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DESIGN OPTIMIZATION OF ZVS AND ZCS
QUASI-RESONANT CONVERTERS FOR EM1 REDUCTION
VIVEK AGARWAL
MADHUWANTI JOSH1
Department of Electrical Engineering
Indian Institure of Technology, P o w 4 Bombay 400 076, India
-
Buidts d i n g to the cost these drawbscks tend to undermine what
could ba one of the be& features of resonant converters, that of low
EMI.
'1 he magnitude of peak current and voltage is dependn,t on the
values o f resonating components. In case o f load resonant
converters, the values of L and C are a function o f required voltage
gain( h4 ), the corresponding normalized operating frequency. f.
(ratio of switching fiequmcy to the resonant fraluency) and the
namalized lo@ ( Q ). The relationship between these thrce
quntities is manifested in the finm o f curves of Fig. 2 171, shown
for a wries-parallel t y p of load resonant mverter.
1. INTRODUCTION
One of the major drawbacks of hard switched. high fioquency power
converters is excessive switching losses. Fig. I(a) shows one o f the
m m o n power conversion schemes based on hard switching. The
reason for excessive Iowa during hard switching is the presence of
either a non-zero voltage or curate at the time of device switching.
Fig. I((b) (d) ) shows another set o f power converters which
utilire some sort o f resonance phenomenon across its devices to
achieve fer0 current or voltage switching. These fall under the
category o f resonant or quasi-resonant converters. These converters
are more popular for high frequency applications because it is
pwsible to shape the current and voltage waveforms across the
device to achieve zero current or zero voltage switching, thereby
reducing the switching losses to a great extent.
It is a well known fact that whenever there is a r k a n c e . i t results
in high peeks o f electrical quantities. Thus. the situation is no
different in quasi-resonant converters. The gain versus nornializd
operating frequency curves for ZCS type o f Q H co~ivertersare shown
-
An additional advantage that comes with the zero currenllvoltage
switched resonnnt converters is a reduction in EM1 (Elecho
Magnetic Interference). It i s evident that the hard switched
tcrpologies will cause sudden snapping of currents through the
dcvices causing large disturbances in the electromagnetic fields
as.wiated with the circuits. Thew disturbances (or electromagnetic
noise), in turn a l l i d the other unnponents/devices o f the same
circuit as well as the neighboring circuits. A resonant converter is
cxpcckd IOeliminate this drawback in a 'natural' way.
(c) m - c u n e n t Switching BoonCmvnCec
Fig. I Examples o f hard-switched ( (a) ) and son-switched
c ~ n v ~ t(e(b)
r ~ (d) ).
-
in Fig. 3 [I]. The corresponding curves fop ZVS mifiguration are
shown in Fig. 4 121. As far as the basic deign mcthdolqty i s
concerned, it remains the same fbr both the lwd resonant and OK
converters. However, the full-wave Q K converters o f k a spccial
advantage over the rest. that of load independence. T h i s property. as
explained in tile next seclion. am be us& for design optimi7ation of
these converters.
Clearly. a resonant converter seems to be. a strong candidate Tor most
high frequency applications, but for a major drawback. These
cmiverters suffer from the disadvantage of high voltage and current
pcaks in their resonant tanks. This, in effect causes the device
ratings (0 be much higher than t L i r hard-switched counterparts.
81-900652-0-3/97 RS.40.00 01997 SEMCEI
(4 Lcro-Volupc Switching Cant-
407
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INCEMIC-97 : 7A-2
Proceedings of the International Conference on Electromagnetic Interference and Compatibility '97
in this case. But another look at the curvcs (of Fig. 4)
shows that i t does not matter, since the curves are indcpmdall of 0.
i.e. all the curves overlap. Thus. the operatins poht does not shill
and M = M'. The same thing holds for the set o f curves shown in
Fig. 4, although nat so obvious at the first giance.
'Ihe present paper optimizes the design o f full-wave ZCS and ZVS
type OK converters to get minimum peaks o f current and voltage
and hence lower EMI. Section II describes the optimization
procedure while section 111 gives the simuiation results. Results are
discussed in seczion iV. The paper cuncludes in section V.
over to Q-
11. OITIMIZAIION OF L,ANL) C,
7his sedion describes the design optimization process. The
notaticms which are used to represent various quantities are as
follows. Vi * Input voltage, V,, = Output voltage, f, = Switching
frequency, f, = Resonating frequency, R( = Load resistance, L, =
Resonant indudor C, = Resonant capacitor, Z = Characteristics
inipcdanced(L,/C,), D = Duty cycle.
Clearly, converters represented by curves of Fig. 2 or 3(a) can not hc
optimi7,. Or at least there exists no simple method to do that
without sacrificing output voltage regtilation. It can be shown that
the same holds true for the half-wave mode QR converters also. On
the other hand, full-wave ZVS and ZCS QK converters can be
optimized taking advantage o f the feature mentioned in (11) above.
.
1hc tlicory behind proposed optimization :
To test the theory just developed. QR boost converters ciperating i t i
full-wave mode have been optimally designed and simolated as
reported in the subsequent sections o f the paper.
I hc following ternidrelations will be used oRen in the remaining of
this paper.
Normalized load,
v - o,l&
Iksonant angular frequency,
D
l
>
3
*
.
1he aini of optimization i s as follows:
i%)r a given (specified) gain M' and operating Requency (f,*), we
want to optimize L, and C, in such a way that the currenVvoltage
peaks are minimized. From the curvm, of M versus h,it is clear that
fiir a chosen value o f c) (say c)'), M will correspond to fa' (f,'/fi).
'I'wo important conclusions follow from this:
fir-+
07
Cb>
Fig. 4 The set o f curves (a) and (b) are the design curve3 M S b~r
quasi-resonant zersvoltage-switched boost ccniverter. A careful look
will reveal that just like Fig. 3 (b), these figure also represent a set o f
overiapping M versus f. curves for various Q's. Note that h $ 0 implies
half-wave mode while h 2 0 implies full-wave mode o f operation.
(I)I n Fig. 2 or 3(a), if an attempt is made to vary L, and C, (keepin!
f, crristnnt), 0
' chanRes to Om, and the operating point (M ,f. )
sliifis to a corresponding point on the curve corresponding to Q,.
'1 hus M f M' . I lence one can not vary (optimize) L, and C, without
varying M, which o f course is not acceptable if a regulated output
voltage is required.
(11) In. Fig. 3(b). however, the situation is different. I t i s possible to
vary L, and C,, keeping fi constant. I t is not that Q'does not change
Design of test convcrters:
A generalized procedure based on the curves shuwn in V i p . 3(h)
and 4. for design of both the ccriverlers i s given bclow. As
discussed earlier, the full wave operation fi* both ZCS and ZVS
converters offers the advantage o f independence of gain ovcr load
current. For the converter to remain in thc full-wave Opneiiun mode
there i s a constraint given by:
(81
408
Madhuwanti and Vivek : Design Optimization of ZVS .and ZCS Quasi-Resonant ...
0
,
depends upon L e gain and fqucncy ratio. Ifwe operate the
converter within the range defined by (2.3) and (2.4), we get
sullicient variation in Q for a cunstant gain and resonant frequency.
Keeping these two conditions in mind the convatas have to be
designed.
I.Delermine the desired gain, VJV,
2.Select a suitable switching frequency.
3.Clime M appropriate value for Q depending on (2.3) and (2.4).
4. For the values found in ( I ) and (3), determine the requirca
hequmcy ratio f/r: using the curves o f Fig. 3(b) (ZCS)and Fig. 4
~
9
-
~
'
(0 p?ms
199*ns
n-8
'b"
E.,
I
i-m. .........
(ZVS).
5. Once f/f, is known, f, can be determined since f, is known.
6. lJse (2.1) and (2.2) to ddermine
oi'timized design valws.
-Jm
&.2.r,
L, and C,. These are the un-
i
i-h\A
0-
I
- - A
A
0-
r
.,*",,
:
nmw
Following the above general procedure. the converters were
designed for the following specifications:
I
Vi==12V,V,,-24V,f,lint
IUOklll.,~=60htn,U=0.5.L= l m l l , C =
(a) ZCS converter :
'I he desired gain 2. From Fig. 3(b), f/t; = 0.5. .'.$
Using the constraint (2.3),
1, < 9c,.
5A(i), un-optimized design.
2OOkhz.
-
Fig. 5 (Mi) Simulation resutts for ZCS ( (A) (0)) and
ZVS ( (E) (tJ) ) cases. showing (i)device current and (ii)
-
voltage across the device obtained using optimized and unoptimized design values. 1\11 the waveforms show (a) 'lime
dcwain waveform (b) Lower order frcquerlcy spectrum
(c)l Iighcr order frequency spectrum.
(2.5)
h a a first step, L, was arbitrarily chosen = 0.397 pH and
corresponding C, = 1.591 pF. It must, however, be pointed out that
these nre only unoptimized values o f L, and C, and are optimized
using repeat& simulations in the next sec2ion.
(b) ZVS converter :
...
'l'he desired gain = 2. therefore from Fig. 4, the corresponding
0.5.
Froni Fig. 4, Q,, * 2.
Iroin equation (2.3).
ZCS case: The optimization is done by varying the values o f 1, nnd
C, using equation (2.5). Repeated simulations were pcrfnrtncd liw
each get of values. The criteria for optimization i s peak current
through the switch. As the characteristic impedance 2 increases. tlic
current reduces. Ilowever. at a particular value of& voltage across
the device starts developing spikes. 'I his puts a limitation on how
much the characteristic impedance can be increased, a point rurtllcr
discussed in the next section.
-
vf;
I, >2.38 pi I .
The switch current and voltage waveforms for vn-optintizd dcsigil
are shown in Figs.JA and513 respeaively. while the correspondinn
waveforms fw the optimized design nre shown in Figs.5Cand R A
comparison FigsJAandSCreveals that current peaks are significantly
reduced in the o p l i m i d case. The frequency spectrum shows that
magnitudes o f both the lower and higher order hnrmonics nre
reduced considcrab!y as compared to thosc is the un-optimi~edcase.
Further, it i s clear from Figs. 5Randsf)Ihat thcre is no change i n
switch voltage waveforms in optimizfd case.
'l'o begin with. I, was randomly chosen = I pH. The corresponding
un-uptimizcd C, i s 0.057 pF.
111 SIMULATION OF THE CONVEI rEHS AND RESULTS
OF OIYTIMIZATION
'IIIcconverters designed in the previous section were simulated
using PSI'ICE. Initially converters are simulated using unoptimized
vducs. Later. the values of Lr and Cr were systematically tuned to
uptiinize the relevant design criteria. The w a v e f m s o f device
current and voltage (across the device) along with their harmonic
spectrum arc shown in Figs. 5(A) - (111, fw both ZCS and ZVS Cases.
ZVS case: The criteria o f optimization in this case is the peak
voltage across the device. Repeated simulations were performed to
optimize the peak value o f device voltage. In contrast to the ZCS
409
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Proceedings of the International Conference on Electromagnetic Interference and Compatibility '97
case, here, one needs to minimize Z,because as 2 decreases, device
voltaKe peak decreases. But, just as in the case o f ZCS, Z can not be
decreased to any arbitrary value because after a certain limit, .the
current through the device shows spikes. a potential source o f E M .
'Ihis point will be further elaborated upon in the next section.
m
I
I\ I
'I'he peak voltage across the device and device current vs Z is
plotted which is shown in Fig. 6. The point on the curve for
which peak voitage across the device is minimum and current spikes
are zero or very less gives the optimum value o f 2 The forbidden
7 ~ n eindicates the 2 values for which very high current spikes are
present.
. . .
n 9201s
The waveforms o f device current and voltage at un-optimum values
of L, and C, are shown in Figs.58and SF respectively. while their
counterparts for optimum L, and C, values are shown in Figs. 50 and
s i t . The canparison o f voltage waveforms in Figs. SF and si1 shows
that the voltage peaks are r e d u d substantially without making any
difference in the current waveforms shown in Figs.5~andSO. The
harmonic spectra o f switch voltage shows a significant magnitude
reduction in Iowa as well as higher order harmonics. A major
observation, then. is that ZCS and ZVS cases are duals of each
other.
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I
IV. DISCUSSION O F RESULTS
i
. --
ah
VlU
.
e...
.
i
I
I
I
i
The ZCS case:
In %CSconverter, there are two major c
a
m of EM:
( I ) The voltage BETOSS the switch being a square wave, it causes
capacitive cwpling between the device and heat sink due to a large,,
Fig. 5 (cont.)
m,
I
'
i~
. .-... ....
;
!
:
.......
MI?
I er
fl
A- . .._...
OlMlfZ
'
__
A. __ -
i
,A-2- 1
O&oB
0-
r w N I
.
j
'
8
I mnh
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Fig. 5 (cont.)
~~~,~~~~~~~~~~~~~~
13"
'-
1-
Slyii), un-optimized design.
410
5C(i). optimized design.
Cdvldt.
(2) 1 he current through the devise is not perfectly sinusoidal. 'Ihere
are higher order harmonics along with thc switching kquency
which get conducted in the circuit. If the frequency o f qmation is
too high, these higher harmonic components may even become a
source of radiated EMI. The megnitde of the current harmonics
depends u p the magnitude o f switch currmt.
Since the current peaks are reduced with optimized values o f
resonant elements. the magnitude o f current harmonics also reduces.
Apart from reduction in magnitude o f current harmoniu. the
reduction in peak reduces the required current rating and current
stress on the device. The voltage waveform remains unchenyed. So
there is no change in the corresponding harmonica level.
It is clear that one would be tempted to reduce the current peaks to
very low values. Ideally speaking, one should be able to do it uplo
any arbitrary level. Unfortunately. this i s not possible because o f the
limit imposed by undesirable voltage spikes across the device. As the
value of inductance (and hence 2) i s increased voltage spikes appear
across the device. These spikes develop because o f the fact that for a
given pulse width, above a critical value of Z. m e non-zero
current is present in the switch at the turn off time. These spikes
can be avoided using proper closed loop amtrol o f pulse width. In
fact one might feel tempted to enter L e forbidden zone in order to
further optimize the design. But that will lead nowhere since the
converter will enter half-wave mode. Ilaice,the desirable option is
to avoid the forbidden m e canpletely.
Madhuwanti and Vivek : Design Optimization of ZVS and ZCS Quasi-Resonant ...
'I he LVS case:
!
I
In ZVS converter, the E
M arises mainly becauseof the following:
(I). 'Ihe squarewave switch current will be rich in harmonics. If the
switching frequency is relatively Iowa. they will be a source of
coriducted EMI. If the convater operating bequency is very high,
tlie impedance offered ty circuit's inductmm will be significantly
high and h a m cooduced EM1 will k less. Hawever, circuit will
becano a nourw of radiated EM.
'
I
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I!
!/
,
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!
89ms
W%S
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11.1
,
r.ai
(2). 'Ihe voltage waveform is nearly sinusoidal. Advantage ofZVS is
that capacitive coupling due to device capacitance is minimum since
dV/dt at the time of device switching is nearly zero. However, EM1
is prescnt due to quasi-sinusoidal voltage which contains multipla
of operating frequency harmonics of voltage. The voltage
hirmmics cause a current of the same beuuenw
. - to flow in the
circuit (conducted EMI).
,IL.--I I_ _ _...--A
-_
aia
voltage which the device needs to handle. Apart kom reducing the
device voltage dress, latter is particularly advantageous for devices
sucii as MOSFE'Is (suitable for high frequency applications), since
02"
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.
.
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0w i z
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Fig. 5 (cont.)
Fig. 5 (cont.)
SU(ii), optimized design.
41 1
5Qii). un-optimized design.
.
I
Proceedings of the lntemational Confeence on Eiectmrnagnetic .Interference and Compatibility '97
will be taken up in a future wurk. The EM1 pcrfcwmance Iias bcmi
investigated for ZCS and ZVS converters by PSPICE simulation of
the unoptimised and optimized designs and comparing their
perfwmance. These resuk have been presented a i d expiaird.
h i g n curves have been presented shuwitrg the pcrfwntancc of
converter for various values of Z.
b
i
,
'
Another advantage of uptimimation i s reduction in device ratings and
stresses on the power devices.
.*,,
i
I
i'
Optimization can not be done to any arbitrary level. 'Iliere are limits
(forbidden zones) which have been identified in this paper. It has
been shown that if these limits are exceeded, tlie performance call
deteriorate rather than improving. Closed loop control of the
converter may stretch these limits slightly, but not too much as the
:
;
,
_..--.A _.----.
02Mllr
MI.
*
04h0k
*
r.
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_. OAW k
1.
8
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1
I Ilh5Il,
IIMlb
Fig. 5 (cont.)
10Mllr)
2 5Mllt
5G(i), optimized design.
14111,
converters enter half-wave mode ifoptimiped beyond a certain point.
The optimization aiteria and procedure uced here seem9 to he
suffrcient for most spplicatims. Hut s better option will be tu cwne
up with some kind of mathematical formulae and standard de+
curves fw optimized performance. Only the most promirimit facttac
(like the peak current and voltage) have heen awiciderd in thic
work. Efforts are on to arrive at coirtpretteiisive ~1ptimi7ati011
fwmulae taking in to account other factrws. 1he snme will hc*
reported in a future paper.
15Mlb
IPOV
6Cb). Once again, it is recommended that the designer &e? enter
the region marked "forbidden" to get the benefit o f reduced device
voltage peaks as well as staying clear of undesired current spikes. It
may be armed once more that if the system is owated in CM
loop, the &sign can be furtkr optimized. But i t must be kept in
mind that as we try to further optimize the converters (entering the
forbiddm zone), the converter enters half-wave mode, which of -IDp",
course i s not acccpcabie.
*)%*
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.
899hns
WOWM
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V. CONCLUSIONS
It i s a common bclicf that resonant converters are farmaMe for good
EM1 performance. Ilowever. this niny not be the cast?, if a proper
sclcctittn of tlie resonant tank component values is not made. A
;
variation in the values oft, and C, (keeping the resonant frequency,
cowtatit) causcs large variations in fhe peaks of the current and
voltages. Unfortunately, the optimii~itiono f L, and C, values is not
easy in general in cases such as load resonant mvetters and QR ~ i z - - - .
converters operated i n half-wave mode. I h e configurations. like the
%<'S arid %VS Q K converters, are special cases when operated in full l c l * ' *
wave mode. 'lhe optiiniiation i s easily possible in these case
1
bccause of their load insensitive feature.
<)tie of the most favorable outcorries of using an optimized design i s
tlic improvement in the EM1 performance of tlie converters. 'Ihis i s
a r e d of reduction o f current and voltage peaks. Both lower and
'
Iiiplier order Iiarmonics are reduced without making an adverse
eliect on any otfier parameters of the circuit. If the operating
frequency is low, the circuit i s prone to conducted noise, while it -;*
becomes a w r c e of radiated noise, as the operating frequency is
iitriectsed. I
he latter can be explained usincq the antenna theory and
\
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1..
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J. J. ~
A
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ISWIZ
loh(f(r
Fig. 5 (cot~t.)
I
wc
1DMil,
Sti(ii). optiniiied desip.
412
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1 IMII.
Madhuwanti and Vivek : Design Optimization of ZVS and ZCS Quasi-Resunant ...
P d 00-
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C w r d md Vottage n ~h trim-
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I
T-r-- -
111 K
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1
t-
I
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ChruMetohc**udan*
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10
2
2 (ohrs)
12
14
3
25
<a)
15
10
fig. G Peak device current and voitage (across the device) versus the
characteristic impedance for (a) ZCS case and (b) ZVS case. The
optimum value in both the ptots i s denoted by a ‘@‘ sign. Note that
thc hcmndary of the forbidden m e is an approximate one and in
Rcncral one has to lune i t stightly to avoid getting undesirable vdtage
(as i n ZCS) and currcnt (as in ZVS) spikes.
413