CN109756124A - A kind of current feed type half-bridge resonance topological structure for wireless power transmission - Google Patents

A kind of current feed type half-bridge resonance topological structure for wireless power transmission Download PDF

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CN109756124A
CN109756124A CN201910053507.6A CN201910053507A CN109756124A CN 109756124 A CN109756124 A CN 109756124A CN 201910053507 A CN201910053507 A CN 201910053507A CN 109756124 A CN109756124 A CN 109756124A
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capacitor
diode
circuit
inductance
bridge
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CN109756124B (en
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周洪
关世琦
李刚
李佳
邓其军
胡文山
周东国
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Shenzhen Huayu Wireless Power Supply Technology Co Ltd
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Shenzhen Huayu Wireless Power Supply Technology Co Ltd
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    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02BCLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
    • Y02B70/00Technologies for an efficient end-user side electric power management and consumption
    • Y02B70/10Technologies improving the efficiency by using switched-mode power supplies [SMPS], i.e. efficient power electronics conversion e.g. power factor correction or reduction of losses in power supplies or efficient standby modes

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Abstract

The present invention provides a kind of current feed type half-bridge resonance topological structures for wireless power transmission, including transmitting terminal and receiving end, the transmitting terminal includes quasi- current source, half-bridge circuit inverter and CLC resonant network, the quasi- current source is connected by the half-bridge circuit inverter with the CLC resonant network, the receiving end includes resonance circuit and voltage-multiplier circuit, the resonance circuit is connected with the voltage-multiplier circuit, the CLC resonant network includes first capacitor, second capacitor and transmitting coil, second capacitor is in parallel with the first capacitor after connecting with the transmitting coil, the receiving coil that the resonance circuit includes and the transmitting coil cooperates and the third capacitor being electrically connected with the receiving coil.Provided by the present invention for the current feed type half-bridge resonance topological structure of wireless power transmission, current feed type inductive power transfer system (IPT) circuit is made to be suitable for medium power applications.

Description

A kind of current feed type half-bridge resonance topological structure for wireless power transmission
Technical field
The present invention relates to wireless power transmission field more particularly to a kind of current feed types for wireless power transmission half Bridge resonant topology.
Background technique
Wireless energy transfer system (WPT) is current research hotspot, is divided into inductive power transfer system and condenser type Electric energy transmission system.Inductive power transfer system (IPT) is a kind of radio energy biography realized using electromagnetic coupling theory Transferring technology, in aerospace, communications and transportation, medical instrument, robot, illumination, portable electronic product, mine and submerged applications Equal fields have a wide range of applications.
If the control of Fig. 1, the inverter of the current feed type push-pull current multiple circuit based on IPT system are usually to pass through What Frequency-variable Modulation was completed.Switching frequency is only determined by inverter output voltage, and is completed by the zero crossing of sensing output voltage, this Facilitate zero voltage switch (ZVS) turn-on and turn-off.However, due to the no-voltage of inverter output, the master of this control method Limiting is starting converter.Since the zero crossing of inverter output voltage is single operating point, to accurately detect The point, and closed while one metal-oxide half field effect transistor (MOSFET) of unlatching under sensor and the undelayed situation of control Another MOSFET, this is the challenge being difficult.If controlled inaccurately in circuit, shunt capacitance will pass through one MOSFET, and the crystal diode of other MOSFET is short-circuit.But if inverter output voltage is lower, and operate switching frequency Rate is lower, and control circuit delay can be ignored, this is not just a big problem.But in high power applications, inversion The output voltage amplitude of device is very big, can steeply rise after zero crossing.Therefore, if MOSFET is not switched on, and in zero crossing It completely closes, then resonant capacitance will be by MOSFET and crystal diode short circuit, this will lead to a large amount of power loss.Due to The application of these reasons, these topological structures is normally limited to low-power.In order to make current feed type IPT circuit be suitable for medium function Rate application, the invention proposes a kind of new current feed type half-bridge resonance topological structures, solve this limitation.
Summary of the invention
It is an object of the invention to overcome the defect of the prior art, a kind of electric current feedback for wireless power transmission is provided Electric-type half-bridge resonance topological structure, so that current feed type IPT circuit is suitable for medium power applications.
The present invention is implemented as follows:
The present invention provides a kind of current feed type half-bridge resonance topological structure for wireless power transmission, including including hair End and receiving end are penetrated, the transmitting terminal includes quasi- current source, half-bridge circuit inverter and CLC resonant network, the quasi- current source It is connected by the half-bridge circuit inverter with the CLC resonant network, the receiving end includes resonance circuit and voltage multiplie electricity Road, the resonance circuit are connected with the voltage-multiplier circuit, and the CLC resonant network includes first capacitor, the second capacitor and hair Ray circle, second capacitor is in parallel with the first capacitor after connecting with the transmitting coil, the resonance circuit include with The receiving coil of the transmitting coil cooperation and the third capacitor being electrically connected with the receiving coil.
Preferably, keeping inverter output power factor lag, regardless of load current, it is always ensured that inverter is opened The Sofe Switch of pass is connected;The value for selecting first capacitor and the second capacitor, so that the amplitude of inverter output current is lower, and selects The value of third capacitor, so that voltage-multiplier circuit input terminal voltage is maximum value.
Preferably, the receiving coil is connected with the third capacitor.
Preferably, the voltage-multiplier circuit includes third diode, the 4th diode, the 4th capacitor and the 5th capacitor, The third diode is connected with the 4th capacitor, and the 4th diode is connected with the 5th capacitor, and the third diode is just Pole, the 4th diode cathode be connected with the cathode of the third capacitor.
Preferably, the quasi- current source includes DC power supply, the first DC inductance and the second DC inductance, described first DC inductance and the second DC inductance are parallel with one another and connect with the DC power supply, first DC inductance and second straight The other end of galvanic electricity sense is connected with the half-bridge circuit inverter.
Preferably, not coupled between first DC inductance and the second DC inductance.
Preferably, the half-bridge circuit inverter includes first switch device, second switch device, first diode and Second diode.
Preferably, the first switch device is the first field-effect tube, the second switch device is the second field-effect Pipe, the drain electrode of first field-effect tube is connected with first DC inductance, the source electrode of first field-effect tube with it is described The anode of first diode is connected, and the drain electrode of second field-effect tube is connected with second DC inductance, and described second The source electrode of effect pipe is connected with the anode of second diode, the first diode, the second diode cathode and institute The cathode for stating DC power supply is connected.
Preferably, the first capacitor anode is connected with the drain electrode of first field-effect tube, the first capacitor is negative Pole is connected with the drain electrode of second field-effect tube.
The invention has the following advantages:
1, provided by the present invention for the current feed type half-bridge resonance topological structure of wireless power transmission, using (C) (CL) series parallel resonance circuit can be suitably used for medium power applications.
2, provided by the present invention for the current feed type half-bridge resonance topological structure of wireless power transmission, pass through direct current mother Line inductance Ld1And Ld2Natural short-circuit protection is provided, and also limits the peak value and circulating current for passing through element.Electric current is shared (half-bridge) configuration further reduced the average and peak point current by element, to reduce conduction loss.Current feed type Circuit also provides voltage gain, and voltage multiplie increases by 2 times of additional gain.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this Some embodiments of invention for those of ordinary skill in the art without creative efforts, can be with Other attached drawings are obtained according to these attached drawings.
Fig. 1 is a kind of push-pull converter circuit based on IPT system;
Fig. 2 is IPT circuit provided in an embodiment of the present invention and current feed type half-bridge converter;
Fig. 3 is the equivalent circuit of IPT system converter provided in an embodiment of the present invention.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts all other Embodiment shall fall within the protection scope of the present invention.
Such as Fig. 2-Fig. 3, the embodiment of the present invention provides a kind of current feed type half-bridge resonance for wireless power transmission and opens up Flutter structure, including transmitting terminal and receiving end, the transmitting terminal includes quasi- current source, half-bridge circuit inverter and CLC resonant network, The quasi- current source is connected by the half-bridge circuit inverter with the CLC resonant network, and the receiving end includes resonance electricity Road and voltage-multiplier circuit, the resonance circuit are connected with the voltage-multiplier circuit, and the CLC resonant network includes first capacitor CP, the second capacitor CSWith transmitting coil L1, the second capacitor CSWith the transmitting coil L1After series connection with the first capacitor CP Parallel connection, the resonance circuit include and the transmitting coil L1The receiving coil L of cooperation2And with the receiving coil L2It is electrically connected The third capacitor C connect2
The present invention is that radio energy transmission system application is proposed, analyzed and develops a kind of new power electronic system, specifically To propose a kind of with the shared current feed type topology with voltage multiplication characteristic of electric current.The topology uses new series connection simultaneously Row CLC resonant network is analyzed.Resonant network of the invention can reduce the rated value of plate external circuit device, and allow using Compared with conventional serial LC resonance network, the device with low conduction impedance and low cost.This is to attempt to utilize shunting electricity for the first time Multiplication current feed-type circuit and CLC resonant network is pressed to realize IPT.Inverter output power factor lag is kept, no matter is loaded How is electric current, is always ensured that the Sofe Switch conducting of inverter switching device.
If Fig. 1-such as Fig. 2, Fig. 1 are a kind of push-pull converter circuit based on IPT system, Fig. 2 is the circuit of the present embodiment Topological structure, it is different from the push-pull converter circuit based on IPT system, in the present embodiment, the DC inductance of the quasi- current source Between do not couple, and in transmit circuit, compensating electric capacity does not use traditional parallel LC resonance circuit, but will compensation Capacitor is divided into two parts, develops series-parallel CCL resonant tank, i.e. the second capacitor CsWith transmitting coil L1Series connection, then with first capacitor CpIt is in parallel.As shown in Fig. 2, transmitting coil circuit impedance (impedance of i.e. entire transmitting terminal) is because of series capacitance due to high leakage current And significantly reduce, effective launcher line circle impedance (i.e. the impedance of CLC resonant network) is reduced to [ω L1-1/(ωCs)].Therefore, One capacitor CpThe sub-fraction for only needing provide total reactive power demand maintains all advantages of current feed type converter, The low harmonic content etc. in low current stress and coil current i.e. at half-bridge circuit inverter switching device.
Half-bridge circuit inverter inputs square wave current to CLC resonant network.The group of transmitting coil side network (i.e. transmitting terminal) Part is designed to make half-bridge circuit inverter output end electric current IiIt is minimum value for given output power, first capacitor in parallel CpLower impedance is provided for higher harmonic current.Therefore, the higher hamonic wave I of inverter output currentiPass through first capacitor Cp With transmitting coil L1Obtain almost simple sinusoidal current.Due to intercoupling, receiving coil L2It can obtain and mutual inductance M, transmitting coil electricity Flow I1The proportional voltage with transmitting coil working frequency.However, it is necessary to which capacitive character reactive compensation appropriate compensates receiving end The influence of the high leakage inductance of coil.In the present invention, connect third capacitor C2Compensating power.Finally, in the network of receiving end Power supply rectify and feedback load by voltage-multiplier circuit.
Such as Fig. 2, preferably, the receiving coil L2With the third capacitor C2Series connection is used to compensating power.
Preferably, the voltage-multiplier circuit includes third diode D3, the 4th diode D4, the 4th capacitor C01With the 5th Capacitor C02, the third diode D3 and the 4th capacitor C01It is connected, the 4th diode D4 and the 5th capacitor C02It is connected, institute State the cathode of positive, the described 4th diode D4 of third diode D3 with the third capacitor C2Cathode be connected, this Embodiment is two voltage-multiplying circuits, for rectifying and amplifying voltage.
Preferably, the quasi- current source includes DC power supply Vd, the first DC inductance Ld1With the second DC inductance Ld2, institute State the first DC inductance Ld1With the second DC inductance Ld2It is parallel with one another and with the DC power supply VdSeries connection, first direct current Inductance Ld1With the second DC inductance Ld2The other end be connected with the half-bridge circuit inverter, the first DC inductance Ld1With Two DC inductance Ld2Do not coupled between inductance, natural short-circuit protection be provided, but also limitation led to the peak value for crossing element and Circulating current.
Preferably, the half-bridge circuit inverter includes the first field-effect tube S1, the second field-effect tube S2, the one or two pole Pipe D1 and the second diode D2, the drain electrode of the first field-effect tube S1 and the first DC inductance Ld1It is connected, described first The source electrode of field-effect tube S1 is connected with the anode of the first diode D1, the drain electrode of the second field-effect tube S2 and described the Two DC inductance Ld2It is connected, the source electrode of the second field-effect tube S2 is connected with the anode of the second diode D2, and described the One diode D1, the second diode D2 cathode with the DC power supply VdCathode be connected, further reduced and pass through member The average and peak point current of part, to reduce conduction loss.
Preferably, the first capacitor CPThe positive drain electrode with the first field-effect tube S1 is connected, first electricity Hold CPCathode is connected with the drain electrode of the second field-effect tube S2, shunt capacitance CpLower resistance is provided for higher harmonic current It is anti-.
The present embodiment is used for the exploitation and verifying of experimental prototype with the design example of a 1.2kW IPT system.
Step 1: Fig. 3 is equivalent circuit shown in Fig. 2, and wherein input/output port is respectively current source IiAnd voltage source Vr.Using power balance theory, it is contemplated that due to fundametal compoment, active power is flowed in exchange side (i.e. receiving end), exchanges side Voltage-multiplier circuit input terminal voltage VrWith voltage-multiplier circuit output end voltage V0Have relationship as follows:
Because of the passive rectification of diode, voltage-multiplier circuit input terminal voltage VrWith receiving coil electric current I2It is same phase.? In this analysis, receiving coil electric current I2Or voltage-multiplier circuit input terminal voltage VrPhase be designated as fixed phase.In transmitting terminal Kirchhoff's current law (KCL) (KCL) is applied in network, half-bridge circuit inverter output end electric current IiIt is transmitting coil electric current I1And warp Cross the electric current I of first capacitorPThe sum of
Wherein, M is the mutual inductance between transmitting coil and receiving coil, and j is imaginary unit, and ω is angular frequency, CpFirst electricity Hold, CsFor the second capacitor, L1For transmitting coil inductance, ViFor half-bridge circuit inverter output end voltage.Kiel is applied in receiving end Hough voltage law (KVL), voltage-multiplier circuit input terminal voltage VrFor
Wherein, L2For receiving coil inductance, C2For third capacitor.
Select first capacitor CpWith the second capacitor CsValue so that half-bridge circuit inverter output end electric current IiAmplitude is lower, And select third capacitor C2, voltage-multiplier circuit input terminal voltage VrFor maximum value.This is by second in elimination (2) and (3) It completes.According to formula (2) and (3), required capacitor is calculated as
Wherein, ω01For transmitting coil resonant frequency, ω02Receiving coil resonant frequency.
By making half-bridge circuit inverter switching frequency ω0(=2 π f0), transmitting coil resonant frequency ω01And receiving coil Resonant frequency ω02It is equal to realize effective power transmission.KVL is applied in receiving end loop, transmitting coil electric current I1Meter It is
Wherein, V0For voltage-multiplier circuit output end voltage, ω0For half-bridge circuit inverter switching frequency, the meaning of j and M are same On.
In transmitting terminal application KVL and KCL, formula (4) and (5), the electricity between transmitting coil and two series capacitances Root mean square (RMS) value of pressure is
Wherein, V1For transmitting coil both end voltage, VsFor the second capacitor both end voltage, I0For voltage-multiplier circuit output end electricity Stream, V0、L1、ω0、Cs, j and M the meaning be same as above.
According to the equivalent circuit of Fig. 3, it can be deduced that half-bridge circuit inverter output end voltage ViWith electric current IiFor
Wherein, Cp, I0, V0, L1, ω0, Cs, the meaning of j and M is same as above.
From formula (8) as can be seen that due to concatenated second capacitor CsPresence, occur?.With it is existing Parallel L-C topological structure is compared, this is the major advantage of proposed topological structure.Half-bridge is obtained from formula (8) and (9) The output power factor of circuit inverterFor
Wherein,For the phase angle of electric current,For the phase angle of voltage, ω0、M、I0、V0、L1、CsAnd CpThe meaning be same as above.
When switching device is metal-oxide half field effect transistor (MOSFET), half-bridge circuit inverter input terminal power factor It lags critically important, because regardless of load current, all can ensure that zero voltage switch (ZVS) is connected.Similarly, when selection switchs When device is insulated gate bipolar transistor (IGBT), power factor is in advance for realizing that Sofe Switch is very when device turns off Important.
From figure 3, it can be seen that the RMS value of half-bridge circuit inverter switching device electric current directly depends on the DC current of input Id.The size of the peak value blocking voltage of half-bridge circuit inverter switching device and diode also exports electricity with half-bridge circuit inverter peak value It presses identical.Therefore, it can be deduced that the rated value of the voltage and current of half-bridge circuit inverter switching device and diode
Wherein, ViFor half-bridge circuit inverter output end voltage, IdFor the DC current of input, IS1For half-bridge circuit inversion The load current value of device switch S1, IS2For the load current value of half-bridge circuit inverter switching device S2, ID3For third diode D3's Load current value, ID4For the load current value of the 4th diode D4,It is hindered for the peak reverse of half-bridge circuit inverter switching device S1 Power-off pressure,For the peak reverse blocking voltage of half-bridge circuit inverter switching device S2.
Step 2: in topological structure shown in Fig. 3, half-bridge electricity not can control by the modulation of fixed frequency variable duty ratio Road inverter output power, this is because basic exchange device is two, S1 and S2.Due to the electric current in inverter input terminal The minimum duty cycle in source, switch is restricted to 0.5.However, the duty ratio of switch is fixed as 0.5, inverter but can change Switching frequency is to reach required output power.The impedance of inverter output end, that is, the resistance being input in transmitting terminal resonant network Anti- ZiFor
Wherein, ReFor the equivalent load resistance of voltage-multiplier circuit input terminal, j, ω, M, L1、L2And CpThe meaning be same as above, and And its derivation formula is
Wherein, I0、V0The meaning is same as above, R0For the equivalent load resistance of voltage-multiplier circuit output end.
According to formula (2), the active-power P of half-bridge circuit inverter outputinvFor
Wherein, Ii、Re、ZiAnd IdThe meaning is same as above.
Step 3: consider the specified charge power of inductive power transfer system (P) and specified charging current (I).Load EV The voltage rating and charging current of (electric car) battery be it is known, in the present embodiment, load EV (electric car) battery Voltage rating is 325V.The present embodiment is a 1.2kW inductive power transfer system, and therefore, specified charge power (P) is 1.2KW, specified charging current I's is calculated as 1200W/325V=3.7A.
Step 4: half-bridge circuit inverter is selected according to switching device, diode, IPT pad size and other conditions Nominal switching frequency.In the present embodiment, specified transmitting coil RMS current is in 11.5A or so.Therefore, required mutual inductance value M For 42 μ H.
It should be understood that the part that this specification does not elaborate belongs to the prior art.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention Within mind and principle, any modification, equivalent replacement, improvement and so on be should all be included in the protection scope of the present invention.

Claims (9)

1. a kind of current feed type half-bridge resonance topological structure for wireless power transmission, it is characterised in that: including transmitting terminal And receiving end, the transmitting terminal include quasi- current source, half-bridge circuit inverter and CLC resonant network, the quasi- current source passes through The half-bridge circuit inverter is connected with the CLC resonant network, and the receiving end includes resonance circuit and voltage-multiplier circuit, institute It states resonance circuit to be connected with the voltage-multiplier circuit, the CLC resonant network includes first capacitor, the second capacitor and emission lines Circle, second capacitor is in parallel with the first capacitor after connecting with the transmitting coil, the resonance circuit include with it is described The receiving coil of transmitting coil cooperation and the third capacitor being electrically connected with the receiving coil.
2. being used for the current feed type half-bridge resonance topological structure of wireless power transmission as described in claim 1, feature exists In: S1. keeps inverter output power factor lag, regardless of load current, is always ensured that the Sofe Switch of inverter switching device Conducting;S2. the value of first capacitor and the second capacitor is selected, so that the amplitude of inverter output current is lower, and selects third electric The value of appearance, so that voltage-multiplier circuit input terminal voltage is maximum value.
3. being used for the current feed type half-bridge resonance topological structure of wireless power transmission as described in claim 1, feature exists In: the receiving coil is connected with the third capacitor.
4. being used for the current feed type half-bridge resonance topological structure of wireless power transmission as claimed in claim 3, feature exists In: the voltage-multiplier circuit includes third diode, the 4th diode, the 4th capacitor and the 5th capacitor, the third diode It is connected with the 4th capacitor, the 4th diode is connected with the 5th capacitor, positive, described four or two pole of the third diode The cathode of pipe is connected with the cathode of the third capacitor.
5. being used for the current feed type half-bridge resonance topological structure of wireless power transmission as described in claim 1, feature exists In: the quasi- current source includes DC power supply, the first DC inductance and the second DC inductance, first DC inductance and second DC inductance is parallel with one another and connects with the DC power supply, the other end of first DC inductance and the second DC inductance It is connected with the half-bridge circuit inverter.
6. being used for the current feed type half-bridge resonance topological structure of wireless power transmission as claimed in claim 5, feature exists In: it is not coupled between the first DC inductance and the second DC inductance described in S1..
7. being used for the current feed type half-bridge resonance topological structure of wireless power transmission as claimed in claim 5, feature exists In: the half-bridge circuit inverter includes first switch device, second switch device, first diode and the second diode.
8. being used for the current feed type half-bridge resonance topological structure of wireless power transmission as claimed in claim 7, feature exists In: the first switch device is the first field-effect tube, and the second switch device is the second field-effect tube, first effect Should the drain electrode of pipe be connected with first DC inductance, the source electrode of first field-effect tube and the anode of the first diode It is connected, the drain electrode of second field-effect tube is connected with second DC inductance, the source electrode of second field-effect tube and institute The anode for stating the second diode is connected, cathode of the cathode with the DC power supply of the first diode, the second diode It is connected.
9. being used for the current feed type half-bridge resonance topological structure of wireless power transmission as claimed in claim 8, feature exists In: the first capacitor anode is connected with the drain electrode of first field-effect tube, the first capacitor cathode with described second The drain electrode of effect pipe is connected.
CN201910053507.6A 2019-01-21 2019-01-21 Current feed type half-bridge resonance topological structure for wireless power transmission Active CN109756124B (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111413542A (en) * 2020-04-26 2020-07-14 中铁电气化局集团有限公司 Target working frequency obtaining method, system, device, computer equipment and medium

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104242657A (en) * 2014-08-29 2014-12-24 南京航空航天大学 Non-contact resonant converter with primary side parallel and series connection compensation and secondary side series connection compensation

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104242657A (en) * 2014-08-29 2014-12-24 南京航空航天大学 Non-contact resonant converter with primary side parallel and series connection compensation and secondary side series connection compensation

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111413542A (en) * 2020-04-26 2020-07-14 中铁电气化局集团有限公司 Target working frequency obtaining method, system, device, computer equipment and medium
CN111413542B (en) * 2020-04-26 2022-07-08 中铁电气化局集团有限公司 Target working frequency obtaining method, system, device, computer equipment and medium

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