Improved Full Bridge Converter with Low Peak Voltage on Rectifier Diodes

XUE Kai-chang (薛开昶), FAN Peng (范 鹏), LIN Jun (林 君), ZHOU Feng-dao (周逢道), LIU Chang-sheng (刘长胜)

College of Instrumentation and Electrical Engineering, Jilin University, Changchun 130026, China

Improved Full Bridge Converter with Low Peak Voltage on Rectifier Diodes

XUE Kai-chang (薛开昶), FAN Peng (范 鹏), LIN Jun (林 君)*, ZHOU Feng-dao (周逢道), LIU Chang-sheng (刘长胜)

CollegeofInstrumentationandElectricalEngineering,JilinUniversity,Changchun130026,China

To suppress peak voltage on rectifier diodes in a full bridge (FB) converter, the mechanism of peak voltage was analyzed and an improved FB converter was proposed. One reason for peak voltage is the resonance of the transformer’s leakage inductance and the rectifier diodes’ junction capacitances. The other reason is that the fast reverse recovery current of the rectifier diodes flows through the transformer’s leakage inductance. An H bridge composed of four diodes, an auxiliary inductance, and a clamping winding were adopted in the proposed converter, and peak voltage was suppressed by varying the equivalent inductance, principally in different operating modes. Experimental results demonstrate that the peak voltage of rectifier diodes decreases by 43%, the auxiliary circuit does not lead to additional loss, and the rising rate, resonant frequency, and amplitude of the rectifier diodes’ voltage decrease. Peak voltage and electromagnetic interference (EMI) of rectifier diodes are suppressed.

fullbridge(FB)converter;rectifierdiodes;peakvoltage;efficiency;electromagneticinterference(EMI)

Introduction

Full bridge (FB) converter is used widely in middle and high power application[1-3]. However, rectifier diodes have high peak voltage. It is well known that peak voltage is related to the reverse recovery current of rectifier diodes, the leakage inductance of transformer, and the junction capacitances of rectifier diodes[4]. However, this is insufficient for analyzing the mechanism of peak voltage. In addition, few research has presented further analysis in the power electronics domain.

The main method of suppressing peak voltage is to add a resistor capacitor (RC) damping network in parallel with each rectifier diode. Compared with this method, the method of adding a resistor capacitor diode (RCD) damping network[5]decreased the additional loss and the complexity of the auxiliary circuit. Because the RCD network kept the rectifier diode’s voltage slightly lower when the reverse recovery current of the rectifier diode was high, the additional loss was decreased. Because an FB converter needed only one RCD network, the number of damping networks decreased and the complexity decreased. However, RC and RCD damping networks are loss networks and have great loss at high frequency. The FB converter in Ref. [6] suppressed the peak voltage by adding one transistor and one capacitor around the rectifier diodes. Because the capacitor is large and the auxiliary circuit does not include resistive components, peak voltage and loss are low. The disadvantage was that the auxiliary transistor needed to be controlled. Many zero-voltage and zero-current-switching FB (ZVZCS-FB) converters and zero-voltage-switching FB (ZVS-FB) converters were presented in Refs. [5, 7-16], and they could suppress the peak voltage on rectifier diodes. Because the main purpose of these converters was to increase efficiency, few analyses had been done on the mechanism of peak voltage, and peak voltage suppression was just an additional function. The ZVZCS-FB converters in Refs. [7-8] suppressed peak voltage by adding auxiliary winding. However, auxiliary winding had leakage inductance, which decreased the dynamic response to transient voltage variation. The ZVZCS-FB converters in Refs. [9-11] and the ZVS-FB converter in Ref. [5] suppressed peak voltage by adding clamping diodes and capacitors around the rectifier diodes. However, the converters in Refs. [5, 9-11] had a relatively narrow range of output voltage. The ZVS-FB converters in Refs. [12-13] employed saturated inductance or magnetic amplifiers in series with rectifier diodes. In addition to suppressing peak voltage, they could suppress the electromagnetic interference (EMI) of rectifier diodes. Both saturated inductance and magnetic amplifiers had high core loss at high frequency, which leaded to tough thermal dissipation. The ZVS-FB converter in Ref. [14] with one auxiliary inductance and two clamping diodes in the primary were proposed. The suppressive effectiveness on peak voltage was obvious. However, the circulating current in clamping diodes caused great additional loss. Further work was evident in Refs. [15-16]. The ZVS-FB converters in Refs. [15-16] decreased the circulating current, decreasing additional loss. However, the converters in Refs. [14-16] were based on phase-shifted pulse width modulation (PWM), which was different from PWM used in an FB converter.

This study analyzes the mechanism of peak voltage on rectifier diodes by adopting the diode lumped charge mode[17-20]from the semiconductor physics domain and proposes an improved FB converter. The proposed FB converter uses this analysis of peak voltage; however, other researchers can use this analysis to propose other reasonable strategies. The auxiliary circuit in the proposed FB converter consists of passive components, is uncontrolled, and has low loss. Operating modes of the proposed FB converter are analyzed, and suppressive principles of peak voltage on rectifier diodes are illustrated. Experimental results on a 1.5 kW prototype verify the low peak voltage in the proposed FB converter.

1 Rectifier Diodes in FB Converter

1.1 Operation principle of FB converter

Because rectifier diodes are treated as ideal components in textbooks when the operation principle of FB converter is analyzed, peak voltage on rectifier diodes, obtained from analysis, is lower than practical value, obviously. Therefore, this section presents an analysis focused on rectifier diodes.

Figure 1 shows the circuit of an FB converter. V1-V4are power transistors. T1is a transformer. Primary and secondary turns areN1andN2, and the turns ratio isn=N2/N1.Ls1andLs2are primary and secondary leakage inductances. D1-D4are rectifier diodes.LandCcompose the output filter.Ris the load resistance andCbis the blocking capacitor.vsecis the secondary voltage.ViandVoare input and output voltages, respectively. To analyze the operating modes, several assumptions are made as follows.

(1)Cbis large enough to be disregarded.

(2) D1-D4have the same characteristics.

(3) The output is treated as a current source.

Fig.1 FB converter

Figure 2 shows the operation waveforms in a switching cycle. There are six operating modes within a half cycle. Operating modes and equivalent circuits are shown in Figs.3 and 4, respectively. Duringt0-t6, D2and D3are studied. Reverse recovery characteristics of D2and D3are shown in Fig.5.

In Figs.2-5，V2is the secondary steady-state voltage andV2=nVi.iDxandvDxare the current and voltage of the rectifier diode Dx, wherex∈{1, 2, 3, 4}.VRMandIRMare the reverse recovery peak voltage and current of rectifier diodes.Lris the equivalent leakage inductance reflected to the secondary andLr=Ls2+n2Ls1.i1andCjare the reverse recovery current and the junction capacitance of one rectifier diode.i2is the current flowing throughCj.vandiare the voltage and current of D2or D3.IFis forward current.tSis the time ofifrom -0.1IRMto -IRM.tFis the time ofifrom -IRMto -0.1IRM.trris the reverse recovery time.Qrris the reverse recovery charge.

Fig.2 Operation waveforms of FB converter

Fig.3 Operating modes of FB converter: (a) before t0; (b) t0-t1; (c) t1-t2; (d) t2-t3; (e) t3-t4; (f) t4-t5

Fig.4 Equivalent circuits of FB converter: (a) before t0; (b) t0-t1; (c) t1-t2; (d) t2-t3; (e) t3-t4

Fig.5 Reverse recovery characteristics of diode

Mode 1 (beforet0) [Figs.3(a) and 4(a)]: D1-D4are freewheeling. The current in each diode isIo/2; namely,IFin D2and D3isIo/2.

Mode 2 (t0-t1) [Figs.3(b) and 4(b)]: V1and V4turn on att0. The arrows in Fig.3(b) indicate the flowing direction of practical current, and the symbol “+” or “-” indicates that the current increases or decreases; this definition is used below, too.iD2andiD3linearly decrease, and the decreasing slope is

a=-diD2/dt=-diD3/dt=V2/(2Lr),

(1)

iD1andiD4linearly increase, and the increasing slope isa.iD2andiD3are down to 0 att1.

Mode 3 (t1-t2) [Figs.3(c) and 4(c)]:iD2andiD3linearly decrease with the slopea.iD1andiD4linearly increase with the slopea.iD2andiD3are down to -IRMatt2[17-20].

IRM=aτ1[1-e-(IF+IRM)/(aτ)],

(2)

whereτandτ1are the constants for expressing diode characteristics. Their calculation is shown in Appendix A.

Mode 4 (t2-t3) [Figs.3(d) and 4(d)]:iD1-iD4all decrease along the direction of the arrows. In Fig.4(d), 2i1, 2i2, and 2Cjindicate the combination of D2and D3.i1andCjare expressed as Eqs. (3) and (4), respectively[17-20].

i1=IRMe-(t-t2)/τrr,

(3)

whereτrris the recovery time constant. The calculation ofτrris shown in Appendix B.

Cj=Cj0/(1-v/Vb)m,

(4)

whereCj0is the junction capacitance atv=0,Vbis barrier potential (typical value is 1 V)， andmis the gradient coefficient of PN junction (typical value is 1/3-1/2).

At the end of this mode, 2i=0, where 2i=-(2i1+2i2)=iD2+iD3. During this mode, peak voltage generates on D2and D3. Detailed analysis will be shown in section 1.2.

Mode 5 (t3-t4) [Figs.3(e) and 4(e)]:Lrand 2Cjkeep resonant, and the resonant voltage amplitude decays as the parasitic resistance.

Mode 6 (t4-t5) [Fig.3(f)]: V1and V4turn off att4, and primary current flows through the body diodes of V2and V3.iD2andiD3increase with the slopea, andiD1andiD4decrease with the slopea. Att5,iD1-iD4reachIo/2; namely,IF=Io/2.

1.2 Analysis of peak voltage on rectifier diodes

In Mode 4 (t2-t3)， because of the characteristics ofi1andCjdefined by Eqs. (3) and (4), it is difficult to calculate the peak voltage, approximate analysis is made and shown in Appendix C. If the influence of parasitic resistance is disregarded, the peak voltage is higher than 2V2.

In a light load, because 2i1is small, the influence of 2i1can be disregarded; the peak voltage mainly depends on the resonance ofLrand 2Cj. In a heavy load,IRMis large, and 2Cjcan get charged fast; the influence of 2Cjcan be disregarded, so the peak voltage mainly depends on d(2i1)/dtand the value ofLr.

In a heavy load, 2i1is large, and the peak voltage is much higher than 2V2. The peak voltage can be calculated in the following manner. From Eq. (2), the change rate ofican be expressed as

ab=-di/dt≈-di1/dt=IRMe-(t-t2)/τrr/τrr.

(5)

The maximum ofabcan be expressed as

abmax=IRM/τrr.

(6)

The peak voltage on D2and D3is

VRM=V2+2abmaxLr.

(7)

2 Rectifier Diodes in the Proposed FB Converter

2.1 Operation principle of proposed FB converter

To suppress peak voltage of the rectifier diodes, an improved FB converter, shown in Fig.6, is proposed. Compared with an FB converter, the proposed converter adds auxiliary windingN3, diodes D5-D8, capacitorsCrandC1, and auxiliary inductanceLR. In Fig.6,Ls3is the leakage inductance of auxiliary winding.N3is the turns of auxiliary winding. Turns ration1=N3/N1.

Fig.6 The proposed FB converter

To simplify analysis of the operating modes, several assumptions are made as follows.

(1)-(3) are the same as (1)-(3) in section 1.1.

(4)Cris far larger than 2Cj.

(5)n1is slightly less than 1.

(6)LRis far larger thanLs1,Ls2, andLs3.

(7)C1is disregarded because it does not affect the analysis directly.

Fig.7 Operation waveforms of the proposed FB converter

Mode 1 (beforet0): the primary is not working. D1-D4are freewheeling. The current in each diode isIo/2; namely,IFin D2and D3isIo/2.

Mode 2 (t0-t1) [Figs.8(a) and 9(a)]: V1and V4turn on att0.iD2andiD3linearly decrease, and the decreasing slope is

a=-diD2/dt=-diD3/dt=V2/[2(Lr+LR2)],

(8)

iD1andiD4linearly increase, and the increasing slope isa.iD2andiD3are down to 0 att1.

Mode 3 (t1-t2) [Figs.8(b) and 9(b)]:iD2andiD3linearly decrease with the slopea.iD1andiD4linearly increase with the slopea.iD2andiD3are down to -IRMatt2. The expression ofIRMis the same as Eq. (2).

Mode 4 (t2-t3) [Figs.8(c) and 9(c)]:iD2andiD3recover from -IRM. The expressions ofi1andCjare the same as Eqs. (3) and (4) and the secondary current chargesCr.vsecrises toV2/n1at the end of this mode.

Mode 5 (t3-t4) [Figs.8(d) and 9(d)]: D6and D7turn on att3and the voltage ofN3is clamped toVi.iD2andiD3recover to 0. At the end of this mode, the secondary current reduces toIo. During this mode, peak voltage generates on D2and D3. Detailed analysis will be shown in section 2.2.

Mode 6 (t4-t5) [Figs.8(e) and 9(e)]: D6and D7turn off att4.Lr+LR2andCr+2Cjkeep resonant. The voltage ofCris

vCr(t)=vsec=V2+(V2/n1-V2)cos ωr(t-t4),

(9)

Mode 7 (t5-t6) [Fig.8(f)]: V1and V4turn off att5.IodischargesCr.vCr(t6)=0 at the end of this mode.

Fig.8 Operating modes of the proposed FB converter: (a) t0-t1; (b) t1-t2; (c) t2-t3; (d) t3-t4; (e) t4-t5; (f) t5-t6

Fig.9 Equivalent circuits of the proposed FB converter: (a) t0-t1; (b) t1-t2; (c) t2-t3; (d) t3-t4; (e) t4-t5

2.2 Peak voltage suppression of rectifier diodes

According to analysis in Section 1.2, peak voltage is caused by either reverse recovery current or resonance; peak voltage is always related toLs1andLs2. However,Ls1andLs2are determined by intrinsic transformer characteristics, and cannot be eliminated. In order to suppress the influence ofLs1andLs2, the proposed converter addsN3, D5-D8, andLR. Suppression of peak voltage is achieved by varying the equivalent inductance in different operating modes.

2.2.1 Suppressing peak voltage caused by 2i1

When the current of rectifier diodes varies fromIFto -IRM(t0-t2in Figs.4 and 9); the equivalent inductance increases from the previousLrtoLr+LR2.adecreases (shown by Eqs. (1) and (8)).IRMdecreases (shown by Eq. (2)), andabmaxdecreases (shown by Eq. (6)). When the current of rectifier diodes recovers from -IRMto 0 (t2-t3in Fig.4 andt3-t4in Fig.9), the equivalent inductance varies from the previousLrtoLe3+Ls2, andLrandLe3+Ls2are approximately equal. Becauseabmaxdecreases andLris approximately equal in Eq. (7), peak voltage decreases. This is one side of the suppression principle for peak voltage caused by 2i1.

In addition,Crcan absorb the reverse recovery charge, which decreases the change rateabof the current flowing throughLe3+Ls2and then decreases the peak voltage (shown by Eq. (7)). This is the other side of the suppression principle for peak voltage caused by 2i1.

2.2.2 Suppressing peak voltage caused by resonance

Figure 10(a) shows the series resonance circuit. When the initial voltage ofCrais 0 and the initial current ofLraisIa, the peak voltage ofCrais always 2Va. On this condition,CraandLracan be any fixed values[21].

Fig.10 Analysis of resonance circuits: (a) series resonance circuit; (b) series resonance circuit with clamping

Based on the above analysis, the suppression principle of peak voltage caused by resonance in the proposed converter is analyzed as follows.

3 Experimental Results

Two prototypes of the topologies were built and were shown in Figs.1 and 6. V1-V4are 1HW30N160R2. D1-D4are DSEI30-10. D5-D8are HFA15PB60. Experimental parameters are shown in Table 1.

Table 1 Detailed parameters of experiment

ParametersViVoIofLRLrValue300V250V6A35kHz16.5μH2.5μHParametersLCCbC1,Crnn1Value410μH1000μF6μF10nF1.10.9

The voltage waveforms of the rectifier diode D2in the FB converter and proposed converter are shown in Figs.11(a) and 11(b), respectively. Resonant details of rectifier diodes’ voltage waveforms are shown in Fig.12. Figures 12(a) and 12(b) show the waveforms in the FB converter and the proposed converter, respectively. Figures 11 and 12 are obtained by TDS2012B oscilloscope.

(a) (b)

(a) (b)

Results shown in Figs.11 and 12 are summarized in Table 2. In Table 2,tr,To, andVrp-pare the rising time, resonant period, and peak-to-peak value of resonant voltage, respectively.

Table 2 Experimental results of waveforms

ParametersV2/VVRM/Vtr/nsTo/nsVrp-p/VFBconverter330840100180840ProposedFBconverter330480360480200

Figure 11 shows that the peak voltage,VRM, in the FB converter is 155% higher thanV2and peak voltage in the proposed converter is 45% higher thanV2. Peak voltage in the proposed converter is 43% lower than in the FB converter. Hence, the proposed converter can suppress peak voltage. Figure 11(b) also shows thatiN3has short conducting time within a cycle, so D5-D8andN3have low auxiliary loss.

Figure 12 shows that the resonant voltage,vD2, has lowerVrp-p, resonant frequency and dvD2/dtthan in the FB converter. Hence, the proposed converter also can suppress the EMI on rectifier diodes. The reason for lowerVrp-pis that D6and D7clamp the voltage ofN3toVi, and then clamp the voltage ofN2duringt3-t4in the proposed converter. The reason for lower resonant frequency and dvD2/dtis mainly that the resonant capacitor increases from 2Cjduringt2-t4in the FB converter toCr+2Cjduringt2-t4in the proposed converter.

Table 3 shows the efficiency of the FB converter and the proposed converter whenVo=250 V andIo=1.2-6 A; namely, when powerPo=0.3-1.5 kW. The efficiency of the proposed converter is slightly higher than the FB converter. This is because that theCrkeeps the rectifier diodes voltage at a slightly lower value when the reverse recovery current of the rectifier diodes is high.

Table 3 Experimental results on efficiency

Power/kWFBconverter/%ProposedFBconverter/%0.383.883.80.688.688.90.989.690.31.289.690.31.590.890.4

4 Conclusions

This paper has analyzed the mechanism of peak voltage and has presented an improved FB converter. Two reasons for the peak voltage on rectifier diodes are the reverse recovery current of rectifier diodes flowing through the transformer’s leakage inductance and the resonance between the rectifier diodes’ junction capacitances and the transformer’s leakage inductance. The proposed converter adds one winding, four diodes, one inductance, and two capacitors and suppresses peak voltage on rectifier diodes by varying the equivalent inductance in different operating modes. Experimental results verify that peak voltage decreases by 43%. Despite the EMI on rectifier diodes being suppressed, further work is necessary to increase effectiveness.

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Appendix A

Equation (2) is the implicit expression ofIRM， andIRM=f(IF,a). It is difficult to extract the two constantsτ1andτdirectly. Thus, an approximate calculation is made. Whenais small,

1≫e-(IF+IRM)/(aτ).

(A-1)

Thus, whenaadopts a small value,τ1can be calculated by readingIRMfrom the diode specification and using the approximate Eq. (A-2).

IRM≈aτ1.

(A-2)

Whenaadopts a large value, becauseτ1is known,τcan be calculated according to Eq. (2) by readingIFandIRMfrom the diode specification.

Appendix B

In Refs. [17-20],τrris treated as a constant; but when the reverse voltage,VR, is higher than 10% of the breakdown voltage,VBR,τrris not a constant. Generally,VR≈0.5VBRin practical operation, soτrrshould be calculated on the condition thatVR≈0.5VBR.tFis not shown in the specification and needs to be calculated by indirect calculation. From Fig.5 and the properties ofefunction, Eqs. (B-1) and (B-2) can be known

Qrr≈IRMtrr/2,

(B-1)

trr=tS+tF, tS≈IRM/a, tF=2.3τrr.

(B-2)

The reverse recovery charge can use Eq. (B-3) for fitting

(B-3)

wherec1,c2, andc3are three unknown parameters. The value ofc1,c2andc3can be calculated by reading three groups ofa,IFandQrrfrom the specification.

By solving Eqs. (B-1)-(B-3),

(B-4)

whereaandIRMcan be adopted from Eqs. (1) and (2).

Appendix C

(1) On the condition thatCj=Cj1,i1=I1, andILr(t2)=2(IF+IRM),vcan be expressed as Eq. (C-1).Cj1andI1are constant values that are the values ofCjandi1, respectively, whenv=-V2.

(C-1)

The peak ofvis -2V2.

(2) Whenvrises from 0 to -V2，practicalCjandi1are larger thanCj1andI1. Thus, the peak of the current flowing throughLris smaller than in a practical situation.

(3) Whenvrises from -V2to -VRM，practicalCjandi1are smaller thanCj1andI1. Hence, the peak voltage ofvis lower than in a practical situation.

Appendix D

IfvCrarises from 0 toVawhen time changes from 0 tota1

vCra(t)=Va(1-cosωra1t),

(D-1)

iLra1(t)=Ia+(Va/Zra1)sin ωra1t,

(D-2)

After combiningvCra(ta1)=Vawith Eqs. (D-1) and (D-2), it can be obtained thatiLra1(ta1)=Ia+Va/Zra1. According to the known initial conditions atta1, afterta1:

vCra(t)=Va+(VaZra2/Zra1)sin[ωra2(t-ta1)],

(D-3)

Foundation items: National Natural Science Foundation of China (No.41004027); Cooperation Innovation Projects of Ministry of Education, China (No. OSR-02-01)

TM464 Document code: A

1672-5220(2015)01-0062-06

Received date: 2013-11-26

* Correspondence should be addressed to LIN Jun, E-mail: lin_jun@jlu.edu.cn