topologies and operating principles of basic full-bridge ...the dual-switch forward converter,...

1Topologies and OperatingPrinciples of Basic Full-BridgeConverters

1.1 Introduction

1.1.1 Development Trends of Power Electronics Technology

High-frequency switching is one of the most important features of power electronicstechnology, enabling power electronics converters to meet the required specificationsand performance. High-frequency power devices and components, including magneticdevices and capacitors, are the basic elements of high-frequency power electronics.Metal-oxide-semiconductor field-effect transistors (MOSFETs) and insulated-gatebipolar transistors (IGBTs) have become the dominant choices for the implementationof power switches, and MOSFETs with low gate charges and low junction capacitorsfurther boost the development of high-frequency power electronics. Recently, therehas been significant progress in the development of silicon carbide (SiC)-based powerdevices, including SiC diodes [1], SiC MOSFETs, and SiC IGBTs [2], and SiC-basedcommercial products have become strong competitors to Si-based fast-recoverydiodes and MOSFETs in medium power conversion applications. Gallium nitride(GaN) power devices have drawn attention for achieving ultra-fast switching. Fur-thermore, recent progress in the development of amorphous, microcrystalline coresand high-frequency ferrites has been significant.

Circuit topology is another important aspect of high-frequency power electronics.Switching losses in switching devices have been drastically reduced through thesystematic development of resonant converters [3, 4], quasi-resonant converters[5], and multi-resonant converters [5, 6], zero-voltage-switching (ZVS) pulse-widthmodulation (PWM) and zero-current-switching (ZCS) PWM converters [7, 8],

Soft-Switching PWM Full-Bridge Converters: Topologies, Control, and Design, First Edition. Xinbo Ruan.© 2014 Science Press. All rights reserved. Published 2014 by John Wiley & Sons Singapore Pte. Ltd.

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2 Soft-Switching PWM Full-Bridge Converters

zero-voltage-transition (ZVT) and zero-current-transition (ZCT) converters [9, 10],and resonant dc link inverters (RDCLIs) [11] that partially or fully achieve ZVSand ZCS. As a result, the operating switching frequency has increased by an orderof magnitude and more. High-frequency switching is also the key contributor tominiaturization and modularization, due to the significant gain in efficiency of powerconversion that it can offer, in addition to the high insulation and high thermalconductivity of the structure employed. Therefore, the success of high-frequencypower electronics can be attributed to the advent of high-frequency power devicesand components, soft-switching technologies, mechanical structures, materials, andrelated technologies.

1.1.2 Classification and Requirements of Power Electronics Converters

Power electronics converters are a family of electrical circuits that convert electricalenergy from one level of voltage/current/frequency to another using semiconductordevices, passive components, and advanced control methods. According to the formof conversion, power electronics converters can be classified into four different types[12]: (i) dc–dc converters, which convert a dc input voltage into a dc output volt-age of a different magnitude and possibly opposite polarity, or with galvanic isolationof the input and output ground references; (ii) dc–ac inverters, which transform adc input voltage into an ac output voltage of controllable magnitude and frequency;(iii) ac–dc rectifiers, which convert an ac input voltage into a dc output voltage, andare capable of controlling the dc output voltage and/or ac input current waveform;and (iv) ac–ac cycloconverters, which convert an ac input voltage into an ac outputvoltage of controllable magnitude and frequency. These four kinds of power electron-ics converter can be unidirectional or bidirectional. The unidirectional ones can onlyconvert electrical power from a defined input terminal to a defined output terminal,while the bidirectional ones can convert electrical power in either direction betweentwo defined terminals.

The primary objective of power electronics converters is to meet the correspond-ing electrical specifications and regulatory requirements. While meeting the electricalspecifications, a power electronics converter should idealy achieve high efficiency,high power density, high reliability, and low cost. High efficiency not only leadsto energy saving but also results in a reduced heat dissipation requirement. Highpower density means compact size at the required output power, which is very impor-tant for aerospace applications and compact portable appliances. Power convertersof high reliability are more competitive in the commercial market and can be essen-tial for critical applications that require operation under adverse working conditionsand long mean-time-between-failure (MTBF). Moreover, the overall cost is a key fac-tor for commercial power supply applications. Power electronics converters are oftenrequired to have good maintainability, including reduced technical requirements forrepair personnel and shortened repair times.

Topologies and Operating Principles of Basic Full-Bridge Converters 3

1.1.3 Classification and Characterization of dc–dc Converters

Dc–dc converters are an important kind of power electronics converter. With thedevelopment of power electronics technology, computer science and technology, andinformation technology, dc–dc converter-based switching-mode power supplies havebeen widely used. The dc–dc converter is thus the key basic building block in powerelectronics and has attracted a great deal of research attention in the past few decades.

According to the presence of galvanic isolation between input and output,dc–dc converters can be divided into two classes: non-isolated and isolated. Basicnon-isolated dc–dc converters include buck, boost, buck–boost, Cuk, Zeta, andsingle-ended primary inductor converter (SEPIC) converters. Other examples includethe dual-switch buck–boost converter, the full-bridge converter, and so on.

Isolated dc–dc converters are derived from non-isolated dc–dc converters by incor-porating transformers and output rectifier circuits. Isolated buck-derived convertersinclude forward, push–pull, half-bridge, and full-bridge. The forward converters canbe single-switch or dual-switch versions. Isolated boost-derived converters includepush–pull, half-bridge, and full-bridge versions. Isolated buck-boost converters areflyback converters, which can also be single-switch or dual-switch versions. Cuk,Zata, and SEPIC converters also have isolated versions.

With the power devices having the same voltage and current ratings, the outputpower of the dc–dc converter is proportional to the number of power switches.Thus, the isolated dc–dc converter with two power switches (dual-switch forward,push–pull, and half-bridge) can handle twice as much power as an isolated dc–dcconverter with only one power switch, such as the single-switch forward converter,and only half as much power as a converter with four power switches, such as thefull-bridge converter. Thus, the full-bridge converter can handle the largest poweramong all the isolated buck-derived converters, and it has been widely used inhigh-input-voltage and medium- to high-power conversion applications.

Resonant converters, quasi-resonant converters, and multi-resonant converters canachieve ZVS or ZCS for power switches without using additional auxiliary powerswitches. However, such soft-switching converters are different from the conventionalPWM converters and they have the disadvantages of high voltage/current stress, largecirculating energy, and variable switching frequency. For ZVS-PWM and ZCS-PWMconverters, the operating frequency is constant and additional auxiliary powerswitches are needed. Also, the voltage/current stress of both the main and auxiliarypower switches is relatively high. For ZVT and ZCT converters, the operatingfrequency is also fixed. However, the additional auxiliary power switches are usedonly for achieving ZVT or ZCT for the main power switches and do not contribute topower processing. Among the isolated buck-derived converters, the converters withtwo or four power switches can achieve ZVT or ZCT without additional auxiliaryswitches, provided an appropriate control scheme is employed. Such simplicitymakes them popular choices in practical applications. This book intends to describesystematically the soft-switching techniques for isolated buck-derived full-bridge


converters. For brevity of illustration, the isolated buck-derived full-bridge converteris simply called a “full-bridge converter.”

1.2 Isolated Buck-Derived Converters

In order to give some insights into the characteristics of the isolated buck-derivedconverters and to reveal the relationships among them, this section begins by deriv-ing the forward converter from the basic buck converter. It then goes on to derivethe dual-switch forward converter, push–pull converter, half-bridge converter, andfull-bridge converter.

1.2.1 Forward Converter

1.2.1.1 Derivation of a Single-Switch Forward Converter

The buck converter is the most basic of the dc–dc converters. It is shown inFigure 1.1a, where Vin is the input dc voltage, Q is the power switch, DFW is the free-wheeling diode, and Lf and Cf are the output filter inductor and output filter capacitor,respectively. In order to achieve galvanic isolation, the transformer Tr is insertedbetween Q and DFW, as shown in Figure 1.1b. The primary and secondary windingturns of Tr are Np and Ns, respectively, and the corresponding turns ratio is K=Np/Ns.When Q conducts, the input voltage Vin is applied on the transformer primarywinding. The transformer is thus magnetized and the magnetizing flux 𝜙m increases.

Vin

Vin

VinVinQ

DFW DFW

DFW

DFW

Cf

Cf

Cf

Cf

Lf Lf

Lf

Lf

DR

Dr

DR

RLd

RLd

RLd

RLd

Vo

Vo

Vo

VoQ * *vp vsec

vp

vp

vsec

vsec

vrect

vrect

vrect

Np

Np

Np

Ns

Ns

Nr

Ns

Tr

Tr

Tr

(a) Buck converter (b) Transformer inserted

Q * *Magnetic

Reset Circuit

(c) Magnetic core reset circuit and rectifier diode included

* *

Q

*

(d) Single-switch forward converter with magnetic reset winding

–– –

+

–

+

–

+

–

+

–

+

–

+

–

+

–

+

–

+

+ +

–

+

–

+

Figure 1.1 Derivation of the single-switch forward converter


(a) Without magnetic core reset circuit (b) With magnetic core reset circuit

ϕmt0

0 Ts 2Ts

Qt

0 t

vrect

vp

ϕm

Vin/K

0 Ts 2Ts

t0

Qt

0 t

vrect

vp

/KVin

Figure 1.2 Waveforms of the primary voltage and magnetizing flux of the transformer

When Q is turned off, the filter inductor current is freewheeling through diode DFW.The conducting diode short-circuits the transformer secondary winding, forcing theprimary winding voltage to zero and thus keeping 𝜙m unchanged. Therefore, in aswitching period, 𝜙m has a net increase, and as time elapses, the magnetic core willsaturate, leading to destruction of the power switches. The waveforms of the primaryvoltage vp and magnetizing flux 𝜙m of the transformer are sketched in Figure 1.2a.

In order to avoid saturating the transformer, the magnetizing flux should be resetbefore the end of each switching period. Thus, a magnetic core reset circuit is manda-tory. This circuit applies a negative voltage across the primary winding of the trans-former when Q is turned off, as shown in the shaded area in Figure 1.2b. However, thisnegative voltage will be reflected to the secondary winding and will force the free-wheeling diode DFW to conduct, shorting the secondary winding. In order to avoidshort-circuiting the transformer, a diode DR can be inserted in series with the sec-ondary winding, as shown in Figure 1.1c. Thus, a magnetic core reset circuit can beformed by a reset winding Nr and a reset diode Dr. Exchanging the positions of powerswitch Q and the transformer primary winding, the basic single-switch forward con-verter is formed, as shown in Figure 1.1d. In practical applications, the turns of thereset winding and primary winding are usually designed to be equal, and thus the volt-age stress of the power switch is 2Vin and its maximum duty cycle is limited to 0.5, inorder to achieve magnetic core reset of the transformer.

1.2.1.2 Derivation of a Dual-Switch Forward Converter

As the power switch sustains twice the input voltage, the single-switch forwardconverter is suitable for low-input-voltage applications. For high-input-voltage appli-cations, it may be difficult to find an appropriate power switch with such a highvoltage rating. For example, with a single-phase input ac voltage of 220 V± 20%, therectified input voltage with power factor correction is 380 V. The voltage stress of thepower switch is 760 V and a power switch with voltage rating of 1000 V is required.MOSFETs with such a high voltage rating have poor performance at high frequencies,


and the drain-source conduction resistor Rds(on) is relatively large. Although IGBTscan be adopted, the switching frequency is limited to tens of kilohertz due to the pres-ence of the current tail. At high frequencies, the turn-off loss will be relatively high,causing degradation in efficiency.

For the sake of employing the available power switches with better performance,it is desirable to reduce the voltage stress of the power switch. As indicated before,when the turns of primary winding and reset winding are equal, the power switch ofa single-switch forward converter must withstand twice the input voltage. If powerswitch Q is replaced by two power switches Q1 and Q2, as shown in Figure 1.3a, thevoltage stress of Q1 and Q2 will be the input voltage Vin. Exchanging the positionsof Q1 and the primary winding leads to the circuit shown in Figure 1.3b. In order toensure the voltage stress of Q1 and Q2 is Vin, a diode D2 is inserted between point Aand the negative rail and a diode D1 between point B and the positive rail, as shownin Figure 1.3c. When both Q1 and Q2 are turned off, the transformer is magneticallyreset through the reset winding Nr and the transformer primary voltage vAB is −Vin.In fact, the transformer can be magnetically reset through the primary winding viaD1 and D2. Therefore, the path constituting reset winding Nr and reset diode Dr isredundant and can be removed. The simplified circuit is redrawn in Figure 1.3d, givingthe well-known dual-switch forward converter. In this circuit, the voltage stress of the

(a)

(c)

(b)

(d)

* *

Tr

Vin

DRQ1D1

D2 Q2

Lf RLd

Np NsDFW Cf

Vo–

+

* *

*

Vin

DR

Q1

Q2

Dr

Lf RLd

NpNr

NsDFW Cf

Vo–

+Tr

* **

NrA

B

Vin

DRQ1

D1

D2 Q2

Dr

Lf RLd

Np NsDFW Cf

Vo

–

+Tr

* **

A

B

Vin

DR

Dr

Q1

Q2

Lf RLd

Np

Nr

NsDFW Cf

Vo–

+Tr

Figure 1.3 Derivation of the dual-switch forward converter: (a) using two power switchesin place of one power switch, (b) exchanging the positions of Q1 and the transformer primarywinding, (c) adding two diodes to ensure the two power switches sustain the input voltage, and(d) final configuration of the dual-switch forward converter


two power switches is Vin, which is half that of the single-switch forward converter.Moreover, D1 and D2 are the reset diodes, and also provide the path for regenerationof the leakage inductor energy to the input voltage when Q1 and Q2 are turned off.

1.2.2 Push–Pull Converter

For the single-switch forward converter, when the primary winding and reset wind-ing have the same number of turns, the duty cycle should be bounded below 0.5 toensure magnetic core reset. Therefore, the magnitude of the secondary rectified volt-age should be larger than twice the output voltage. This secondary rectified voltagecontains a large amount of harmonics, necessitating the use of a large output inductor.In order to reduce the magnitude of the secondary rectified voltage and hence theoutput filter inductor, we can use two single-switch forward converters connected inparallel at the input side and the secondary rectifier, sharing the freewheeling diodeand the output filter, as shown in Figure 1.4a. Note that the two forward converters

V

(c)

(a) (b)

in

* *

*

* **

DR1 DFW

DR2

Dr1

Dr2

Ns1Np1

Ns2

Nr1

Nr2

Tr1

Tr2

Lf RLd

Cf

Q1

Q2

–

+

–

+

–

+

–

+

–

+

–

+

vp1

vp2

vsec1

vsec2

vrect Vo

Vin

* *Tr

*

* **

DFW

DR2

Dr1 D1

D2Dr2

Ns2Np2Np2

Nr1

Nr2

Cf

Q1

Q2

–

+

–

+

–

+

––

+

–

+

DR1Ns1Np1Lf RLd

+

vp1

vp2

vsec1

vsec2

vrect Vo

Vin

*

* *

*

iDR1 iLf

iDR2

DFW

DR2D1 D2

Ns1

Ns2

Np1 Np2

Tr

Cf

Q1 Q2

–

+

–

+

DR1 Lf RLd

vrect Vo

Figure 1.4 Derivation of the push–pull converter: (a) two single-switch forward convertersconnected in parallel at the input side and the secondary rectifier, sharing the freewheelingdiode and the output filter, (b) the two transformers sharing a magnetic core, and (c) finalconfiguration of the push–pull converter


0 Ts 2TsTs/2 3Ts/2

Vin/Kvrect

t0

ϕm2

vp2

0

Vin

t

vp1

ϕm1t0

Vin

Vin

Vin

tQ1 Q2 Q2Q1 Q1

Figure 1.5 Key waveforms of two interleaved forward converters

are required to operate in an interleaving manner; that is, power switches Q1 and Q2operate at the same switching frequency with a time difference of half the switchingperiod, as shown in Figure 1.5.

Referring to Figure 1.4a, if we let the two transformers share a magnetic core andconnect an antiparallel diode D2 across Q2, as shown in Figure 1.4b, the primary wind-ing Np2 and diode D2 can provide the magnetic core reset function for the transformerwhen Q1 is turned off. Likewise, by connecting an antiparallel diode D1 across Q1,the transformer core can be magnetically reset through the primary winding Np1 andD1 when Q2 is off. This makes the two core reset circuits redundant and they can beremoved. The simplified circuit is re-sketched in Figure 1.4c, showing what is usuallyreferred to as the push–pull converter.

It should be noted that the transformer of the push–pull converter cannot be magnet-ically reset when Q1 or Q2 is off because the current of the output filter inductor will befreewheeling through diode DFW, which clamps all of the transformer winding at 0 V.When Q1 conducts, the transformer is positively magnetized; when Q2 conducts, thetransformer is negatively magnetized; and when both Q1 and Q2 are off, the voltagesacross the transformer windings are zero and the magnetic flux of the transformerremains unchanged. Figure 1.6 shows the key waveforms of the push–pull converter.For the forward converter, including the single-switch and dual-switch versions, themagnetizing current can only flow in a single direction, as when the magnetizing cur-rent decays to zero, it cannot flow in the reverse direction. For the push–pull converter,


vp1, −vp2

ϕmt0

0 Ts 2TsTs/2 3Ts/2

Vin

Vin

Vin/Kvrect

t0

Q1 Q1 Q1Q2 Q2 t

Figure 1.6 Key waveforms of the push–pull converter

the magnetizing current of the transformer flows bidirectionally. If the flux swing isconstrained by the core loss rather than by the saturation flux density, the utilizationof the transformer of the forward converter is the same as that of the push–pullconverter.

As in the single-switch forward converter, the two switches of the push–pull con-verter must withstand a voltage of 2Vin. Since the push–pull converter is equivalent tothe interleaved parallel connection of two single-switch forward converters, the ripplefrequency of the secondary rectified voltage vrect is twice the switching frequency andits duty cycle can reach unity, as shown in Figure 1.6. With the same input and outputvoltages, the required magnitude of vrect of the push–pull converter is only half thatof the forward converter. Thus, the primary-to-secondary-winding-turns ratio of thepush–pull converter is twice that of the forward converter.

Referring to Figure 1.4c, when both switches are off, the output filter inductor cur-rent can freewheel through DFW or flow through the two secondary windings viarectifier diodes DR1 and DR2. Therefore, DFW is redundant and can be removed. WhenDFW is removed, we get:

iDR1 + iDR2 = iLf (1.1)

For an ideal transformer, the magnetizing current is zero; that is:

iDR1 − iDR2 = 0 (1.2)

According to Equations 1.1 and 1.2, we have:

iDR1 = iDR2 = iLf∕2 (1.3)

Hence, when both the power switches are off, the output filter inductor current isshared by the two rectifier diodes DR1 and DR2, with DFW removed.


1.2.3 Half-Bridge Converter

Figure 1.7a shows two single-switch forward converters connected in series at theinput side and in parallel at the secondary rectifiers, sharing the freewheeling diodeand the output filter, where Cd1 and Cd2 are two input dividing capacitors. The valuesof the two capacitors are equal and quite large, and the voltage across each is Vin/2.Power switches Q1 and Q2 operate at the same switching frequency with a time dif-ference of half the switching period Ts/2. If the two transformers share a magneticcore and an antiparallel diode D2 is connected across Q2, the transformer core canbe magnetically reset through primary winding Np2 and D2 when Q1 is off. Likewise,inserting an antiparallel diode D1 across Q1, the transformer core can be magneticallyreset through primary winding Np1 and D1 when Q2 is off. Thus, the two magnetic corereset circuits are redundant and can be removed, as shown in Figure 1.7b. Exchang-ing the positions of Q1(D1) and primary winding Np1 leads to the circuit shown inFigure 1.7c. There is current flowing through each of the two primary windings when

* *

Q1

DR1

* Tr1

DFW

Dr1

NP1 NS1

Nr1vp1

+

_

+

_vsec1

Lf

Cf

RLd

Vo

+

_vrect

+

_

* *

Q2

DR2

*

Tr2

Dr2

Np2 Ns2

Nr2vp2

+

_

+

_vsec2

Cd1

Cd2

Vin

* *

Q1

DR1

*

TrDFW

Dr1

Np1 Ns1

Nr1vp1

+

_

+

_vsec1

Lf

Cf

RLd

Vo

+

_vrect

+

_

* *

Q2

DR2

*

Dr2

Np2 Ns2

Nr2vp2

+

_

+

_vsec2

Cd1

Cd2

Vin

D1

D2

(a) (b)

*

Q1

Np1

*

Q2

Np2

D1

D2

Tr

Tr

DR1

DR2

*

*

Ns1

Ns2

Cd1

Cd2

VinVin

vrect+

Lf

Cf

RLd

Vo

+

__

DFW

*

Q1

Np

Q2

D1

D2

Tr

Tr

DR1

DR2

*

*

Ns1

Ns2

Cd1

Cd2

vrect+

Lf

Cf

RLd

Vo

+

__

DFW

(c) (d)

Figure 1.7 Derivation of the half-bridge converter: (a) two single-switch forward convertersconnected in series at the input side and in parallel at the secondary rectifiers, sharing thefreewheeling diode and the output filter, (b) the two transformers sharing a magnetic core,(c) the positions of Q1 and primary winding Ns interchanged, and (d) the final configurationof the half-bridge converter


Q1 and Q2 conduct in turn. Since the nonpolarity-marked terminals of the two primarywindings are connected, the polarity-marked terminals have the same voltage poten-tial and can be connected. It is obvious that the two primary windings are in parallel,and one of them can be removed. Figure 1.7d shows the final configuration of the con-verter, which is the half-bridge converter. As in the case of the push–pull converter,the freewheeling diode DFW can be removed and DR1 and DR2 conduct simultaneouslywhen Q1 and Q2 are off.

The half-bridge converter is equivalent to two single-switch forward converters con-nected in series at the input side. Thus, the voltage applied on the input side of eachforward converter is half the input voltage Vin/2 and the magnitude of the primarywinding voltage is Vin/2, which is half that of the push–pull converter. Key waveformsof the half-bridge converter are given in Figure 1.6, with Vin replaced by Vin/2. As inthe push-pull converter, the transformer of the half-bridge converter is bidirectionallymagnetized.

The voltage stress of the power switches in the half-bridge converter is 2 ⋅Vin/2=Vin;in fact, it can be seen from Figure 1.7d that when either switch is conducting, the othermust withstand Vin.

1.2.4 Full-Bridge Converter

The dual-switch forward converter was derived in Section 1.2.1 and is redrawn inFigure 1.8a for convenience. This converter has an alternative configuration, shownin Figure 1.8b. When both switches conduct, the transformer is negatively magnetized;when the switches are off, the transformer is magnetically reset through diodes D1 andD4. The two kinds of dual-switch forward converter can be connected in parallel at theinput sides and the output rectifier, as shown in Figure 1.8c, where Q1(Q4) and Q2(Q3)operate at the same frequency and with a time difference of Ts/2. If the two transform-ers share a magnetic core and an antiparallel diode is connected to each switch, asshown in Figure 1.8d, then the transformer can be magnetically reset through primarywinding Np2 and the antiparallel diodes of Q2 and Q3, or through primary windingNp1 and the antiparallel diodes of Q1 and Q4. Consequently, diodes D1 to D4 can beremoved. Since the two primary windings have the same voltage waveforms, points A1and A2 and points B1 and B2 can be connected, respectively. Thus, the two primarywindings are in parallel, and one can be removed, resulting in the circuit shown inFigure 1.8e. This is the full-bridge converter. Similarly, the freewheeling diode DFWcan be removed. For brevity of illustration, the antiparallel diodes of Q1 to Q4 arelabeled D1 to D4.

The transformer of the full-bridge converter is bidirectionally magnetized, and themagnitude of the primary winding voltage is Vin, which is the same as that of thepush–pull converter and twice that of the half-bridge converter. The voltage stress ofthe power switches of the full-bridge converter is Vin, which is the same as that of thedual-switch forward converter.


*Np

Tr

D2

Q4

Q1

Vin Vin

D3

*

DR

DFW

Lf

Cf

RLd

Vo

+

_Ns

*Np

Tr

D1

Q3

Q2

D4

*

DR

DFW

Lf

Cf

RLd

Vo

+

_

Ns

(a) (b)

*Np1

Tr1

D2

Q4

Q1

Vin

D3

*Np2

Tr2

D1

Q3

Q2

D4

*

*

Ns1

Ns2

DR1

DR2

DFWLf

Cf

RLd

Vo

+

_vrect+

_*Np1

Tr1

Q4

Q1

Vin

*Np2

Tr2

Q3

Q2

*

*

Ns1

Ns2

DR1

DR2

DFWLf

Cf

RLd

Vo

+

_vrect

+

_

A1

B1

A2

B2

(c) (d)

Q1

Vin

D1

Q3 Q4

Q2 D2

D4D3

*Np

DR1

DR2

*

*

Ns1

Ns2

vrect+

Lf

Cf

RLd

Vo

+

__

DFW

(e)

Figure 1.8 Derivation of the full-bridge converter: (a) dual-switch forward converter,(b) alternative configuration of the dual-switch forward converter, (c) two kinds of dual-switchforward converter connected in parallel at the input sides and the output rectifier, (d) thetwo transformers sharing a magnetic core, and (e) final configuration of the full-bridgeconverter

1.2.5 Comparison of Isolated Buck-Derived Converters

From the derivation of the forward converter (including single-switch and dual-switchversions), the push–pull converter, the half-bridge converter, and the full-bridge con-verter, it can be concluded that all of these isolated converters are originated from thebuck converter. Table 1.1 provides a comparison.


Table 1.1 Comparison of isolated buck-derived converters

Convertertype

Voltagestress ofpower

switches

Primary-to–secondary-winding-turns ratio

Currentstress ofpower

switches

Numberof powerswitches

Totalpower

handlingcapacityof powerswitches

Ripplefrequency of

secondaryrectifiedvoltage

Maximumduty

cycle ofsecondaryrectifiedvoltage

Single-switchforward

2Vin K0 Io/K0 1 2VinIo/K0 fs 0.5

Dual-switchforward

Vin K0 Io/K0 2 2VinIo/K0 fs 0.5

Push–pull 2Vin 2K0 Io/(2K0) 2 2VinIo/K0 2fs 1Half-bridge Vin K0 Io/K0 2 2VinIo/K0 2fs 1Full-bridge Vin 2K0 Io/(2K0) 4 2VinIo/K0 2fs 1

1. Voltage stress of power switches: The power switches of the single-switch for-ward converter and the push–pull converter have to withstand twice the input volt-age, while the power switches of the dual-switch forward converter, the half-bridgeconverter, and the full-bridge converter are required to withstand the input voltage.Thus, the single-switch forward converter and the push–pull converter are suit-able for low-voltage applications, while the dual-switch forward converter, thehalf-bridge converter, and the full-bridge converter are suitable for high-voltageapplications.

2. Transformer primary-to-secondary-winding-turns ratio: The maximum dutycycle of the forward converter (including single-switch and dual-switch versions)is limited to 0.5 and the maximum duty cycle of the push–pull converter, thehalf-bridge converter, and the full-bridge converter can reach unity. Under condi-tions of the same input and output voltages, if the transformer winding turns ratio ofthe forward converter is K0, the transformer-winding-turns ratios of the push–pullconverter and of the full-bridge converter should be 2K0. For the half-bridge con-verter, although its duty cycle can reach unity, the magnitude of the primary voltageis half of the input voltage, so its transformer-winding-turns ratio is K0.

3. Current stress of power switches: Neglecting the output filter inductor currentripple, the current stresses of the power switches of the forward converter and ofthe half-bridge converter are both Io/K0, while the current stresses of the powerswitches of the push–pull converter and of the full-bridge converter are bothIo/(2K0), where Io is the output current.

4. Total power handling capacity of power switches: The power handling capacityof a power switch is defined as the product of the voltage stress and current stressimposed on the power switch. From the preceding analysis, it can readily beseen that the total power handling capacity (i.e., the number of power switches


multiplied by each power switch’s power handling capacity) of the five isolatedbuck-derived converters is 2VinIo/K0. This means that for the same input andoutput, the total power handling capacities of switches of all five converters arethe same. In other words, if the power switches have the same voltage and currentratings, the output power the converter can handle is proportional to the numberof power switches. Of the five isolated buck-derived converters, the full-bridgeconverter has the most power switches (four) and the highest power handling capa-bility. Therefore, the full-bridge converter has been widely used in medium-to-high-power-conversion applications.

5. Output filter: For the forward converter, the ripple frequency of the secondaryrectified voltage is the switching frequency fs and the maximum duty cycle islimited to 0.5. For the push–pull converter, the half-bridge converter, and thefull-bridge converter, the secondary rectified voltage has a ripple frequency of 2fsand a maximum duty cycle of 1. Therefore, for the same output voltage, the sec-ondary rectified voltages of the push–pull converter, the half-bridge converter, andthe full-bridge converter have smaller amounts of high-frequency harmonics thanthat of the forward converter, and thus the required output filter is much smaller.

1.3 Output Rectifier Circuits

Section 1.2 presented the derivations of the forward converter (including single-switchand dual-switch versions), the push–pull converter, the half-bridge converter, andthe full-bridge converter. The output rectifier circuit of the forward converter is ahalf-wave rectifier circuit, while those of the push–pull converter, the half-bridgeconverter, and the full-bridge converter are full-wave rectifier circuits. In fact, sincethe push–pull converter, the half-bridge converter, and the full-bridge converterall transfer energy from the input to the load during both the positive and the neg-ative half-periods, they can all also adopt the full-bridge rectifier circuit and thecurrent-doubler rectifier circuit. In this section, the half-wave rectifier circuit, thefull-bridge rectifier circuit, and the current-doubler rectifier circuit will be derivedfrom the half-wave rectifier circuit. The purpose of this is to reveal the relationshipamong these output rectifier circuits.

1.3.1 Half-Wave Rectifier Circuit

Figure 1.9a and Figure 1.9b show the positive and negative half-wave rectifier circuits,respectively. The two half-wave rectifier circuits can only transfer energy to load in thepositive or negative half-period of transformer primary voltage vp. The key waveformsare depicted in Figure 1.10, from which it can be seen that:

1. The output voltage Vo can be derived as:

Vo = DhVpm∕K (1.4)


Tr

DR1 DFW1

*

Lf

Cf

RLd

*Vo

+

_vp

+

_vsec1

+

_vrect

+

_

iLf

Tr

DR2

**DFW2

Lf

Cf

RLd

Vo

+

_

vp

+

_vsec2

+

_

vrect

+

_

iLf

(a) positive half-wave rectifier circuit (b) negative half-wave rectifier circuit

Figure 1.9 Two kinds of half-wave rectifier circuit

t

t

vrect

Ts/2 Ts

0

0

iLf

vsec1

0

t

Vpm/K

Vo

Io

Vpm /K

0

Vpm /K

t

t

vrect

0

0

iLf

vsec2

0

t

Vpm/K

Vo

Io

0

Vpm/K

Ts/2 Ts

Vpm/K

(a) Positive half-wave rectifier circuit (b) Negative half-wave rectifier circuit

Figure 1.10 Waveforms of two kinds of half-wave rectifier circuit

where Vpm is the magnitude of the transformer primary voltage, Dh is the dutycycle of the half-wave rectifier circuit, which is the ratio of the width of thepositive (or negative) half-period to the switching period, and K is the primary-to-secondary-winding-turns ratio.

2. The ripple frequency of the rectified voltage and output filter inductor current isthe switching frequency.

3. The voltage stress of both the rectifier diode and the freewheeling diode is Vpm/K.

1.3.2 Full-Wave Rectifier Circuit

If the transformer is expected to transfer energy to the load during both positive andnegative half-periods, the positive and negative half-wave rectifier circuits should becombined, as shown in Figure 1.11a. As illustrated in Section 1.2, when vp is equal tozero, the output filter inductor can freewheel through freewheeling diodes DFW1 andDFW2 or through two secondary windings via DR1 and DR2. Therefore, DFW1 and DFW2


DR2

DFW1DR1

DFW2

Lf

Cf

RLd

Vo

+

_vrect

+

_

Tr

*

*

* vsec1

+

_

vsec2

+

_

vp

+

_

Tr

DR2

*

*

Lf

Cf

RLd

*

DR1

Vo

+

_vsec1

+

_

vsec2

+

_

vp

+

_

vrect

+

_

(a) With freewheeling diodes (b) Without freewheeling diodes

Figure 1.11 Full-wave rectifier circuit

t

t

vrect

0

vsec1vsec2

0

Vpm/K

Vo

Vpm/K

Vpm/K

0

iLf

t

Io

0 Ts/2 Ts

0

iDR1

t

Io

iDR2

Figure 1.12 Key waveforms of the full-wave rectifier circuit

are redundant and can be removed, as shown in Figure 1.11b. Thus, the full-waverectifier circuit is obtained. Figure 1.12 shows the key waveforms of the full-waverectifier circuit, from which we see that:

1. The output voltage Vo is given by:

Vo = 2DhVpm∕K = DyVpm∕K (1.5)

where Dy is the duty cycle of the secondary rectified voltage, which is the ratioof the pulse width of the secondary rectified voltage to half the switching period.Here, Dy is twice the duty cycle of the half-wave rectifier circuit; that is, Dy = 2Dh.

2. The ripple frequency of the rectified voltage and the output filter inductor currentis twice the switching frequency.


3. The voltage stress of the two rectifier diode is 2Vpm/K. During the freewheelingperiod, the two rectifier diodes share the output filter inductor current.

From Equations 1.4 and 1.5, it can be seen that the output voltage of the full-waverectifier circuit is twice that of the half-wave rectifier circuit when Dh is the same. Thisis because with the full-wave rectifier circuit, voltage is applied on the output filter inboth the positive and the negative half-periods. If the output voltage stays the same, thetransformer-turns ratio of the full-wave rectifier circuit is twice that of the half-waverectifier circuit and the voltage stresses of the rectifier diodes of the two kinds ofrectifier circuit are equal. Compared with the half-wave rectifier circuit, the ripplefrequency of the secondary rectified voltage is doubled and the switching-frequencyharmonics are significantly reduced. Thus, the output filter can be drastically reduced.

1.3.3 Full-Bridge Rectifier Circuit

In the full-wave rectifier circuit, the transformer has two secondary windings, witheach one only conducting for a half-period. If the secondary winding can conductcurrent during both positive and negative half-periods, the utilization is increasedand one secondary winding can be removed, leading to a simple configuration of thetransformer. Figure 1.13a shows the rectifier circuit with only one secondary winding

TrDR1

DFW1

*

Lf

Cf

RLd

*

DR2

DFW2

Vo

+

_vp

+

_vsec

+

_

TrDR1

DFW1

*

Lf

Cf

RLd

*

DR2

DFW2

DR3

DR4

Vo

+

_vp

+

_vsec

+

_

(a) (b)

(c) (d)

vp

+

_vsec

+

_

Tr

DFW1

*

Lf

Cf

RLd

*

DFW2

Vo

+

_

DR1 DR2

DR3 DR4

Tr**

DR1 DR2

DR3 DR4

Lf

Cf

RLd

Vo

+

_

vp

+

_vsec

+

_

iLf

vrect

+

_

Figure 1.13 Derivation of the full-bridge rectifier circuit: (a) preliminary bidirectional rec-tifier circuit with one secondary winding, (b) bidirectional rectifier circuit with one secondarywinding, (c) full-bridge rectifier circuit with freewheeling diodes, and (d) full-bridge rectifiercircuit


t

t

vrect

0

vsec

0

Vpm/K

Vo

Vpm/K

Vpm/K

0

iLf

t

Io

0 Ts/2 Ts

0

iDR1

t

Io

iDR2iDR3 iDR4

Figure 1.14 Key waveforms of the full-bridge rectifier circuit

conducting current bidirectionally, where DR1 and DFW1 are the rectifier diode andfreewheeling diode of the positive half-wave rectifier circuit, respectively, and DR2and DFW2 are the rectifier diode and freewheeling diode of the negative half-wave rec-tifier circuit, respectively. However, such an arrangement leads to short-circuit of thesecondary winding; diodes DR4 and DR3 should be inserted to avoid this, as shownin Figure 1.13b. Redrawing the circuit in Figure 1.13b as Figure 1.13c, it can easilybe seen that the output filter inductor current can freewheel through DFW1 or DFW2,or through the branch consisting of DR1 and DR3, or through the branch consisting ofDR2 and DR4. Therefore, DFW1 and DFW2 are redundant and can be removed, leadingto the well-known full-bridge rectifier circuit, as shown in Figure 1.13d.

Figure 1.14 shows the key waveforms of the full-bridge rectifier circuit, from whichwe can conclude the following:

1. The expression of the output voltage is the same as Equation 1.5.2. As in the full-wave rectifier circuit, the ripple frequency of the rectified voltage

and output filter inductor current is twice the switching frequency.3. The voltage stress of all of the rectifier diodes is Vpm/K. During the freewheeling

period, the rectifier diodes share the output filter inductor current.

1.3.4 Current-Doubler Rectifier Circuit

The positive and negative half-wave rectifier circuits are redrawn in the forms shownin Figure 1.15a and Figure 1.15b, respectively. If the two rectifier circuits share the


DR1

DR1

DR2 DR2

DR1

RLd RLd RLdDFW1

DFW2

**Np Ns Np Ns Np Ns

Cf CfCf

Vo Vo Vo

io

iLf 2

iLf1Tr Tr Tr

Lf1

Lf 2

Lf 1

vrect

Lf 2

+

_ **

+

_ **

+

_

+

_

(a) (b) (c)

Figure 1.15 Derivation of the current-doubler rectifier circuit: (a) positive half-wave rectifiercircuit, (b) negative half-wave rectifier circuit, and (c) current-doubler rectifier circuit

t

t

0

0

Vo

Io

Io

Io/2

Ts/2 Ts

iDR2

iLf 2iLf 1

iDR1

0 t

00 t

vsecVpm/K

Vpm/K

Vpm/K

vrect

iLf 1+iLf 2

Figure 1.16 Key waveforms of the current-doubler rectifier circuit

same set of transformer, rectifier diode, and freewheeling diode, the current-doublerrectifier circuit is obtained, as shown in Figure 1.15c, where two output filter inductorcurrents are supplied to the output filter capacitor and load. Figure 1.16 shows thekey waveforms of the current-doubler rectifier circuit, whose characteristics are asfollows:

1. It can be treated as the parallel of the positive and negative half-wave rectifiercircuits. The expression of the output voltage is thus the same as that of the


half-wave rectifier circuit; that is, Equation 1.4. In other words, with the sametransformer-turns ratio, the output voltage of the current-doubler rectifier circuitis half that of the full-wave rectifier circuit or the full-bridge rectifier circuit.

2. The two output filter inductor currents pulsate at the switching frequency with aphase shift of 180∘ and the output current io is the sum of the two output filter induc-tor currents and ripples at twice the switching frequency. Since two output filterinductor currents have a phase shift of 180∘, the current ripples at the switching fre-quency and its odd multiples are cancelled in the output current, which means thatthe ripple of io is smaller than the individual output filter inductor current ripple.

3. The voltage stress of the two rectifier diodes is Vpm/K. Under conditions of thesame input and output voltages, and with the same duty cycle Dh, the transformer-winding-turns ratio of the current-doubler rectifier circuit is half that of thefull-wave rectifier circuit and the full-bridge rectifier circuit. Therefore, the volt-age stress of the rectifier diodes is equal to that of the full-wave rectifier circuit anddouble that of the full-bridge rectifier circuit.

From this analysis, it can be concluded that the full-wave rectifier circuit, thefull-bridge rectifier circuit, and the current-doubler rectifier circuit can be derivedfrom the half-wave rectifier circuit. Table 1.2 compares the three kinds of rectifiercircuit, which can be described as follows:

1. Transformer primary-to-secondary-winding-turns ratio: The full-wave recti-fier circuit and the full-bridge rectifier circuit can be treated as a series connec-tion of positive and negative half-wave rectifier circuits, while the current-doublerrectifier circuit can be treated as a parallel connection of positive and negativehalf-wave rectifier circuits. Therefore, when operating with the same duty cycleDh and transformer primary-to-secondary-winding-turns ratio, the output voltageof the full-wave rectifier circuit and the full-bridge rectifier circuit is twice thatof the current-doubler rectifier circuit. In other words, if under the same input andoutput voltages, the transformer-turns ratio of the full-wave rectifier circuit and thefull-bridge rectifier circuit is K0, that of the current-doubler rectifier circuit shouldbe K0/2.

Table 1.2 Comparison of three kinds of rectifier circuit

Rectifier circuit type Transformerprimary-to-secondary-turns ratio

Voltagestress ofrectifierdiodes

Currentstress ofrectifierdiodes

Number ofrectifierdiodes

Total powerhandling

capacity ofrectifier diodes

Full-wave rectifier K0 2Vin/K0 Io 2 4VinIo/K0Full-bridge rectifier K0 Vin/K0 Io 4 4VinIo/K0Current-doubler rectifier K0/2 2Vin/K0 Io 2 4VinIo/K0


2. Voltage stress of rectifier diodes: The voltage stress of the rectifier diodes of thefull-wave rectifier circuit and the current-doubler rectifier circuit is 2Vin/K0, whilethat of the rectifier diodes of the full-bridge rectifier circuit is Vin/K0, where Vin isthe input voltage.

3. Current stress of rectifier diodes: Neglecting the output filter inductor currentripple, the current stress of the rectifier diodes in all three rectifier circuits is theoutput current Io.

4. Total power handling capacity of rectifier diodes: The power handling capacityof a rectifier diode is defined as the product of the voltage stress and the currentstress of the rectifier diode. From the preceding discussion, it can be seen thatthe total power handling capacity of the rectifier diodes (i.e., the power handlingcapacity of each rectifier diode multiplied by the number of rectifier diodes in allthree rectifier circuits) is equal to 4VinIo/K0.

1.4 Basic Operating Principle of Full-Bridge Converters

1.4.1 Topologies of Full-Bridge Converters

Since the transformer of the full-bridge converter transfers energy from the inputto the load during both the half-periods, the rectifier circuit of the full-bridge con-verter can be either the full-wave rectifier circuit, the full-bridge rectifier circuit, orthe current-doubler rectifier, as shown in Figure 1.17.

1.4.2 Pulse-Width Modulation Strategies for Full-Bridge Converters

Figure 1.18 shows the commonly used PWM strategies for the full-bridge converter.In the basic PWM strategy, the two diagonal switches of the two legs turn on and offsimultaneously, as shown in Figure 1.18a. The two switches in one bridge leg canalso be operated in a PWM fashion, and the two in the other bridge leg in a comple-mentary manner with 50% duty cycle, as shown in Figure 1.18b. Figure 1.18c showsthe well-known phase-shift control, where the switches of each bridge leg operatecomplementarily with 50% duty cycle and a phase-shift is introduced between thetwo legs. Regulation of the output voltage can thus be achieved by controlling thephase-shift.

1.4.3 Basic Operating Principle of a Full-Bridge Converterwith a Full-Wave Rectifier Circuit and a Full-BridgeRectifier Circuit

Regardless of the kind of PWM strategy adopted, the operating principle of thefull-bridge converter with a full-wave rectifier circuit is the same. In the following,the basic strategy is used for illustration. Figure 1.19 shows the key waveforms of the


*

*

*

+

_

+

_

A B

C

D

A B

*

*

DR2+

_

+

_

*

+

_

O

C

ip

A B

*

Vin

Vin

Vin

vrect

vrect

Tr

Tr

Np Ns

Tr

Np Ns

Lf

Lf

iLf

iLf

Lf1

iLf1

Lf 2

iLf2

Cf

Cf

ip

ip

io

Q2

Q4

Q2

Q4

Q1

Q1

D1 D2

D4

D2

D4

Q2

Q4

D2

D4

DR1

DR1

DR3

DR2

DR1

DR4

RLd

Cf

RLd

RLd

D3

D1

D3

Q3

Q3

Q1 D1

D3Q3

(a) With full-wave rectifier circuit

(b) With full-bridge rectifier circuit

(c) With current-doubler rectifier circuit

Vo

Vo

Vo

Figure 1.17 Full-bridge converter with different output rectifier circuits


t

t0

t

t0

(b) One leg PWM operated and the other operatingin symmetrical complementary manner

tQ1 Q3 Q1

t0

Q4 Q2 Q4

Q1 Q3

Q2

Q1

Q4Q4

Q1 Q3

Q2

Q1

Q4Q4

(a) Diagonal switches turning on and off simultaneously

(c) Phase-shifted control

Ts/2 TsTon

Ts/2 TsTon

Ts/2 TsTon

Figure 1.18 Widely used modulation strategies for the full-bridge converter

full-bridge converter with a full-wave rectifier circuit, while the equivalent circuits ofthe topological modes are depicted in Figure 1.20.

When the diagonal switches Q1 and Q4 are conducting, as shown in Figure 1.20a, thevoltage across the midpoints of the bridge legs vAB is equal to Vin, the secondary rec-tifier diode DR1 conducts, and the secondary rectified voltage vrect is equal to Vin/K,where K is the transformer primary-to-secondary-winding-turns ratio. The voltageapplied across the output filter inductor Lf is Vin/K−Vo, which causes the inductorcurrent iLf to increase linearly. The primary current ip is equal to the output filterinductor current reflected to the primary side (i.e., ip = iLf/K), and correspondinglyit increases linearly. Also, ip flows through Q1 and Q4.

When the diagonal switches Q2 and Q3 are conducting, as shown in Figure 1.20b,vAB =−Vin, DR2 conducts, vrect =Vin/K, and iLf increases linearly.

When all of the power switches are off, the primary current ip is zero and theoutput filter inductor current freewheels through the two rectifier diodes as shown inFigure 1.20c. The two rectifier diodes shares the output filter inductor current (i.e.,iDR1 = iDR2 = iLf/2). Since both rectifier diodes are conducting, the two secondarywinding voltages are clamped to zero. Thus, vrect = 0 and the voltage applied to theoutput filter inductor is −Vo. This negative voltage makes iLf decay linearly. If the


t

t

0

0

0 t

00 t

t0

0 t

t

t

0

0

0 t

00 t

t0

0 t

Q1&Q4 Q2&Q3 Q1&Q4 Q1&Q4 Q2&Q3 Q1&Q4

Ts/2 TsTs/2 Ts

VinVinvAB vAB

ip ip

Vin

Vo

Io

Io

Vo

Io

Vin/K Vin/K

Vin

vrect

iLf

iDR1 iDR4

iDR1iDR4

iDR2 iDR3

iDR2iDR3

iLf

vrect

(a) Continuous current mode (b) Discontinuous current mode

Figure 1.19 Key waveforms of the full-bridge converter with full-wave rectifier circuit

load is light or the output filter inductor is small, iLf may decay to zero before one pairof diagonal switches is turned on; it is then kept at zero, as shown in Figure 1.20d.Under this condition, the full-bridge converter operates in discontinuous currentmode (DCM). The corresponding waveforms are sketched in Figure 1.19b.

The operating principle of the full-bridge converter with a full-bridge rectifier cir-cuit is similar to that of one with a full-wave rectifier circuit. The key waveforms aregiven in Figure 1.19, where the rectifier diode current waveforms are shown. For theequivalent circuits, the primary side is the same, while the secondary side is shownin the dashed block in Figure 1.20. The difference between the two rectifier circuitsis that, for the full-bridge rectifier circuit, when all of the power switches are off,the output filter inductor current freewheels through the four rectifier diodes, whilethe secondary winding current is zero.

1.4.4 Basic Operating Principle of a Full-Bridge Converterwith a Current-Doubler Rectifier Circuit

The full-bridge converter with a current-doubler rectifier circuit is shown inFigure 1.17c. The operation of a converter adopting the basic PWM strategy (see


*

*

*

+

_

+

_

B

B

*

*

+

_

+

_

A B

*

*

+

_

+

_

*

*

*

+

_

+

_

*

*

+

_

+

_

*

*

*

+

_

+

_

C

D *

*

*

+

_

+

_

D

C

*

*

+

_

+

_

Vin

ip

ip

ip

ip

Vin

Q1 D1

DR1

DR1

DR1 DR2

DR3 DR4

DR2 DR2

DR2

DR3 DR3DR4

D3Q3

A

Q1 D1

D3Q3

A

A

BA

Q2

Q4

D2

D4

BQ2

Q4

D2

D4

BVin

Q1 D1

D3Q3

AQ2

Q4

D2

D4

CTr

Tr

Tr

Tr

Np Ns

DR1

DR2

D

vrect

vrect

Lf

iLf

Lf

iLf

Lf

iLf

Lf

iLf

Cf

Cf

Cf

Cf

RLd

RLd

RLd

RLd

Vo

Vo

Vo

Vo

Vo

B

ip

DR1DR2

DR4

A

TrNp Ns

Np Ns Ns

vrect

vrect

vrectip

DR1 DR2

DR3 DR4

BA

Tr

Lf

iLf

Cf

RLd

VoNp vrect

ip

Vin

DR1

Q1 D1

D3Q3

A BQ2

Q4

D2

D4

Tr

Lf

iLfCf

RLd

vrect

Lf

iLf

Cf

RLd

Vo

ipC

TrDR1

DR2

D

vrect

Lf

iLfCf

RLd

Vo

(a) Q1 and Q4 are conducting (b) Q2 and Q3 are conducting

(c) All power switches are off (d) Output filter inductor current is zero

Figure 1.20 Equivalent circuit of switching modes of the full-bridge converter


Figure 1.18a) is different from that of one adopting either of the other two PWMstrategies (see Figure 1.18b,c).

1.4.4.1 Basic PWM Strategy

At Heavy LoadThe key waveforms of the full-bridge converter with a current-doubler rectifier circuitunder heavy load condition are shown in Figure 1.21a. When the diagonal powerswitches Q1 and Q4 conduct, the secondary rectifier diode DR1 also conducts, as shownin Figure 1.22a. During this interval, vAB =Vin and vCO =Vin/K. The voltage across Lf1is Vin/K−Vo and iLf1 increases linearly, while the voltage across Lf2 is −Vo and iLf2decreases linearly. The primary current ip is equal to iLf1 reflected to the primary side(i.e., ip = iLf1/K) and increases linearly. The output current io is the sum of the twooutput filter inductor currents (i.e., io = iLf1 + iLf2) and also increases linearly.

t0

0 t

00 t

t0

0

0

t

t

t0

Vin

0 t

0 t

t0

0

0

t

t

0

Q1&Q4 Q2&Q3 Q1&Q4 Q1&Q4 Q2&Q3 Q1&Q4

Vin Vin

Vin

vABvAB

vCO

ip ip

vCO

Io

Io/2

Vo Vo

KVo

Vin/K

Vin/K

iDR1 iDR2

iDR1 iDR2

Ts/2 TsTon Ts/2 TsTon Tr

iLf 1

iLf 1 iLf 2

iLf 2

iLf 1+iLf 2

iLf 1+iLf 2

(a) At heavy load (b) At light load and iLf 1 and iLf 2 keep positive

Figure 1.21 Key waveforms of the full-bridge converter with current-doubler rectifier circuitunder the basic PWM strategy


t0

0 t

0 t

t0

0

0

t

t

0

t0

0 t

00 t

t0

0

0

t

t

Q1&Q4 Q2&Q3 Q1&Q4 Q1&Q4 Q2&Q3 Q1&Q4

Vin Vin

Vin

ip

KVo

Vo

vAB vAB

vCO

ip

vCOVin/K Vin/K

iLf 1 iLf 1iLf 2 iLf 2iLf 1+iLf 2 iLf 1+iLf 2

iDR1iDR1

iDR2iDR2

Ts/2 TsTon Ts/2 TsTon

(d) Discontinuous current mode (c) iLf 1 and iLf 2 are bidirectional

Figure 1.21 (Continued)

When Q1 and Q4 are turned off, iLf1 and iLf2 flow through DR2 and DR1, respectively,and ip becomes zero, as shown in Figure 1.22b. At this point, the voltages acrossthe two output filter inductors are all −Vo, making iLf1 and iLf2 decay linearly. Sinceboth DR1 and DR2 are conducting, vCO = 0 and the secondary winding voltage is zero.Correspondingly, the primary voltage vAB = 0.

The operation when Q2 and Q3 are conducting is similar to that when Q1 and Q4 areconducting, which is omitted here.

At Light Load when Output Filter Inductor Currents are Positive as DiagonalSwitches ConductAs just discussed, when Q1 and Q4 are turned off, iLf1 and iLf2 freewheel through DR2and DR1, respectively, and both decay linearly, as shown in Figure 1.22b. If the load isvery light or the output filter inductor is not large enough, iLf2 will decay to zero andDR1 will turn off naturally, as shown in Figure 1.22c. Following this, iLf2 is kept at zerountil Q2 and Q3 are turned on, as shown in the dashed lines within interval [Tr,Ts/2]in Figure 1.21b. During this interval, vAB =−KVo and vCO = 0. Similarly, when iLf1decays to zero, it stays at zero, as shown in the dashed lines in Figure 1.21b. Duringthis interval, vAB =KVo and vCO =Vo.


*

+

_

* O **

*

*

+

_ *

+

_

*

C

ip

Vin

DR2

DR1

Q1 D1

D3Q3

A BQ2

Q4

D2

D4

Tr

Lf1

iLf1

Lf 2

iLf 2

Cf

RLd

VoNp Ns

io

Q

O

C

ip

Vin

DR2

DR1

Q1 D1

D3Q3

A BQ2 D2

D4

Tr

Lf 1

iLf1

Lf 2

iLf 2

Cf

RLd

VoNp Ns

io

O

C

ip

Vin

DR2

DR1

Q1 D1

D3Q3

A BQ2

Q4

D2

D4

Tr

Lf1

iLf1

Lf 2

iLf 2

Cf

RLd

VoNp Ns

io

Q4

+

_

O

C

ip

Vin

DR2

DR1

Q1 D1

D3Q3

A BQ2 D2

D4

Tr

Lf 1

iLf1

Lf 2

iLf 2

Cf

RLd

VoNp Ns

io

(a) Q1 and Q4 are conducting (b) All switches are off and iLf 2 >0

(c) All switches are off and iLf 2 = 0 (d) All switches are off and iLf 2 < 0

Figure 1.22 Equivalent circuits of switching modes of the full-bridge converter withcurrent-doubler rectifier circuit under the basic PWM strategy

At Light Load when Output Filter Inductor Current becomes Negativeas Diagonal Switches ConductWhen Q1 and Q4 are conducting, iLf1 increases, iLf2 decays, and ip is equal to thereflected iLf1 (i.e., ip = iLf1/K). If the load becomes lighter, iLf2 will cross zero and con-tinue flowing in the negative direction. When Q1 and Q4 are turned off, iLf1 freewheelsthrough DR2 and decays linearly. Moreover, iLf2 flows through the secondary windingand is reflected to the primary side (i.e., ip =−iLf2/K). Thus, ip is positive and flowsthrough D2 and D3, as shown in Figure 1.22d. During this interval, vAB =−Vin and thevoltage across Lf2 is Vin/K−Vo, forcing iLf2 to increase linearly. When iLf2 increasesto zero, ip reduces to zero correspondingly. Since all the power switches are off, ipcannot flow in the reverse direction and must be kept at zero, which makes iLf2 stay atzero until Q2 and Q3 are turned on. It can be seen from Figure 1.21c that, compared


with Figure 1.21b, there are additional portions in vAB and vCO, shown as the dashedarea. Thus, Vo is equal to the average value of vCO, and clearly Vo is dependent notonly on the duty cycle but also on the load.

If the load continues to reduce, the hatched area shown in Figure 1.21c increasesto reach the turn-on instant of diagonal two switches, as shown in Figure 1.21d. Thismeans that at the turn-on instant of Q2 and Q3, iLf2 is still negative. When iLf2 increasesto zero, it can continue to flow in the positive direction, and it is continuous. Underthis condition, vAB becomes an ac square voltage with 180

∘ electrical degree, whilevCO becomes a pulse voltage with a magnitude of Vin/K and a pulse width of Ts/2. Theaverage value of vCO is equal to Vin/(2K). Since Vo is the average value of vCO, it isequal to Vin/(2K) and is independent of the duty cycle.

This analysis illustrates that, employing the basic PWM strategy, the output volt-age of the full-bridge converter with a current-doubler rectifier circuit is dependantnot only on the duty cycle but also on the load. Furthermore, the output voltage willlose control at light load. Therefore, the basic PWM strategy is not suitable for thefull-bridge converter with a current-doubler rectifier circuit.

1.4.4.2 Phase-Shifted Control

Figure 1.23 shows the key waveforms of the full-bridge converter with a current-doubler rectifier circuit when the phase-shifted control is adopted. At heavy load,the operation is the same as that adopting the basic PWM strategies, as shown inFigure 1.23a.

At light load, when Q1 and Q4 are conducting, iLf2 decays and becomes negative.When the leading-leg switches Q1 is turned off and Q3 is turned on, iLf1 is freewheelingthrough DR2 and decays linearly and iLf2 flows through the secondary winding and isreflected to the primary side (i.e., ip =−iLf2/K). Here, ip flows through D3 and Q4, asshown in Figure 1.24a. At this time, vAB = 0 and the voltage across Lf2 is still −Vo,meaning iLf2 continues to decay. Figure 1.23b shows the key waveforms under thiscondition.

If the load becomes lighter, the two output filter inductor currents decay linearlywhen vAB = 0. When iLf1 =−iLf2, DR2 is turned off, and iLf1 and iLf2 are kept unchanged.Thus, io = 0. At this time, the full-bridge converter operates in DCM. It should be notedthat, for the current-doubler rectifier circuit, “DCM” refers to the sum of the two out-put filter inductor currents flowing into the load being in discontinuous conduction;the two output filter inductor currents are not zero. Correspondingly, continuing cur-rent mode (CCM) refers to when the sum of two output filter inductor currents iscontinuous.

From this analysis, the following conclusions can be drawn:

1. When the phase-shifted control is adopted, regardless of whether the operationis in CCM or DCM, the output voltage of the full-bridge converter with a


t0

Vin

0 t

00 t

t0

0

0

t

t

t

t0

0 t

00 t

t0

0

0

t

t

t

iDR1

iDR1

iDR2

iDR2

iLf 1iLf 1

iLf 2

iLf 2

iLf 1+iLf 2

iLf 1+iLf 2

Vin

Vin/K

Vin

Vin

Vin/K

Q1 Q3 Q1 Q1 Q3 Q1

Q2 Q4Q4 Q2 Q4Q4

vAB

vCO

ip

vAB

vCO

ip

Io

Io

Io/2

Ts/2 TsTonTs/2 TsTon

(a) At heavy load (b) At light load and iLf 1 and iLf 2 are bidirectional

Figure 1.23 Key waveforms of the full-bridge converter with current-doubler rectifier circuitunder phase-shifted control

current-doubler rectifier circuit can be regulated by controlling the duty cycle.This is different from the basic PWM strategy.

2. If the output filter inductor current becomes negative in active mode (vAB =+Vin or−Vin), it will be reflected to the primary side when vAB = 0. The induced primarycurrent increases linearly. This can be used to achieve ZVS for the lagging leg,which will be discussed in Chapter 8.

The operation of the full-bridge converter with a current-doubler rectifier circuitemploying the PWM modulation strategy shown in Figure 1.18b is the same as thatusing a phase-shifted control. Details are omitted here.


t0

0 t

00 t

t0

0

0

t

t

t

0 t

Q1 Q3

Q2

Q1

Q4Q4

Ts/2 TsTon

Vin

Vin

Vin/K

vAB

vCO

ip

iDR1

iDR2

iLf 1 iLf 2iLf 1+iLf 2

(c) DCM

Figure 1.23 (Continued)

*

*

+

*

*

ip

Vin

Q1 D1

D3Q3

A

+

_

C

DR2

DR1

BQ2

Q4

D2

D4

Tr

Lf1

iLf1

(a) iLf1 > _ iLf 2 (a) iLf1 =

_ iLf 2

Lf 2

iLf 2

Cf

RLd

VoNp Ns

io ip

Vin

Q1 D1

D3Q3

A

+

_

C

DR2

DR1

BQ2

Q4

D2

D4

Tr

Lf1

iLf1

Lf 2

iLf 2

Cf

RLd

VoNp Ns

io

Figure 1.24 Equivalent circuits when Q3 and Q4 are conducting


1.5 Summary

This chapter introduced some development trends in the switching techniques,classifications, and requirements of power electronics converters, as well as thetypes and characteristics of dc–dc converters. The forward converter (includingsingle-switch and dual-switch versions), push–pull converter, half-bridge converter,and full-bridge converter were derived from the buck converter, in order to help read-ers understand more clearly the relationships among various isolated buck-derivedconverters. Meanwhile, the full-wave rectifier circuit, the full-bridge rectifier circuit,and the current-doubler rectifier circuit were derived from the half-wave rectifiercircuit. Again, the emphasis was on the relationships among these rectifier circuits.The basic operation of the full-bridge converter with full-wave rectifier circuit,full-bridge rectifier circuit, and current-doubler rectifier circuit was analyzed. Thebasic background necessary for study of the operation and design of soft-switchingPWM full-bridge converters has thus been provided.

References

1. Spiazzi, G., Buso, S., Citron, M. et al. (2003) Performance evaluation of a Schottky SiC power diodein a boost PFC application. IEEE Trans. Power Electron., 18 (6), 1249–1253.

2. Zhang, Q., Callanan, R., Das, M.K. et al. (2010) SiC power devices for microgrids. IEEE Trans.Power Electron., 25 (12), 2889–2896.

3. Oruganti, R. and Lee, F.C. (1985) Resonant power processors, part I: state plane analysis. IEEETrans. Ind. Appl., 21 (6), 1453–1461.

4. Oruganti, R. and Lee, F.C. (1985) State-plane analysis of parallel resonant converters. Proceedingof the IEEE Power Electronics Specialists Conference, pp. 56–73.

5. Lee, F.C. (1988) High-frequency quasi-resonant and multi-resonant converter technologies. Proceed-ing of the IEEE International Conference on Industrial Electronics, pp. 509–521.

6. Tabisz, W.A. and Lee, F.C. (1988) Zero-voltage-switching multi-resonant technique – A novelapproach to improve performance of high frequency quasi-resonant converters. Proceeding of theIEEE Power Electronics Specialists Conference, pp. 9–17.

7. Hua, G. and Lee, F.C. (1991) A new class of zero-voltage-switched PWM converters. Proceeding ofthe High Frequency Power Conversion Conference, pp. 244–251.

8. Barbi, I., Bolacell, J.C., Martins, D.C. and Libano, F.B. (1990) Buck quasi-resonant converter oper-ating at constant frequency: analysis, design and experimentation. IEEE Trans. Power Electron.,5 (3), 276–283.

9. Hua, G., Leu, C.S., Jiang, Y.M. and Lee, F.C. (1992) Novel zero-voltage-transition PWM converters.Proceeding of the IEEE Power Electronics Specialists Conference, pp. 55–61.

10. Hua, G., Yang, E.X., Jiang, Y.M. and Lee, F.C. (1993) Novel zero-current-transition PWM convert-ers. Proceeding of the IEEE Power Power Electronics Specialists Conference, pp. 538–544.

11. Divan, D.M. (1989) The resonant dc link converter – a new concept in static power conversion. IEEETrans. Ind. Appl., 25 (2), 317–325.

12. Erickson, R.W. and Maksimovic, D. (2001) Fundamentals of Power Electronics, 2nd edn, KluwerAcademic Publishers, Boston, MA.

topologies and operating principles of basic full-bridge ...the dual-switch forward converter,...

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