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: - Changing the position of the capacitor from the output to the position between the positive output
and input connectors, leads to an interesting modification of the traditional Boost converter. The inrush current,
when the converter is applied to a stable voltage source e.g. batteries in cars or a battery-buffered DC micro-
grid, is suppressed, and the voltage stress across the capacitor is reduced. To reduce the switching losses and to
reduce the disturbances caused by fast voltage rise- and fall-times, a zero voltage switching (ZVS) concept is
applied and explained step by step and some interesting aspects of the converter are shown. All explanations
are supported by calculations and simulations done with LTSpice.
Key-Words: - DC/DC converter, Boost converter, modified Boost converter, zero voltage switching ZVS,
stable input voltage, didactical paper,
Received: August 29, 2022. Revised: August 27, 2023. Accepted: September 24, 2023. Published: October 27, 2023.
1 Introduction
This paper is one of a series of didactic papers
which show important Power Electronic concepts
applied to the modified Boost converter. The
modification consists in the position of the
capacitor. In the normal Boost converter (Figure 1),
the capacitor is in parallel to the output connectors
and in the modified one (Figure 2) between the
positive input and output connectors.
Fig. 1: Boost converter.
An analyzes of the modified Boost converter
can be found in, [1]. The interesting features are
reduced voltage across the capacitor and no inrush
current, when the converter is applied to an input
voltage. The second feature is especially important,
when the converter is applied to a constant input
voltage source like batteries in cars or to a battery or
super-capacitor buffered DC micro-grid. In, [2], the
concept of quasi-resonant zero current switching
(QRZCS) is applied to the modified Boost
converter. ZCS reduces the switching losses
considerably.
Fig. 2: Modified Boost converter.
In, [3], the application of the Boehringer network on
the modified Boost converter is treated. The
Boehringer network is a turn-off snubber which
reduces the turn-off losses of the converter. It
should especially be marked that new very fast
switches have lower switching losses, but due to the
fast switching produce electromagnetic
compatibility (emc) problems which are reduced by
using a snubber in parallel to the active switch. The
simplest one is an RCD-snubber, which defines the
voltage rise across the active switch, but produces
additional losses which reduce the efficiency of the
converter. The Boehringer turn-off snubber has
principally (when the used components are ideal) no
losses. Now in this paper a ZVS concept is treated
which is valid for the turn-on and the turn-off of the
active switch. The basics of power electronic
converters can be found in the textbooks, [4], [5],
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Felix A. Himmelstoss
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[6]. Figure 1 shows the classical Boost converter
with an input voltage source U1 and a load
represented by the resistor R. Figure 2 shows the
modification by changing the position of capacitor
C.
From the vast literature about ZVS a few ones
will be cited here. In, [7], the application of a totem-
pole PFC is treated. It is also possible to apply the
ZVS concept to dual active bridge converters, [8], to
synchronous Buck converters, [9], to T-type totem-
pole rectifiers, [10], to isolated step up/down
bidirectional DC/DC converters, [11], [12], to
clamped-switch quasi Z-source dc/dc Boost
converters, [13]. A multi time-scale analytical
model of the ZVS Buck Converter is used in, [14].
In, [12]. a closed-form solution for ZVS for the
cascaded Buck plus Boost converter is derived and a
non-isolated high step-down DC–DC converter with
low voltage stress and zero voltage switching is
treated in, [15]. An extensive system is shown in,
[16].
To generate a ZVSMBoC (zero voltage
switching modified Boost converter) some changes
have to be done on the original circuit. First: the
main switch must be a current bidirectional one
(when MOSFETs are used, the body diode is
already an antiparallel diode). Second: small
capacitors have to be added in parallel to the
electronic switches (the transistor and the diode).
Figure 3 shows the topology drawn exemplarily
with MOSFETs, the attached values are used in the
simulations. The capacitor C is taken so large that
the voltage across it can be taken as constant during
a switching period. Therefore, it is represented by
the voltage source UC. The active switch is called
S2 because the circuit can also be built by a half-
bridge and in this case the upper switch is always
called S1.
Fig. 3: Simulation circuit of the ZVSMBo converter.
Figure 4 shows the important waveforms of the
converter. In the upper picture the output voltage,
the input voltage, and the control signal are shown.
The middle part shows the voltage across the active
switch, and in the bottom part the current through
the inductor can be seen. Turn on and off happens
always by ZVS, so no switching losses occur across
the transistor.
Fig. 4: ZVSMBoConverter (up to down): output
voltage (violet), input voltage (blue), control signal
(turquoise); voltage across the active switch (green),
current through the coil (red).
2 Sequence of the Modes in Steady
State
The large capacitor between input and output is
modelled by a voltage source UC. One can
distinguish several modes.
2.1 M1: Active Switch S2 is on, the Current
Increases
The sequence of the modes starts with the
conducting low side switch S2 (mode M1, Figure 5).
The current through the inductor increases linearly
with the derivative
L
U
dt
diL1
. (1)
The capacitor C2 is discharged (and not drawn
because of the short circuit by S2) and the whole
output voltage U2 must be across the capacitor C1
during this mode.
Fig. 5: Equivalent circuit mode M1.
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2.2 M2: Transistor S2 is Turned Off, C1
and C2 Change Their Charges
When the current through the coil reaches the
desired value ILP, the switch S2 is turned off, C2 is
being charged and C1 is discharged, the current
through the inductor can be taken constant during
this mode (Figure 6).
Fig. 6: Equivalent circuit mode M2
The current through the coil commutates into
the parallel capacitors of the active and the passive
switches. The capacity value of the capacitors C1
and C2 is the sum of the output capacitor of the
switch plus the value of the added capacitor. The
current through the coil can be taken constant during
this mode (the commutation time is short compared
to the on-time of switch S2). The lower capacitor C2
is being charged and the upper capacitor C1 is being
discharged. When the capacitors have equal values,
half of the current discharges C1 and the other half
charges C2. The voltage across both capacitors is
always equal to the output voltage U2. When the
voltage across C2 reaches the output voltage, diode
D1 turns on and the current through the inductor
now flows to the output (load and capacitor). This is
the beginning of mode M3.
To calculate the commutation time Tcom, we
assume that the current is constant during this time
and the two capacitors form a single capacitor (both
capacitors are efficient in parallel)
LP
com I
UCC
T221
. (96 ns with 15 A) (2)
From this equation the capacitors can be
calculated for a desired rate of voltage change and a
given peak current. Both capacitors should have the
same value
2
21 2U
IT
CC LPcom
. (3)
Figure 7 shows the current through the coil and
the voltage across the active switch. One can see
that the voltage through the inductor is nearly
constant during M2, and the voltage rises linearly
across the switch.
2.3 M3: the Voltage Across the Active
Switch Reaches the Output Voltage, D1
Turns On
When the voltage across the switch reaches the
output voltage, diode D1 turns on (Figure 8 shows
the equivalent circuit). Now the difference between
the input and the output voltages (that is the voltage
across C) is across the inductor and the current
decreases linearly. Within the time interval
12 UU
IL
TLP
down
(3.1 µs) (4)
the current reaches zero.
Fig. 7: Voltage rise across the active switch during
mode M2 (the mode is marked by the cursors), up to
down: current through the coil (red), voltage across
the transistor S2 (green).
Fig. 8: Equivalent circuit mode M3.
Figure 9 shows the current through the coil and
the voltage across the switch. The mode is marked
by the cursors.
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Fig. 9: Current through the coil decreases during
mode M3 (the mode is marked by the cursors), up to
down: current through the coil (red), voltage across
the transistor S2 (green).
2.4 M4: Diode D1 Turns Off, the Capacitors
Change Their Charges
When the current reaches zero, the diode D1 turns
off. The voltage across the inductor is still negative
(the negative capacitor voltage at this moment), the
current decreases and the capacitor C1 is charged
and the capacitor C2 is discharged in a resonant
way. When the diode turns off, the discharge/charge
process of the capacitors starts. This process can be
described by a simple resonant circuit. The sum of
the voltages of the snubber capacitors C1 and C2 is
always equal to the output voltage U2. If the values
of the capacitors are equal, one half of the current
through the inductor charges C1 and the other half
discharges C2.
Fig. 10: Equivalent circuit mode M4.
The state equations can be written according
Figure 10 for the current through L1 and the voltage
across C1 using the original directions (current
through the coil from left to right) according to
1
1
1L
uU
dt
di CC
L
0)0(
L
i
(5)
1
12/
C
i
dt
du L
C
0)0(
1
C
u
(6)
or written in matrix form
0
0
2
1
1
0
1
1
1
1
1
1
1L
U
u
i
C
L
u
i
dt
dC
C
L
C
L
. (7)
With the help of the Laplace transformation
0
)(
)(
2
1
1
1
1
1
1
1sL
U
sU
sI
s
C
L
sC
C
L
(8)
one gets the time functions
t
CLL
C
Ui CL
111
1
12
1
sin
, (9)
t
CL
Uu CC
11
12
1
cos1
. (10)
(The angular frequency is 2.236e6 s-1, the
frequency is 3.559e-5 Hz.)
After a quarter wave (0.702 µs) the current
reaches its minimum (-2.15 A) which is in
accordance to the simulation (Figure 11). At this
moment the voltage across the inductor changes its
direction and the current through it increases again.
The time to charge the capacitor C1 completely TCh
can be found by
ChCChCT
CL
UUTu
11
21 2
1
cos1)(
(11)
12
1
11 arccos2 UU
U
CLTCh
(0.937 µs) (12).
Fig. 11: Mode M4a (marked by the cursors), up to
down: voltage across the coil (blue); voltage across
the active switch S2 (green), current through the coil
(red), control signal (black, always off).
In Figure 12 the time elapsing which the voltage
across the coil needs to reach the input voltage from
zero, is marked by the cursers. The voltage across
the active switch, which is equal to the voltage
across C2, is also shown besides the current through
the coil and the control signal.
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Fig. 12: Mode M4b (marked by the cursors), up to
down: voltage across the coil (blue); voltage across
the active switch S2 (green), current through the coil
(red), control signal (black, always off).
2.5 M5: Diode D2 Turns On
When the voltage across the active switch reaches
zero (precisely a little bit negative, because of the
forward voltage of the diode), the diode D2 (this is
the body diode of the MOSFET, or the diode
antiparallel to the active switch e.g. an IGBT) turns
on (equivalent circuit Figure 13). From now on the
current through the inductor increases linearly.
When the current reaches zero again (precisely a
little bit later because of the turn-off delay of the
diode), the body diode of the transistor turns off and
a ringing occurs.
Fig. 13: Equivalent circuit mode M5.
2.6 M6: Ringing
When the diode D2 turns off, a ringing starts
because the current is a little bit positive (due to the
reverse recovery of the diode). The frequency can
be calculated according to
)(
1
2
1
211 CCL
f
. (356 kHz) (13)
Figure 14 shows the output voltage, the input
voltage, the control signal, the voltage across the
active switch, and the current through the coil. The
cursers mark the interval when the voltage reaches
zero and when the switch is turned on again.
Fig. 14: Up to down: output voltage (violet), input
voltage (blue), control signal (turquoise); voltage
across the active switch (green), and current through
the coil (red).
When the active switch is turned again, the
converter is once more in mode M1. In Figure 14
the active switch is turned on, when the voltage
across the switch reaches a minimum again. One
can interpret such an operation as a discontinuous
mode. When the switch is turned on, and the diode
D2 is conducting for the first time after the voltage
across the switch reaches zero, one can name this
operation continuous mode. Mode M1 follows
immediately after M5 (as in Figure 4).
When the active switch is turned on before the
body diode turns off, the converter is again in mode
M1. When S1 is turned on later, a ringing occurs.
To avoid a fast charge/discharge of the capacitors,
the turn on of S2 should be done, when the voltage
across S2 has a minimum.
Figure 15 shows the u-Zi diagram of the
converter (u is the voltage across the switch, which
is equal to the one across C2, and Zi is the product
between the characteristic impedance and the
current through the coil). The characteristic
impedance of the resonance circuit can be calculated
according to
21 CC
L
Z
(22.4 Ω). (14)
Zi forms the ordinate, and the voltage the abscissa.
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Fig. 15: U-Zi diagram of the converter when turned
on again at zero voltage.
The vertical line starting from the origin follows
mode M1 (the current increases and the voltage
across the switch is zero). When the switch is turned
off, M2 starts and is represented by the little bowed
line (the voltage across the switch increases now
until it reaches the output voltage). Now the diode
D1 turns on and mode M3 can be seen as the
vertical line going down to zero. When zero is
reached, the segment of a circle represents mode
M4. M5 is the vertical line up to the origin. The
following circle displays mode M6. During M5 the
line is little bit on the negative side (caused by the
forward voltage of the diode).
Figure 16 shows the u-Zi diagram, when the
transistor is turned on during the ringing at a voltage
of Vto (40 V). Now losses occur entailed by the
transfer of the energy stored in the capacitors
2
1
2
22
2
,
CVUCV
Etoto
onC
(1.31e-5 Ws) (15)
into heat. The current is also not zero (but compared
to real hard switching very low). Therefore, it is
advantageous that the turn-on should occur always
at low voltage. Figure 17 shows a signal diagram for
this case (equal to Figure 16).
Fig. 16: U-Zi diagram of the converter when turned
on again during the ringing with losses.
Fig. 17: Operation with turn on not precisely at zero
voltage, (up to down): voltage across the coil (blue),
voltage across the active switch (green), current
through the coil (red), control signal (black).
2.7 Restriction
To charge/discharge the capacitors C1 and C2 the
output voltage must be higher than two times the
input voltage. This is because the voltage across the
capacitor UC is used for the charge/discharge
process at the end of a cycle. Therefore, UC must be
higher than the input voltage; only in this case C1
can be fully charged and C2 fully discharged. The
voltage transformation ratio must be higher than two
to make the ZVS concept possible.
3 ZVS half-bridge Modified Boost
Converter
When the onward voltage of the diode is higher than
that of an active switch (e.g. a MOSFET), the
replacement of the diode by an active switch
reduces the onward losses. The sequence of the
modes is the same as for the single switch converter.
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Only mode M3 consists of two parts. After the diode
turns on (Figure 8), the high-side switch is turned
on, shunts the diode D1 (Figure 18) and turns it off.
Now the current is flowing through the active switch
S1.
Fig. 18: Equivalent circuit mode M3-part 2.
When the current reaches zero again (or a little
bit after), the switch can be turned off. The current
through the coil reverses and commutates into the
capacitors C1 and C2, C1 is charged and C2 is
discharged. When the voltage across C2 reaches
zero, D2 turns on. Now one can turn on S2 with
zero voltage and the circuit is again in mode M1.
In Figure 19 the simulation circuit of the ZVS half-
bridge modified Boost converter is depicted (in this
example the values of the capacitors are reduced).
Fig. 19: Simulation circuit of the ZVS half-bridge
modified Boost converter.
Fig. 20: ZVS half-bridge modified Boost converter,
up to down: voltage across the coil (blue), voltage
across the active switch (green), current through the
coil (red), control signal for switch S2 (black),
control signal for switch S1 (turquoise).
Figure 20 shows the signals. Switch S1 is turned
off a little bit later after the current has reached zero.
When looking at the voltage across the coil, one can
see that the voltage across it increases by the
forward voltage of the diode before S2 is turned on
again and the next cycle starts.
4 Conclusion
The modified Boost converter has several
interesting features
No inrush current when applied to a stable
input voltage source
Reduced voltage stress across the capacitor
Continuous but pulsed input current
High step-up ratios possible
As this paper is a didactic one, some new additional
interesting features are found
The voltage transformation rate must be
higher than two
The second active switch S1 is only
significant, when the forward voltage of the
diode is larger than that of an active switch
Without the second switch S1, no high-side
driver is necessary and the control amount
is reduced
The converter is especially useful for driving loads,
which need a supply voltage which is two times
higher than the input voltage found in DC micro
grids, or in cars (electro mobility).
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Felix A. Himmelstoss
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Volume 18, 2023
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The author contributed in the present research, at 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 conflict 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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