Quasi Resonant Zero Current Switching Modified Boost Converter
(QRZCSMBC)
FELIX A. HIMMELSTOSS
Faculty of Electronic Engineering and Entrepreneurship,
University of Applied Sciences Technikum Wien,
Hoechstaedtplatz 6, 1200 Vienna,
AUSTRIA
Abstract: - The inrush current of the Boost converter can reach high values when attached to a stable input
source like a car battery or a battery buffered micro-grid. To avoid the inrush current, a modification of the
converter by placing the capacitor between the output and input can be done. To reduce the switching losses,
the quasi resonant zero current switching QRZCS concept is used. The active switch of the converter has a
constant on-time and a variable off-time or frequency. The inrush current is studied and the function of the
QRZCS converter is treated with the help of mathematical descriptions and with the uZi diagram. LTSpice
simulations are used to prove the considerations.
Key-Words: - DC/DC converter, modified Boost converter, inrush current, zero current switching ZCS, uZi
diagram, LTSpice simulations
Received: April 21, 2022. Revised: March 15, 2023. Accepted: April 16, 2023. Published: May 26, 2023.
1 Introduction
When the capacitor of the Boost converter is not
connected between the output connectors, but
between the positive input and the positive output
connectors, we call this topology modified Boost
converter. A comprehensive study can be found in
[1]. This circuit (Fig. 1) has two interesting features.
First, the voltage stress at the capacitor is reduced
and second, the inrush current is avoided. The
disadvantage of the converter is the fact that
changes in the input voltage effect immediately the
output voltage. The converter is therefore useful
when a stable input voltage is available, like a
battery buffered micro-grid. In this study, the inrush
current of the modified and of the normal Boost
converters are compared and the modified converter
is extended to a zero current switching ZCS quasi
resonant QR converter. The basic studies on quasi-
resonant DC/DC converters go back to [2], [3]. The
concept was applied to many topologies (c.f. e.g.,
[4], [5], [6], [7], [8], and there cited references), but
not as we know to the modified Boost converter.
The main idea of the ZCS is to avoid switching
losses by switching on and off the transistor with no
current. With an inductor in series to the switch, the
current starts at zero, when the transistor is turned
on. With the help of a resonance circuit, the current
through the switch reaches zero within a predefined
time interval, and now the transistor is turned off
again with zero losses.
Fig. 1: Modified Boost converter
2 Inrush Current
The inrush current of a converter used on a stable
supply can lead to high current and to saturation of
the magnetic devices.
2.1 Inrush Current of the Boost Converter
The inrush current of the normal Boost converter
(Fig. 2) is very high when applied to a battery or a
battery stabilized micro-grid. When the input
voltage is applied to the converter, the loop
consisting of U1, L, D, and the output is closed.
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Felix A. Himmelstoss
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Fig. 2: Boost converter
2.1.1 Inrush Current with No Load
When no load is applied to the output of the
converter, the inrush current can be described by
KVL (Kirchhoff’s voltage law) by
t
idt
Cdt
di
LU
0
1
1
(1)
which leads to the sinusoidal current
t
CLL
C
Ui 1
sin
1
. (2)
The peak current is therefore
L
C
UI IN 1
(3)
and the output capacitor is charged up to two times
the input voltage. A simulation of the inrush current
and the output voltage is depicted in Fig. 3. The
inductor of the converter has a value of 47 µH, the
capacitor has a value of 330 µF, and the input
voltage is chosen to 24 V.
Fig. 3: Boost converter inrush current with no load,
up to down: current through the inductor (equal to
the current which comes out of the source, red), the
voltage across the output (green)
2.1.2 Inrush Current with Consideration of the
Load
The state equations can be written according to
L
uU
dt
di CL
1
0)0(
L
i
(4a)
C
Rui
dt
du CLC
0)0(
CR
u
(4b)
Transformation into the Laplace domain leads to the
matrix equation
0
)(
)(
11
1
1
sL
U
sU
sI
CR
s
C
L
s
C
L
. (5)
With the help of Crammer’s law, the current in the
Laplace domain can be written according to
CLCR
ss
CLRs
U
L
U
sIL11
)(
2
11
(6)
Until the current reaches zero again for the first time
it can be described by a damped ringing with the
damping factor
CR2
1
(7)
and the angular frequency
22
4
11
RC
CL
. (8)
After the first half wave, the diode turns off and the
current decreases by an e-function until the output
voltage reaches the input voltage. The time constant
depends on the load and the value of the output
capacitor
RC
. (9)
Fig. 4: Boost converter: inrush current (red). The
voltage across the output (green) with the attached
load
From Fig. 4 one can see that the peak of the inrush
current is about the same as that of the one that
occurs when no load is connected. The difference is
that the output capacitor is now discharged by the
load until the diode turns on again when the output
voltage is lower than the input voltage. The ringing
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Felix A. Himmelstoss
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56
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is caused by the diode. For estimating the inrush
current, (3) leads to a good approximation.
The normal concept to reduce the inrush current
is to insert a resistor to limit the current and to shunt
it by a mechanical contact, when the output
capacitor is charged, or to use an NTC resistor
which reduces its value when it gets warm; but this
second method leads to additional losses. When
using an electronic switch instead of the mechanical
contact this can be used as a fuse to turn off the
converter in case of overload or short circuit.
2.2 Inrush Current of the Modified Boost
Converter
When the modified Boost is applied at the input
voltage and no load is connected, no inrush current
occurs. When the load is already connected then an
inrush limited by the load occurs, but no dangerous
overcurrent. Fig. 5 shows the current through the
inductor and the current through the capacitor (same
values as in Fig. 4). The steady state values are the
input voltage divided by the load resistor for the
inductor current and zero for the current through the
capacitor. The maximum current through the
inductor is about two times the steady state value.
But the input current which is drawn from the input
source is nearly constant all the time and is equal to
the steady state value of the current through L1.
Fig. 5: Inrush of the modified Boost converter, up to
down: output voltage (green), the voltage across the
capacitor (blue), current through the inductor (red),
input current (grey), current through the capacitor
(violet)
3 Quasi Resonant ZCS Boost
Converter
One possibility to achieve a QRZCS converter
(Fig. 6) is to connect an inductor LR in series to the
active switch and a capacitor CR parallel to the
diode. The devices are supposed to be ideal.
Fig. 6: Zero current switching quasi resonant
modified Boost converter
3.1 QRZCSMBC Described by the Sequence
of the Modes
For the description of the function, the capacitor C
is modelled by a constant voltage source UC, and
the inductor L1 is modelled by a current source I0.
The function is described starting from the free-
wheeling stage mode M0 (Fig. 7).
Fig. 7: Equivalent circuit during M0 (free-wheeling)
Mode M1 (Fig. 8) starts when the active switch is
turned on.
Fig. 8: Equivalent circuit during M1 (the current
commutates from the diode into the active switch)
The current in the resonance coil increases
according to the differential equation
R
LR L
U
dt
di 2
. (10)
The current increases linearly. When it reaches the
current I0, the diode D turns off. Now a new
equivalent circuit is valid. The duration of mode M1
lasts
2
0
1U
LI
TR
M
. (11)
When the current in the switch reaches I0, the
current through the diode reaches zero, too, and
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Felix A. Himmelstoss
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turns off. Now the resonant capacitor has to be
included in the equivalent circuit (Fig. 9).
Fig. 9. Equivalent circuit during M2 (resonant
stage).
The circuit can be described by the state equations
and their initial values according to
R
CRLR L
Uu
dt
di 2
0
)0( IiLR
(12.a)
R
LRCR C
Ii
dt
du 0
0)0(
CR
u
. (12.b)
The mode M2 can be described by the state
description
R
R
CR
LR
R
R
CR
LR
C
I
L
U
u
i
C
L
u
i
dt
d
0
2
0
1
1
0
. (13)
Laplace transformation leads to
R
R
CR
LR
R
R
sC
I
I
sL
U
sU
sI
s
C
L
s
0
0
2
)(
)(
1
1
. (14)
With Crammer’s rule and with the Laplace
correspondences one can write for the resonance
current in the time domain
t
LCL
C
UIi
RRR
R
LR 1
sin
20
. (15)
Fig. 10 shows the sequence of the modes starting
with Mode M0. During M1 the current reaches I0,
during M2a the current through LR is positive, and
during M2b negative. During M2b one must turn off
the active switch to achieve ZCS. During M3 CR is
discharged by I0 until the diode D turns on and the
circuit is again in the free-wheeling mode M0.
When the current is negative, one can turn off
the active switch, and the current commutates into
the body diode.
The current reaches zero within the time TM1a.
aM
RRR
R
aM T
LCL
C
UITi 2202
1
sin0)(
(16)
resulting in
R
R
RRaM C
L
U
I
LCT
2
0
2arcsin
. (17)
Fig. 10: Sequence of the modes: voltage across the
resonant capacitor (green), the control signal (blue),
and current through the resonant inductor (red)
With
xx arcsinarcsin
(18)
one gets (the sinus is already in the third quadrant)
R
R
RRaM C
L
U
I
LCT
2
0
2arcsin
. (19)
The next time when the current reaches zero, which
is the last possibility to turn off the switch at zero
current, is attained at
R
R
RRbMaM C
L
U
I
LCTT
2
0
22 arcsin
4
3
. (20)
Note that the sine wave is already in the fourth
quadrant.
The voltage across the resonant capacitor can be
calculated according to
t
LC
Uu
RR
CR 1
cos1
2
. (21)
When the current reaches zero, the body diode turns
off and mode M3 begins. The current I0 discharges
linearly the resonant capacitor, and when the voltage
reaches zero the free-wheeling diode D turns on and
the circuit is again in the free-wheeling mode M0.
3.2 QRZCSMBC Described by the uZi
Diagram
A very clear way to understand the resonance effect
of the converter is by using the u-Zi diagram, [9]
(Fig. 11).
When the active switch is turned on, the current
increases, and the voltage across CR is still zero
(mode M1, perpendicular line). When the current
reaches I0, the diode turns off, and the resonant
mode M2 starts. To get the midpoint (center) of the
circle, one must look at the equivalent circuit Fig. 9
and ask oneself to which endpoint a damped ringing
would lead.
One can see that the current through the
inductor LR would be I0 and the voltage across CR
would reach the output voltage. Now one can draw
the circle starting from the point (0, ZI0). When the
circle reaches the voltage axis and the current gets
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Felix A. Himmelstoss
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negative, one can turn off the active switch, and the
current commutates into the diode in parallel to the
active switch (body diode when a MOSFET is
used). The last possibility to turn off the switch is
before the current gets positive again. Mode M2 can
be separated into two parts M2a and M2b, but the
describing equations are the same. Mode M3 starts
when the circle hits again the voltage axis. Now M3
can be described by a horizontal line (the capacitor
is discharged linearly by I0) until it reaches the
origin and Mode M0 starts again.
Fig. 11: uZi diagram of the ZCSQRMBC
From the resonance angular frequency
T
LC RR
21
(22)
one can calculate the period of the resonance
RRLCT
2
. (23)
With the Schlussrechnung
bM
aM
RR
T
T
LC
22
21
........
........
2.......2
(24)
one gets
RRaM LCT 12
(25)
RRbM LCT 22
. (26)
One can calculate the duration of M2 by measuring
the angles φ1 and φ2.
With the help of the definition of the cosine in a
rectangular triangle one can calculate the angles
2
02
2
cos U
ZI
. (27)
The angles for M2a and M2b are
2
0
2arccos2 U
ZI
(28)
2
02
1arccos
2
3
)
22
(U
ZI
, (29)
respectively. The durations are therefore
RRaM LC
U
ZI
T
2
0
2arccos
2
3
(30)
RRbM LC
U
ZI
T
2
0
2arccos2
. (31)
3.3 QRZCSMBC Dimensioning Hints
The converter is useful when the load current (and
the mean value of the current through the coil) does
not change very much. The basic converter is
dimensioned like a normal Boost converter. When
the electronic switch is turned on, the input voltage
is across the main inductor, and the current
increases by ΔI. The on-time is given by
1
U
LI
Ton
. (32)
The on-time Ton is fixed and must be chosen
according to the ZCS condition
02
1
sin It
LCL
C
U
RRR
R
. (33)
The amplitude of the sinus wave must be larger than
the current through the coil to secure that the current
through the active switch becomes negative. For the
nominal point, one gets a good choice with (30, 31)
RR
bM
aMon LC
T
TT 2
3
2
2
2
. (34)
During the off-time the current decrease by the same
value ΔI (in the steady state). L can be calculated
with the help of (32). During the on-time, the load
current discharges the capacitor by
onon TT
LoadC dt
R
U
C
dtI
C
u
0
2
0
11
. (35)
For an allowable voltage ripple ΔuC, the capacitor
can be calculated according to
C
onLoad
u
TI
C
. (36)
The capacitor will be chosen larger to compensate
for the series resistor of the device and the tolerance.
This has to be proved with the datasheet. The
chosen capacitor will be approximately two times
the value got by (36).
For the resonance elements one gets from
t
LCL
C
UIi
RRR
R
LR 1
sin
20
(37)
for the characteristic resistor
0
2
I
U
C
L
Z
R
R
(38)
and for the period
M0
M1
Z.I
Z.i
phi
(U ,Z.I )
U
M2b
M3
M2a
U
1
phi2
2 0
2CR
0
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RRLCT
2
. (39)
Calculating LR from the two equations and setting
them equal leads to
R
RR C
T
C
I
U
L2
2
2
0
2
4
. (40)
This results in the equation for CR
2
0
2U
I
T
CR
. (41)
4 Simulation
First, we simulate the converter with constant
current through the inductor and constant voltage
across the capacitor. The small RC snubber in
parallel to the active switch damps the ringing
between the resonance inductor LR and the parasitic
output capacitor of the transistor. Fig. 12 shows the
simulation circuit and the voltage across the
transistor, the current through the resonance
inductor, and the voltage across the resonance
capacitor.
.
Fig. 12: QRZCSMBC simulation circuit, up to
down: voltage across the active switch (green);
current through the resonance coil (red), the voltage
across the resonance capacitor
Fig. 13 shows the current through the resonance
inductor LR over the voltage across the resonance
capacitor CR. The ringing caused by the output
capacitor of the transistor can also be seen here.
Fig. 14 shows the real converter with an
inductor, capacitor, and load resistor. The higher the
duty cycle, the higher the output voltage, the higher
the load current, and the higher the current through
the main inductor.
Fig. 13: Resonant current over the voltage of the
resonance capacitor, parameters like in Fig. 12
Fig. 14: Current through the active switch (dark
green), current through the inductor (violet); output
voltage (turquoise), input voltage (blue), the control
signal (grey); current through the resonant coil (red),
the voltage across the resonant capacitor (green)
(duty cycle 42 %)
When the current through the main coil is too
high, so that the zero switching condition is no more
valid, the switch is turned off under current and
additional losses occur. This is depicted in Fig. 15.
The definition of duty cycle, that is the on-time
of the active switch referred to as the period, is used
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Felix A. Himmelstoss
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here for convenience. Fig. 16 shows the converter
with low output voltage and current.
Fig. 15: Current through the active switch (dark
green), current through the inductor (violet); output
voltage (turquoise), input voltage (blue), the control
signal (grey); current through the resonant coil (red),
the voltage across the resonant capacitor (green)
(duty cycle 70 %)
Fig. 16: Current through the active switch (dark
green), current through the inductor (violet); output
voltage (turquoise), input voltage (blue), the control
signal (grey); current through the resonant coil (red),
the voltage across the resonant capacitor (green)
(duty cycle 28 %)
To get a comparison with the normal modified
Boost converter, it was simulated using the same
coil and capacitor values as used for the
QRZCSMBC. The efficiency is about 1.4 % lower
than for the ZCSQR converter. No optimization was
done. A Schottky diode was used. The efficiency is
improved because of the reduction of the switching
losses, but the additional resonance current leads to
higher forward losses.
4 Conclusion
The QRZCSMBC has several interesting features:
No inrush current when applied to the input
source
Reduced voltage stress across the capacitor
Nearly no switching losses
But increased forward losses
Overall improved efficiency
The circuit is especially useful for powerful
batteries and battery-buffered micro-grids.
References:
[1] F.A. Himmelstoss, J.P. Fohringer, B. Nagl, and
A.F. Rafetseder: A new Step-Up Converter
with Reduced Voltage Stress Across the Buffer
Capacitor, 10th International Conference on
Optimization of Electrical and Electronics
Equipment, OPTIM’06, Vol. 2, pp. 141-146.
[2] F. C. Lee, High-frequency quasi-resonant
converter technologies, Proceedings of the
IEEE, vol. 76, no. 4, pp. 377-390, April 1988.
[3] D. Maksimovic and S. Cuk, A general
approach to synthesis and analysis of quasi-
resonant converters, IEEE Transactions on
Power Electronics, vol. 6, no. 1, pp. 127-140,
Jan. 1991.
[4] K. Deepa and M. Vijaya Kumar, Performance
analysis of a DC motor fed from ZCS-quasi-
resonant converters, IEEE 5th India
International Conference on Power Electronics
(IICPE), Delhi, India, 2012, pp. 1-5.
[5] S. Sooksatra and W. Subsingha, Analysis of
Quasi-resonant ZCS Boost Converter using
State-plane Diagram, 2020 8th International
Electrical Engineering Congress (iEECON),
Chiang Mai, Thailand, 2020, pp. 1-4.
[6] S. Sooksatra and W. Subsingha, ZCS Boost
Converter with Inductive Output Filter, 2020
International Conference on Power, Energy
and Innovations (ICPEI), 2020, pp. 77-80.
[7] D. K. Mandal, S. Chowdhuri, S. K. Biswas and
S. S. Saha, A Soft-Switching DC-DC Boost
Converter for Extracting Maximum Power
from SPV Array, IEEE 5th International
Conference on Computing Communication and
Automation (ICCCA), 2020, pp. 363-368.
[8] P. P. Abkenar, A. Marzoughi, S. Vaez-Zadeh,
H. Iman-Eini, M. H. Samimi and J. Rodriguez,
A Novel Boost-Based Quasi Resonant DC-DC
Converter with Low Component Count for
Stand-Alone PV Applications IECON –IEEE
Industrial Electronics Society, 2021, pp. 1-6.
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DOI: 10.37394/23201.2023.22.8
Felix A. Himmelstoss
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Volume 22, 2023
[9] (text in German) F. Zach, Leistungselektronik,
Frankfurt: Springer, 6th edition 2022.
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The idea, the text, the calculations, the simulations
and the drawings were done by the author; Fig. 11
was thankfully drawn by Dr. Karl Edelmoser.
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 authors have 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
https://creativecommons.org/licenses/by/4.0/deed.en
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