Page 1

Circuit Properties of Zero-Voltage-Transition PWM Converters 35

JPE 8-1-4

Circuit Properties of Zero-Voltage-Transition PWM Converters

Amir Ostadi*, Xing Gao* and Gerry Moschopoulos†

†*Dept. of Electrical and Electronics Eng., University of Western Ontario, London, Ontario, Canada

ABSTRACT

A zero-voltage-transition (ZVT) pulse width modulated (PWM) converter is a PWM converter with a single main power

switch that has an auxiliary circuit to help it turn on with zero-voltage switching (ZVS). There have been many

ZVT-PWM converters proposed in the literature as they are the most popular type of ZVS-PWM converters. In this paper,

the properties and characteristics of several types of ZVT-PWM converters are reviewed. A new type of ZVT-PWM

converter is then introduced, and the operation of a sample converter of this type is explained and analyzed in detail. A

procedure for the design of the converter is presented and demonstrated experimentally. The feasibility of the new

converter is confirmed with results obtained from an experimental prototype. Conclusions on the performance of

ZVT-PWM converters in general are made based on the efficiency results obtained from the experimental prototypes of

various ZVT-PWM converters of different types.

Keywords: Zero-voltage transition, PWM converters, Switch-mode power supplies, High-frequency converters

1. Introduction

High switching frequencies are used in power

converters to reduce the size and weight of their magnetic

and filter components, thus reducing overall converter size

and weight. Operating at higher switching frequencies,

however, increases switching losses, which reduces

converter efficiency. Converters operating with high

switching frequencies are, therefore, typically implemented

with zero-voltage switching (ZVS) to minimize these

problems. With ZVS, converter switches are made to

operate with a zero-voltage turn-on and turn-off.

In recent years, the most widely used single-switch

pulse-width modulated (PWM) ZVS power converters

have been so called zero-voltage-transition (ZVT) PWM

converters. There have been many previously proposed

ZVT-PWM converters (i.e.

certain common properties. These converters have an

auxiliary circuit connected in parallel to the main switch to

help it turn on with ZVS and a snubber capacitor to help

the switch turn off with ZVS, as shown in Fig. 1. They

operate in the same manner as regular PWM converters,

but with reduced switching losses. This reduction is due

to the fact that the auxiliary circuit operates for only a

small portion of the switching cycle and is activated just

before the main converter switch is about to be turned on.

Since the auxiliary circuit is on for such a short time, a

device with better switching characteristics than that used

as the main switch can be chosen, as conduction losses are

not an issue.

[1]-[14]) and they all share

Manuscript received Oct. 1, 2007; revised Nov. 19, 2007

†Corresponding Author: gmoschopoulos@eng.uwo.ca

Tel: 519-661-2111, Fax: 519-850-2436, Univ. of Western Ontario

*Dept. of Elec. and Comp. Eng. Univ. of Western Ontario

Page 2

36 Journal of Power Electronics, Vol. 8, No. 1, January 2008

The objectives of this paper are as follows:

(i) To review the basic circuit properties of ZVT-PWM

converters for design engineers who may not be

familiar with them;

(ii) To determine if it is possible to maximize the

efficiency of these converters using these circuit

properties.

In this paper, the properties and characteristics of

several types of ZVT-PWM converters are reviewed. A

new type of ZVT-PWM converter is then introduced and

the operation of an experimental converter of this type is

then demonstrated. The feasibility of the new converter is

confirmed with results obtained from an experimental

prototype. Conclusions on the performance of the

converter and on the performance of ZVT-PWM

converters in general are made based on efficiency results

obtained from experimental prototypes

ZVT-PWM converters that are representative of different

types.

of other

2. Non-Resonant and Resonant Auxiliary

Circuits in ZVT-PWM Converters

There have been many auxiliary circuits that have been

previously proposed for use in ZVT-PWM converters [14].

With few exceptions, auxiliary circuits in ZVT-PWM

converters are generally one of three types: non-resonant

circuits, resonant circuits that have an LC resonant

network placed in series with the auxiliary circuit switch,

or dual circuits that are a combination of the first two

types. The operation of a ZVT-PWM boost converter with

an experimental non-resonant and an experimental resonant

auxiliary circuit is reviewed in this section of the paper.

The operation of a ZVT-PWM boost converter with an

experimental dual circuit will be reviewed in the next section.

2.1 Non-Resonant Auxiliary Circuit

Consider the converter shown in Fig. 2 which is an

example of a ZVT-PWM converter with a non-resonant

auxiliary circuit [1]. The auxiliary circuit consists of a switch,

S2, an inductor, Lr, a capacitor, Cr, and two diodes, D2 and

D3. The circuit is a non-resonant circuit because there is no

capacitor in series with the auxiliary circuit inductor.

V in

C s1

C o

R

L in

S 1

D 1

Auxiliary

Circuit

a

b

c

Fig. 1 General structure of a ZVT PWM boost converter

Vin

Cs1

Lr

Co R

Lin

S1

S2

D1

D2

Cr

D3

Fig. 2 ZVT-PWM boost converter with non-resonant auxiliary

circuit

Iin

Vo

D1

Lr1

S2

Iin

C s1

S 2

L r1

I in

S2

Lr1

S1

(a) [t0-t1] (b) [t1-t2] (c) [t2-t3]

Iin

D2

Lr1

S1

Cr

I in

S 1

Iin

Cs1

(d) [t3-t4] (e) [t4-t5] (f) [t5-t6]

Vo

D3

Cr

Iin

Cs1

Iin

V o

D 1

(g) [t6-t7] (i) t > t7

Fig. 3 Modes of operation of a ZVT-PWM boost converter with

a non-resonant auxiliary circuit

Page 3

Circuit Properties of Zero-Voltage-Transition PWM Converters 37

Fig. 3 shows circuit diagrams of the modes of operation

that the converter shown in Fig. 2 goes through during a

switching cycle. For these diagrams, the input inductor, Lin,

is assumed large enough to be considered as a constant

current source, Iin, and the output capacitor, Co, is large

enough to be considered as a voltage source, Vo.. Typical

waveforms that illustrate the converter's operation are

shown in Fig. 4.

The converter works as follows: Before the auxiliary

switch S2 is turned on to help the main switch S1 turn on

with ZVS, current flows through the main power boost

diode D1. At some time t = t0, the auxiliary switch S2 is

turned on and current begins to be diverted from D1 to the

auxiliary circuit. Since there is an inductor in series with

the switch, it is turned on with zero-current switching

(ZCS) as the inductor slows down the rate of current rise

in the switch. At t = t1, there is no current flowing in D1

and capacitor Cs1 begins to discharge as the voltage across

it is now not clamped to the output voltage. Cs1 is totally

discharged at some time t = t2 and the body diode of S1

conducts current. S1 can be turned on with ZVS as the

voltage across Cs1 is almost zero.

Once S1 has been turned on, S2 can be turned off at

some time t = t3. When this happens, the current through

Lr is diverted to D2 and charges capacitor Cr and the

current in S1 stops flowing through the body diode and

instead flows through the switch. When the current

through Lr becomes zero at some time t = t4, the converter

then operates like a conventional PFC boost converter. S1

is turned off at t = t5 and capacitor Cs1 is charged until D3

begins to conduct at t = t6. Cr is eventually discharged

through D3 and current then flows through D1 at t = t7 until

S1 is turned on again to start a new switching cycle.

The following facts, which are true for all ZVT-PWM

converters with non-resonant auxiliary circuits, should be

noted:

(i) The current flowing through the auxiliary switch is

interrupted when the switch is turned off. Although

the switch has a hard turn-off that somewhat offsets

the gain in efficiency that is derived by having the

auxiliary circuit in the circuit, these turn-off losses are

still less than the turn-on losses of the main power

switch in a conventional PWM converter.

(ii) The operation of the auxiliary circuit in the converter

does not affect the voltage or current stress of the

main power switch or the main power boost diode.

Other non-resonant auxiliary circuits that can be used

in ZVT-PWM converters were proposed in [2], [4], [8], [9];

some of these are shown in Fig. 5. Regardless of how

these circuits may look, the fundamental circuit properties

of all non-resonant circuits are the same. The only real

difference is in the way that energy is transferred out of

the auxiliary circuit after the auxiliary switch is turned off.

2.2 ZVT-PWM Converter with Resonant Auxiliary

Circuit

Consider the converter shown in Fig. 6, which is an

example of a ZVT-PWM converter with a resonant

auxiliary circuit [5], [6]. The auxiliary circuit consists

S 1

S 2

V s1

I s1

I Lr

I in

V Cr

t 5 t 7

t 6

V o

t 0 t 1 t 2 t 3 t 4

Fig. 4 Typical waveforms of a ZVT-PWM boost converter

with a non-resonant auxiliary circuit

b

c

a

b

c

a

Fig. 5 Other non-resonant auxiliary circuits

Page 4

38 Journal of Power Electronics, Vol. 8, No. 1, January 2008

of a switch, S2, an inductor, Lr, a capacitor, Cr, and three

diodes, D2, D3 and D4. The purpose of D3 is to keep

current from flowing through the body diode of S2 so that

current can flow through D4, which is a faster device. The

circuit is a resonant circuit because there is a capacitor in

series with the auxiliary circuit inductor.

Fig. 7 shows the circuit diagrams of the modes of

operation that the converter shown in Fig. 6 goes through

during a switching cycle, while Fig. 8 shows typical

waveforms that illustrate the converter’s operation. The

converter works as follows: The auxiliary switch S2 is

turned on with ZCS at t = t0 and current begins to be

diverted from D1 to the auxiliary circuit. At t = t1,

capacitor Cs1 begins to discharge as there is no current

flowing in D1 and is totally discharged at some time t = t2

when the body diode of S1 conducts current. S1 can then

be turned on with ZVS.

Initially, during the time interval from t0 to t2 when

current is flowing through S2, the current through S2 rises,

but then begins to drop as capacitor Cr is being charged -

especially as Cs1 is being discharged and the net voltage

across Lr1 is negative. At t = t3, auxiliary circuit current

ILr2 becomes less than the input current Iin and, thus, the

current through S1 changes direction and stops flowing

through the body diode. ILr2 continues decreasing until it

becomes zero at t = t4 then reverses direction and flows

through D4 and S1, so that Cr can discharge; switch S2 can

be turned off softly while this is happening. At t = t5,

current stops flowing in the auxiliary circuit as the voltage

across Cr has become negative and there is no path for Cr

to discharge. The operation of the converter becomes

Vin

Cs1

Co

R

Lin

S1

D1

Cr

Lr

D2

S2

D4

D3

Fig. 6 ZVT-PWM boost converter with a resonant auxiliary

circuit

D 1

D 3

L r1

S 2

C r

I in

V o

Cs1

D 3

L r1

S2

C r

I in

S1

S2

D3

Lr1

Cr

I in

(a) [t0-t1] (b) [t1-t2] (c) [t2-t3]

C r

(d)[t3-t4] (e) [t4-t5] (f) [t5-t6]

S 1

S 2

D 3

L r1

I in

D 4

S1

L r1

C r

I in

I in

S1

(g)[t6-t7] (h) [t7-t8] (i) t > t8

Fig. 7 Modes of operation of a ZVT-PWM boost converter

with a resonant auxiliary circuit

I in

C s1

V o

D2

C r

I in

C s1

Vo

D1

I in

S1

S2

Vs1

Is1

ILr

Iin

Vo

VCr

t0t1t2t3

t 6

t4

t8

t7

t5

Fig. 8 Typical waveforms of a ZVT-PWM boost converter

with a resonant auxiliary circuit

Page 5

Circuit Properties of Zero-Voltage-Transition PWM Converters 39

identical to that of the converter shown in Fig. 2 until the

start of the next switching cycle.

The following facts, which are true for all ZVT-PWM

converters with resonant auxiliary circuits, should be

noted:

(i) The series inductor-capacitor components in the

auxiliary circuit force the auxiliary switch current to

drop to zero naturally so that there is no current

flowing through the auxiliary switch when the switch

is turned off. The switch is turned off softly while

current is flowing through diode D4, which is

anti-parallel to it.

(ii) The operation of the auxiliary circuit in the converter

results in an increase in the peak current stress of the

main power switch S1 due to the auxiliary circuit

current that flows through D4 when it is in its negative

resonant half-cycle. This circulating current increases

both the peak current stress of the main switch and

conduction losses.

Other resonant auxiliary circuits that can be used in

ZVT-PWM converters were proposed in [3], [7], and [10];

some of these are shown in Fig. 9. Regardless of how

these circuits may look, the fundamental circuit properties

of all resonant circuits are the same. The only real

difference is in the way that energy is transferred out of

the auxiliary circuit to the load. In general, the more

sophisticated the auxiliary circuit, the more efficiently this

process will occur.

3. Dual Auxiliary Circuits in ZVT-PWM

Converters

In recent years, dual auxiliary circuits that combine the

advantages of resonant and non-resonant converters while

reducing the drawbacks of each have been proposed (i.e.

[11-13]). The auxiliary switch in these circuits has the soft

turn-off of switches in resonant auxiliary circuits, but

without the increase in main switch peak current stress and

conduction losses as is the case with non-resonant circuits.

An example of a boost converter with a dual auxiliary

circuit is shown in Fig. 10 [13]. This auxiliary circuit can be

considered to be dual since it has two parallel branches: a

non-resonant branch consisting of components: Lr1, Lr2, D3,

D4 and a resonant branch consisting of components: Lr2, Cr

D4. In general, a dual auxiliary circuit can be formed by

combining any one non-resonant auxiliary circuit with any

one resonant auxiliary circuit then eliminating all

redundant components; a procedure for doing so was

presented in [13]. In the dual circuit shown in Fig. 10, the

circuit has been formed by combining the non-resonant

auxiliary circuit presented in Section II.A with the

resonant circuit presented in Section II.B then eliminating

all redundant components.

The equivalent circuit for each mode is shown in Fig.

11 and the converter waveforms are shown in Fig. 12. The

converter works as follows: At t0, the auxiliary switch S2

is turned on with ZCS. The current through Lr1, Lr2 and Cr

increases as current is being diverted away from the boost

diode, D1. The mode ends at t = t1 when the current

flowing through D1 is zero. At t1, the capacitor across the

main switch, Cs, begins to be discharged through the

auxiliary circuit. Current ILr1, and voltage VCs continue to

increase. ILr2 reaches its maximum value and begins to

decrease when VCs drops below VCr. Cs. is still being

discharged until it is totally discharged at t= t2, when the

main switch body-diode begins to conduct.

At t2, the body-diode of the main switch begins to

conduct as ILr2 is larger than Iin; this allows the main

b

c

a

b

c

a

Fig. 9 Other resonant auxiliary circuits

Vin

Cs1

Co R

Lin

S1

D1

Cr

D3

Lr1

Lr2

D4

S2

D2

Fig. 10 ZVT-PWM boost converter with a dual auxiliary

circuit

Page 6

40 Journal of Power Electronics, Vol. 8, No. 1, January 2008

D 1

L r1

switch S1 to be turned on with ZVS. Current ILr1 and

voltage VCr continue to increase. Some time during this

mode, a resonant process involving the resonant branch of

the auxiliary circuit begins and currents ICr and ILr2 start to

decrease. It continues to do so until t = t3, when the main

switch S1 can be turned on with ZVS. At t3, current stops

flowing through the body-diode of main switch S1 and

starts flowing through the switch. The resonant process

that began earlier continues as current ILr1 and voltage VCr

continue to increase and currents ICr and ILr2 continue to

decrease.

At t = t4, ILr2 becomes zero and ILr1 = ICr as diode D4

blocks any negative resonant current that would otherwise

flow. The auxiliary switch can be turned off with ZCS as

there is no current flowing through it. The current through

the main switch is equal to iin and the energy from

inductor Lr1 is transferred to Cr until t=t5 when the current

through Lr1 becomes zero and diode D3 prevents the

current from reversing direction. The operation of the

converter from time t5 onwards (Fig. 11(f)-(i)), when

current no longer flows in the auxiliary circuit, is exactly

the same as that of the ZVT-PWM converter with the

non-resonant auxiliary circuit discussed in Section II.A

(Fig. 3(f)-(i)).

It can be seen from Fig. 11(e) that the switch in the dual

auxiliary circuit, like the switch in any dual auxiliary

circuit, is turned off softly while current is diverted away

from the switch by the resonant branch, but without any

circulating current fed back into the main power switch as

it is contained in the auxiliary circuit.

4. An Off-Tuned Dual Auxiliary Circuit

Presently, dual auxiliary circuits are the most efficient

V o

D 3

D 4

L r2

S 2

C r

I in

I in

D 3

L r1

D 4

L r2

S 2

C r

I in

C s1

I in

D 3

D4

Lr2

Lr1

S 1

S2

Cr

(a) [t0-t1] (b) [t1-t2] (c) [t2-t3]

D 3

L r1

I in

D 4

L r2

S 1

S 2

C r

I in

D 3

L r1

S 1

C r

I in

S1

(d) [t3-t4] (e) [t4-t5] (f) [t5-t6]

(g) [t6-t7] (h) [t7-t8] (i) t > t8

Fig. 11 Modes of operation of a ZVT-PWM boost converter

with a dual auxiliary circuit

I in

C s1

Vo

D2

C r

I in

C s1

Vo

D1

I in

S1

S2

Vs1

Is1

ILr2

ILr1

Vs2

Is2

Iin

VCr

t0t1t2t3

t6 t8

t7

t4

t 5

t9

Vo

Iin

Vo

Fig. 12 Typical waveforms of a ZVT-PWM boost converter

with a dual auxiliary circuit

Is2

ta

tb

td t e

tc

tf

Iin

t

Non-Resonant

Resonant

Fig. 13 Auxiliary switch current waveforms of a ZVT-PWM

boost converter

Page 7

Circuit Properties of Zero-Voltage-Transition PWM Converters 41

type of auxiliary circuits in ZVT-PWM converters because

they have lower switching losses than non-resonant

auxiliary circuits and lower conduction losses than

resonant auxiliary circuits. One question that can be asked,

however, is whether it is possible to further improve the

efficiency of dual auxiliary circuits - what would it take to

maximize the efficiency of auxiliary circuits in

ZVT-PWM converters?

To answer this question, consider the auxiliary switch

current waveforms shown in Fig. 13. If the auxiliary

switch S2 is turned on at some time ta to discharge the

capacitance across the main power switch S1, then it is

turned off at time tc. If the switch is in a non-resonant

auxiliary circuit, tc is when the auxiliary switch current Is2

is greater than the input current Iin after tb; if it is a dual

auxiliary circuit, tc is at time te ; if it is in a resonant

auxiliary circuit, tc is some time between te and tf . In the

case of a resonant auxiliary circuit, current would continue

to flow through the anti-parallel diode across the switch

until tf.

Let us say that the auxiliary switch is turned off at time

tc in Fig. 13. If this is done, it can be seen that the switch

will be turned off with some current flowing through it,

but this current will still be significantly less than it would

be if the switch were turned off at tc than it would be if it

were in a non-resonant circuit. Moreover, any increase in

conduction losses would be fairly small. Turning the

switch off at tc would also result in the switch conducting

even less current than it would if it were in a dual

auxiliary circuit and significantly less current that it would

if it were in a resonant auxiliary circuit. Interrupting the

resonant cycle of the auxiliary switch current would

reduce the current circulating in the auxiliary circuit.

Although the turn-off losses in the auxiliary switch are

greater than those of a switch in a dual or resonant

auxiliary circuit, these losses are more than offset by the

reduction in conduction losses.

In terms of circuit implementation, an auxiliary circuit

can be made to operate in this way if the resonant branch

of the dual circuit is "off-tuned" so that the current through

the auxiliary switch is reduced, but not completely

eliminated, before it is turned off. This is in contrast to the

"appropriate" tuning of the resonant branch in a dual

auxiliary circuit so that the auxiliary switch turns off with

zero current. Fig. 14 shows an example a ZVT-PWM

boost converter with an off-tuned variation of the dual

auxiliary circuit in Fig. 10.

Just like a dual auxiliary circuit, the circuit in Fig. 14

has a non-resonant branch and a resonant branch. The

non-resonant branch consists of components Lr1, D3 and

D4, and the resonant branch consists of components Lr2, Cr,

D4. Components D2 and Cr* are added to provide a path

where the remaining auxiliary switch current can be

diverted when the switch is turned off. This is needed as

the switch does not turn off softly. Energy from Lr1 and Lr2

is transferred to Cr*. Diodes D6 and D5 allow the voltages

across capacitors Cr and Cr*, respectively, to return to zero

every cycle by transferring the energy in these capacitors

to the output each cycle.

Fig. 15 shows the circuit diagrams of the modes of

operation that the converter shown in Fig. 14 goes through

during a switching cycle. The converter's modes of

operation are as follows:

Mode 1 (t0-t1): At t0, the auxiliary switch S2 is turned

on and current begins to be diverted away from the boost

diode, D1. S2 turns on with ZCS due to the presence of

inductors in both circuit branches. The equations that

define this mode are given in equs. (1) to (3):

di

Lv

=+

2

(1)

r

dt

or cr

V

dt

2

o

V

di

L

=

1

1

(2)

dt

dv

Ci

cr

r

=

2

(3)

The solutions to the above equations are given below by

equs. (4) to (7).The resonant frequency in this mode is

given by (8).

(

ω

)()

tVv

ocr

0

cos1

−=

(4)

oc

Vtv

s

=

)(

(5)

V in

C s1

Co

R

L in

S 1

D 1

D 6

D 3

D 2

D 4

L r1

S 2

D 5

Cr

Lr2

C r

*

Fig. 14 A ZVT-PWM boost converter with an off-tuned dual

auxiliary circuit

Page 8

42 Journal of Power Electronics, Vol. 8, No. 1, January 2008

D 1

L r1

Lr1

t

L

V

i

r

o

1

1=

(6)

() t

0

VCi

or

02

sin ωω=

(7)

where

rrC

2

L

1

0=ω

(8)

Mode 2 (t1-t2): At t = t1, the current flowing through D1

is zero and the capacitor of the main switch Cs1 begins to

be discharged through the auxiliary circuit. The current

through Lr1 continues to rise during this interval. The

current through Lr2 rises until the voltages across

capacitors Cs1 and Cr become equal, and then starts

decreasing. The equations that define this mode are given

in equs. (9) to (12):

dt

di

Lv

rcs

1

1

=

(9)

dt

di

Lvv

rcc

rs

2

2

+=

(10)

dt

dv

Ci

rc

r

=

2

(11)

dt

dv

CIii

s c

s in−=+21

(12)

Equation (13) defines the voltage across the capacitor

Cr. The other parameters (i1, i2 and

s c

v

) are defined based

on equs. (14) to (16):

(

ω

)(

ω

)(

ω

)(

ω

) t

2

BtAtBtAv

ddddcr

211

sin cos sincos

2211

+++=

(13)

dt

dv

Ci

rc

r

=

2

(14)

2

2

2

dt

vd

CLvv

r

rs

c

rrcc

+=

(15)

()

3

3

21

dt

vd

CCL

dt

dv

CCi

rr

c

srr

c

sr

−+−=

(16)

where

2

4

4

2

4

1

2

1

1

ωωω

ω

−+

=

d

(17)

2

4

4

2

4

1

2

1

2

ωωω

ω

−−

=

d

(18)

and A1 ,A2 ,B1 ,B2 ,D1,D2, ω1, and ω2 are given below

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

C

+

L

=

r

CL

s

CL

r

CLL

srr

rrr

21

121

2

1

)(

ω

(19)

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

=

rsrr

CCLL

(

21

4

2

1

ω

(20)

)

V

( )

t

1

()

⎟⎟

⎠

⎟

⎞

⎜⎜

⎝

⎜

⎛

−

+−

=

rrdd

o

r

crrd

CL

VCL

A

2

22

2

2

1

1

)

V

2

2

1

ωω

ω

(21)

(

( )

t

1

()

⎟⎟

⎠

⎟

⎞

⎜⎜

⎝

⎜

⎛

−

+−

=

rrdd

o

r

crrd

CL

VCL

A

2

22

2

2

2

21

1

1

ωω

ω

(22)

( )

t

1

()

⎟

⎠

⎟

⎟

⎟

⎟

⎞

⎜

⎝

⎜

⎜

⎜

⎜

⎛

−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−

=

rddd

rr

d

C

I

CL

ω

B

112

2

22

2

2

2

1

1

ωω

ω

(23)

V o

D 3

D 4

S 2

C r

L r2

I in

D3

D 4

S 2

C r

L r2

I in

Cs1

I in

D3

D4

Lr1

S1

S2

Cr

Lr2

(a) [t0-t1] (b) [t1-t2] (c) [t2-t3]

D 3

L r1

I in

D 4

S 1

S 2

C r

L r2

I in

D 3

L r1

D 2

S 1

C r

L r2

C r

*

I in

D3

Lr1

S1

Cr

Lr2

(d) [t3-t4] (e) [t4-t5] (f) [t5-t6]

(g) [t6-t7] (h) [t7-t8] (i) [t8-t9] (j) t > t9

I in

S 1

I in

C s1

V o

D 5

D 6

C r

C r

*

I in

Cs1

Vo

D1

Iin

Fig. 15 Modes of operation of a ZVT-PWM boost converter

with an off-tuned dual auxiliary circuit

Page 9

Circuit Properties of Zero-Voltage-Transition PWM Converters 43

( )

t

1

()

⎟

⎠

⎟

⎟

⎟

⎟

⎞

⎜

⎝

⎜

⎜

⎜

⎜

⎛

−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−

=

rddd

rr

d

C

I

CL

ω

B

221

1

22

2

2

2

2

1

ωω

ω

(24)

Mode 3 (t2-t3): Cs1 is totally discharged at t = t2 and the

main switch body-diode begins to conduct as the

combined current flowing through both auxiliary circuit

branches is greater than the input current Iin. The current

through Lr1, ILr1, is constant because the voltage across the

inductor is zero during this mode. Voltage VCr continues

to increase as current ILr2 passes through it and ILr2

continues decreasing because of the negative voltage

across the inductor. While current is flowing through the

body-diode of S1, this switch can be turned on with ZVS.

The equations that define this mode are given in equs. (25)

to (27):

0

2

2

=+

dt

di

Lv

rcr

(25)

0

1

1

=

dt

di

Lr

(26)

dt

dv

Ci

rc

r

=

2

(27)

Ci

r

=

2

The solutions to the above equations are given below by

equs. (28) to (30). The resonant frequency in this mode is

given by (31).

( )

t

2

(

ω

)

( )

t

2

ω

(

ω

) t

0

C

I

tVv

r

cc

rr

2

0

sin

0

cos

+=

(28)

( )

2

t

11

Ii =

(29)

( )

t

2

(

ω

) ( )

t

2

(

ω

) t

0

VCtIi

rcr

0022

cos sin

ω−=

(30)

rrCL2

0

1

=

ω

(31)

Mode 4 (t3-t4): At t = t3, the combined current flowing

through both branches of the auxiliary circuit reaches the

input current Iin as the resonant process that began in

Mode 3 continues. This results in current ceasing to flow

through the body-diode of S1 and beginning to flow

through the switch itself. Current ILr1 still remains constant

because the voltage across it is zero when current is

passing through the main switch. Voltage VCr continues to

increase during Mode 4 as current ILr2 continues to

decrease. The voltage and current equations associated

with this mode of operation are as follows where the

resonant frequency was defined in the last mode of

operation:

( )

C

r

0

ω

( )

2

11

tIi =

(33)

( )

VCttIi

r

0

03

22

sin

( )

t

3

(

ω

)(

ω

) t

0

tI

tVv

cc

rr

32

0

sincos

+=

(32)

()( )

t

3

() t

0

rc

cos

ωωω+=

(34)

Mode 5 (t4-t5): At t = t4, the auxiliary switch S2 is

turned off and the current in both auxiliary circuit

branches flows through diode D2 to charge Cr*. The

equations associated with this mode are

di

Lv

r

cr

dt

1

1

* =

(35)

dt

di

Lvv

rc

c

r

r

2

2

*

+=

(36)

dt

dv

rc

(37)

0

*

*

r

21

=++

dt

dv

Cii

rc

(38)

Equ. (39) defines the voltage across Cr and the

equations for the other parameters can be derived from

this equation as follows:

()()()() t

2

BtAtBtAv

ddddcr

211

sincos sincos

2211

ωωωω+++=

(39)

dt

dv

Ci

rc

r

=

2

(40)

2

2

2*

r

dt

vd

CLvv

r

r

c

rrc

c

+=

(41)

()

3

3

*

r

2

*

r

1

dt

vd

CCL

dt

dv

CCi

rr

c

rr

c

r

−+−=

(42)

Page 10

44 Journal of Power Electronics, Vol. 8, No. 1, January 2008

where

2

4

4

2

4

1

2

1

1

ωωω

ω

−+

=

d

(43)

2

4

4

2

4

1

2

1

2

ωωω

ω

−−

=

d

(44)

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

++

=

rrrr

rrrr

L

r

CCL

CLCLL

*

21

*

112

2

1

)(

ω

(45)

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

=

rrrr

CCLL

(

*

21

4

2

1

ω

(46)

)

V

( )

C

()

⎟

⎠

⎟

⎞

⎜

⎝

⎜

⎛

−

−

=

rrdd

crrd

ω

L

tCL

A

r

2

22

42

2

1

12

2

1

ω

ω

(47)

()

V

( )

C

()

⎟

⎠

⎟

⎞

⎜

⎝

⎜

⎛

−

−

=

rrdd

crrd

ω

L

tCL

A

r

2

22

42

2

2

21

1

1

ω

ω

(48)

( )

t

4

()

( )

L

( )

t

4

()

⎟⎟

⎠

⎟

⎟

⎟

⎞

⎜⎜

⎝

⎜

⎜

⎜

⎛

−

+

−

⎟

⎠

⎞

⎟

⎟

⎟

⎟

⎞

⎜

⎝

⎛

⎜

⎜

⎜

⎜

⎛

−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−

=

rddd

r

ω

r

rddd

r

ω

r

d

C

C

2

ItI

C

I

CL

ω

B

112112

2

*

2

221

22

2

2

2

2

1

1

ωωω

ω

(49)

( )

t

4

()

( )

L

( )

t

4

()

⎟⎟

⎠

⎟

⎟

⎟

⎞

⎜⎜

⎝

⎜

⎜

⎜

⎛

−

+

−

⎟

⎠

⎟

⎟

⎟

⎟

⎜

⎝

⎜

⎜

⎜

⎜

−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−

=

rddd

r

ω

r

rddd

r

ω

r

d

C

C

2

ItI

C

I

CL

ω

B

221221

1

2

*

2

221

22

2

2

2

2

1

ωωω

ω

(50)

Mode 6 (t5-t6): At t=t5, current stops flowing through

D2 and Cr*. This is usually because current in the resonant

branch has reversed direction and has diverted the

non-resonant branch current away from D2 so that the

current flowing "up" the resonant branch is equal to the

current flowing "down" the non-resonant branch. A

resonant circuit between Lr1, Lr2 and Cr is created and

current continues to flow in the auxiliary circuit until the

current through Lr1 and Lr2 becomes zero. Diode D3

prevents the current from reversing direction and

Capacitor Cr has a negative voltage at the end of this mode.

The equations that define this mode are

di

Lv

dtdt

di

L

rcr

r

2

2

1

1

+=

(51)

dt

dv

Cii

rc

r

−=−=

21

(52)

and they can be solved to give

( )

t

5

(

ω

)

( )

t

5

ω

(

ω

) t

0

C

I

tVv

r

cc

rr

0

2

0

sin cos

+=

(53)

( )

t

5

(

ω

) ( )

t

5

(

ω

) t

0

VCtIi

rcr

0022

sincos

ω−=

(54)

where

()

rrr

CLL

21

0

1

+

=

ω

(55)

It should be noted that Mode 6 may be bypassed if

Mode 5 ends with the current in each auxiliary branch

falling to zero by the end of the Mode, but this rarely

happens. It may also be possible for the converter to

temporarily slip into Mode 5 if the voltage across Cr is

more "negative" than that across Cr*. If this happens, then

the converter may slip back and forth between Modes 5

and 6 until current stops flowing in the auxiliary circuit.

Mode 7 (t6-t7): At t=t6, current is no longer flowing in

the auxiliary circuit. The converter operates in the same

way as a standard PWM boost converter during this mode.

Mode 8 (t7-t8): At t = t7, the main switch S1 turns off

with ZVS as capacitor Cs1 slows down the rate of voltage

increase as it begins to be charged by Iin.

Mode 9 (t8-t9): At t = t8, either the sum of VCs1 and VCr

is equal to Vo, which causes D6 to conduct, or the sum of

VCs1 and VCr* is equal to Vo, which causes D5 to conduct.

Eventually, during this mode, both D5 and D6 conduct as

both these capacitors are discharged by the input current

while Cs1 is being charged.

Mode 10 (t>t9): At t=t9, Cr and Cr* are both fully

discharged and Iin starts flowing through D1. The converter

operates like a standard PWM converter until the auxiliary

switch is turned on at the start of the next switching cycle.

5. Design of an Off-Tuned Auxiliary

Circuit

Simple, experimental prototypes of a PWM boost

converter implemented with the non-resonant, resonant,

dual and off-tuned auxiliary circuits discussed in this

paper were built so that a comparative study of the

Page 11

Circuit Properties of Zero-Voltage-Transition PWM Converters 45

performance of these converters could be made. In order

to show how the off-tuned auxiliary circuit shown in Fig.

14 was designed, a design procedure is presented and

demonstrated with a sample in this section of the paper. It

is based on an analysis of the steady-state characteristics

of the converter, which can be determined from the mode

equations derived in Section IV, as shown in [7]. The

procedure is iterative and the example shown represents

the final iteration. The design of the components of the

main power boost converter (i.e. the main boost switch)

will not be discussed as it is the same as that of a standard

PWM boost converter, nor will that of capacitor Cr* as it

is basically a snubber capacitor that has little impact on

the operation of the auxiliary circuit.

For the example, the auxiliary circuit is to be designed

for a boost converter with the following parameters: Lin =

1 mH, S1 - IRFP460A MOSFET, and D1 - HFA25TB60

diode. The converter operates according to the following

specifications: Input voltage Vin = 100 - 250V, output

voltage Vo = 400V, maximum output power Po = 500 W,

switching frequency fsw=100 kHz. The value of Cr* is 1.2

nF. The estimated efficiency for this final iteration is

η=95%.

The auxiliary circuit should be designed to operate

under the worst case operating condition, which is when

the input current is at its maximum average value. This

occurs at maximum load Po = 500 W, when the input

voltage is at its minimum value, Vin = 100 V. The

maximum input current can be found from the given

specifications and is

A 26. 5

V 100 95. 0

W 500

in

V

o

P

in

I

=

⋅

= =η

(56)

The auxiliary circuit is activated when the input current

waveform is at its lowest point, just before the main

switch is to be turned on. Since the input inductor is Lin =

1 mH and the duty cycle for a boost converter is:

100400

===

o

V

75 . 0

400

−

−

ino

VV

D

(57)

The peak-to-peak input current ripple when Vin = 100 V

can be determined to be

A

kHz mH

1

fL

DV

I

sw in

in

pp in

75. 0

100

75 . 0

⋅

100

,

=

⋅

==

−

(58)

The auxiliary circuit should designed with Vo = 400 V

and Iin = 5.26 - (0.5)(0.75) = 4.89 A.

The next step is to determine Cr, Lr1, and Lr2. Based on

an analysis of the auxiliary circuit, performed in previous

iterations not shown here, it was determined that selecting

either Cr or Lr2 first would be most useful in limiting the

range of values for the other parameters as they are both in

the resonant branch, which dominates the initial modes of

operation. A value of Cr = 10 nF was determined to be

suitable and this narrowed the range of possible sets of Lr1

and Lr2 component values to the ones shown in the graphs

of steady-state characteristic curves in Fig. 16. The graphs

have been plotted using the modal equations in Section IV

using the procedure described in [7] and are as follows:

(i) ZVS time window: In order for the main power switch

S1 to turn on with ZVS, there must be some window of

time during which it can do so. This window can be

defined to be the difference between ta, which is the

earliest time when the auxiliary switch can be turned on

after the output capacitance of the main switch has

been completely discharged, and tb, which is the latest

time that the auxiliary switch can be turned on before

this capacitance begins to recharge. This window is at

its narrowest at the maximum input current that the

converter encounters; if S1 can be turned on with ZVS

under this condition, then it can also be done when the

input current is lower. Curves of ta and tb vs Lr2 for

various values of Lr1 are shown in Figs. 16(a) and

16(b).

(ii) Peak auxiliary switch current: The peak current

flowing in the auxiliary circuit should be as small as

possible to reduce current stress. This current is most

likely to reach its peak sometime during Modes 3 or 4

of operation. Curves of the peak auxiliary switch

current IS2,pk vs Lr2 for various values of Lr1 are shown

in Fig. 17(a).

(iii) Auxiliary circuit conduction time: The amount of

time that the auxiliary circuit is in operation should be

as small as possible to reduce conduction losses due to

Page 12

46 Journal of Power Electronics, Vol. 8, No. 1, January 2008

current circulating in the converter. A measure of this

time can be an approximation of the length of time

from Mode 1, when S2 is turned on, to Mode 7, when

current stops flowing in the auxiliary circuit, t6,

t0-6.Curves of t0-6 vs Lr2 for various values of Lr1 are

shown in Fig. 17(b).

As it is impossible to satisfy all the above criteria,

several compromises must be made. For example,

although both minimum auxiliary peak current and

conduction time are desired, these two parameters are

inversely proportional so that minimizing one of these

parameters maximizes the other and vice versa. The same

relationship is true for the worst-case ZVS time window

and the peak switch current - the longer the window, the

higher the peak must be and vice versa. Based on the

graphs in Fig. 16 and the above-mentioned criteria, Lr1 =

18 µH and Lr2 = 2 µH can be used.

6. Experimental Results

The operating conditions of the converters with the

non-resonant, resonant, dual and off-tuned auxiliary

circuits were input voltage Vin = 100 V -250 V, Vo = 400 V,

maximum power Po,max = 500 W, switching frequency fsw

= 100 kHz. The following components were common to

all converters: main switch S1 - IRFP460, auxiliary switch

(a)

(b)

Fig. 17 (a) Peak current through Lr1 and Lr2, ILr1,pk and ILr2,pk vs

Lr2 (b) Conduction time tLr1 and tLr2 vs Lr2

(a)

(b)

Fig. 16 Steady-state characteristic curves: (a) S1 turn-on time

ta vs Lr2 (b) S1 turn-on time tb vs Lr2

Page 13

Circuit Properties of Zero-Voltage-Transition PWM Converters 47

S2 - IRF840, boost diode D1 - HFA25TB60, input inductor

Lin - 1 mH, and output capacitor Co - 470µF. All auxiliary

circuit diodes were MUR420 devices. The inductor and

capacitor values for the non-resonant auxiliary circuit

were Lr1 = 13 µH and Cr = 1.2 nF. The inductor and

capacitor values for the resonant auxiliary circuit were Lr1

= 5.8 µH and Cr = 1.2 nF. The inductor and capacitor

values for the dual auxiliary circuit were Lr1 = 30µH, Lr2 =

7.5µH, and Cr = 4.4 nF. The inductor and capacitor values

for the off-tuned auxiliary circuit were Lr1 = 18µH, Lr2 =

2.1µH, Cr = 10.5 nF, and Cr* = 1.2 nF .

Fig. 18(a) shows typical waveforms of the drain to

source voltage Vds1 and current Is1 of switch S1. It can be

seen that the switch voltage drops to zero and the switch

can turn on with ZVS. Fig. 18(b) shows typical waveforms

of the drain to source Vds2 and the gate to source voltage

Vgs2 of the auxiliary switch S2. It can be seen that when the

switch is turned off, current that was flowing through the

switch is transferred to capacitor Cr* and the voltage

across the switch rises slowly as this capacitor is being

charged. Fig. 18(c) shows the boost diode waveforms.

Fig. 19 shows the efficiency of the boost converters

with the four different auxiliary circuits. It can be seen

from Fig. 19 that the off-tuned dual circuit is generally the

most efficient circuit. This is because this circuit has the

advantages of the non-resonant and resonant circuits, but

not the disadvantages. It also operates with less current

circulating in it than the dual circuit. The following, more

general conclusions can also be made from Fig. 19:

(i) The off-tuned auxiliary circuit (Fig. 14) is an

off-tuned version of the dual auxiliary circuit (Fig. 10),

which is itself derived from the non-resonant circuit

(Fig. 2) and the resonant circuit (Fig. 6). The

off-tuned circuit is the most efficient of this set of

four circuits. It can, therefore, be stated as a circuit

property that if any non-resonant circuit is combined

with any resonant circuit to form a dual circuit that is

then off-tuned, then the off-tuned circuit will likely be

the most efficient of that set of four circuits.

(ii) The improvement in efficiency of the off-tuned

circuit compared to the dual circuit is greater when

the converter operates under low line, heavy load

conditions when the converter is operating with

maximum current. Under operating conditions when

the converter is operating with little current, the

current circulating in the dual circuit will be small so

that the conduction losses will be fairly small and the

dual circuit may be more efficient.

(iii) It should also be noted that the off-tuned circuit

presented in this paper may be less efficient than the

circuits belonging to some other, more sophisticated

set of resonant, non-resonant, and dual circuits. There

are many possible non-resonant and resonant

auxiliary circuits that can be combined to form any

number of possible dual circuits. The off-tuned circuit

presented in this paper is, therefore, not the only

(a)

(b)

(c)

Fig. 18 Experimental waveforms (a) Main switch voltage

Vds1 and current Is1, scale (Vds1: 100 V/div, Is1: 2

A/div, 1 µs/div) (b) Auxiliary switch voltage Vds2

and gate to source voltage Vgs2, scale (Vds1: 100

V/div, Vgs1: 10 V/div, 1 µs/div) (c) Main boost

diode D1 voltage VD1 and current ID1: (V:100V/div,

I:2A/div, 1µs /div V)

I

V

Vds

Vgs

V

I

Page 14

48 Journal of Power Electronics, Vol. 8, No. 1, January 2008

possible circuit of its type and another off-tuned

circuit can be derived from a different combination of

non-resonant and resonant

Regardless of the set of resonant, non-resonant, and

dual circuits, the off-tuned circuit derived from the set

will likely be the most efficient circuit of the set.

(iv) A corollary of this property would be that any of the

dozens of previously proposed non-resonant auxiliary

circuits can be made even more efficient if

implemented with a resonant branch and then

off-tuned, thus decreasing auxiliary circuit switching

losses without significantly increasing auxiliary

circuit conduction losses. This is especially true for

non-resonant circuits as there have been considerably

auxiliary circuits.

more non-resonant than resonant circuits proposed

and off-tuned circuits are considerably more efficient.

(v) The maximum improvement in efficiency of the

off-tuned circuit when compared to the dual circuit is

shown in Fig. 19. This represents the maximum gain

in efficiency that can be achieved with ZVT-PWM

converter structures as almost all previously proposed

auxiliary circuits are non-resonant, resonant, or dual.

It may be possible to achieve higher converter

efficiencies, but it would take an approach that is

completely different than the ZVT-PWM converter

approach that has been studied for many years by

power electronics experts. The efficiencies of

off-tuned auxiliary circuits are probably the maximum

that can be achieved with the ZVT-PWM approach in

single-switch PWM converters.

(vi) As a general circuit property, the more components

that an auxiliary circuit has, the more efficient it will

be, but the more it will cost. It is up to a circuit

designer to determine the cost benefits of one type of

converter over another for his or her particular

application as efficiency may be the most important

factor in one application, overriding cost considerations,

while cost may be the primary factor in another.

7. Conclusion

Most auxiliary circuits in single switch ZVT-PWM

converters are either non-resonant, resonant, or dual. The

auxiliary switch in any non-resonant auxiliary circuit turns

off with considerable current flowing through it; thus, it

has switching losses that partially offset any gains in

efficiency due to the reduction of turn-on losses in the

main converter switch. The auxiliary switch in any

resonant circuit can be made to turn off softly, but at the

expense of an increase in conduction losses due to a

considerable amount of circulating current flowing in the

auxiliary circuit. Moreover, the main switch has a higher

peak current stress than that found in conventional PWM

converters as it must conduct the circulating current in the

auxiliary circuit in addition to the input current. Dual

auxiliary circuits combine the advantages of non-resonant

and resonant auxiliary circuits so that the auxiliary switch

can turn off softly as in resonant auxiliary circuits, but

86

88

90

92

94

96

100 200 300 400 500

Output Power (W)

(a)

Eff. (%)

Resonant

Non-Resonant

Dual

Off-Tuned

88

100

90

92

94

96

98

125 150

Input Voltage (V)

(b)

175 200 225 250

Eff. (%)

Resonant

Non-Resonant

Dual

Off-Tuned

Fig. 19 Converter efficiency (a) Efficiency vs. output power, Vin

= 100 V. (b) Efficiency vs. input voltage, Po=500 W

Page 15

Circuit Properties of Zero-Voltage-Transition PWM Converters 49

without the main switch peak current stress and with less

circulating current. At the present time, dual circuits are

the most efficient type of auxiliary circuits.

In this paper, the fundamental circuit principle of

"off-tuning" was presented as a way of maximizing the

efficiency of auxiliary circuits. The circulating current in

dual auxiliary circuits can be reduced even further by

"off-tuning" the resonant branch so that there are some

auxiliary switch turn-off losses, but less than those found

in non-resonant circuits. The paper reviewed the operation

of auxiliary circuits in ZVT-PWM converters, and then

discussed the properties and characteristics of the new

off-tuned type of auxiliary circuits. There are many

possible off-tuned auxiliary circuits as there are presently

many previously proposed non-resonant and resonant

circuits.

Experimental results obtained from 500W, 100 kHz

prototype converters confirmed the feasibility of a

ZVT-PWM boost converter

experimental off-tuned auxiliary circuit and a comparison

was made between the experimental circuit and the

original non-resonant, resonant, and dual circuits from

which it was derived. Based on this comparison, several

general circuit properties were determined. It was

concluded that an off-tuned circuit will be the most

efficient circuit of the set of non-resonant, resonant, and

dual circuits from which it was derived, but it also has the

most components. It is up to a circuit designer to

determine the cost benefits of one type of converter over

another for his or her particular application.

References

[1] R. Streit and D. Tollik, “A high efficiency telecom rectifier

using a novel soft-switching boost-based input current

shaper,” in IEEE INTELEC Conf. Rec., 1991, pp. 720-726.

[2] G. Hua, C.-S. Leu, Y. Jiang, and F. C. Lee, “Novel

zero-voltage transition PWM Converters,” in IEEE Trans.

on Power Elec., vol. 9, no. 4, pp. 213-219, Mar. 1994.

[3] L. Yang and C. Q. Lee, “Analysis and Design of Boost

Zero-Voltage-Transition PWM Converter”, in IEEE APEC

Conf. Rec.,1993, pp.707-713.

[4] J. Gegner and C. Q. Lee, “Zero-voltage-transition

converters using an inductor feedback technique," in IEEE

APEC. Conf. Rec., 1994, pp. 862-868.

operating with an

[5] K. M. Smith, Jr. and K. M. Smedley, “A comparison of

voltage-mode soft-switching

converters," in IEEE Trans. on Power Elec., vol. 12, no. 2,

pp. 376-386, Mar. 1997.

[6] C.-J Tseng and C.-L.Chen, “Novel ZVT-PWM converter

with active snubbers”, in IEEE Trans. on Power Elec., vol.

13, no. 5, pp. 861-869, Sept. 1998.

[7] G. Moschopoulos, P. Jain, G. Joos, and Y.-F. Liu, “Zero

voltage switched PWM boost converter with an energy

feedforward auxiliary circuit”, in IEEE Trans. on Power

Elec., vol. 14, no. 4, pp. 653-662, July 1999.

[8] T.-W. Kim, H.-S. Kim, and H.-W. Ahn, “An improved

ZVT PWM boost converter”, in IEEE PESC. Conf. Rec.,

2000, pp. 615-619.

[9] J.-H. Kim, D. Y. Lee, H. S. Choi, and B. H. Cho, "High

performance boost PFP (power factor preregulator) with an

improved ZVT (zero voltage transition) converter," in

IEEE APEC Conf. Rec., 2001, pp. 337-342.

[10] N. Jain, P. K. Jain, and G. Joos, “A zero voltage transition

boost converter employing a soft switching auxiliary

circuit with reduced conduction losses”, in IEEE Trans. on

Power Elec., vol. 19, no. 1, pp. 130-139, Jan. 2004.

[11] M. L. Martins, H. A. Grundling, H. Pinheiro, and J. R.

Pinheiro, and H. L. Hey, "A ZVT PWM boost converter

using an auxiliary resonant source," in IEEE APEC Conf.

Rec., 2002, pp. 1101-1107.

[12] C.-M. Wang, "Novel zero-voltage-transition PWM dc-dc

converters" in IEEE Trans. on Ind. Elec., vol. 53, no. 1, pp.

254-262, Feb. 2006.

[13] W. Huang and G. Moschopoulos, “A new family of

zero-voltage-transition PWM converters with dual active

auxiliary circuits,” in IEEE Trans. on Power Elec., vol. 21,

no. 2, pp. 370-379, Mar. 2006.

[14] M. L. Martins, J. L. Russi, and H. L. Hey,

"Zero-voltage-transition PWM converters: a classification

methodology" in IEE Proc. Elec. Power Appl., vol. 152, no.

2, pp. 323-334, Mar. 2005.

methods for PWM

Amir Ostadi received a B.Sc. degree from

Sharif University of Technology, Tehran,

Iran, in Electrical Engineering. Currently, he

is working towards his M.Sc. degree in

Electrical Engineering, at the University of

Western Ontario, London, Ontario, Canada.

His research interests include wind power generation, application

of power electronics in power systems, power system

restructuring, and power system stability.

Page 16

50 Journal of Power Electronics, Vol. 8, No. 1, January 2008

Xing Gao received the M.E.Sc degree in

Electrical & Computer Engineering from

University of Western Ontario, London,

Canada in 2006. He also received the M.E.Sc

degree and the B. Eng degree with distinction

from University of Inner Mongolia, China in

1985 and 1982 respectively. He has been a power electronics

design engineer for many years in Canada and in the United

States. He is currently working in Boston, US as a senior design

engineer.

Gerry Moschopoulos received the Bachelor

of Engineering, Master's of Applied Science

and Ph.D degrees from Concordia University

in Montreal, Quebec, Canada in 1989, 1992,

and 1997 respectively. From 1996 to 1998,

he was a design engineer in the Advanced

Power Systems division of Nortel Networks in Lachine, Quebec,

Canada, working on developing power supplies and systems for

telecom applications. From 1998 to 2000, he was a research

engineer at Concordia University working on power converter

operating with soft-switching and active power factor correction.

Since 2000, he has been with the Department of Electrical and

Computer Engineering at the University of Western Ontario in

London, Ontario, Canada, where he is presently an associate

professor. He is also a member of the Professional Engineers of

Ontario