A Non-Insulated Resonant Boost Converter
Peng Shuai∗ , Yales R. De Novaes† , Francisco Canales† and Ivo Barbi‡
∗ ISEA-Institute
for Power Electronics and Electrical Drives, RWTH-Aachen University, Aachen, Germany
Email: Peng.Shuai@isea.rwth-aachen.de
† ABB Corporate Research, Dättwil, Switzerland
Email: {yales.de-novaes, francisco.canales}@ch.abb.com
‡ INEP-Power Electronics Institute, UFSC-Federal University of Santa Catarina, Florianópolis, SC, Brazil
Abstract— In this paper, a resonant boost converter is analyzed and verified through experimentation. Switching losses
are reduced since the converter operates at ZCS (Zero Current
Switching). The analysis presented here covers its operation
with variable switching frequency but only below the resonant
frequency. The range of its voltage gain goes from 1 to 2 and
the energy conversion efficiency (including filtering at input) is
around 97% for the lowest input voltage. Its envisioned that
it could be applied as a front-end converter when a backend inverter is needed, for instance with batteries, photovoltaic
converters or fuel cells, perform partial output voltage regulation
only.
I. I NTRODUCTION
Nowadays, resonant techniques have widely been utilized
in power electronics converters. Compared with the conventional PWM converters, the switching losses of the resonant
converters are significantly reduced due to the soft-switching
properties. This allows for increasing the switching frequency
to levels as high as 1 MHz and drastically increasing the power
density compared to hard switched converters. Electromagnetic interference is usually less critical for resonant converters
since there are no spikes during commutations (or they are
reduced). Although resonant commutations have been utilized
long time ago with thyristor semiconductors, the resonant
conversion evoluted from resonant converters to quasi-resonant
converters and multi-resonant converters [1] [2] [3]. Resonant
converters contain resonant L-C networks and the voltage and
current of this networks vary sinusoidally in one or more
commutation intervals [4]. The commutation of the switches
is usually with zero-voltage switching (ZVS) or zero current
switching (ZCS).
In this paper, a two-switch non-insulated DC-DC boost
converter using resonant technique is proposed, investigated
and validated at 1 kW and maximum switching frequency of
100 kHz. The only switching losses of this converter occur
because of the energy stored in the parasitic capacitance of
the active switch. The original document where this topology
is proposed among other resonant and PWM converter is [6].
But by coincidence, the commutation cell of this converter can
be extracted from the PWM multilevel converter presented
by [16], however the capacitor has a different functionality
since in the resonant converter it is completely charged and
discharged during operation. This topology can also be seen
in [9] where a snubber for the NPC inverter is presented. It
978-1-4244-4783-1/10/$25.00 ©2010 IEEE
becomes more clear if one looks at half of the modulation
cycle of the inverter operating with no load.
In this work, the analysis is carried in detail by describing
every topological stage and its equivalent equations. The
equation of the static characteristic is obtained describing the
voltage gain as function of the load current and switching
frequency. The voltage gain of this converter can be controlled
by controlling the switching frequency, the minimum value
is 1 and the maximum is 2. Since the maximum gain is
limited, it is envisioned that this converter could be a good
option if the primary energy source would be a battery or
photovoltaic string and the output of this converter would be
connected to an inverter. By doing so, assuming a variating
input voltage, the resonant converter could regulate the output
voltage partially, limit the lowest value seen by the inverter.
This is depicted in Fig. 1, where the resonant converter
regulates the voltage from 1 to 2 pu, and the inverter accepts
the variation from 2 to 2.5 pu without compromising its output
voltage and current quality. In an application, for instance,
ideally the input voltage could variate from 200 V to 500V, and
the resonant converter boosts and regulates its output voltage
to 400V while the input voltage is lower than 400V. When the
input voltage is higher than 400V, then the converter could be
by-passed.
Fig. 1: Input voltage variation and regulation range.
II. C ONVERTER O PERATION P RINCIPLE
The converter topology investigated in this paper is shown
in Fig. 2. The resonant tank of this non-insulated converter
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is composed of the resonant inductor Lr and the resonant
capacitor Cr . Two switches and two diodes are represented
as ideal devices. In addition, it is assumed that the output
capacitor Co is large enough, so that the output voltage Vo is
kept constant during one switching cycle. The control signals
Vi
After mathematical transformation and calculation, one can
obtain the following equations:
io
Ds1
Lr
By assuming that the initial condition for this stage is:
iLr (t0 ) = 0
vCr (t0 ) = 0
iLr (t) =
Vo Co
C
r
Ds 2
√
Ro
S2
Fig. 2: Converter Topology.
iLr (t) =
Lr
Vi
iLr
Ds 2
S1
Ro
Vi
Lr
iLr
Ds1
io
Ds 2
Cr Vo Co
Lr
Vi
iLr
Ds 2
Ro
S1
Stage 1
Vo Co
C
r
S1
Ro
Vi
Lr
iLr
S2
io
Ds 2
Cr Vo Co
Ro
S1
S2
Stage 4
Fig. 3: Representation of the main topological stages.
vCr (t) = 1 − cos(ω0 t)
(8)
At t0 , S1 is turned off and S2 is switched on, diode Ds2
is conducting. During this stage, the resonant capacitor Cr is
charged by the source to the voltage level of the output voltage
Vo . Due to the resonance, the current through the resonant
inductor Lr increases sinusoidally from 0 to a certain value,
which is supposed to be I1 . This stage can be described with
the following two equations:
diLr
+ vCr (t)
dt
dvCr (t)
dt
(10)
where I1 is defined as the final condition of the inductor
current at t1 (I1 is parameterized). At this time instant, the
resonant capacitor voltage is equal to the output voltage Vo ,
therefore:
vCr (t1 ) = G
(11)
ω0 Δt10 = π − arccos(G − 1)
A. Switching Stage 1 [t0 ,t1 ]
iLr (t) = Cr
(7)
Where G = Vo /Vi is also the voltage gain of the converter.
From (10) and (11) the duration of this topological stage can
be calculated as:
Stage 5
Vi = L r
iLr (t) = sin(ω0 t)
vCr (t1 ) = 1 − cos(ω0 t1 )
Ds1
(5)
At the end of this stage, at the time instant t1 , the following
equations are valid:
iLr (t1 ) = I1
(9)
Stage 2
io
iLr (t)
Vi /Zr
vCr (t) =
S2
S2
Ds1
(4)
vCr (t)
(6)
Vi
So, for this topological stage, by applying (5) and (6) to
(3) and (4), the parameterized inductor current and capacitor
voltage of the resonant tank are:
of the two switches are two complementary signals with 50%
duty cycle. Each switch turns on for a half of the switching
cycle and in each half cycle there are three switching stages
according to the operation of the resonant tank. The operation
stages of the converter in a switching cycle are illustrated in
Fig. 3.
V Co
Cr o vCr (t) = Vi [1 − cos(ω0 t)]
(3)
Where ω0 = 1/ Lr Cr is the resonant angular frequency. The
inductor current can be parameterized as a function of
the input
voltage and the resonant circuit impedance (Zr = Lr /Cr ),
and the resonant capacitor voltage can be parameterized as a
function of the input voltage, as follows:
S1
iLr
Vi sin (ω0 t)
Lr
ω0
Where Δt10 = t1 − t0 .
As usually done in resonant converter analysis [10], a vector
z can be defined as per (13).
z = vCr (t) + jiLr (t)
(13)
The real part of the vector z stands for the voltage on the
resonant capacitor while the imaginary part represents the
current through the resonant inductor. So the first stage can
be described by the following vector:
(1)
(2)
(12)
z1 = 1 − cos(ω0 t) + j sin(ω0 t) = 1 − e−jω0 t
(14)
This vector shall be utilized in a next section to build a stateplane.
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B. Switching Stage 2 [t1 ,t2 ]
F. Stage 6 [t5 ,t6 ]
At t1 , the resonant capacitor voltage vCr is equal to the
output voltage Vo , the diode Ds1 turns on. So in this stage
vCr is clamped as Vo , while the current through the inductor
iLr drops lineally to zero, since the output voltage is higher
than the input voltage, a negative voltage is applied across Lr .
By similar mathematical calculation, the vector in a state-plane
can be derived as:
At the end of stage 5, the current drops to 0 and there
is no voltage across the resonant capacitor. Thus, in this last
stage there is no current through Lr and no voltage across Cr .
Therefore, the vector of this stage is equal to zero:
z2 = G + j[I1 − (G − 1)ω0 (t − t1 )]
I1
G−1
(23)
And the duration is:
ω0 Δt65 = π − ω0 Δt43 − ω0 Δt54
(15)
(24)
G. Summary of the switching behavior
The duration of this stage can be calculated as following:
ω0 Δt21 =
z6 = 0
The main waveforms of voltages and currents of the components are shown in Fig. 4. The waveforms of the two switches
(16)
C. Stage 3 [t2 ,t3 ]
Gate signal for S1
vCr
As the current becomes 0 at the end of the second stage,
Ds2 blocks, so there is no current through Lr , and the voltage
across Cr remains at Vo as in stage 2. In this stage, no current
is circulating in the circuit. The vector to describe this stage
is then quite simple:
z3 = G
iLr
Gate signal for S2
(17)
The end of this switching stage is half of the whole switching
cycle, which means ω0 t3 = π. So:
ω0 Δt32 = π − ω0 Δt10 − ω0 Δt21
vS 1
(18)
iS 1
D. Stage 4 [t3 ,t4 ]
At the beginning of this stage, S1 is turned-on and Ds1
starts to conduct the resonant current. Ds2 remains blocked.
The resonant capacitor is discharged, so the voltage across it
drops from Vo to 0. At the same time, the current through the
inductor increases from 0 to I1 . The operation of the converter
is similar as in the first stage. One can obtain similar vector
as for the first stage:
z4 = G − 1 − cos(ω0 t) − j sin(ω0 t) = G − 1 − e
−jω0 t
vS 2
iS 2
vDs1
iDs1
(19)
This stage has the same duration of the first stage:
ω0 Δt43 = π − arccos(G − 1)
(20)
vDs 2
iDs 2
E. Stage 5 [t4 ,t5 ]
The operation of the converter in this stage is quite similar
as in stage 2, difference is that the resonant capacitor voltage
keeps at zero. The vector related to this stage is:
z5 = j[I1 − (G − 1)ω0 (t − t4 )]
(21)
The duration of stage 5 is also the same as stage 2, so:
ω0 Δt54 =
I1
G−1
(22)
t0
t1
t2
t3
t4
t5
t6(Ts )
t
Fig. 4: Converter waveforms based on analysis with ideal
components.
and two diodes are complementary with each other in each
switching cycle. The ZCS (Zero Current Switching) can be
clearly seen when looking to the instantaneous values of the
voltages and currents of the active switches. In regarding the
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resonant circuit, the voltage across the resonant capacitor vCr
is charged to Vo and then clamped at this value during the first
half switching cycle. Then in the second half switching cycle
the resonant capacitor is discharged and then vCr becomes
zero. The frequency of the current through the resonant
inductor iLr is twice of the switching frequency. The average
value of the current through Ds1 diode is dependent on the
switching frequency, then the output voltage can be regulated
by the ratio between the switching frequency and the resonant
frequency.
Based on the analysis above, the complete state-plane graph
for the vector z in a switching cycle can be depicted. The
real axis is the parameterized resonant capacitor voltage vCr ,
while the imaginary axis is the resonant inductor current iLr ,
see Fig. 5. Following the direction of the arrows the variations
of the current and voltage during the switching cycle can be
seen. The maximum value of the inductor current can be found
characteristic of the converter and is depicted in Fig. 6 for
several values of μ0 . The ideal gain is limited between 1 and
2 for the full range of frequency variation. This means that the
output voltage cannot be lower than the input voltage (there
would be forward conduction of both diodes), and cannot be
higher the twice the input voltage.
0.5
ioAVG
0.4
P0 0.01
P0 0.02
P0
0.3
0.04
P0 0.06
P0 0.08
P0 0.1
0.2
P0 increases
0.1
1
I1
0
0.8
1
z5
0.6
z1
z4
1.2
1.4
G
1.6
1.8
2
Fig. 6: Converter gain as a function of the average output
current, having the frequency ratio as parameter.
z2
iLr (Z0t )
0.4
It is important to highlight that in this study it is assumed
that the switching frequency is always lower than the resonant
frequency, i.e. fs ≤ f0 or 0 < μ0 ≤ 1. By using the
resonant impedance Zr to parameterize the load resistance,
the following ratio can be introduced:
0.2
z3
z6
0
G 1
0
vCr (Z0t )
1
1.5
ro = Ro /Zr
Fig. 5: State-Plane Graph.
(29)
With this ratio, the following equation can be derived:
in the graph as: iLr (ω0 t)max = 1, when vCr (ω0 t) = 1 or
vCr (ω0 t) = G − 1.
III. C ONVERTER E XTERNAL C HARACTERISTIC
Based on the switching behavior of the converter, the
parameterized average output current can be calculated by the
following equations:
t4
t2
iLr (t)dt +
iLr (t)dt + (25)
ioAV G = fs (
t
t3
t5 1
iLr (t)dt
(26)
+
G = ro ioAV G
By substituting (28) and (29) into (30), (31) can be obtained.
μ0
ro + 1
(31)
G=
2π
The relationship described by (31) is shown in Fig. 7. It can be
2
G
t4
where fs is the switching frequency of the converter.
fs =
ioAV G
1
Ts
G
= μ0
2π(G − 1)
(30)
(27)
ro
0.1
ro
0.5
ro
1
ro
ro
5
2S
ro
10
ro
ro
20
100
1.8
ro ž
1.6
1.4
1.2
(28)
1
0
In this equation μ0 = 2πfs /ω0 , which is the ratio between
the switching frequency fs and the resonant frequency f0 . The
time instants can be obtained by the switching stage duration
calculated previously. This equation describes the external
0.2
0.4
P0
0.6
0.8
1
Fig. 7: Dependence of Gain G on frequency ratio and gain.
seen that, for a constant load and constant input voltage, the
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output voltage changes linearly with μ0 . This means the output
voltage can be easily to control. Now, if it is necessary to
operate the converter over the full range of gain variation, the
relation (32) has to be respected. If a wide range of frequency
variation is required, then ro should be equal to 2π.
ro ≥ 2π
(32)
IV. E XPERIMENTAL VALIDATION
In order to verify the theoretical analysis and to verify the
concepts, a prototype rated at the following specifications has
been built and tested:
Output power: Po = 1kW
Regulated output voltage: Vo = 400V
Input voltage: 200V ≤ Vi ≤ 400V
ro = 2π → Zr = Ro /ro = 25.46Ω
Resonant inductor and capacitor: Lr = 39.69μH, Cr =
61.2nF
Resonant frequency: f0 = 102.1kHz
Output capacitor: Co = 110μF
Another constrain added to the specification is that the
converter should be able to withstand an input voltage of
500 V. In this case, above 400V there will not be regulation
of the output voltage and this converter could be bypassed
by an additional diode or a mechanical switch. A supposed
application where this makes sense would be a two stages
converter where the second stage could be an inverter able
to regulate its AC variables while having its input voltage
variating from 400 to 500V maximum. The utilized silicon
semiconductor devices were rated at 600 V as breakdown
voltage.
Fig. 8 shows the resonant inductor current iLr , resonant
capacitor voltage vCr and the input and output voltage for
operation at maximum power and minimum input voltage.
As expected, since this frequency is almost the resonant
frequency, the waveforms of the resonant tank are sinusoidal.
The input voltage is 200V while the output voltage is 400V,
the maximum gain G=2 is reached. The peak of vCr is equal
to the output voltage while the peak of iLr is approximately
7.8A as calculated from Vi /Zr.
Vo (Ch 2)
Vi (Ch3)
iLr (Ch1)
vCr (Ch 4)
(Ch1 & Ch4)
Fig. 8: iLr , vCr , Vi and Vo @ fs = 100kHz, Po = 1kW .
Fig 9 is showing the active switch commutations. The turnon is depicted in Fig. 9 (a). From this figure it can be seen that
there are reduced switching losses since the current increases
sinusoidally from zero. The only switching losses occur due
to the intrinsic capacitance of the active switch, in this case
MOSFET. The turn-off behavior is shown in Fig. 9 (b). As the
instantaneous values of current and voltage are not overlapping
the turn-off losses can be neglected.
vS 1 (Ch3)
(Ch2 & Ch3)
iS 1 (Ch 2)
Turn-on
Gate Signal(Ch4)
(a) Turn-on
iS 1 (Ch 2)
vS 1 (Ch3)
(Ch2 & Ch3)
Turn-off
Gate Signal(Ch4)
(b) Turn-off
Fig. 9: Commutation of the switching devices at fs =
100kHz.
The waveforms of the diode current and reverse voltage are
shown in Fig. 10. The reverse recovery of the diode can hardly
be found from the waveform, so almost no loss is produced
by the reverse recovery current.
Fig. 11 illustrates the behaviors of the current and voltage
of MOSFET at fs = 50kHz. The oscillations in the MOSFET voltage and current waveforms are due to the parasitic
capacitance.
In order to verify the operation at high input voltage, the
converter has been tested at fs = 5kHz and full power,
the waveforms can be found in Fig. 12. At this switching
frequency, the input voltage is quite close to the output voltage.
As the designed specification, the input voltage can vary from
200V to 400V, while keeping the output voltage at 400V and
the output power at 1kW.
The efficiency curve of this converter, considering the
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vCr (Ch 4)
Vo (Ch 2)
iLr (Ch1)
Vi (Ch3)
(Ch1 & Ch4)
vDs1 (Ch3)
vCr (Ch 4)
iDs1 (Ch 2)
Turn-on
iLr (Ch1)
Turn-off
(Ch1 & Ch4)
(Ch2 & Ch3)
Fig. 10: Diode reverse voltage and current @ fs
100kHz, Po = 1kW .
=
Fig. 12: iLr , vCr , Vi and Vo @ fs = 5kHz, Po = 1kW .
0.98
0.975
iS 1 (Ch 2)
vS 1 (Ch3)
0.97
K
0.965
0.96
(Ch2 & Ch3)
Turn-on
vCr (Ch 4)
Turn-off
0.955
iLr (Ch1)
0.95
0
100
200
300
400
500
600
700
800
900
1000 [W ]
Output Power
Fig. 13: Efficiency curve of 1kW prototype by power variation.
(Ch1 & Ch4)
0.986
0.984
Fig. 11: MOSFET current and voltage behaviors @ fs =
50kHz, Po = 1kW .
0.982
Trend line
0.98
K
0.978
0.976
0.974
variation of the output power while keeping the input and
output voltage constants and gain equal to 2 is depicted in
Fig. 13. At nominal power the efficiency is about 97 %. The
highest efficiency over the load range is at around 60% of
the full load, which is about 97.8%. The efficiency curve has
also been obtained considering input voltage variation, while
keeping the ouput voltage constant at 400V and output power
at 1 kW. The results are presented in Fig. 14. As expected for
this converter, for higher input voltage the efficiency is higher.
V. C ONCLUSION
A two-switches boost resonant converter capable of
stepping-up the input voltage by 2 times has been analyzed
and proposed in this paper. The utilized mechanism to control
the power flow is implemented by variating the switching
frequency, while keeping it below the resonant frequency. Both
active switch commutations are soft and the only switching
losses occur due to the energy stored in the parasitic capacitance of the active switch.
Detailed analysis and experimentation shown that this converter has potential for application where high efficiency and
simplicity are needed while its limited gain would not be a
drawback. With an appropriate dimensioning of the resonant
0.972
0.97
0.968
0.966
10k
20k
30k
40k
50k
60k
70k
80k
90k
100k[ Hz ]
fs
Fig. 14: Efficiency as a function of switching frequency (or
input voltage) with constant output power and voltage.
components, the converter reactive energy circulation could
be kept at low values, not compromising the efficiency. An
efficiency around 97 % was obtained by utilizing 600 V
MOSFETs (80 mΩ ).
Due to its reduced switching losses, this converter has
potential for applications where high power density is required.
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