Quasi-resonant Zero Voltage Switching Modified Boost Converter
FELIX A. HIMMELSTOSS
Faculty of Electronic Engineering and Entrepreneurship,
University of Applied Sciences Technikum Wien,
Hoechstaedtplatz 6, 1200 Vienna,
AUSTRIA
Abstract: - To reduce the switching losses in a DC/DC converter the quasi-resonant concept can be applied to
the converter. With an additional resonant capacitor and an additional resonant inductor, the voltage across or
the current through the electronic switch is influenced, so that the switching of the transistor can be done at zero
voltage or zero current. The zero voltage switching concept is applied to the modified Boost converter. The
modification concerns the position of the bulk capacitor. It is not connected between the output terminals but
between the positive input and output connectors. This reduces the voltage stress of the capacitor and avoids the
inrush current when connected to a stable DC grid or large batteries. The converter is explained step by step
with the help of equivalent circuits and calculations. A very instructive method to analyze resonant circuits is
the uZi diagram which is also applied. LTSpice simulations are used to prove these considerations.
Key-Words: - DC/DC converter, Boost converter, modified Boost converter, zero voltage switching ZVS, uZi
diagram, LTSpice simulations.
Received: April 13, 2024. Revised: August 19, 2024. Accepted: September 18, 2024. Published: October 24, 2024.
1 Introduction
The zero current switching (ZCS) and the zero
voltage switching (ZVS) methods were invented to
reduce or eliminate the switching losses in a DC/DC
converter. All basic converters are treated in the
important paper [1], which can be traced back to the
conference paper [2]. A topology study to
synthesize and analyze quasi-resonant converters [3]
was also done at this early period. Another
important paper concerning quasi-resonant
converters, their topologies, and their characteristics
is [4]. Looking at the more recent literature one
finds that the quasi-resonant concept is also applied
to a single switch single input bipolar output
converter, [5]. A comprehensive reliability
assessment of the quasi-resonant Buck can be found
in [6]. A quasi-resonant pre-stage for an induction
motor drive is shown in [7]. Transient analysis of a
quasi-resonant converter based on the equivalent
small parameter method considering different time
scales can be found in [8]. Quasi-resonant
converters are also treated in a review concerning
renewable energy and electric vehicle charging
applications, [9]. A ZVS QR boost converter with
variable input voltage and load is studied in [10]. A
ZVS quasi-resonant Buck converter is treated in
[11]. In [12] a novel Boost-based quasi-resonant
DC/DC converter with low component count for
stand-alone photovoltaic applications is treated.
[13], shows a novel high voltage gain quasi-resonant
step-up DC/DC converter with soft-switching. In
[14] the EMI (electromagnetic interference)
emission of DC/DC converters using bi- and
unidirectional QRZVS topologies is studied. The
extremely fast switching of modern semiconductor
components also requires methods to reduce
electromagnetic disturbance. So QRZVS DC/DC
converters have a large field of application [15].
In this paper, the quasi-resonant ZVS (QRZVS)
concept is applied to the modified Boost converter
(MBoC). Simply by changing the position of the
bulk capacitor C of a Boost converter from the
output terminals to connect the positive input and
output terminals, a modified Boost converter
(MBoC) is built (Figure 1).
Fig. 1: Modified Boost converter
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Felix A. Himmelstoss
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The MBoC has two interesting features: reduced
stress of the bulk capacitor C and no inrush current
when connected to a stable input voltage like
batteries or a DC grid. To reduce the switching
losses, the quasi-resonant concept can be used. Here
the zero voltage switching (ZVS) concept is applied
to the MBoC. In his lectures, the author explains
interesting concepts in Power Electronics by
applying them to the MBoC. This has the advantage
that the basic circuit is simple, and has some
interesting features, that cannot be found in the
textbooks and in the basic literature.
There are several possibilities to change an
MBoC into a quasi-resonant zero voltage switching
modified Boost converter (QRZCSMBoC). The
here-used method is very easy to remember. To turn
off an active switch without losses, a capacitor has
to be connected in parallel to the electronic switch
so that the current can commutate from the
transistor. Without such a parallel path the voltage
across the switch must rise until the diode can turn
on, and that means that the voltage must go up to the
output voltage (and even higher, because of the
forward recovery effect of the diode and due to the
parasitic inductance in the loop). Using an RCD
snubber, the capacitor is connected with a series
diode in parallel to the electronic switch. To avoid a
large current peak when the transistor is turned on
again, the diode of the snubber blocks. For
discharging the capacitor of the snubber a resistor is
connected in parallel to the diode of the snubber.
The energy stored in the capacitor is transformed
into heat. There exist several snubber concepts
which feed the energy into the output. The basic
concepts can be found in [16] and can be applied to
the MBoC. To reduce the turn-on losses, an
additional network must be connected to the switch
which has a series inductor. So the current through
the switch rises with a derivative limited by this
inductor. This inductor produces an overvoltage
across the transistor when it turns off. A diode in
series with a resistor or an avalanche diode
connected in parallel to this inductor limits the
overvoltage across the active switch, and the energy
stored in the inductor is dissipated into heat. The
RCD snubber can also be used to dissipate the
energy of the turn-on inductor, but this produces a
damped ringing with high frequency. It should be
mentioned that loss-free turn-on snubbers also exist.
To achieve a QRZVS converter only an
additional resonant capacitor CR and a resonant
inductor LR are necessary. The circuit diagram is
shown in Figure 2. No additional resistors have to
dissipate energy and no additional diodes are
necessary. The capacitor CR is connected in
parallel, and the coil LR is connected in series to the
electronic switch.
Fig. 2: Quasi-resonant zero voltage switching
modified Boost converter (QRZVSMBoC)
2 Step-by-step Explanation of the
Converter
The function of the QRZVSMBoC is now explained
for steady state and ideal components (no parasitic
resistors, ideal switching). The bulk capacitor C is
taken so large that the voltage across it does not
change significantly during one period and can be
taken constantly. Also, the main inductor L is so
large that the current through it can be taken
constant, too. The cycle of operation can be divided
into several modes. We start with mode M0 where
the transistor is on and the diode is off.
2.1 M0: S on
Figure 3 shows the equivalent circuit of this mode.
The current through the main inductor flows
through the transistor. As this current is constant,
the resonant inductor produces no voltage and
therefore has no meaning and is not displayed in the
equivalent circuit. The resonant capacitor is short-
circuited by the electronic switch and has no effect
in this mode and is therefore also not included in the
equivalent circuit.
Fig. 3: Equivalent circuit of mode M0
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2.2 M1: S Turns Off
Mode M1 starts when the electronic switch S turns
off. The current can commutate out of the switch
and into the resonant capacitor CR. As the current is
constant, LR has no effect and is not included in the
equivalent circuit (Figure 4).
Fig. 4: Equivalent circuit of mode M1
The circuit is described by the differential
equation:
R
CR C
I
dt
du 0
. (1)
The resonance capacitor is charged by the
current source I0 and increases linearly. When the
voltage reaches U2, diode D turns on and mode M2
begins. The duration of mode M1 lasts
2
0
1U
I
C
TR
M
. (2)
2.3 M2: Resonance
The equivalent circuit of mode M2 is shown in
Figure 5.
Fig. 5: Equivalent circuit of mode M2
The circuit can now be described by the state
equations and their initial values
R
CRCLR L
uUU
dt
di
1
0
)0( IiLR
(3)
R
LRCR C
i
dt
du
2
)0( UuCR
(4)
It is easier to use
21 UUUC
. (5)
The two state equations can be combined into a state
space equation in matrix form:
0
0
1
1
02
R
CR
LR
R
R
CR
LR L
U
u
i
C
L
u
i
dt
d
. (6)
To solve this equation Laplace transformation can
be used:
2
0
2
)(
)(
1
1
U
I
sL
U
sU
sI
s
C
L
s
R
CR
LR
R
R
. (7)
The easiest way to calculate the state variables is to
use Crammer’s law:
RR
R
R
CR
LC
s
U
C
I
sL
U
s
sU 1
1
)(
2
2
0
2
(8)
leading to:
t
LCC
L
IUu
RRR
R
CR 1
sin
02
. (9)
The ZVS condition is:
20 U
C
L
I
R
R
. (10)
The amplitude of the ringing must be higher
than the output voltage so that the voltage across the
transistor (and at the resonant capacitor) reaches
zero. The resonant current results in:
RR
R
R
RR
C
LR
LC
s
sI
s
C
L
s
sU L
I
sL
UU
sI 1
1
1
1
)(
2
0
2
0
1
,
(11)
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Felix A. Himmelstoss
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t
LC
Isi
RR
LR 1
cos)( 0
. (12)
From the analytical geometry, one can see that
when iLR is multiplied by the characteristic
impedance of the resonant circuit Z
R
R
C
L
Z
(13)
t
LC
ZIZi
RR
LR 1
cos
0
(14)
and looking at the voltage across the resonant
capacitor (9), this can be interpreted as a circle in
Cartesian coordinates with the center of the circle at
U2 and zero. In Cartesian coordinates a circle is
described by:
2
0
2
0
2)( YyXxR
(15)
where R is the radius, and X0 and Y0 are the
coordinates of the center point. In our case, we have
to interpret the x-axis as the uCR-axis and the y-axis
as the ZiLR-axis. One can write
t
LCC
L
It
LCC
L
IZI
RRR
R
RRR
R1
cos
1
sin 22
0
22
0
2
0
(16)
and with
1cossin 22
(17)
one gets
R
R
C
L
IIZ 2
0
2
0
2
(18)
which is thereby proved. When the voltage reaches
zero the ringing ends and mode M3 starts.
2.4 M3: Increase of the Current through the
Resonance Coil
Figure 6 shows the equivalent circuit of mode M3. It
can be divided into two parts. During M3a the
current is negative and flows through the
antiparallel diode of the switch. During this mode,
the electronic switch has to be turned on again.
During M3b the current is positive and flows
through the turned-on electronic switch.
Fig. 6: Equivalent circuit of mode M3
First the current flows through the body diode
of the MOSFET or through a diode which is
connected in antiparallel to the active switch. Now
one can turn on the switch at zero voltage. When the
current changes its direction, the current will
commutate into the electronic switch (e.g. an
IGBT), or when a MOSFET is used as a switch, the
current starts to commutate immediately when the
channel of the transistor is turned on. When the
current through the switch reaches the current
through the main inductor I0, the diode D turns off
and mode M0 is reached again. Figure 7 shows the
QRZVSMBoC in a steady state; depicted are the
current through the resonant coil, the voltage across
the resonant capacitor, the output voltage, and the
control signal. The data that were used for the
simulation are CR=0.2 µF, LR=3.6 µH, U1=24 V,
U2=50 V, I0=15 A. In Figure 8 the current source is
replaced by an inductor with the value 100 µH. Now
the current is not constant. Figure 8 shows the
QRZVSMBoC in a steady state with realistic values.
One can see the concept is functioning. The current
through the main inductor L, the current through the
resonant coil, the voltage across the resonant
capacitor, the output voltage, and the control signal
are depicted.
Fig. 7: QRZVSMBoC in steady state, up to down:
the current through the resonant coil (red); the
voltage across the resonant capacitor (green), the
output voltage (blue), the control signal (turquoise)
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Fig. 8. QRZVSMBoC in steady state with realistic
values, up to down: the current through the main
inductor L (violet), the current through the resonant
coil LR (red); the voltage across the resonant
capacitor CR (green), the output voltage U2 (blue),
the control signal (turquoise)
3 Description of the Converter with
the Help of the uZi Diagram
The uZi diagram is a very helpful tool for describing
resonant processes. A detailed description can be
found in [17], it was also used in [18] for the
QRZCSMBoC. The axes of coordinates in a
Cartesian coordinate system are the voltage across
the resonant capacitor in the horizontal and the
current through the resonant inductor multiplied
with the characteristic impedance Z in the vertical.
During mode M0 the electronic switch is turned
on and the current I0 flows through the switch and
also through the resonant inductor which is in series
to the transistor. The resonant capacitor is in parallel
to the switch, so the voltage across it must be zero.
Mode M0 is a point with the coordinates (0, ZI0).
When the electronic switch S is turned off,
mode M1 begins. The current commutates into the
resonant capacitor and it is linearly charged by the
current I0 through the main inductor until the
voltage reaches the output voltage and the diode
turns on. In the uZi diagram, this mode can be
drawn as a horizontal line starting from the point
(0,ZI0) and ending at the point (U2, ZI0).
M2 starts when the diode is forward-biased
because the voltage across the resonant capacitor
(and the transistor) reaches the output voltage. Now
a resonance occurs. As shown in (16) this can be
interpreted as a circle. One only needs one point, the
end of mode M1, and the center point which was
found at (U2, 0) to draw the circle. One can find this
center point also by a simple consideration. Looking
at the equivalent circuit (Figure 5) and including a
damping resistor in the resonant circuit (this resistor
is built by the parasitic resistors of the components),
one has to find the endpoint. In reality, the trajectory
of such a resonant circuit will be not a circle but a
spiral line ending at the center point of the circle
with ideal components. At the steady state no
current must flow through the resonant inductor to
avoid a change of the voltage across the resonance
capacitor and the voltage across the resonant
capacitor must be equal to the output voltage, the
sum of the input voltage U1 and the voltage across
the bulk capacitor UC. The spiral is shown in
Figure 9. A damping resistor of 2 mΩ is included in
the resonant circuit. Within 10 ms the final value,
the center point of the circle in the uZi diagram is
reached.
Mode M2 ends when the voltage across the
resonant capacitor reaches zero. The voltage cannot
be negative because of the diode which is connected
antiparallel to the switch (e.g. the body diode of the
MOSFET). Now one can again turn on the active
switch with ZVS.
Figure 10 shows the uZi diagram of the
QRZVSMBoC. This can be sketched with a ruler
and a pair of compasses. Here the simulation
according to Figure 11 was used for drawing the red
line. The simulation with the data used for the time
diagrams (Figure 7) is depicted in Figure 11. Keep
in mind that the Zi-axis is scaled in volts. The point
where the switch is turned on is marked. The
voltage before was a little bit negative because the
current flew through the antiparallel diode.
Fig. 9: Phase diagram during M2: right 10 ms
(parasitic resistor 2 mΩ)
Fig. 10: QRZVSMBoC: uZi diagram
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Fig. 11: QRZVSMBoC: simulation of the uZi
diagram, data as in Figure 7
Using the uZi avoids a lengthy calculation and
is very informative.
The duration of mode M1 can be calculated
with (2). The duration of M2 can be calculated by
the rule of proportion. From the angular frequency
of the resonant circuit:
RRLC
T
f12
2
(19)
one gets the duration of the complete circle of 2π:
RRLCT
2
. (20)
The angle
2/3
is passed through during
the duration of M2. Therefore, the duration of mode
M2 lasts:
RRM LCTT
2
3
2
2/3
2
. (21)
From (15) one can write with the center point
(X0, 0) and searching the y-value when the x-value
is zero:
22
0
2yXR
. (22)
With the radius of the circle ZI0, the circle cuts
the ZiLR axis at:
)0(
2
2
2
0
22
0
2 CRLR uZiUIZXRy
. (23)
Now one can calculate the value of the angle ψ
according to:
0
2
2
2
0
2
arcsin ZI
UIZ
. (24)
During Mode M3a the current is negative
(flowing through the diode which is antiparallel to
the switch, e.g. the body diode of the MOSFET) and
during this mode, the transistor has to be turned on
again. The voltage across the resonant inductor is
equal to the output voltage and mode M3a lasts
according to:
2
2
2
2
0
2
3ZU
UIZ
LT Ra
. (25)
After the time interval:
2
0
3U
I
LT Rb
(26)
the converter reaches again mode M0.
The control of the converter can be done by
controlling the length of mode M0. The off-time of
the switch can only last until the converter is again
in mode M3a. The QRZVSMBoC is controlled by
the frequency with variable on-time of the switch.
4 Conclusion
The ZVS concept has for higher frequencies a
significant advantage compared to the ZCS concept.
When the switch is turned on in the ZCS concept,
the current starts at zero, but the voltage across the
switch is not zero. The parasitic capacitor of the
switch is charged and now is discharged very fast.
So some additional losses occur depending on the
switching frequency, the parasitic capacitor, and the
square of the voltage across the switch at the
moment of turn-on. The discharge peak also
produces a fast-changing magnetic field which can
induce disturbing voltages (EMC). Both
disadvantages are avoided by the ZVS concept. It
should be mentioned that in this paper only the full
wave mode was treated. In the half-wave mode an
additional diode must be included leading to higher
onward losses. Summarizing one can say that the
QRZVSBoC has interesting features:
No inrush current
Reduced voltage stress across the bulk
capacitor
No switching losses
Higher onward losses
Nevertheless, improved efficiency
Fix turn-off time and variable on-time
Applicable for high switching frequency
The converter is especially useful for
applications with relatively low input voltages and
high frequencies. The higher the switching
frequency the smaller the passive components of the
converter.
References:
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Volume 23, 2024
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elektronischer Einwegschalter von ihrer
Verlustleistungsbeanspruchung beim
Ausschalten), [Online],
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(QRZCSMBC), WSEAS Transactions on
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55-62,
https://doi.org/10.37394/23201.2023.22.8.
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The author contributed to the present research, in all
stages from the formulation of the problem to the
final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The author has no conflicts of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
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