmitting end of a wireless power transmission system according to an embodiment of the present application;

[0041] Figure 4 is a schematic diagram of a transmission of a wireless power transmission system according to an embodiment of the present application;

[0042] Figure 5 is a schematic diagram of branch transmission of a wireless power transmission system according to an embodiment of the present application;

[0043] Figure 6 is a schematic diagram of another branch transmission of a wireless power transmission system according to an embodiment of the present application;

[0044] Figure 7 is a schematic diagram of compensation adjustment of a wireless power transmission system according to an embodiment of the present application;

[0045] Figure 8 is a parameter configuration example of a wireless power transmission system according to an embodiment of the present application. DETAILED DESCRIPTION

[0046] In order to make the purposes, technical solutions, and advantages of the present application clearer, the present application is described and explained below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only intended to explain the present application and not to limit the present application. Based on the embodiments provided by the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort fall within the scope of the present application.

[0047] It is obvious that the accompanying drawings in the following description are only some examples or embodiments of the present application, and for those of ordinary skill in the art, the present application can be applied to other similar scenarios without creative effort based on the accompanying drawings. In addition, it can be understood that although the efforts made in the development process can be complex and lengthy, for those of ordinary skill in the art related to the content disclosed in the present application, some design, manufacture or production changes based on the technical content disclosed in the present application are only routine technical means and should not be understood as insufficient disclosure of the content disclosed in the present application.

[0048] In the present application, the phrase "embodiment" means that the specific features, structures or properties described in conjunction with the embodiment can be included in at least one embodiment of the present application. The appearance of this phrase at various places in the specification does not necessarily mean the same embodiment, nor is it an independent or alternative embodiment that is not mutually exclusive with other embodiments. It is explicitly and implicitly understood by those of ordinary skill in the art that the embodiments described in the present application can be combined with other embodiments without conflict.

[0049] Unless otherwise defined, technical terms and scientific terms used in the present application shall have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. The terms "a", "an", "one", "this", and similar referents in the context of describing the application are to be construed to be inclusive of both the singular and the plural, unless otherwise indicated. The terms "comprising", "comprises" and "comprised of" as well as "containing", "containing" and "contains" are inclusive and do not exclude other steps, elements or ingredients. The terms "connected", "coupled", "linked", and the like, as well as the terms "connected", "coupled", "linked", and the like, are not restricted to physical or mechanical connections or couplings, but can include electrical connections or couplings, whether direct or indirect. The term "multiple" means two or more. The term "and / or" describes associated objects in association with the associated objects, and means that there can be three relationships, for example, "A and / or B" can mean that A exists alone, A and B exist together, and B exists alone. The character " / " generally represents an "or" relationship between the associated objects. The terms "first", "second", "third", and the like only distinguish similar objects, and do not represent a specific order for the objects.

[0050] Wireless power transmission, also known as wireless power transmission or contactless power transmission, refers to a transmission mode in which the transmitting end converts electrical energy into other forms of relay energy (such as electromagnetic field energy, laser, microwave and mechanical wave, etc.), transmits a distance in the air, and then converts the relay energy into electrical energy through the receiving end to realize wireless power transmission. The relay energy form in the power transmission process of the embodiments of the present application is preferably magnetic coupling type. By loading a high-frequency power supply to the transmitting coil, the transmitting coil generates a high-frequency magnetic field under the excitation of the power supply. The receiving coil generates a current under the action of the high-frequency magnetic field, thereby realizing wireless power transmission.

[0051] Figure 1 is a schematic diagram of a series-series type wireless power transmission system according to the related art, as shown in Figure 1 , the output power P out is calculated based on the following calculation model:

[0052] Z out = R L + jX out (1)

[0053]

[0054] Wherein:

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] In the calculation model shown in the above formula, i z1 represents the current of the coil in the energy transmission process; Z eq represents the equivalent impedance from the receiving end to the transmitting end, Re(Z eq ) represents the equivalent resistance of the receiving end; X r and X t respectively represent the reactance of the receiving end and the transmitting end; f represents the working frequency of the inverter. In addition, ω represents the inverter angular frequency; M represents mutual inductance; k represents the coupling coefficient between L1 and L s ; v fa1 represents the input sinusoidal voltage of the transmitting end; R L represents the equivalent load, L1, L S represents the transmitting end coupling coil, the receiving end coupling coil, C1, C S represents the compensation capacitor, Z out represents the equivalent output impedance, X out represents the equivalent reactance introduced by the rectifier.

[0061] Based on the above calculation model, when the condition shown in the following formula (3) is met, the energy transmission capability of the wireless power transmission system reaches the optimal level:

[0062]

[0063] That is, when v fa1 and i z1 are in the zero phase angle state ZPA, the energy transmission capability can reach the optimal level.

[0064] Therefore, the embodiments of the present application realize the resonance control of the wireless power transmission system by making v fa1 and i z1 be in the zero phase angle state ZPA. Specifically, Figure 2 is a structural schematic diagram of the wireless power transmission system according to the embodiments of the present application, as shown in Figure 2 , the adaptive resonance type wireless power transmission system of the embodiments of the present application comprises:

[0065] The transmitting end is used for exciting the transmitting coil to generate an alternating electromagnetic field by high-frequency alternating current generated after inverting the accessed direct current power, and specifically comprises: a direct current power, an inverter, a transmitting coil L1 and a resonance capacitor C1 which are electrically connected in series; wherein the inverter is a half-bridge inverter, and further comprises two series-connected switch tubes S1 and S2 which are used for generating a high-frequency square-wave voltage v1.

[0066] The receiving end is used for picking up energy from the alternating electromagnetic field generated by the transmitting coil through a receiving coil by magnetic field coupling, and converting the energy into direct current to supply a load, and specifically comprises: a receiving coil L s , a capacitor C s and a class-E rectifier which are electrically connected in sequence. Figure 2 The class-E rectifier of the embodiment of the present application further comprises: an inductor L e , a capacitor C e , a diode D e , a capacitor C o and an equivalent load R o , the inductor L e is connected in parallel with the capacitor C s , the capacitor C e is connected in series with the capacitor C s , the diode D e is connected across the capacitor C e , the capacitor C o is connected in parallel with the capacitor C e , the equivalent load R o is connected in parallel with the capacitor C o , and the capacitor C e is connected across the switch tube S a and the capacitor C a .

[0067] The transmitting end further comprises a self-adapting reactance compensation network which at least comprises an auxiliary inverter and an energy storage capacitor C i2 , the auxiliary inverter is electrically connected with the transmitting coil, and the energy storage capacitor is connected in parallel with the auxiliary inverter, the energy storage capacitor C i2 is used for generating an auxiliary direct current voltage V i2 , the capacitor and the auxiliary inverter constitute an alternating voltage source, and the phase angle of the alternating voltage source is constrained to be ±90° to make the voltage and current of the transmitting coil always work in a resonance state. Specifically, the auxiliary inverter is a half-bridge inverter, and further comprises two series-connected switch tubes S3 and S4 which are used for generating high-frequency square-wave voltages, respectively. Figure 2The adaptive reactive compensation circuit further comprises a capacitor C2, a capacitor C3 and an inductor L3, the capacitor C2 is electrically connected with the resonance capacitor C1, the capacitor C3 is connected in parallel with the capacitor C2, and the inductor L3 is connected in series with the capacitor C3 and the auxiliary inverter.

[0068] In order to realize the constraint of the phase angle of the alternating voltage source, in some embodiments, the phase angle of the alternating voltage source is represented as a calculation model as follows:

[0069] The constraint is realized through a parameter configuration as follows:

[0070] and |c i | and |d r | have the same order of magnitude.

[0071] wherein a r , d r are real numbers, b i , c i are imaginary numbers, and R eq is the equivalent load of the receiving end, and the specific parameter configuration order of magnitude is exemplified as shown in Figure 8 , but is not limited to the parameter configuration shown in Figure 8 . The parameter configuration can also be flexibly configured based on the above constraint conditions.

[0072] Based on the transmitting end configured as above, the adaptive reactive compensation circuit absorbs the impedance mismatch reactive power caused by device aging, temperature drift or control strategy, and adjusts the current amplitude and phase, adaptively eliminates unnecessary capacitive impedance and inductive impedance, thereby improving the energy density and impedance adjustment ratio, and realizing better system robustness.

[0073] The working principle of the transmitting end of the wireless power transmission system with the above structure is combined, and the equivalent impedance of the receiving end is shown in Figure 3 . In an ideal state, L1 and C1 are in complete resonance state, therefore, as shown in Figure 3 , the wireless power transmission system is simplified and analyzed as follows in the embodiments of the present application:

[0074] Firstly, it is assumed that the electrical elements in the circuit are ideal devices such as switch tubes, capacitors and inductors, and there is no stray resistance in the circuit, the energy storage capacitor C i2 is a large capacitor, the capacitor capacity is sufficient to generate the required auxiliary DC voltage V i2 , and the auxiliary DC voltage V i2 is constant. Therefore, when the transmitting end starts to work, C i2 does not store charge, and V i2 value is 0; as C i2Energy accumulation in the voltage V i2 Gradually increase; simultaneously, the corresponding high-frequency square wave voltage v2 will generate another current in inductor L3 to adjust i. z3 The amplitude and phase; when the stray resistance in switching transistors S3 and S4 and C i2 If all components are ignored and there are no energy-consuming components, if V i2 Stable, i z3 The phase angle between v2 and v2 becomes 90°.

[0075] Based on this, the transmission principle at the transmitting end during power transmission is as follows: Figure 4 As shown in the figure, v1 represents the AC square wave generated by the DC power supply at the transmitting end through the inverter, and v2 represents the energy storage capacitor C. i2 The DC voltage is inverted by the auxiliary inverter to generate an AC square wave, V fa1 and V fa2 These are functions related to waveforms v1 and v2, respectively, and are specifically represented by the following calculation model:

[0076]

[0077]

[0078] in, Indicates v fa1 and v fa2 The phase difference between them.

[0079] Based on the aforementioned calculation model, refer to Figure 4 As shown, Z1 is the impedance of the branch corresponding to the transmitting coil L1 and resonant capacitor C1, Z2 is the impedance of the branch corresponding to capacitor C2, and Z3 is the impedance of the branch corresponding to inductor L3 and capacitor C3. The impedance of each branch is expressed as follows: (5) Calculation model:

[0080]

[0081] According to the superposition principle, the currents generated by each voltage source will not affect each other; therefore, the reference... Figure 5 , Figure 6 The figures shown are v fa1 v fa2 The principle of current transmission generated by a separate voltage source:

[0082] Figure 5 In the middle, Z t1 Indicates v fa1 Input impedance:

[0083]

[0084] At this time, by v fa1 The generated current i11 Current i 12 And by v fa2 The generated current i 13 The following formula is used to calculate:

[0085]

[0086]

[0087]

[0088] Similarly, Figure 6 In the middle, input anti-Z t2 Current i 23 and current i 22 And by v fa1 The generated current i 21 It can be calculated using the following formula:

[0089]

[0090]

[0091]

[0092]

[0093] final, Figure 4 The total current in each branch can be calculated using the following formula:

[0094]

[0095] Based on the above, when the wireless transmission system is in a fully resonant state, v fa1 and i z1 It should be in the ZPA state and must satisfy the conditions set by the following formula (15):

[0096]

[0097] Among them, i z1r Defined as the current in the transmitting coil when it is in a fully resonant state, and V fa1 Defined as v fa1 Amplitude. Due to v fa1 It is a known quantity, i 11 It can be calculated using the above formula (7), from v fa2 Provide to ensure v fa1 and i z1 The required current i for achieving full resonance 21r The following calculation model can be obtained from (16):

[0098] i 21r =i z1r -i 11 (16)

[0099] Required auxiliary voltage v fa2r The following calculation model can be obtained by calculating from (11) and (13):

[0100]

[0101] To simplify (17), Z1+Z eq It can be reconverted using the following formula (18):

[0102] Z1+Z eq =(Z1+Im(Z) eq ))+Re(Z eq )=Z′1+R eq (18)

[0103] Where Z′1 represents Z1 and Z eq Total reactance, R eq Z represents the equivalent load at the receiving end. eq This is the equivalent impedance from the receiver to the transmitter.

[0104] Substituting equations (6), (10), and (18) into equation (17), we obtain the following formula:

[0105]

[0106] in,

[0107] Therefore, its phase angle This can be represented by the following calculation model:

[0108]

[0109] Since the product of an even number of imaginary numbers is a real number, and the product of an odd number of imaginary numbers is an imaginary number, therefore, a r d r and It is a real number, and b i c i and It is an imaginary number.

[0110] when i z1 When operating in a fully resonant state, the output of equation (20) above is used to maintain v fa1 v fa2r Phase angle, will and R eq a r b id r Substituting into (19), we can obtain the following formula:

[0111]

[0112] Therefore, the denominator in equation (20) remains 0 and is unrelated to the choice of resonance parameters. In other words, It should be fixed at 90° or -90° to compensate for v. fa1 and i z1 The fully resonant state is specifically represented as:

[0113]

[0114] Once equations (21) and (22) are satisfied, the imaginary part of equation (19) will become much larger than the real part. Specifically, v fa2r phase angle It should be fixed at 90° or -90° to ensure v fa1 and i z1 It can always operate in a fully resonant state.

[0115] Therefore, when the Z of the wireless power transmission system of this application embodiment... eq When Z1, Z2, and Z3 are affected by external factors, based on the constraint parameter configuration described above, that is... And |c i | and |d r | Having the same magnitude, under this constraint... The symbol will only be used with c i It has the following relationship:

[0116]

[0117] Because at full resonance v fa2 The phase angle is fixed, making v fa2 The amplitude can be automatically adjusted, and adaptive resonance enables high-speed impedance regulation without monitoring and control circuitry. Specific adjustment effects include, for example... Figure 7 As shown:

[0118] According to the superposition principle, the currents generated by each voltage source will not affect each other. (Refer to...) Figure 5 The image shows v fa1 The generated current, including current i 11 Current i 12 Current i 13 ;refer to Figure 6 The image shows v fa2 The generated current, including current i 21 Current i22 , the current i 23 ; wherein, the reference Figure 7 , the current i 11 has a lagging phase difference with the phase of the voltage v1, the current i 21 has a leading phase difference with the phase of the voltage v2, the current i 11 , the current i 21 , the current i z1 has a compensated phase difference with the phase of the voltage v1, and is adjusted to a zero phase angle state ZPA, in which state a high energy density wireless power transmission can be achieved to meet the needs of dynamic charging or underwater submersible places, therefore, compared with the conventional WPT system which requires precise design of resonant capacitance and inductance or complex frequency control strategy, the topology of the embodiments of the present application is highly flexible in parameter selection and is conducive to simplifying the control circuit.

[0119] The above-described embodiments only express several implementation manners of the present application, and the description is relatively specific and detailed, but it should not be understood as a limitation on the scope of the patent. It should be pointed out that for ordinary skilled persons in the art, several modifications and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application should be subject to the appended claims.

Claims

1. An adaptive resonant wireless power transfer system, characterized by, Comprising: The transmitting end is used for exciting the transmitting coil by high frequency AC power generated after inverting the accessed DC power to generate alternating electromagnetic field, and further comprises: DC power, inverter and transmitting coil connected in series L 1 and resonance capacitor C 1; a receiving end for picking up energy from the alternating electromagnetic field generated by the transmitting coil through magnetic field coupling effect by a receiving coil, and converting into direct current through rectification to supply the load; wherein the transmitting end further comprises: an adaptive reactive compensation circuit comprising at least an auxiliary inverter and an energy storage capacitor, the auxiliary inverter being electrically connected to the transmitting coil, and the energy storage capacitor being connected to the auxiliary inverter, the capacitor and the auxiliary inverter constituting an alternating voltage source, and by constraining the phase angle of the alternating voltage source to be ±90°, the voltage and current of the transmitting coil are always operated in a resonant state, the adaptive reactive compensation circuit further comprising: Capacitance C 2, electrically connected resonant capacitance C 1; capacitor C 3, the capacitor is connected in parallel C 2; and inductance L 3, connecting the capacitors in series C 3 and connecting the auxiliary inverter Phase angle of the alternating voltage source is represented as a calculation model as follows: ， phase angle of the ac voltage source by constraining the parameter configuration by , and and have the same order of magnitude; wherein , is a real number, , is an imaginary number, R eq is the equivalent load of the receiving end, the real number , , imaginary number , is calculated by the following calculation model, respectively: wherein, Z 1 ' denotes the total reactance of , is the equivalent impedance of the receiving end to the transmitting end, Z 1 is the inductance of the transmitting coil L 1 and the resonance capacitance C 1, Z 2 is the capacitance of the branch C 2, Z 3 is the inductance of the branch L 3 and the capacitance C 3.

2. The adaptive resonant wireless power transfer system of claim 1, wherein, The inverter and the auxiliary inverter are half-bridge inverters, each comprising two series-connected switching tubes, and each used for generating a high-frequency square-wave voltage and .

3. The adaptive resonant wireless power transfer system of claim 1, wherein, The , Z2, Z3 are calculated by the following calculation model:

4. The adaptive resonant wireless power transfer system of any one of claims 1-3, wherein, The receiving end further includes: receiving coils connected in sequence. L s ,capacitance C s And Class E rectifiers.

5. The adaptive resonant wireless power transfer system of claim 4, wherein, the E-class rectifier further comprising: inductance L e shunt the capacitor C s ; capacitor C e , the capacitor C s ; Diode D e And connected to the capacitor C e Two ends; capacitor C o in parallel with the capacitor C e ; Equivalent load R o And the capacitor C o , the capacitor C e Two ends are also connected with switch tube S a And capacitor C a .

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