DIRECT BUCK-TYPE AC/AC CONVERTER BASED ON
SWITCHED-CAPACITOR
Telles Brunelli Lazzarin, Marcos Paulo Moccelini, Ivo Barbi
Federal University of Santa Catarina - UFSC, Power Electronics Institute - INEP
PO box 5119, ZIP code 88040-970, Florianpolis, SC, BRAZIL
telles@inep.ufsc.br, moccelini@inep.ufsc.br, ivobarbi@inep.ufsc.br
Abstract—Switched-capacitor (SC) converters —
mainly non-isolated DC-DC converters — have been a
very important research topic for many years. Recently,
switched capactitors have also been applied in direct ACAC conversion, and studies have presented two different
bidirectional SC ac-ac converters, which intended to
replace the conventional auto-transformer in commercial
and residential applications. The analysis of one of
the presented converters shows that, by sacrificing the
bidirectionality, the circuit can be shortened, resulting in
a reduction of its overall cost and size. The proposed
change modifies the behavior of the converter in each
operational stage, thus a new analysis is needed. Therefore,
this paper studies, describes, analyzes, designs and tests
the proposed new topology. The paper also compares the
new converter with the previous topology and presents
its advantages, disadvantages and applications. In order
to demonstrate the performance of that converter, the
design example and experimental results of a prototype
of 1 kW, 220/110 V input/output voltages, and switching
frequency of 100 kHz, are reported herein. The maximum
and nominal efficiencies shown by the prototype were
97.6% and 96.1%, respectively.
Keywords—buck-type, direct ac-ac converter, switchedcapacitor.
I.
I NTRODUCTION
It is common to find commercial and residential devices
that use a different voltage from the one available in the
electrical grid, and, thus, generally a low power/low voltage
autotransformer must be employed as a solution. However,
as the auto-transformer is an electromagnetic transformer,
it suffers from low efficiency, audible noise and the heavy
weight of the magnetic core. Another important matter to take
into consideration is the global shortage of copper, commonly
used to construct the windings of the transformer [1], [2], [3].
The Switched-Capacitor (SC) has been an important
research topic for many years, mainly in relation with nonisolated DC-DC static power conversion [4], [5]. The main
applications of the SC converters are: power supplies for
mobile electronics systems [6], [7]; electric vehicles [8];
battery equalizer circuits [9] and voltage-balancing circuits
for multilevel inverters [10], [11]. As SC power converters
are composed only of capacitors and electronic switches, it
is possible to achieve smaller size and weight comparing to
common switched-mode power supplies, which use magnetic
devices. Also, the SC converter behavior can be described by
simple equivalent circuits.
978-1-4799-0272-9/13/$31.00 ©2013 IEEE
230
The switched capacitor principle was recently extended
to AC-AC static conversion for the first time [1]. In the
article, a brief analysis and experimental results for a stepdown/step-up converter with rated power of 600 W, 220/110
V, 60 Hz, switching frequency of 50 kHz and a measured
peak efficiency of 95.6% were presented. The converter
supplies a differential output voltage and it employs two
SC’s and eight unidirectional switches. Another publication
[2] proposed a new bi-directional topology with rated power
of 1 kW, 220/110 V or 110/220 V, 60 Hz and switching
frequency of 100 kHz and a measured peak efficiency of
97.8% were presented. The converter employs two fixed
capacitors and one SC, it supplies an output voltage which
has a common reference with the input voltage, and it uses
four bi-directional switches.
The purpose of this paper is to present the theoretical
analysis and practical results for a reduced version of the
topology presented in [2]. By sacrificing the bi-directionality
of the converter, one of the fixed capacitors can be removed
from the circuit, reducing its overall cost and size. The
absence of one of the capacitors changes the behavior of
the circuit in each operational stage, thus a new analysis is
needed.
II.
T HE PROPOSED SWITCHED - CAPACITOR AC-AC
CONVERTERS
The original topology introduced by [2] consists of four
bidirectional switches (S1 , S2 , S3 , S4 ) and three capacitors:
the SC C1 and the fixed capacitors C2 and C3 (Figure 1).
S1
I
N
/
O
U
T
C2
S2
C1
S3
C3
S4
O
U
T
/
I
N
Fig. 1. Original bidirectional converter topology proposed in [2].
The new proposed SC AC-AC converter topology is
shown in Figure 2 (a). It is obtained by the elimination
of one of the fixed capacitors from the original circuit,
C2 . The elimination of C2 takes away the bidirectionality
characteristic of the converter and therefore only the stepdown operation becomes possible. The elimination of the
capacitor C3 instead of C2 is possible for a step-up operation
S1
S1
S1
S1
S2
I
N
O
U
T
C1
S3
C3
S4
O
U
T
/
S2
O
U
T S3
C1
/
I
N
C2
vi
I
N
/
I
N
S4
(a) Buck-type topology
(b) Boost-type topology
Fig. 2. Unidirectional topologies.
S2
S2
vi
C1
S3
S3
C3 vo
C3 vo
S4
S4
(a)
(b)
Fig. 4. Buck converter topological states.
(boost-type), as shown in Figure 2 (b). Both cases must be
feeding on a source with voltage characteristics. This paper
studies in detail the step-down version (buck-type) presented
in Figure 2 (a).
III.
/
O
U
T
C1
T HEORETICAL ANALYSIS
A detailed low-frequency (input voltage frequency) and
high-frequency (switching frequency) theoretical analysis of
the step-down converter is presented in this section.
A. Topological stages
The proposed converter presents two topological stages
during its operation, which are controlled by the switch gate
signals shown in Figure 3. The switches S1 and S3 operate
together, as well as S2 and S4 . The duty-cycle of all the
switches is 0.5, and S1 /S3 gate signals are complimentary of
the S2 /S4 gate signals. The switching logic is very simple and
can be achieved with a single UC3525 IC.
B. High-frequency (HF) analysis
The operational stages of the converter are discussed in
this section. The closed-switch resistance non-ideality (Ron ),
as well as a load resistance Ro >> Ron are taken into
consideration. The analysis is detailed only for the positive
half-cycle of the input voltage because the operational stages
are very similar in the negative half-cycle; however, the
voltages and the directions of the currents in the elements
are the opposite from those of the positive half-cycle.
C 1 2Ron
S3
C 1 2R on
S1
S3
S1
C3
vi
Ro
C3
vi
Δt1A
Ro
Δt1B
(a) First stage (∆t1 )
S2
S2
2R on
2Ron
C3
C1
Ro
C3
Ro
C1
S4
S4
Δt2A
Δt2B
(b) Second stage (∆t2 )
Fig. 5. Buck converter operational stages in the positive half-cycle.
Fig. 3. Gate signals of the bi-directional switches.
In the first stage, S1 and S3 are turned on, and S2 and S4
are turned off. The converter operates with C1 and C3 seriesconnected, as shown in Figure 4 (a). In this stage, the circuit
becomes a simple voltage divider and output voltage is vi/2.
In the second stage, S2 and S4 are turned on, and S1
and S3 are turned off. The converter works with C1 and C3
parallel-connected, as shown in Figure 4 (b). In this stage, the
input voltage source is disconnected from the circuit and the
capacitor C1 works to maintain a voltage equilibrium with
C3 .
Therefore, the SC C1 applies and maintains a voltage in
C3 equal to vi/2, i.e., the converter supplies an output voltage
equal to vi/2.
231
•
•
First stage (∆t1 ) — starts when the switches S1
and S3 are closed. During ∆t1A , the capacitors are
series-connected and receive energy from the voltage
source. When the current in C3 reaches zero, it starts
discharging (∆t1B ). C1 charges during the whole
stage. The switches S1 and S3 are then opened and
the stage is concluded. Figure 5 (a) illustrates this
topological stage. The currents in S1 , S2 , S3 , S4 , C1
and C3 and the voltages vi , vo and across C1 during
this stage (∆t1 ) are presented in Figure 6 (a) for the
positive half-cycle and in Figure 6 (b) for the negative
half-cycle.
Second stage (∆t2 ) — starts when the switches S2 and
S4 are closed. The capacitors are parallel-connected
and the voltage source is disconnected from the circuit.
C1 charges C2 during ∆t2A . When the current in C2
reaches zero, both capacitors start discharging (∆t2B ).
The opening of S2 and S4 marks the end of the stage.
Figure 5 (b) illustrates this topological stage. The
currents and the voltages during this stage (∆t2 ) are
also presented in Figure 6 (a) for positive half-cycle
and Figure 6 (b) for negative half-cycle.
vi
Gv =
vo
vC3
vi
=
=
= 0.5
vi
vi
2 × vi
vi_max/2
vi
+
input voltage. The theoretical LF waveforms of the proposed
converter are shown in Figures 7 (a), 7 (b) and 7 (c).
_
vi_max
vi
vi_max /2
vo
iS3
iS3
ωt
(b) Capacitor voltages
ωt
vS1 =vS2 =vS3 =vS4
vi_max/2
0
(a) Input and output voltages
0
0
vC1 =vC3
0
0
iS1
(1)
ωt
iS1
(c) Switch voltages
Fig. 7. Main low frequency waveforms.
iS2
0
iS4
D. Equivalent model
According to [2], an equivalent circuit for the proposed
converter, shown in Figure 8, can be obtained. The calculations are based on (2) — presented in [12] —, where fs is the
switching frequency, Req is the equivalent resistance and D,
the duty-cycle.
0
iS2
iS4
iC1
iC3
iC1
iC3
0
0
Req =
1
×
fs C
−1
1 − e (2fs Ron C)
vo
vC1
−(1−D)
−D
DTS
Δt2B
(1-D)TS
(a)
Δt1A
(2)
0.5vi
vC1
vo
Δt1A Δt1B Δt2A
1
1 − e (2fs Ron C) + e (2fs Ron C) + e (2fs Ron C)
0.5vi
Δt1B Δt2A
DTS
Req
Δt2B
(1-D)TS
vi_eq
Ceq
Ro_eq
vo
(b)
Fig. 6. High-frequency waveforms: (a) positive half-cycle, (b)
negative half-cycle.
Fig. 8. Equivalent circuit of the proposed converter.
C. Low-frequency (LF) analysis
Considering C1 and C3 equal capacitors, the voltage across
each one of them tends to be vi/2 in both series and parallel
stages. The maximum voltage across the switches is also vi/2.
As vo is the voltage across C3 and vC3 is ideally vi/2, the
voltage gain (Gv ) is calculated by (1).
Thus, the converter presents the behavior of a voltage
divider for any type of input voltage (AC or DC). Therefore,
if a sinusoidal voltage is connected to the input of the
converter, it outputs a sinusoidal voltage equal to half the
232
As shown in [2], the lowest Req is obtained with D =
0.5 and, consequently, the voltage drop and energy losses
are minimized for that duty-cycle value. Eq. (3) shows the
calculation of Req for a 50% duty-cycle.
−1
Req(D=0.5) =
1 + e /(2fs Ron C)
1
×
fs C
1 − e − 1/(2fs Ron C)
(3)
Table I summarizes the calculated value of the circuit
elements.
TABLE I
Circuit elements
Parameter
Proposed converter
Original converter [2]
Ceq
CeqL = 2C
CeqL = 3C
Req
ReqL = Req
ReqL = Req
Vi
Vi
2
2
Vi
eq
IV.
E XPERIMENTAL R ESULTS
In order to verify the proposed converter operation, a
prototype was built in laboratory. The experimental results
and a comparison with the original bidirectional converter is
presented within this section. Table II shows the converter
specifications, which are similar to the specifications of the
original converter, since that allows a better comparison. The
waveforms were recorded with rated power output and a 0.4
duty-cycle (0.1 dead-time).
TABLE II
Converter specifications
Description
Input Voltage
Output Voltage
Output Power
Input Voltage Frequency
Switching Frequency
Capacitors
MOSFET Ron
Fig. 10. Input and output voltages (100 Hz).
Figure 7. The voltage stresses on internal components is one
half of the input voltage vi . Figure 12 shows vS1 detailed
at switching frequency, which reveals the waveform does not
present overvoltage.
Value
220 V
110 V
1000 W
60 Hz
100 kHz
20 µF
0.06 mΩ
Figures 9 and 10 show the input and output voltages. As
expected, the converter works with a voltage gain of 0.5, i.e.,
vo is one half of vi . The frequency of the input voltage is
60 Hz in Figure 9 and, in Figure 10, is 100 Hz. This shows
the converter operates normally for different input voltage
frequencies.
Fig. 11. Voltages across S1 , C1 and C3 (vo ).
Fig. 9. Input and output voltages (60 Hz).
The voltages across the switch S1 and capacitors C1 and
C3 can be seen in Figure 11. Those experimental waveforms
are very similar to the theoretical waveforms presented in
233
Figure 13 shows the voltage and current outputs supplied
by the converter at rated power (1 kW) with a resistive load.
The measured output voltage was 106.6 V, which correponds
to a regulation near 96.9%.
The input voltage and the input current at the rated power
can be seen in Figure 14. The input current ii presents
a high frequency component and it leads the voltage by
approximately 10◦ , which is expected due to the topological
stages of the converter and the circuit being capacitive.
If the voltage source can not supply the high frequency
component of the input current, a filter must be added to
the converter. The frequency of the current ripple is high
(100 kHz), and, thus, a small LC filter is sufficient. That
configuration was also tested, with C = 10µF and L = 5µH.
The current is supplied by the source, i.e., before the LC
filter, can be also seen in Figure 14. The current is is
approximately sinusoidal and without distortion.
TABLE III
Results comparison
Description
Peak efficiency
Efficiency (1 kW)
Power factor (1 kW)
Voltage regulation
Original [2]
97.8%
96.2%
96.9%
96.9%
Proposed
97.6%
96.1%
98.5%
96.9%
original bidirectional converter. A negligible loss of efficiency
(due to the disconnection of the voltage source in the second
operational stage), similar regulation and higher power factor
are observed in the new converter results, as Table III shows.
Fig. 12. Voltage across S1 detailed at 100 kHz.
Fig. 15. Efficiency
The experimental efficiency curve plotted in Figure 15
shows that, for a wide range of loads, the experimental
efficiency is higher than 96%. The measured efficiency at
rated power was 96.1% and the efficiency peak were 97.6%
and occurred at approximately 400 W. Figure 15 also shows
the efficiency curve of the original converter studied in
[2], making evident the proposed circuit reduction does not
decrease significantly the efficiency of converter.
Fig. 13. Output voltage and current.
Fig. 14. Input voltage (vi ), current supplied by the source (is ) and
converter input current (ii ).
Fig. 16. Regulation
Figures 15, 16 and 17 show the efficiency, regulation and
power factor, respectively, of the proposed converter and the
234
The output regulation curve can be seen in Figure 16. A
voltage drop of less than 3.5% was noted for rated power
compared to the no-load output voltage. Again, the proposed
and original converters showed similar results.
The input power factor curves plotted in Figure 17 show
that the power factor is close to one at rated power, but
it drops considerably as active power decreases. That is a
consequence of the capacitive circuit and the parameters
chosen. The comparison between the original and proposed
converters demonstrates that the latter performs better in
terms of input power factor, measured 98.5% at rated power.
Those characteristics were expected due to fact the total
capacitance of the circuit was reduced.
Fig. 17. Power Factor
V.
C ONCLUSIONS
A new switched-capacitor AC-AC converter was proposed
with the following characteristics: no inductors or other
magnetic elements present, only capacitors and switches employed; operation in open-loop; common reference between
input and output voltages; and step-down operation with a
voltage gain of 0.5.
The proposed converter topology was based on another
SC AC-AC converter, but with the number of capacitors
reduced. Consequently, the cost and size of converter were
also reduced, although, as a disadvantage, the converter
became unidirectional.
The paper presented the theoretical analysis of the converter and its operation was verified through experimental
results. The measured maximum and rated power efficiencies were 97.6% and 96.1%, respectively. The voltage
gain measured in rated power was 0.485. A comparison
between the new and the original converter showed that
both presented similar performance. Therefore, the proposed
converter presents the advantage of a reduced number of
capacitors and the disadvantage of being unidirectional.
Those characteristics indicate the new converter is an
appropriate alternative solution for the auto-transformer in
unidirectional and low cost applications.
235
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