ZERO-VOLTAGE SWITCHING IN HIGH FREQUENCY POWER
CONVERTERS USING PULSE WIDTH MODULATION
C. P. Henze+
Unisys Corporation'
P.0. BOX 64525, U2N26
S t . P a u l , MN 55164
H. C. M a r t i n *
D. W. P a r s l e y "
Unisys C o r p o r a t i o n *
640 N. S p e r r y Way, FlH12
S a l t L a k e C i t y , UT 84116
ABSTRACT
P
A z e r o - v o l t a g e s w i t c h i n g t e c h n i q u e is d e s c r i b e d ,
mploying a resonant-transition during a switching
i n t e r v a l o f s h o r t b u t f i n i t e d u r a t i o n , which may b e
a p p l i e d t o c o n v e n t i o n a l power c o n v e r t e r t o p o l o g i e s
allowing e f f i c i e n t operation a t very high switching
frequencies
while
retaining
the
fundamental
c h a r a c t e r i s t i c s of t h e conventional topology.
'I.
+ m
6
INTRODUCTION
F i g u r e 1. The c a n p o s i t e s w i t c h is used i n p l a c e o f
t h e c o n v e n t i o n a l power s w i t c h and t h e f r e e w h e e l i n g
d i o d e i n NRT s w i t c h i n g power c o n v e r t e r s .
Q u a s i - r e s o n a n t power c o n v e r t e r t o p o l o g i e s h a v e been
developed u s i n g a resonant-switch
concept t h a t
i n h e r e n t l y r e d u c e s (or e l i m i n a t e s ) t h e f r e q u e n c y
d e p e n d e n t s w i t c h i n g losses o f t h e power c o n v e r t e r
allowing e f f i c i e n t o p e r a t i o n a t very high switching
f r e q u e n c i e s . Q u a s i - r e s o n a n t power c o n v e r t e r s may b e
described
as
zero-current
switching
Cl1
or
zero-voltage
s w i t c h i n g C21 r e s o n a n t - s w i t c h
power
or
converters.
Furthermore,
zero-current
zero-voltage
buck, b o o s t ,
buck-boost
and
Cuk
quasi-resonant
t o p o l o g i e s may b e d e r i v e d f r a n a
c o n v e n t i o n a l n o n - r e s o n a n t t o p o l o g y by r e p l a c i n g t h e
conventional
switch
with
the
appropriate
resonant-sui tch.
However, c o n d u c t i o n l o s s e s a r e i n c r e a s e d i n t h e
p a r e r c o n v e r t e r and s y n c h r o n o u s r e c t i f i c a t i o n is
r e q u i r e d ( w h i c h is u s e f u l f o r low o u t p u t v o l t a g e
a p p l i c a t i o n s 1.
2. BASIC CONCEPT
Although q u a s i - r e s o n a n t
converters a r e w e l l suited
f o r and p r e s e n t l y used i n many h i g h f r e q u e n c y power
processing
applications,
two d i s a d v a n t a g e s are
a s s o c i a t e d with t h e resonant switch concept. Since
f r e q u e n c y m o d u l a t i o n is used t o c o n t r o l t h e o u t p u t
characteristics,
new t e c h n i q u e s and methods m u s t be
developed
f o r feedback c o n t r o l
and
stability
a n a l y s i s ; furthermore,
i n p u t and o u t p u t f i l t e r
d e s i g n is more complex. Because i n t e r n a l waveforms
have l a r g e s i n u s o i d a l c a n p o n e n t s ,
the off-state
v o l t a g e stress on s e m i c o n d u c t o r d e v i c e s is i n c r e a s e d
and t h e c o n d u c t i o n losses i n b o t h a c t i v e and p a s s i v e
components a r e i n c r e a s e d .
The c a n p o s i t e s w i t c h o f F i g u r e 1 is used f o r b o t h
t h e power s w i t c h and t h e s y n c h r o n o u s s w i t c h .
The
c a n p o s i t e s w i t c h is modeled by: a n i d e a l s w i t c h t h a t
may
c a r r y c u r r e n t i n e i t h e r d i r e c t i o n and is
c o n t r o l l e d by a n e x t e r n a l s i g n a l , a n a n t i - p a r a l l e l
i d e a l d i o d e Dsw, and a p a r a l l e l c a p a c i t o r Csw. A
power f i e l d - e f f e c t - t r a n s i s t o r (FET) may b e used t o
implement t h e c a n p o s i t e s w i t c h b e c a u s e t h e FET
c o n t a i n s a n a n t i - p a r a l l e l d i o d e and a s i g n i f i c a n t
drain-to-source
Capacitance;
however,
i n scne
applications, a f a s t e r
anti-parallel
diode o r
a d d i t i o n a l p a r a l l e l c a p a c i t a n c e may b e r e q u i r e d .
I t
s h o u l d by r e c o g n i z e d t h a t i n sane a p p l i c a t i o n s t h e
drain-to-source
c a p a c i t a n c e may l i m i t t h e maximum
a w i t c h i n g f r e q u e n c y a t which FETs m a y b e used t o
implament ZVRT s w i t c h i n g .
a
zero-voltage
switching
T h i s paper d e s c r i b e s
t e c h n i q u e , Employing a r e s o n a n t - t r a n s i t i o n d u r i n g a
switching i n t e r v a l of s h o r t but f i n i t e d u r a t i o n ,
which may be a p p l i e d t o c o n v e n t i o n a l power c o n v e r t e r
topologies allowing e f f i c i e n t operation a t very high
switching
frequencies
while
retaining
the
fundamental c h a r a c t e r i s t i c s
of t h e conventional
topology.
Specifically,
zero-voltage
r e s o n a n t - t r a n s i t i o n (NRT) s w i t c h i n g c o n v e r t e r s may
u s e pulse width modulation f o r output c o n t r o l , t h e
power
transistor parasitic capacitor
switching
losses a r e e l i m i n a t e d , and t h e o f f - s t a t e v o l t a g e
stress o f t h e power t r a n s i s t o r is n o t i n c r e a s e d .
An example z e r o - v o l t a g e
switching interval using a
r e s o n a n t - t r a n s i t i o n i s i l l u s t r a t e d i n F i g u r e s 2 and
3 f o r a p a i r o f canposite switches.
Zero-voltage
s w i t c h i n g is a c c o m p l i s h e d by r a p i d l y t u r n i n g o f f t h e
lower s w i t c h ( F i g u r e 221) which m u s t be c a r r y i n g a
positive
current
IL (with
respect
to
the
a n t i - p a r a l l e l d i o d e ) fran a c u r r e n t s o u r c e ( w h i c h i n
p r a c t i c e is t h e i n d u c t o r i n t h e power c o n v e r t e r ) .
This forces t h e current IL t o cannutate fran t h e
i n t e r n a l i d e a l switch t o t h e pal-allel c a p a c i t o r s
w h i l e t h e v o l t a g e a c r o s s t h e c a n p o s i t e s w i t c h is
e s s e n t i a l l y zero ( F i g u r e 2 b ) .
The v o l t a g e a c r o s s
lower s w i t c h Vsu2 i n c r e a s e s u n t i l t h e a n t i - p a r a l l e l
3.3
CH2504-9/88/0000-0033$1.00 0 1988 IEEE
a)
b)
IL
6
6
b
F i g u r e 2. I n t h i s example o f a ZVRT s w i t c h i n g t r a n s i t i o n , t h e c u r r e n t which is i n i t i a l l y
c a r r i e d by t h e l o w e r i d e a l s w i t c h I L ( a ) is t r a n s f e r r e d t o t h e p a r a l l e l c a p a c i t o r s
a l l o w i n g a z e r o v o l t a g e t u r n o f f . Charging of t h e p a r a l l e l c a p a c i t o r s c a u s e s t h e v o l t a g e
a c r o s s t h e l o w e r s w i t c h V s w p t o rise ( b ) u n t i l t h e upper a n t i - p a r a l l e l d i o d e c o n d u c t s ( c )
a l l o w i n g t h e upper i d e a l s w i t c h t o b e t u r n e d on a t z e r o v o l t a g e ( d ) .
be l a r g e enough t o c o m p l e t e l y c h a r g e t h e s w i t c h
capacitors f r m t h e i n i t i a l to t h e final voltage
vsw
,
on
I
swl
off
swz
tb
I
LIL*
I
I
I
I
I
I
I
I
I
I
V-
!
t
I
I
>>
2Csw Vsw2
(1)
Thus, t h e i n d u c t o r may b e approximated by a c o n s t a n t
IL( t s w ) d u r i n g
the
switching
current
source
i n t e r v a l . The b l a n k i n g time m u s t b e l o n g enough t o
a l l o w t h e s w i t c h i n g t r a n s i t i o n t o be completed ( f o r
t h e minimum v a l u e o f i n d u c t o r c u r r e n t ).
I
I
on
off--/
.
I
tb
I
>
2CswVsw
(2)
IL( t s u )
I
zero
*
I
I
a
I
I
I
I
I
I
,
H
I f these conditions a r e not m e t ,
s w i t c h i n g losses
will
r e s u l t frm
dissipatively
charging
and
discharging t h e switch capacitors.
I
I
b
F i g u r e 3. I d e a l waveforms for
s w i t c h i n g i n t e r v a l o f F i g u r e 2.
B
the
C
'
example
S i m i l a r zero-voltage
s w i t c h i n g t e c h n i q u e s h a v e been
employed i n l o s s l e s s s n u b b e r s f u l l b r i d g e c i r c u i t s
C3,41. I n t h i s c a s e t h e m a g n e t i z i n g c u r r e n t o f t h e
transformer
p r o v i d e s t h e e n e r g y t o c h a r g e and
d i s c h a r g e t h e c o m p o s i t e s w i t c h c a p a c i t a n c e 'during
t h e blanking i n t e r v a l .
Furthermore, t h i s concept
h a s been a p p l i e d t o a c o n s t a n t f r e q u e n c y r e s o n a n t
power c o n v e r t e r i n which o p e r a t i o n above r e s o n a n c e
provides
p r o p e r c u r r e n t waveforms t o implement
z e r o - v o l t a g e s w i t c h i n g C51.
d
NRT
d i o d e i n t h e u p p e r c o m p o s i t e s w i t c h is forward
b i a s e d ( F i g u r e 2 c ) and c a r r i e s t h e c u r r e n t IL. The
upper s w i t c h may now b e d r i v e n i n t o t h e on s t a t e by
the
control
(gate)
signal
cmpleting
the
z e r o - v o l t a g e s w i t c h i n g t r a n s i t i o n ( F i g u r e 2d 1.
3. ZVRT SWITCHINTI CONVERTERS
The p r o c e s s o f c a n n u t a t i n g c u r r e n t from t h e upper t o
t h e lower c o m p o s i t e
switch
with
zero-voltage
r e s o n a n t - t r a n s i t i o n s w i t c h i n g is i d e n t i c a l e x c e p t
t h a t t h e c u r r e n t IL m u s t b e o f o p p o s i t e p o l a r i t y
during t h e switching interval.
In
general, a zero-voltage
resonant-transition
switching
t o p o l o g y may b e o b t a i n e d
frm
the
1 ) r e p l a c i n g both t h e
c o n v e n t i o n a l t o p o l o g y by:
power s w i t c h and t h e f r e e w h e e l i n g d i o d e w i t h a new
c a n p o s i t e power s w i t c h which c o n t a i n s a p a r a l l e l
c a p a c i t a n c e and a n a n t i - p a r a l l e l d i o d e , 2 ) o p e r a t i n g
b o t h t h e power s w i t c h and t h e s y n c h r o n o u s s w i t c h ( i n
a
place
of
the
freewheeling
diode)
in
br-k-before-make
mode w i t h a s h o r t b u t f i n i t e
During t h e s w i t c h i n g i n t e r v a l , t h e s w i t c h c a p a c i t o r s
and t h e i n d u c t o r form a L-C r e s o n a n t c i r c u i t . To
implement a
proper
switching
transition, the
i n d u c t o r e n e r g y a t t h e # t a r t o f t h e t r a n s i t i o n must
34
waveforms
and t h e s w i t c h v o l t a g e and i n d u c t o r
c u r r e n t waveform a t b o t h n o l o a d and f u l l l o a d .
b l a n k i n g t i m e t b , 3) c h o o s i n g a n a p p r o p r i a t e l y
valued inductor such t h a t t h e i n d u c t o r c u r r e n t w i l l ,
f o r a l l o p e r a t i n g c o n d i t i o n s o f i n t e r e s t , reach a
maximum peak c u r r e n t which is g r e a t e r t h a n z e r o and
a minimum peak c u r r e n t which is less t h a n zero.
"out
ZVRT
A NRT s w i t c h i n g buck,
boost
and
buck-boost
c o n v e r t e r s and r e l e v a n t no l o a d and f u l l l o a d
The i n d u c t o r
waveforms a r e shown i n F i g u r e 4.
c u r r e n t c o n t a i n s a n a c c a n p o n e n t I i p p t h a t is
i n d e p e n d e n t o f t h e o u t p u t c u r r e n t and a dc ccmponent
<IL> t h a t is d e p e n d e n t on t h e o u t p u t c u r r e n t . S i n c e
t h e i n d u c t o r m u s t b e s i z e d s u c h t h a t t h e minimum
peak i n d u c t o r c u r r e n t is a l w a y s n e g a t i v e , a " d e s i g n
i n d u c t a n c e " Ld may b e c a l c u l a t e d as a f u n c t i o n of
t h e r a t i o K o f peak-to-peak
inductor r i p p l e current
I L ~ Pt o t h e a v e r a g e ( o r dc ) i n d u c t o r c u r r e n t < I l m r ~ >
a t f u l l load.
Switchinq B o o s t Converter
"out
2VRT
I
I
"in
(3)
K < I t o r x > = ILPP
Switching Buck-Boost Converter
I'
I
Ll
The d e s i g n i n d u c t a n c e is t h e maximum i n d u c t a n c e t h a t
c a n be used i n t h e c o n v e r t e r which o p e r a t e s w i t h
ZVRT s w i t c h i n g .
The d e s i g n i n d u c t a n c e t h i s i a
s i m i l a r concept t o t h e " c r i t i c a l
i n d u c t a n c e " C63
which d e f i n e s a minimum i n d u c t a n c e t o m a i n t a i n
continuous conduction i n a conventional topology.
However, u s i n g t h e d e s i g n i n d u c t a n c e v a l u e i n a
c o n v e n t i o n a l t o p o l o g y would g u a r a n t e e d i s c o n t i n u o u s
c o n d u c t i o n up t o t h e maximum l o a d c u r r e n t frcm which
<I-.%>
h a s been c a l c u l a t e d .
I +
For a zero-voltage
buck c o n v e r t e r
resonant-transition
-
switching
Vin-Vout
K<Itoax> = ILpp =
DT
( f o r K>2>
(4)
Ld
where D is t h e d u t y r a t i o o f t h e power s w i t c h and T
i s t h e s w t i c h i n g p e r i o d . F u r t h e r m o r e , it h a s been
assumed t h a t t h e b l a n k i n g t i m e is s h o r t c a n p a r e d t o
t h e switching period.
Using
Vout
<Itorx> = Iout(max) =
-
(5)
Ricmin)
where I o u t ( m a x ) is t h e f u l l l o a d o u t p u t c u r r e n t o f
t h e power c o n v e r t e r and s o l v i n g f o r Ld
Ld
-
=
K
Topology
V'
V-
Buck
Vin
0
0
Vout
Vin
Vout
Boost
~
NRT s w i t c h i n g
Figure
4.
buck-boost c o n v e r t e r s w i t h
Vout
Ri(min)T
(6)
Vidmin)
An e x p r e s s i o n f o r t h e d e s i g n i n d u c t a n c e may b e found
f o r t h e b o o s t and buck-boost c o n v e r t e r s u s i n g t h e
same method,
however, t h e a v e r a g e i n d u c t o r c u r r e n t
is n o t e q u a l t o t h e o u t p u t c u r r e n t
i n these
converters.
For
the
zero-voltage
r e s o n a n t - t r a n s i t i o n boost converter
the
design
i n d u c t a n c e Ld is
~~
Buck-Boost
-)
buck,
boost,
and
the
switch control
35
For t h e z e r o - v o l t a g e r e s o n a n t - t r a n s i t i o n
c o n v e r t e r t h e d e s i g n i n d u c t a n c e Ld is
c o n d u c t i o n l o s s e s are i n d e p e n d e n t o f t h e o u t p u t l o a d
c u r r e n t , t h e a c c o n d u c t i o n losses w i l l b e p r e s e n t
even a t zero l o a d c u r r e n t . Thus, i t e x p e c t e d t h a t
t h e power c o n v e r s i o n e f f i c i e n c y a t l i g h t l o a d w i l l
b e r e d u c e d when c m p a r e d t o t h e f u l l l o a d e f f i . c i e n c y
when N R T s w i t c h i n g is used.
buck-boost
I f c o n v e n t i o n a l s w i t c h i n g t e c h n i q u e s a r e used, t h e
t o t a l s w i t c h i n g l o s s e s f o r b o t h power t r a n s i s t o r s a t
f u l l l o a d may b e approximated by
(8)
Prw.conv = 2<CorsVin2
To p r o v i d e n e g a t i v e c u r r e n t t o d r i v e t h e s y n c h r o n o u s
s w i t c h t o power s w i t c h t r a n s i t i o n , K must b e g r e a t e r
t h a n two.
In typical
a p p l i c a t i o n s K i s four
r e s u l t i n g a t h r e e t o we r a t i o i n t h e t u r n - o f f and
t u r n - o n t r a n s i t i o n t i m e s f o r t h e power s w i t c h a t
f u l l load.
I f K is i n c r e a s e d ,
t h e f u l l load
transition
time
ratio
is
decreased b u t t h e
c o n d u c t i o n losses are i n c r e a s e d .
Pac
Pcond =
(
+
3
12
c
Iout(max)2
+
(15)
3
30 V
-
2
( 0 . 1 4 Ohm) = 520 mW
and t a k i n g Coar t o b e 300 pf a t r a n s i t i o n t i m e o f 30
n s e c , t h e c o n v e n t i o n a l s w i t c h i n g loss is
+
( 5 0 V)(1.67 A X 3 0 n s e c ) ) f ' a w
= (3.25 mJ)fsw
Since
RDSOX-,
(10)
520 mW
-=
3.25 m J
RDSon
+
Iout(maX)2RDson
160 KHz
zero-voltage
resonant-transition
switching
will
r e d u c e t h e power loss i n t h e power t r a n s i s t o r s i f
t h e c i r c u i t operates a t a s w i t c h i n g f r e q u e n c y o v e r
160 KHz.
However, a c m p l e t e power l o s s t r a d e o f f
a n a l y s i s s h o u l d a l s o c o n s i d e r t h e losses i n t h e
i n d u c t o r s , c a p a c i t o r s , and t r a n s f o r m e r s a s w e l l a s
t h e volume o f t h e s e c m p o n e n t s .
(11)
12
[ :)
50W
2((300 pfX50 V ) 2
I n t y p i c a l a p p l i c a t i o n s K is f o u r .
Pcond =
4
-
Using e q u a t i o n 3.
Pcond =
2( C o s s v i n z
Iout(max)tr)Vinfsw
As a n u m e r i c a l example, assume t h a t two IRFAJINFI30s
are used i n a 5 0 w a t t power c o n v e r t e r which h a s a n
i n p u t v o l t a g e o f 5 0 Vdc and a r e f l e c t e d o u t p u t
loss
voltage
of
3 0 Vdc.
The a c c o n d u c t i o n
introduced
by
zero-voltage
resonant-transition
s w i t c h i n g is
on t h e o u t p u t
o n l y on t h e
1
-
(14)
- 1oua( max )2RDsOn <
1l P P 2
Iout(max)2
Psw,conv
4
(9)
u h e r e t h e dc component d e p e n d s o n l y
c u r r e n t and t h e a c component depends
internal inductor ripple current.
<
Using e q u a t i o n s 1 2 and 13.
For a buck power c o n v e r t e r o p e r a t i n g a t maximum
o u t p u t power u s i n g ZVRT s w i t c h i n g ,
t h e t o t a l power
l o s s i n b o t h power s w i t c h e s c o n s i s t s o f a dc and a n
a c component
Plc
(13)
To e f f e c t i v e l y u s e ZVRT s w i t c h i n g , t h e s w i t c h i n g
f r e q u e n c y must b e h i g h enough so t h a t t h e a c
c o n d u c t i o n l o s s e s a s s o c i a t e d w i t h NRT s w i t c h i n g a r e
less t h a n t h e s w i t c h i n g l o s s e s t h a t would r e s u l t
f r a conventional switching.
Zero-voltage
resonant-transition
switching
will
e l i m i n a t e ( t o f i r s t o r d e r approximation) switching
l o s s e s i n t h e power t r a n s i s t o r s a t t h e e x p e n s e of
i n c r e a s i n g t h e conduction l o s s e s throughout t h e
power c o n v e r t e r c i r c u i t . The c o n d u c t i o n l o s s e s are
i n c r e a s e d b e c a u s e a l a r g e a c component is r e q u i r e d
i n t h e i n d u c t o r c u r r e n t waveform. A d e t a i l e d t r a d e
o f f a n a l y s i s c a n b e made f o r a g i v e n s e t o f d e s i g n
g o a l s t o d e t e r m i n e i f NRT s w i t c h i n g p r o v i d e s a n
o v e r a l l advantage.
However, t h e d i s c u s s i o n i n t h i s
s e c t i o n w i l l b e l i m i t e d t o t h e power t r a n s i s t o r
losses i n a buck c o n v e r t e r t o d e t e r m i n e t h e minimum
f r e q u e n c y t h a t ZVRT s w i t c h i n g p r o v i d e s a power loss
savings.
+
VinIout(max)tr)fsw
where Cora is t h e o u t p u t c a p a c i t a n c e o f t h e power
t r a n s i s t o r , tr i s t h e a v e r a g e t i m e of t h e s w i t c h i n g
t r a n s i t i o n , and f w is t h e s w i t c h i n g f r e q u e n c y .
4. CONDUCTION LOSS PENALTY
Pcond = Pdc
+
(12)
5. IWERLEAVED FLYBACK CONVERTER
From e q u a t i o n 1 2 i t is c l e a r t h a t t h e a c c o n d u c t i o n
l o s s e s i n t h e power t r a n s i s t o r s t h a t a r e i n t r o d u c e d
by N R T s w i t c h i n g are o n e t h i r d l a r g e r t h a n t h e f u l l
losses.
Because
t h e ac
l o a d dc
conduction
B a s i c NRT s w i t c h i n g c o n v e r t e r s a r e d e s c r i b e d i n
s e c t i o n 3, however, m o s t r e a l a p p l i c a t i o n s r e q u i r e
i n p u t / o u t p u t i s o l a t i o n and v o l t a g e c o n v e r s i o n r a t i o s
36
c o n v e r t e r . The s t a t e - s p a c e a v e r a g i n g t e c h n i q u e E71
is used t o d e v e l o p t h e s m a l l s i g n a l model for t h o
NRT s w i t c h i n g i n t e r l e a v e d f l y b a c k c o n v e r t e r . I t is
assumed t h a t : t h e b l a n k i n g t i m e is s h o r t c m p a r e d t o
t h e s w i t c h i n g p e r i o d , t h e m u l t i p l e winding i n d u c t o r s
are identical,
t h e s t e a d y - s t a t e duty r a t i o i n each
and t h e l e a k a g e
flyback
s e c t i o n is i d e n t i c a l ,
inductance
effects are
insignificant
to
the
low-frequency dynamics o f t h e c o n v e r t e r .
t h a t a r e not obtainable with these baaic topologies.
T r a n s f o r m e r i s o l a t e d ZVRT s w i t c h i n g c o n v e r t e r s a r e
sought.
I n g e n e r a l , t a n s f o r m e r i s o l a t e d buck and
b o o s t d e r i v e d NRT s w i t c h i n g c o n v e r t e r t o p o l o g i e s
c a n b e formed by o p e r a t i n g two i d e n t i c a l c o n v e r t e r
s e c t i o n s i n p a r a l l e l w i t h i n t e r l e a v e d t i m i n g and
u s i n g m u l t i p l e winding i n d u c t o r s f o r i n p u t / o u t p u t
isolation.
Although a c o m p l e t e
discussion
of
i n t e r l e a v e d ZVRT s w i t c h i n g t o p o l o g i e s i s o u t o f t h e
scope of t h i s paper, it advantageous t o i n t r o d u c e
t h e switched-capacitor i n t e r l e a v e d flyback converter
t o e x p e r i m e n t a l l y d e m o n s t r a t e ZVRT s w i t c h i n g i n a
practical application.
The s w i t c h e d - c a p a c i t o r i n t e r l e a v e d f l y b a c k c o n v e r t e r
is
simplified
to
an
equivalent
interleaved
buck-boost
c o n v e r t e r which
passes through four
states i n a c m p l e t e s w i t c h i n g c y c l e a s shown i n
F i g u r e 6 . To implement ZVRT s w i t c h i n g , t h e c u r r e n t
i n a given i n d u c t o r must r e v e r s e p o l a r i t y b e f o r e
t h a t i n d u c t o r is s w i t c h e d t o a new state. A s l o n g
a s t h e i n d u c t o r c u r r e n t is c o n t i n u o u s ,
it may p a s 8
through z e r o without
affecting t h e state-space
averaging process.
The s w i t c h e d - c a p a c i t o r i n t e r l e a v e d f l y b a c k c o n v e r t e r
[61 o f F i g u r e 5 w i l l o p e r a t e w i t h ZVRT s w i t c h i n g i f
t h e design c o n s t r a i n t s described i n Section 3 a r e
m e t . The i n t e r l e a v e d f l y b a c k c o n v e r t e r is u s e f u l
f o r high s w i t c h i n g frequency ( 1 M H z )
applications
which r e q u i r e low o u t p u t v o l t a g e s (5 V and less).
I f t h e d u t y r a t i o f o r b o t h f l y b a c k s e c t i o n s is less
t h a n o n e h a l f and i f a h a l f - c y c l e t i m i n g i n t e r l e a v e
is u s e d , t h e p r i m a r y s i d e f i l t e r c a p a c i t o r C p
a p p e a r s m u l t i p l i e d by t h e s q u a r e o f t h e t r a n s f o r m e r
t u r n s r a t i o n i n t h e o u t p u t c i r c u i t a s Ca.
This
a l l o w s t h e u s e of high v o l t a g e ceramic f i l t e r
Since t h e duty
c a p a c i t o r s on t h e p r i m a r y s i d e .
r a t i o o f t h e o u t p u t r e c t i f i e r t r a n s i s t o r s is a l w a y s
g r e a t e r than one h a l f , t h e conduction l o s s e s f o r a
f i x e d o u t p u t c u r r e n t r e q u i r e m e n t are r e d u c e d by t h e
timing overlap.
The s t a t e - s p a c e a v e r a g e d
v a r i a b l e c i r c u i t is
D- 2
0
0
-
2L
D-2
0
0
-
equation
r,
r!
12
2-D
2-D
-1
- - -
A s m a l l - s i g n a l model d e s c r i p t i o n is i n c l u d e d f o r t h e
NRT s w i t c h i n g i n t e r l e a v e d f l y b a c k c o n v e r t e r t o
demonstrate t h a t t h e small-signal c h a r a c t e r i s t i c s
a r e s i m i l a r t o t h o s e o f t h e c o n v e n t i o n a l buck-boost
2C
2C
the
three
V
DL
V
-
A
d
DL
2L
5 . SMALL-SIGNAL MODEL
for
A
V
RC
-I
2c
i 16)
-
where D i s t h e f r a c t i o n t h a t a power s w i t c h ( Q 2 or
Qs i n F i g u r e 5 ) i s a c t u a l l y o n c m p a r e d t o t h e t o t a l
t i m e t h a t i t c o u l d b e on w i t h i n t.he i n t e r l e a v e d
timing c o n s t r a i n t s .
b
a c t u a l on t i m e
(17)
D =
d u r a t i o n of o n e h a l f c y c l e
Thus, f o r a d u t y r a t i o o f o n e i n t h e i n t e r l e a v e d
f l y b a c k c o n v e r t e r , e a c h power s w i t c h is on f o r a
c o m p l e t e h a l f c y c l e . The f o u r z e r o s I n t h e upper
l e f t c o r n e r of t h e A m a t r i x guarantee t h a t t h e
d e t e r m i n a n t o f A is z e r o , i m p l y i n g l i n e a r dependence
of t h e s t a t e e q u a t i o n s .
This i n turn implies t h a t
t h e o r d e r o f t h e r e s u l t i n g s y s t e m is less t h a n
three.
A c o n c l u s i o n which is n o t s t a r t l i n g when o n e
c o n s i d e r s t h a t t h e i n d u c t o r s form a p a r a l l e l e l a n e n t
f o r two o f t h e f o u r s w i t c h s t a t e s .
al
I
P
A second-order s t a t e - s p a c e
averaged d e s c r i p t i o n can
be developed by t a k i n g t h e c a p a c i t o r v o l t a g e and t h e
sum o f t h e i n d u c t o r c u r r e n t as t h e two s t a t e
variables.
S t a t e s o n e and t h r e e a s well a s s t a t e s
two and f o u r a s shown i n F i g u r e 6 a r e i d e n t i c a l .
The r e s u l t i n g m a t r i x e q u a t i o n is
Figure
5.
The s w i t c h e d - c a p a c i t o r
interleaved
f l y b a c k c o n v e r t e r p r o v i d e s t r a n s f o r m e r i s o l a t i o n and
may b e d e s i g n e d t o o p e r a t e w i t h NRT s w i t c h i n g .
37
I::=
State 1
A
+
(18)
d
--
dt
S i n c e t h e m a t r i x A is n o n s i n g u l a r ,
equatj.on
d e s c r i b e s t h e c i r c u i t as a s e c o n d - o r d e r system.
18
The s t a t e - s p a c e a v e r a g e d e q u a t i o n s may b e coriverted
i n t o t r a n s f e r f u n c t i o n d e s c r i p t i o n s ( a l s o known a s a
g-parameter d e s c r i p t i o n ) o f t h e power c o n v e r t e r
State 2
A
Vo(s)
C v g ( s ) =-if
=
Vg(s)
D
1/LEC
2-D
s2
+
s/RC
~/LEC
+
P
Vo( s )
Gvd(s) = 7
=
d( 8 )
2R
Vin
(
~-D)~LERC
82 +
-
s/RC
SDLE
+
-
~/LEC
A
Iin(s)
Cig(s) = I
\=
Vg(s)
s
D2
2L
82 +
+
1/RC
s/RC
+
1/L&
A
Iin(s)
DVin
Gid(s) = 7
=
d(s)
(2-D)L
-
State 3
s
82 +
+
(2+D)/2RC
s/RC * ~ / L E C
(19
-
22)
where
2L
LE =
)*
(23)
( 2-D
F o l l o w i n g t h e p r o c e d u r e i n t71,
w e obtain t h e
e q u i v a l e n t continuous-time
( o r canonical) c i r c u i t
model of F i g u r e 7.
State 4
-1
d
-
-- v
--
c
L
i
-
+
-
F i g u r e 6 . T h e r e are f o u r states i n a c m p l e t e
s w i t c h i n g c y c l e for t h e i n t e r l e a v e d
buck-boost
c o n v e r t e r which o p e r a t e s w i t h NRT s w i t c h i n g .
By c a s t i n g t h e i n t e r l e a v e d buck-boost ( f l y b a c k )
t o p o l o g y i n t o t h e form o f a c o n t i n u o u s - t i m e c i r c u i t ,
w e have a c o n v e n i e n t means of c a p a r i n g dynamic
c h a r a c t e r i s t i c s of
the
interleaved
buck-boost
t o p o l o g y w i t h t h o s e o f t h e r o o t buck-boost t o p o l o g y .
I f t h e d u t y r a t i o is n o r m a l i z e d t o a s w i t c h c y c l e
t h a t i n c l u d e s b o t h "halves"
of t h e i n t e r l e a v e d
operation, t h e e q u i v a l e n t c i r c u i t of t h e i n t e r l e a v e d
buck-boost
is
identical t o
the
conventional
buck-boost e x c e p t f o r t h e t e r m s LE and J as shown i n
F i g u r e 7. The v a r i a t i o n i n LE n o t a s i g n i i i c a n t
d e p a r t u r e , s i n c e it i s s i m p l y h a l f of t h e v a l u e f o r
a s i n g l e i n d u c t o r t o p o l o g y , which h a s t h e e f f e c t of
placing
the
two i n d u c t o r s o f t h e i n t e r l e a v e d
buck-boost i n p a r a l l e l a t low f r e q u e n c i e s .
More s i g n i f i c a n t is t h e f a c t o r D, p r e s e n t i n J, f o r
t h e i n t e r l e a v e d buck-boost
topology.
T h i s is a
d e p a r t u r e from t h e i n p u t c h a r a c t e r i s t i c s o f t h e r o o t
topology. T h i s d e p a r t u r e a r i s e s because interl.eaved
v e r s i o n h a s s t a t e s i n which i n d u c t i v e e l e m e n t s are
connected
to
both
the
input
and
output
s i m u l t a n e o u s l y - a c i r c u m s t a n c e n e v e r e x p e r i e n c e d by
t h e s i m p l e buck b o o s t c o n v e r t e r .
The t e r m h a s n o
e f f e c t on t h e c o n t r o l t o o u t p u t c h a r a c t e r i s t i c s , b u t
Conv.
Buck-
Boost
Inter.
BuckBoost
F i g u r e 8.
The o u t p u t waveform8 o f t h e d i g i t a l
c o n t r o l l e r are used d r i v e t h e power
switching
t r a n s i s t o r s w i t h a b l a n k i n g i n t e r v a l o f 117.5 n s e c .
F i g u r e 7. The c o n v e n t i o n a l buck-boost c o n v e r t e r and
t h e i n t e r l e a v e d buck-boost
c o n v e r t e r are c m p a r e d
u s i n g t h e c a n o n i c a l c i r c u i t model o f Middlebrook and
t r a c e ) f o r power s w i t c h 122 a r e shown i n F i g u r e 9. A
z e r o - v o l t a g e t u r n on t r a n s i t i o n f o r Q2 is shown i n
The t u r n on
middle photograph
of
F i g u r e 9.
t r a n s i t i o n f o r Q 2 is i n i t i a t e d when Q l is t u r n e d o f f
causing t h e drain-to-source
f o r v o l t a g e f o r Q2 t o
s t a r t t o d r o p 104 n s e c b e f o r e t h e g a t e of Q2 is
d r i v e n h i g h . A s F i g u r e 9 shows, t h e d r a i n t o s o u r c e
v o l t a g e f o r Q2 is a p p r o x i m a t e l y zero when t h e g a t e
a c t u a l l y t u r n s ( c h a n n e l o f ) t h e t r a n s i s t o r on. A
z e r o - v o l t a g e t r u n o f f t r a n s i t i o n f o r Q2 is shown i n
lower p h o t o g r a p h o f F i g u r e 9, where t h e g a t e - t o s o u r c e v o l t a g e is r a p i d l y s w i t c h e d
below
the
threshold v o l t a g e while t h e drain-to-source v o l t a g e
is a p p r o x i m a t e l y z e r o . The c h a r a c t e r i s t i c p l a t e a u
i n t h e gate-to-source
v o l t a g e waveform a s s o c i a t e d
w i t h d r i v i n g t h e FET t h r o u g h t h r e s h o l d is e l i m i n a t e d
u s i n g NRT s w i t c h i n g .
CUk.
it
d o e s a f f e c t t h e i n p u t impedance of t h e c i r c u i t
and hence t h e i n p u t f i l t e r parameters r e q u i r e d f o r
acceptable operation.
7. EXPERIMENTAL VERIFICATION
An e x p e r i m e n t a l i n t e r l e a v e d f l y b a c k c o n v e r t e r i s
u s e d t o e x p e r i m e n t a l l y v e r i f y VZRT s w i t c h i n g .
In
r e f e r e n c e t o F i g u r e 5, e a c h f l y b a c k s e c t i o n o p e r a t e s
a t a s w i t c h i n g f r e q u e n c y of 1 M H z w i t h 500 n s e c
d e l a y ( o r 1800 p h a s e s h i f t ) between s e c t i o n s . Thus,
t h e f r e q u e n c y o f t h e i n p u t and o u t p u t r i p p l e is 2
MHz.
The e x p e r i m e n t a l c i r c u i t o p e r a t e s f r a n a n
i n p u t v o l t a g e s o u r c e o f 55 Vdc ( * / - 1 0 p e r c e n t ) and
p r o v i d e s 40 watts o f o u t p u t power a t 3.3 Vdc.
A e f f i c i e n c y o f 83 p e r c e n t h a s been measured i n t h e
experimental i n t e r l e a v e d flyback c i r c u i t providing
40 Watts o f o u t p u t power a t 3.3 Vdc s w i t c h i n g a t 1
MHz. The e f f i c i e n c y d o e s n o t i n c l u d e t h e 1.15 watt
power loss i n t h e g a t e d r i v e a m p l i f i e r a n d 1.5 w a t t
power loss i n t h e d i g i t a l c o n t r o l l e r .
If the gate
d r i v e and c o n t r o l power is i n c l u d e d , t h e f u l l l o a d
e f f i c i e n c y is r e d u c e d t o 76 p e r c e n t .
A d i g i t a l c o n t r o l l e r C 8 1 is used t o c l o s e t h e
feedback l o o p which is implemented i n a CMOS g a t e
array.
The e r r o r i n o u t p u t v o l t a g e o f t h e power
c o n v e r t e r is sampled and d i g i t i z e d e a c h s w i t c h i n g
cycle
and
used a s t h e i n p u t t o t h e d i g i t a l
c o n t r o l l e r . The d i g i t a l c o n t r o l l e r g e n e r a t e s p u l s e
w i d t h m o d u l a t e d waveforms
with t h e a p p r o p r i a t e
b l a n k i n g i n t e r v a l s t o d r i v e power t r a n s i s t o r s 91
t h r o u g h (16 i n a NRT s w i t c h i n g mode.
Typical
d i g i t a l c o n t r o l l e r o u t p u t waveforms a r e shown i n
The upper waveform o f F i g u r e 8 is
F i g u r e 8.
i n v e r t e d by t h e g a t e d r i v e a m p l i f i e r and used t o
d r i v e b o t h Q1
a n d Q3 s i m u l t a n e o u s l y .
The l o w e r
wavefrcm o f F i g u r e 8 ( w h i c h is n o t i n v e r t e d by t h e
g a t e d r i v e a m p l i f i e r ) i s used t o d r i v e Q2. A
b l a n k i n g t i m e t b o f 117.5 n s e c h a s been s e l e c t e d
(via a digital input port to the digital controller
t i m i n g l o g i c ) f o r b o t h t h e t u r n on and t h e t u r n o f f
transitions.
8. SUMMARY
A
zero-voltage
switching
technique
has
been
d e s c r i b e d which u t i l i z e s a r e s o n a n t
transition
during a short but f i n i t e switching interval.
This
zero-voltage
r e s o n a n t - t r a n s i t i o n (NRT) s w i t c h i n g
t e c h n i q u e c a n b e a p p l i e d t o c o n v e n t i o n a l buck,
boost, and buck-boost
power c o n v e r t e r t o p o l o g i e s
which o p e r a t e w i t h a c o n s t a n t s w i t c h i n g f r e q u e n c y
and u s e p u l s e w i d t h m o d u l a t i o n f o r o u t p u t c o n t r o l .
S i n c e f r e q u e n c y d e p e n d e n t losses are g r e a t l y r e d u c e d
i n t h e power t r a n s i s t o r s , e f f i c i e n t o p e r a t i o n a t
higher switching
frequencies
( o v e r 1 M H z ) is
allowed.
However, c o n d u c t i o n losses are i n c r e a s e d
because
ripple
currents
are
increased
and
The g a t e - t o - s o u r c e
v o l t a g e a t 5 V/div ( u p p e r t r a c e )
<lower
and drain-to-source
v o l t a g e a t 50 V/div
30
s y n c h r o n o u s r e c t i f i c a t i o n is r e q u i r e d .
Experimental
r e s u l t s are p r e s e n t e d f o r a n i n t e r l e a v e d f l y b a c k
c o n v e r t e r which o p e r a t e s w i t h ZVRT s w i t c h i n g a t 1
MHz.
REFERENCES
Cll.
K. H. L i u and F. C . L e e , "Resonant S w i t c h e s
-
A U n i f i e d Approach t o Improve Performance o f
Switching
Converters,"
I EEE
I NTELEC
P r o c e e d i n g s ; pp 344-351, 1984.
9.
ZVRT s w i t c h i n g
waveforms
in
the
Figure
i n t e r l e a v e d f l y b a c k c o n v e r t e r f o r power t r a n s i s t o r
Q2 i n t h e
i n t e r l e a v e d f l y b a c k c o n v e r t e r . The upper
t r a c e is t h e g a t e - t o - s o u r c e v o l t a g e a t 5 V/div and
t h e lower t r a c e is t h e d r a i n - t o - s o u r c e v o l t a g e a t 50
V/div.
The m i d d l e p h o t o g r a p h shows z e r o - v o l t a g e
t u r n - o n and t h e lower p h o t o g r a p h shows z e r o - v o l t a g e
t u r n - o f f a t 20 naec/div.
40
H.
L i u and F.
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t o Modeling
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C87.
C.
P. Henze and N. Mohan, "Modeling and
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G.