CN100438304C - A soft switch reversion conversion circuit for the resonance DC step - Google Patents

A soft switch reversion conversion circuit for the resonance DC step Download PDF

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CN100438304C
CN100438304C CNB2006101051345A CN200610105134A CN100438304C CN 100438304 C CN100438304 C CN 100438304C CN B2006101051345 A CNB2006101051345 A CN B2006101051345A CN 200610105134 A CN200610105134 A CN 200610105134A CN 100438304 C CN100438304 C CN 100438304C
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diode
bus
utmost point
resonance
inverter
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CN1996736A (en
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贺虎成
刘卫国
马瑞卿
李榕
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Northwestern Polytechnical University
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Abstract

This invention discloses one resonance direct flow flexible inverter circuit, which comprises one direct current power, one control circuit, one inverter bridge and drive load, wherein, the direct current power and inverter bridge are added with aid resonance circuit composed of three aid switches, six diodes, three capacitors and one inductance; when the power parts converts from status to another one, the control circuit sends control signal for reasonable aid switch V1, V2 and V3.

Description

A kind of resonance DC link soft-switching inverter circuit
Technical field
The present invention relates to a kind of switch transformed circuit, in particular for the switching inverter circuit of bridge-type inverter.
Background technology
At present, domestic and international most bridge-type inverter adopts hard switching pulse width modulation (PWM) technology, in the PWM inverter, the volume of output transformer, ac filter inductance and radiator accounts for major part, for volume and the weight that reduces inverter, improve the power density of inverter, must improve inverter switching frequency.But power device is after high frequencyization, and switching loss sharply increases, and causes the junction temperature of power device sharply to rise, and has stoped the high frequencyization of power conversion circuit; And the voltage that power device is very big after the high frequencyization, current changing rate (
Figure C20061010513400031
) produce bigger electromagnetic interference (EMI), influence the normal operation of circuit.Power device is opened or the voltage and current peak value of shutdown moment may make the running orbit of power device exceed safety operation area (SOA), thereby causes the damage of power device.Though adopt the switching loss of buffer circuit cpable of lowering power device, it transfers to Resistor-Capacitor Unit consumption with loss, system effectiveness is low.Therefore, people study resonant type soft-switch and solve the problems referred to above.So-called " soft switch technique " is exactly by resonance, make power device its voltage be zero or electric current open or turn-off when being zero, voltage and electric current is overlapping when avoiding the power device switch, thus reduction
Figure C20061010513400032
And switching loss.
But early the resonance DC annulus inverter that proposes exists that switching voltage stress is higher, the resonant inductance loss is big, and the problems such as harmonic wave that cause of discrete pulse-width modulation; And quasi-resonance DC link inverter need preestablish one or several and the relevant threshold value of auxiliary switch control in inductive current, the generation of resonance just can reach the course of work of expection, these threshold value normal conditions are relevant with load current, this has brought difficulty with regard to giving the realization of circuit in full-load range, the control more complicated.
People such as bright posivtive spike disclose " a kind of new dc bus parallel resonance zero voltage transition three-phase PWM voltage source inverter " in the 16th the 6th phase of volume of " electrotechnics journal " calendar year 2001.This technology is added auxiliary resonance circuit 6 in DC link, and this circuit has increased by one by the dc bus switch S on the dc bus in traditional DC link inverter circuit L, two auxiliary switch S of series connection in the other direction AAnd S B, the resonant network that constitutes of booster diode VD and resonant inductance Lr and capacitor C r, the auxiliary switch of all increases all has fly-wheel diode, when the inverter bridge power device need move by reasonable control switch device S A, S B, S L, make dc tache voltage resonance to zero, the inverter bridge power device is finished switch motion during the DC link no-voltage groove, makes dc tache voltage resonance go up after switching process finishes.This technology had both overcome big, the electromagnetic interference important disadvantages of conventional P WM inverter switching device loss, and have following advantage again: 1. all switches are zero voltage switch (ZVS) or Zero Current Switch (ZCS); Though 2. need to increase by three auxiliary switches in the circuit. power requirement is less, can realize the four quadrant running of motor; 3. resonance natural occurring does not need setting threshold; 4. the fly-wheel diode in the inverter bridge also is soft shutoff; 5. the used time of resonant process lacks; 6. can realize PWM and space vector modulation (SVM) technology.But still there is deficiency in this technology: 1. when motor is in no-load condition, the formation of bus no-voltage groove will run into very big difficulty; 2. two big electric capacity that are used to form the DC power supply mid point have increased the inverter volume weight, have limited the further raising of inverter power density.
Summary of the invention
Form difficulty, the not high deficiency of inverter power density in order to overcome prior art bus no-voltage groove, the invention provides a kind of circuit of realizing the soft switching manipulation of inverter bridge power device, improve the operating efficiency and the power density of inverter, reduce electromagnetic interference, simplify control method, be easy to Project Realization.
The technical solution adopted for the present invention to solve the technical problems is: comprise a DC power supply, the load of control circuit, inverter bridge and driving.DC power supply can be to be AC rectification the DC power supply of galvanic rectifier power source or battery strings generation in parallel; Inverter bridge converts direct current to alternating current; Part between DC power supply and the inverter bridge is called DC link.The present invention adds the auxiliary resonance circuit in DC link, comprises first to the 3rd auxiliary switch V1~V3, first to the 6th diode D1~D6, first to the 3rd capacitor C 1, C2, Cr and 1 inductance L r.Second to the 5th diode D2, D3, D4, D5 connect successively, the negative electrode of the second diode D2 meets dc bus first utmost point P1, one end of the anode of the second diode D2 and first capacitor C 1 and the negative electrode of the 3rd diode D3 link to each other, one end of the negative electrode of the 5th diode D5 and second capacitor C 2 and the anode of the 4th diode D4 link to each other, and the anode of the 5th diode D5 meets the 3rd utmost point N of dc bus; The other end of the negative electrode of the first diode D1 and second capacitor C 2 joins, and meets second utmost point P2 of dc bus then, and the anode of the first diode D1 meets the 3rd utmost point N of dc bus; The second and the 3rd auxiliary switch V2, V3 series connection, series connection point links to each other with inductance L r one end, link to each other with the anode of the 3rd diode D3, the negative electrode of the 4th diode D4 simultaneously, another termination dc bus first utmost point P1 of the second auxiliary switch V2, the 3rd utmost point N of another termination dc bus of the 3rd auxiliary switch V3; After linking to each other, the other end of the other end of inductance L r and first capacitor C 1 meets second utmost point P2 of dc bus; The first auxiliary switch V1, two terminations the 6th diode D6 two ends, the negative electrode of the 6th diode D6 meets first utmost point P1 of dc bus, and the anode of the 6th diode D6 meets second utmost point P2 of dc bus; The 3rd capacitor C r two is terminated at second utmost point P2 and the 3rd utmost point N of dc bus.Dc bus first utmost point P1 connects the positive pole of DC power supply; Dc bus second utmost point P2 connects the anode of inverter bridge; Dc bus the 3rd utmost point N connects the negative pole of DC power supply and the negative terminal of inverter bridge.Send the turn-on and turn-off of signal controlling first to the 3rd auxiliary switch V1, V2, V3 by control circuit.
When the power device of inverter bridge need be from a kind of switch state to another kind of on off state, control circuit sends control signal and shifts to an earlier date ZCS conducting the 3rd auxiliary switch V3 and while ZVS stopcock V1, the inductance L r and second capacitor C 2 and the 3rd capacitor C r resonance, make the voltage resonance of dc bus second utmost point P2 drop to zero and remain zero, control circuit turn-offs the 3rd auxiliary switch V3, because inductance L r and first capacitor C, 1 resonance also make excess energy pass through the first diode D1 and the second diode D2 feedback DC power supply, make that the 3rd auxiliary switch V3 is that ZVS turn-offs.The inverter bridge device is finished soft switching manipulation during dc bus second utmost point P2 is in no-voltage, after switching process is finished, control circuit sends control signal makes the second auxiliary switch V2 with the ZCS conducting, resonance takes place in the inductance and first capacitor C 1 and the 3rd capacitor C r, the voltage of dc bus second utmost point P2 rises to DC power supply voltage, the back control circuit ZVS conducting first auxiliary switch V1, simultaneously, turn-off the second auxiliary switch V2, because inductance L r and second capacitor C, 2 resonance also make excess energy pass through the 5th diode D5 and the 6th diode D6 feedback DC power supply, make that the second auxiliary switch V2 is that ZVS turn-offs.Thereby, realized the ZVS switch of inverter bridge power device, simultaneously, the auxiliary switch device also is ZCS or ZVS action.
Switching device in described inverter bridge and the auxiliary resonance circuit is the property a controlled device entirely, comprises power transistor (GTR), igbt (IGBT), power field effect transistor (MOSFET) and Intelligent Power Module (IPM).Like this, switching circuit is directly controlled by control circuit fully, need not increase to open or turn-off auxiliary circuit.
Diode in described inverter bridge and the auxiliary resonance circuit is fast recovery diode or high-frequency diode.Diode not only will have enough withstand voltage, maximal integer mass flow electric current, and requires its reverse recovery time of describing frequency characteristic enough short.
Described the 3rd capacitor C r can be separated into a plurality of electric capacity, is connected in parallel on the two ends of converter bridge switching parts device.When electric capacity disperse be parallel to the switching device two ends time, switching device can directly turn-off, owing to there is electric capacity to cushion energy when turn-offing, turn-offs and is ZVS.Only need resonance is taken place, produce the no-voltage groove, realize converter bridge switching parts ZVS conducting.
Described inverter bridge is H bridge or heterogeneous bridge.The H bridge is used to drive single-phase load, and heterogeneous bridge is used to drive multiphase load.
The invention has the beneficial effects as follows: owing to adopt novel resonance DC link soft-switching translation circuit, the present invention has these advantages: 1. resonant network does not have the restriction of resonance threshold value; 2. used time of resonant process shorter, consumed power is less; 3. the fly-wheel diode of inverter bridge has been realized soft shutoff, has overcome reverse-recovery problems; 4. can realize that PWM control and method are simple, be easy to Project Realization; 5. save the big electric capacity of DC link, improved the power density of inverter; 6. do not have the midpoint potential imbalance problem, be easy to form bus no-voltage groove; 7. can be used for alternating current motors such as induction machine that three-phase or heterogeneous bridge drive, permagnetic synchronous motor, brshless DC motor, can be used for the inductive load that the H bridge drives simultaneously; 8. inverter bridge main switch operation is ZVS, the resonant element switching device be operating as ZVS or ZCS, overcome the EMI problem and improved the operational efficiency of switch converters.9. switch converters may operate in higher switching frequency, strengthened original system efficient, improved power density.
The present invention is further described below in conjunction with drawings and Examples.
Description of drawings
Fig. 1 is inverter circuit figure of the present invention.
Fig. 2 is the circuit diagram of inverter circuit embodiment two of the present invention.
Fig. 3 is the equivalent circuit diagram of inverter circuit of the present invention.
Fig. 4 is the timing waveform of inverter circuit of the present invention.
Fig. 5 is the harmonic motion operation mode circuit diagram of inverter circuit of the present invention.
Fig. 6 is the control flow chart of the embodiment two of inverter circuit of the present invention.
Fig. 7 be the embodiment two of inverter circuit of the present invention capacitor C r voltage (on) and resonance inductive current (descending) simulation waveform figure.
Fig. 8 be the embodiment two of inverter circuit of the present invention electric moter voltage (on) and electric current (descending) simulation waveform.
Fig. 9 be the experiment of the embodiment two of inverter circuit of the present invention survey capacitor C r voltage (on) and resonance inductive current (descending) oscillogram.
Figure 10 be the embodiment two of inverter circuit of the present invention experiment institute measured motor voltage (on) and electric current (descending) oscillogram.
Figure 11 is the resonance DC link soft-switching three-phase inverter circuitry figure of prior art.
Among the figure, E--DC power supply voltage, V1, V2, V3--auxiliary unit switching device,
D1, D2, D3, D4, D5, D6--auxiliary unit diode, C1, C2, Cr auxiliary unit electric capacity,
S1, S2, S3, S4, S5, S6--converter bridge switching parts device,
SD1, SD2, SD3, SD4, SD5, SD6--inverter bridge fly-wheel diode,
The drive signal of ds1, ds2, ds3, ds4, ds5, ds6--converter bridge switching parts device,
The BLDCM--brshless DC motor, TDi--inverter bridge equivalence fly-wheel diode,
The equivalent current of Io--load, u Cr--capacitor C r both end voltage, u C1--capacitor C 1 both end voltage,
u C2--capacitor C 2 both end voltage, i Lr--the electric current of resonant inductance Lr, the drive signal of dV1--switch V1,
The drive signal of dV2--switch V2, the drive signal of dV3--switch V3.
Embodiment
Embodiment one
According to embodiments of the invention one, as shown in Figure 1, provide a kind of novel resonance DC link soft-switching three-phase inverter main circuit, can be used for threephase asynchronous machine, three-phase brushless dc motor, three-phase synchronous motor driving etc.The present invention includes: 4, one control circuits 5 of 1, one resonance auxiliary circuit of a DC power supply, 3, one inductive loads of 2, one known three phase inverter bridges.For the operation principle of auxiliary circuit of the present invention is described, can replace Fig. 1 with equivalent electric circuit Fig. 3, because the inductance of load is much larger than resonant inductance, the load current of inverse switch status transition moment can be thought constant-current source Io, converter bridge switching parts status transition moment, the fly-wheel diode equivalence is TDi.Suppose that converter bridge switching parts needs switch motion, timing waveform such as Fig. 4 of an one switching process, control circuit 5 block V1 drive signal dV1, and output V3 drive signal dV3, inductance and capacitor resonance make dc tache voltage u CrDrop to zero, control circuit 5 blocks V3 drive signal dV3, converter bridge switching parts changes on off state under the converter bridge switching parts drive signal of control circuit 5 outputs, after switching process finishes, control circuit 5 output V2 drive signal dV2 make DC bus-bar voltage resonance to supply voltage, back control circuit 5 output V1 drive signal dV1, and block V2 drive signal dV2, finish switching process one time.The switch motion of following analysis chart 1, it is made up of 10 mode of operations, and Fig. 5 has provided inverter state transition period pattern equivalent electric circuit.
Pattern a[to~t1]
Suppose that this is the initialization state of circuit, V2, V3 disconnect, the V1 conducting, and power supply E provide electric current through V1 to load.I is then arranged Lr(t)=0, u C1(t)=0, u C2(t)=E and u Cr(t)=E.
Pattern b[t1~t2]
During t=t1, stopcock V1 is because the voltage of capacitor C r, C2 can not suddenly change, so this turn-offs the action into ZVS.Open V3 simultaneously, owing to inductive current can not suddenly change, so this opens ZCS.When t=t2, DC bus-bar voltage resonance is zero, i.e. u Cr(t)=0.
Pattern c[t2~t3]
When t=t2, DC bus-bar voltage drops to zero, load current I 0Flow through fly-wheel diode TDi, simultaneously, because of the conducting of diode D1, stoped the carrying out of resonance, electric capacity can not reverse charging, inductance L r, auxiliary switch V3 and diode D1 self-forming loop, and making inductive current is constant.Turn-off V3 this moment, because of capacitance voltage u C1(t)=0 and can not suddenly change, then V3 is the soft shutoff of ZVS.Resonance takes place in inductance L r and capacitor C 1, and electric capacity is recharged voltage and raises, and inductive current descends.When t=t3, electric capacity charges to supply voltage, i.e. u C1(t)=and E, because the unilateral conduction of D3 makes resonance end.
Pattern d[t3~t4]
When t=t3, u C1(t)=and E, resonance is ended, and inductive current is transformed into diode D2, to the power supply feedback energy, makes inductive current be reduced to zero rapidly.When t=t4, inductive current is reduced to zero.
Pattern e[t4~t5]
In t4~t5 stage, inverter bridge fly-wheel diode and load current constitute the loop, and be identical with known inverter operating state.In t2~t5 stage DC bus-bar voltage is zero, and the inverter bridge power switch can be finished the ZVS switching process one time, and this section period can control, after switching process finishes, can carry out busbar voltage.
Pattern f[t5~t6]
When t=t5, open V2 under the ZCS, then the inductive current forward is linear increases, and powers to the load by converter bridge switching parts, and the electric current linearity that flows through fly-wheel diode TDi is reduced, and when t=t6, inductive current and load current equate, make the soft shutoff of TDi.
Pattern g[t6~t7]
When t=t6, inductive current and load current equate and continue to increase, and an inductive current part and load current keep balance, and another part makes inductance and capacitor C r, C1 that natural resonance take place, and capacitor C r voltage rises, and capacitor C 1 voltage descends.In resonant process, DC bus-bar voltage rises to supply voltage E, promptly during t=t7, and u Cr(t7)=E, u C1(t7)=0, diode D6 conducting has limited DC bus-bar voltage u Cr(t) further increase.
Pattern h[t7~t8]
When t=t7, u Cr(t7)=E, i Lr(t7)>I 0So the charging of electric capacity stops, unnecessary inductive current forms the closed-loop path through diode D6, opens V1 this moment and then is the ZVS action, and ZVS turn-offs V2 simultaneously, and then resonance takes place for inductance and capacitor C 2, makes capacitor C 2 chargings.When t=t8, electric capacity charges to supply voltage, i.e. u C2(t)=and E, because the unilateral conduction of D4 makes resonance end.
Pattern i[t8~t9]
When t=t8, u C2(t)=and E, make diode D5 conducting, inductance is to the power supply energy regenerative.Elapsed time T8, inductive current equals load current, and the energy regenerative process finishes.
Pattern j[t9~t10]
When t=t9, i Lr(t9)=I 0, the soft shutoff of diode D6, DC power supply 1 through V1 to the load supplemental current, until i Lr(t)=0, after this load current is all provided by power supply.
When t=t10, inductive current i Lr(t10)=0, circuit state is got back to pattern a again, finishes a switching manipulation.
Embodiment two
Embodiment two in accordance with the principles of the present invention, as shown in Figure 2, provide a kind of novel resonance DC link soft-switching inverter circuit, use it for the three-phase permanent brshless DC motor and drive.The present invention includes: 3, one brshless DC motors 4 of 2, one known three phase inverter bridges of 1, one resonance auxiliary circuit of the present invention of a DC power supply, control circuit 5.Present embodiment two is on the basis of embodiment one, changes inductive load into concrete brshless DC motor, and operation principle is identical with embodiment one, repeats no more herein.At this, mainly the present invention emulation and experiment have been carried out.Choose during emulation and test identical running parameter, brshless DC motor 4 is operated in known star six states, and its parameter is: rated power 40W, rated voltage 24V, number of poles are 4, every phase winding resistance 0.95 Ω, every phase winding inductance 0.829mH.The parameter of resonance auxiliary circuit 2 of the present invention is: capacitor C r=22nF, C 1=10nF, C 2=47nF, resonant inductance L r=20uH.The voltage 24V of known DC power supply 1, the carrier frequency of three phase inverter bridge 3 is 20kHz.Switching device adopts MOSFET, and model is IRF640, and diode adopts fast recovery diode MUR410.The operation principle according to the present invention when its control flow such as Fig. 6, PWM turn-off, is blocked V1 drive signal dV1 at PWM trailing edge control circuit 5, and output V3 drive signal dV3, inductance and capacitor resonance make dc tache voltage u CrDrop to zero, control circuit 5 blocks V3 drive signal dV3, and control circuit 5 turn-offs converter bridge switching parts, and converter bridge switching parts forms continuous current circuit under the effect of current of electric, when PWM opens, at the PWM rising edge, control circuit 5 is opened converter bridge switching parts, control circuit 5 output V2 drive signal dV2, make DC bus-bar voltage resonance to supply voltage, back control circuit 5 output V1 drive signal dV1, and block V2 drive signal dV2, finish the PWM process one time.
Actual effect is as described below:
Fig. 7 is capacitance voltage, the inductive current waveform of the present invention in the auxiliary resonance unit that two times emulation of embodiment obtains, and as can be seen, its sequential with Fig. 4 is consistent.Fig. 8 for the present invention brshless DC motor voltage that two times emulation of embodiment obtains (on) and electric current (descending), brshless DC motor is pressed 120 ° of commutation six state work fully, voltage waveform is near trapezoidal wave, current waveform is near square wave.Dc tache voltage and resonant inductance electric current that Fig. 9 obtains in two times experiments of embodiment for the present invention, it is consistent with inventive principle and simulation result as can be seen.Figure 10 tests the voltage and the current waveform of the brshless DC motor of the open loop control that obtains for two times at embodiment for the present invention, voltage is near trapezoidal wave, electric current approaches square wave, demonstrates brshless DC motor reliable operation when resonant circuit of the present invention drives, stable performance.Comprehensive, novel resonance DC link soft-switching translation circuit of the present invention has these advantages: 1. resonant network does not have the restriction of resonance threshold value; 2. used time of resonant process shorter, consumed power is less; 3. the fly-wheel diode of inverter bridge has been realized soft shutoff, has overcome reverse-recovery problems; 4. can realize that PWM control and method are simple, be easy to Project Realization; 5. saved the big electric capacity of DC link, no midpoint potential imbalance problem; 6. power device has less switch stress; 7. can be used for alternating current motors such as induction machine that three-phase or heterogeneous bridge drive, permagnetic synchronous motor, brshless DC motor, can be used for the inductive load that the H bridge drives simultaneously; 8. inverter bridge main switch operation is ZVS, the resonant element switching device be operating as ZVS or ZCS, overcome the EMI problem and improved the operational efficiency of switch converters.9. switch converters may operate in higher switching frequency, strengthened original system efficient, improved power density.

Claims (5)

1, a kind of resonance DC link soft-switching inverter circuit, comprise a DC power supply, the load of control circuit, inverter bridge and driving, it is characterized in that: between DC power supply and inverter bridge, add the auxiliary resonance circuit, comprise first to the 3rd auxiliary switch (V1~V3), first to the 6th diode (D1~D6), first to the 3rd electric capacity (C1, C2, Cr) and 1 inductance
Figure C2006101051340002C1
Second to the 5th diode (D2, D3, D4, D5) is connected successively, the negative electrode of second diode (D2) connects dc bus first utmost point (P1), one end of the anode of second diode (D2) and first electric capacity (C1) and the negative electrode of the 3rd diode (D3) link to each other, one end of the negative electrode of the 5th diode (D5) and second electric capacity (C2) and the anode of the 4th diode (D4) link to each other, and the anode of the 5th diode (D5) connects the 3rd utmost point (N) of dc bus; The other end of the negative electrode of first diode (D1) and second electric capacity (C2) joins, and connects second utmost point (P2) of dc bus then, and the anode of first diode (D1) connects the 3rd utmost point (N) of dc bus; The second and the 3rd auxiliary switch (V2, V3) series connection, series connection point links to each other with inductance (Lr) end, link to each other with the anode of the 3rd diode (D3), the negative electrode of the 4th diode (D4) simultaneously, another termination dc bus first utmost point (P1) of second auxiliary switch (V2), the 3rd utmost point (N) of another termination dc bus of the 3rd auxiliary switch (V3); After linking to each other, the other end of the other end of inductance (Lr) and first electric capacity (C1) connects second utmost point (P2) of dc bus; First auxiliary switch (V1) two terminations the six or two diodes (D6) two ends, the negative electrode of the 6th diode (D6) connect first utmost point (P1) of dc bus, and the anode of the 6th diode (D6) connects second utmost point (P2) of dc bus; The 3rd electric capacity (Cr) two is terminated at second utmost point (P2) and the 3rd utmost point (N) of dc bus; Dc bus first utmost point (P1) connects the positive pole of DC power supply; Dc bus second utmost point (P2) connects the anode of inverter bridge; Dc bus the 3rd utmost point (N) connects the negative pole of DC power supply and the negative terminal of inverter bridge; Send the turn-on and turn-off of signal controlling first to the 3rd auxiliary switch (V1, V2, V3) by control circuit.
2, a kind of described resonance DC link soft-switching inverter circuit according to claim 1, it is characterized in that: the switching device in described inverter bridge and the auxiliary resonance circuit is the property a controlled device entirely, comprises power transistor, igbt, power field effect transistor and Intelligent Power Module.
3, a kind of described resonance DC link soft-switching inverter circuit according to claim 1, it is characterized in that: the diode in described inverter bridge and the auxiliary resonance circuit is fast recovery diode or high-frequency diode.
4, a kind of described resonance DC link soft-switching inverter circuit according to claim 1, it is characterized in that: described the 3rd electric capacity (Cr) can be separated into a plurality of electric capacity, is connected in parallel on the two ends of converter bridge switching parts device.
5, a kind of described resonance DC link soft-switching inverter circuit according to claim 1, it is characterized in that: described inverter bridge is H bridge or heterogeneous bridge.
CNB2006101051345A 2006-12-07 2006-12-07 A soft switch reversion conversion circuit for the resonance DC step Expired - Fee Related CN100438304C (en)

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