社団法人 電子情報通信学会
THE INSTITUTE OF ELECTRONICS,
INFORMATION AND COMMUNICATION ENGINEERS
信学技報
TECHNICAL REPORT OF IEICE.
EM インバータを用いた共振型 dc/dc コンバータ
関屋大雄†
永島和治†
魏秀欽††
† 千葉大学大学院融合科学研究科 〒 263–8522 千葉市稲毛区弥生町 1–33
†† 福岡大学工学部電子情報工学科 〒 814-0180 福岡市城南区七隈 8-19-1
E-mail: †sekiya@faculty.chiba-u.jp, ††xiuqinwei@fukuoka-u.ac.jp
あらまし
本稿では EM 級インバータを用いた共振型 dc/dc コンバータを提案する. EM 級インバータを用いること
で, 従来の共振型コンバータと比較して, 高周波数動作下における電力変換効率の改善を低コストで達成できる. 著者
らが開発した数値設計手法を適用することで, 複数の拘束条件を満足するコンバータの設計値を高い精度で導出する
ことができる. 回路実験を行い, 動作周波数 1 MHz, 7.5 W の出力において, 88.5 %の電力変換効率を達成した.
キーワード
共振型 dc/dc コンバータ, EM 級インバータ, 電力変換効率, 高周波数
Resonant Converter with Class EM Inverter
Hiroo SEKIYA† , Tomoharu NAGASHIAM† , and Xiuqin WEI††
† Graduate School of Advanced Integration Science, Chiba University
1-33, Yayoi-cho, Inage-ku, Chiba-shi, Chiba, 263–8522 Japan
†† Dept of Electronics Engineering and Computer Science, Fukuoka University
8-19-1, Nanakuma, Johnan, Fukuoka, 814-0180 Japan
E-mail: †sekiya@faculty.chiba-u.jp, ††xiuqinwei@fukuoka-u.ac.jp
Abstract This paper proposes a resonant converter with the class-EM inverter along with its design procedure.
Because the class-EM inverter is applied to the inverter part of the resonant dc/dc converter, the proposed converter
achieves high power conversion efficiency at high frequencies with low cost. By using the numerical design procedure,
the accurate component values for achieving multiple constraint conditions without any analyses. In the laboratory
measurements, the proposed converter achieved 88.5 % power conversion efficiency with 7.5 W output power at 1
MHz operating frequency.
Key words Resonant dc/dc converter, class-EM inverter, power conversion efficiency, high frequency
ing and zero-derivative-voltage switching (ZVS/ZDVS) con-
1. Introduction
ditions. The switch current waveform, however, has a jump
High-frequency resonant dc-dc converters [1]- [6] have at-
at turn-off instant, which is a problem of the class-E inverter.
tracted a great deal of attentions in recent years. They are re-
For solving the current-jump problem, the class-EM inverter
quired to have ability of high power-conversion efficiency op-
was proposed [7], [8]. The class-EM inverter is regarded as
eration at high frequencies, which realize considerable minia-
the improved version of the class-E inverter. The class-EM
turization of power supplies. Generally, resonant converters
inverter achieves not only ZVS/ZDVS at turn-on instant but
consists of two part, which are inverter and rectifier parts.
also zero-current switching and the zero-derivative-current
In other word, the power-conversion-efficiency improvements
switching (ZCS/ZDCS) at the turn-off instant by injecting
of both the inverter and rectifier are important for achieving
to biharmonic frequency current from the auxiliary circuit.
high power-conversion efficiency of the converter.
Because of the smooth switch-current waveform, the class-
The resonant dc-dc converter using the class-E inverter [1]-
EM amplifier achieves higher power conversion efficiency than
This is
the class-E inverter, in particular, when the transistor has a
because the class-E inverter is able to reduce the turn-on
long turn-off-switching time. By allowing the slow switching,
switching losses because of the class-E zero-voltage switch-
the driving power can be reduced. Therefore, the class-EM
[5] is one of the solutions for this requirement.
—1—
Class EM Inverter
iLC1
VDD1
iS1
S1
Dr1
LC1
frequencies. Therefore, the proposed converter also has the
Class E Rectifier
ability to achieve high power-conversion efficiency at high
Main Circuit (k=1)
Lf
C1 L1
+ −
1
v
vS1−+ CS1
i1
D
i
v
+ f
− D
CD
frequencies.
2. 1 Class-EM Inverter
+
− f
v
Cf
R
The class-EM inverter [7], [8] has a main circuit and an auxiliary circuit as shown in Fig. 1. Both circuits has the similar
circuit topology to the class-E inverter. However, the opera-
iLC2
VDD2
LC2
C2
L2
+
− 2
v
i2
tion of the auxiliary circuit is different from the main circuit.
Namely, the auxiliary circuit works as a frequency doubler
iS2
S2
Dr2
and the output current of the auxiliary circuit has a bihar-
vS2+− CS2
monic frequency. Each circuit is composed of input voltage
Auxiliary Circuit (k=2)
VDDk , dc-feed inductance LCk , MOSFET as a switching de(a)
iLC1
VDD1
iS1
RS1
iLC2
VDD2
iS2
RS2
LC1
rLC1
C1 L1
+ −
1
v
+
S1−
v
CS1
LC2
rLC2
C2
L2
rL2
vice Sk , shunt capacitance CSk , and series resonant filter
Lk − Ck . In the above component expressions, k means the
Lf rLf
rL1
main (k = 1) and auxiliary (k = 2) circuits. The series
i1
RD
CD
i
v
+ f
− D
Cf
+
−
vf
R
resonant filters of the main and auxiliary circuits are tuned
to the fundamental and biharmonic frequency of the output
+
− 2
v
i2
voltage, respectively.
Figure 2 shows example waveforms of the proposed converter. In this figure, θ = ωt = 2πf represents the angular
vS2+− CS2
RX
rX
time and f is the operating frequency of the main circuit.
Figure 2(a) shows example waveforms in the class-EM in-
(b)
Fig. 1 The proposed converter. (a) Circuit topology. (b) Equivalent circuit.
verter. The switching device of the main circuit are driven
by Dr1 . When the main switch S1 is in the off-state, the
sum of the currents through dc-feed inductance of the main
circuit, resonant filter of the main circuit, and resonant filter
inverter also improves the power-added efficiency with low
of the auxiliary circuit flows through the main shunt capaci-
cost.
tance CS1 . The current through the main shunt capacitance
This paper proposes a resonant converter with the class-
produces the switch voltage of the main circuit vS1 . At the
EM inverter along with its design procedure. The proposed
switch-turn-on instant of the main circuit, the switch voltage
converter has the class-EM inverter as an inverter part and
vS1 satisfies the ZVS/ZDVS conditions, which are expressed
the class-E rectifier [4], [5] as a rectifier part. By applying
as
the class-EM inverter, the proposed converter achieves high
power added efficiency with low cost compared with the reso-
¯
dvS1 (θ) ¯¯
vS1 (π) = 0,
= 0.
dθ ¯θ=π
(1)
nant converters with the class-E inverter. On the other hand,
Due to the ZVS/ZDVS conditions, there is no jump on the
it is hard to determine the component values of the proposed
switch-voltage and switch-current waveforms at turn-on in-
converter for satisfying the ZVS/ZDVS and ZCS/ZDCS con-
stant.
ditions simultaneously. In this paper, the numerical design
When S1 is in on-state, vS1 is almost zero and the sum of
algorithms proposed in [9] and [10] are applied for designs of
current flows through the switching device. In the nominal
the proposed converter, which provides accurate design val-
operation, both the ZCS and ZDCS conditions are achieved
ues for satisfying the design specifications. By carrying out
at the switch-turn-off instant, namely,
the circuit experiments, effectiveness of the proposed converter and validity of the design procedure are confirmed.
¯
diS1 (θ) ¯¯
iS1 (2π) = 0,
= 0.
dθ ¯θ=2π
(2)
From the ZCS/ZDCS conditions, there is also no jump on the
2. Circuit Description
switch-current and switch-voltage waveforms at the turn-off
instant. This smooth turn-off switching can be achieved by
Figure 1 is the circuit topology of the proposed resonant
injecting the biharmonic current from the auxiliary circuit.
converter. This converter is composed of the class-EM in-
As a result, there is no jump in both the switch-voltage and
verter and the class-E rectifier. Both the inverter and the
switch-current waveforms on the main switch. By realiz-
rectifier can achieve high power-conversion efficiency at high
ing the smooth switch current, the current fall of the main
—2—
ON
π
0
3. Design Procedure
Dr2
Dr1
OFF
θ
2π
OFF
0
ON
π
θ
2π
For achieving high power-conversion efficiency, the condi-
vS2
vS1
tions (1) and (2) need to be achieved in the proposed con-
π
i2
iS1
0
θ
2π
π
i1
0
θ
2π
verter. It is hard to obtain the component values to satisfy
0
π
0
π
θ
2π
these conditions simultaneously. In this paper, the numerical design procedure in [9] is applied for the design of the
θ
2π
proposed converter. By using numerical algorithm, it is possible to obtain high accurate component values without carrying out any analyses. The design procedure in [9] requires
0
π
only the circuit topology and the simulator, which outputs
θ
2π
waveforms of the circuit. In this paper, the circuit topology
(a)
is expressed as differential equations and waveforms of the
Runge-Kutta method to the differential equations.
vo
vD
proposed converter are obtained numerically by applying the
π
0
θ
2π
3. 1 Assumptions and Parameters
0
π
θ
2π
(b)
Fig. 2 Example waveforms of the proposed converter. (a) Waveforms of class-EM inverter. (b) Waveforms of class-E rectifier.
In this paper, the circuit operation in the range of 0 <
=θ<
2π is considered. The proposed converter design is based on
the following assumptions.
(i) The switch S1 , S2 , and diode D have infinite offresistance and on-resistance, which are rS1 , rS2 , and rD , respectively. In addition, the same type of MOSFETs are used
switch current disappears. Therefore, the slow-switching de-
as S1 and S2 . Therefore, rS1 = rS2 = rS can be assumed.
vices are allowed and the cost reduction is possible. These
(ii) The shunt capacitance of each switching device,
are advantages of the class-EM inverter compared with the
namely CS1 , CS2 , and CD includes switching-device para-
class-E inverter.
sitic capacitance.
2. 2 Class-E rectifier
(iii) The equivalent series resistances (ESRs) of the in-
The class-E rectifier consists of an input current source,
ductances are considered. The ESRs of the capacitances are
which is the same as the output current of the inverter, diode
ignored because they are much smaller than ESRs of the
D with a shunt capacitance CD , low-pass filter Lf − Cf , and
inductance in experimental environment.
load resistance R.
Figure 2(b) shows example waveforms of the class-E recti-
(iv) All the passive elements including the switch onresistances work as linear elements.
fier. In the rectifier, the difference of the input current, which
(v) The switch-off duty ratio of the main circuit and
is i1 in the proposed converter, and the output current flows
the auxiliary one are 0.5 and 0.25, respectively and both the
into the diode or its shunt capacitance alternatively. While
switches turn off at θ = 0.
the diode is off, the current flows through the capacitance.
From the above assumptions, the equivalent circuit is illus-
When the diode voltage decreases to the threshold voltage, it
trated as shown in Fig. 1(b). Additionally, the following pa-
turns on. In the diode-off state, the power dissipation caused
rameters defined for obtaining the normalized circuit equa-
in the diode is nearly zero since the diode current is negli-
tions.
gible. While the diode is in the on state, the current flows
through the diode. In this period, the power dissipation in
the diode is kept small because the diode voltage is the same
as the threshold voltage. At the diode turn-off transition,
the capacitor current is zero. Therefore, the derivative of
the diode voltage is also zero as shown in Fig. 2(b). That
√
(a) Ak = fk /f = ωk /ω = 1/ Lk Ck /ω : The ratio of
resonant frequency to operating frequency.
(b) Bk = Ck /CSk : The ratio of resonant capacitance
to shunt capacitance.
(c) Hk = Lk /LCk : The ratio of resonant inductance to
dc-feed inductance.
reduces the switching losses and noises and enables the recti-
(d) Qk = ωLk /R : The loaded quality factor.
fier to operate with high power conversion efficiency at high
(e) J = C1 /CD : The ratio of the main resonant capac-
frequencies.
itance and the shunt capacitance of the rectifier diode.
(f) Dk : The switch-off duty ratio.
—3—
3. 2 Circuit Equations
From (1), (2), and (7)-(9), we have 17 algebraic equations for
From the assumptions and the parameters in the previous
obtaining nominal operation. When these algebraic equations are solved, the components values for obtaining the
subsection, the circuit equations can be formulated as
 di
LC1


dθ


di1



dθ



dvS1



dθ


dv1



dθ


di
LC2




 dθ
di2

























H1
Q1 R (VDC1 − vS1 − rLC1 iC1 )
1
Q1 R (vS1 − v1 − vD − rL1 i1 )
A21 B1 Q1 R(iC1 − vS1 − i1 + i2 )
RS1
A21 Q1 Ri1
2H2
Q2 R (VDC2 − vS2 − rLC2 i2 )
2
, (3)
Q2 R (vS2 − v2 − vS1 − rL2i2 )
2
A2 B2 Q2 R
vS2 − i )
(i
−
C2
2
2
RS2
A22 Q2 R
i2
2
vD − i )
2
A1 JQ1 R(i1 − R
f1
D
1 (v − v − r i )
f
Lf f 1
ωLf D
1 (i − vf )
ωCf f 1
R
=
=
=
=
=
=
dθ
dvS2
dθ
dv2
dθ
dvD
dθ
dif 1
dθ
dvf
dθ
=
=
=
=
=
where rLCk , rLk and rLf are ESRs of the inductors as shown
in Fig. 1(b). Additionally, RSk and RD are the resistances
of the switches Sk and the diode D, which are expressed as
(
RD =
Bk , Q2 and J are set as unknown parameters in the algebraic
equations. The other parameters are given as design specifications. The numerical algorithm for solving these algebraic
equations are presented in [9]. By using the algorithm, we
can obtain the component values with high accuracy.
4. Design Example and Experimental Result
In this section, experimental results along with a detailed
design procedure are shown.
First, the following design
specifications were given: f = 1 MHz, VDD1 = 10 V,
VDD2 = VDD1 /2 = 5 V, Vos = 20 V, R = 50Ω, D1 = 0.5,
D2 = 0.25, H1 = H2 = 0.07, and Q1 = 10. By considering
the operating frequency of 1 MHz, the low-pass filter of the
rectifier was designed as Lf = 3.18 µH and Cf = 470 nF.
IRFZ24N MOSEFETs and 20KHA20 shottky barrier
RSk =
and
constraint conditions can be obtained. In this paper, x0 , Ak ,
rS
if Sk is in on state
∞
if Sk is in off state,
(4)
diode were used as the switching devices of the inverter and
that of rectifier, respectively. Therefore, rS = 0.07Ω and
rD = 0.28Ω could be obtained from the datasheets. The
(
cores of L1 and L2 were Micrometal Powder Core T200
rD
for vD < 0
for vD >
= 0,
∞
(5)
#2 and T106 #2, respectively and 0.8mm-diameter copper
winding wires were used for making inductors. From these
respectively. When we define x(θ)=[x1 , x2 , · · ·, x11 ] =[iC1 ,
conditions, the ESRs of the resonant inductances can be es-
i1 , vS1 , v1 , iC2 , i2 , vS2 , v2 , vD , if 1 , vf ] ∈ R , (3) can be
timated by using analytical equations in [10].
T
T
11
From the above, the major loss factors, which are the
rewritten as
power losses on the switch-on resistances and ESRs of res-
dx
= f (θ, x, –),
dθ
(6)
onant inductors, could be included in the circuit equations.
where λ is a set of the system parameters as –=[A1 , A2 , B1 ,
Therefore, we can predict the power conversion efficiency
B2 , H1 , H2 , Q1 , Q2 , J, VDD1 , VDD2 , R, rLC1 , rLC21 , rL1 ,
from
rL2 , rLf , rS , rD , f , D1 , D2 ] ∈ R .
T
22
η=
3. 3 Constraint Conditions for Designs
Because the class-EM conditions are defined on steadystate waveforms, the boundary conditions between θ = 0
and θ = 2π should be achieved as
x(2π) − x(0) = 0
∈ R11 .
(7)
PO
Vo2
=
,
PI
(VDD1 IDD1 + VDD2 IDD2 )R
(10)
where input IDDk is
IDDk
1
=
2π
Z
2π
iLCk dθ.
(11)
0
Following the design procedure in the previous section, the
component values were obtained numerically for these design
For achieving high power-conversion efficiency, the class-EM
specifications. Table 1 gives the calculated component values
switching conditions (1) and (2) are considered. Addition-
and the estimated power conversion efficiency.
ally, the ZVS condition for auxiliary switch is considered for
power-conversion efficiency enhancement [8], namely,
vS2 (π/2) = 0.
By using the obtained component values, the circuit experiment was carried out. Figure 3 shows the waveforms
(8)
from numerical predictions and experimental results. Additionally, Table 1 gives the measurement results. In these
The output voltage should be the same as the specified volt-
figure and table, the component values were measured by
age Vos . Therefore, we also have
HP 4284A LCR meter, input voltage, input current, and
Vo − Vos =
1
2π
Z
2π
vf dθ − Vos = 0.
0
output voltage were measured by IWATSU VOAC7523 digi(9)
tal multimeter, and waveforms are obtained from Tektronix
—4—
Table 1 Numerical Predictions and Experimental Measurements
Dr1 (V)
π
θ
2π
Calculated Measured Difference
0
0
50
π
θ
2π
vS1 (V)
vS1 (V)
0
0
50
Dr1 (V)
10
10
π
θ
2π
0
0
3.5
π
θ
2π
iS1 (A)
iS1 (A)
0
0
3.5
π
θ
2π
π
θ
2π
1.5
00
π
θ
2π
π
π
θ
2π
θ
2π
00
π
π
θ
2π
θ
2π
1.14 mH
1.07 mH
−6.14 %
L1
79.6 µH
78.8 µH
−0.968 %
CS1
3.68 nF
3.68 nF
0.00 %
C1
337 pF
336 pF
−0.297 %
LC2
94.1 µH
96.3 µH
2.33 %
L2
6.59 µH
6.58 µH
−0.152 %
CS2
2.2 nF
2.19 pF
−0.455 %
C2
1.18 nF
1.18 nF
0.00 %
CD
2.35 nF
2.35 nF
0.00 %
Lf
318 µH
316 µH
−0.629 %
Cf
470 µF
470 µF
0.00 %
R
50 Ω
49.8 Ω
−0.40 %
rS
0.07 Ω
−
−
rD
0.28 Ω
−
−
rLC1
−
0.2 Ω
−
1.7 %
rL1
1.22 Ω
1.20 Ω
rLC2
−
0.042 Ω
−
rL2
0.15 Ω
0.18 Ω
20.0 %
rLf
−
0.21 Ω
−
-1.5
1.5
-1.5
1.5
0
0
-1.5
60
-1.5
60
vD (V)
π
θ
2π
vD (V)
0
0
0
1.5
i1 (A)
i2 (A)
00
50
i2 (A)
vS2 (V)
00
i1 (A)
0
0
10
vS2 (V)
00
50
θ
2π
Dr2 (V)
π
Dr2 (V)
00
10
LC1
π
θ
2π
00
25
π
π
θ
2π
vo (V)
00
π
θ
2π
(a)
1 MHz
1 MHz
0.0 %
10.0 V
10.0 V
0.0 %
VDD2
5.0 V
5.0 V
0.0 %
IDD1
0.698 A
0.68 A
−2.58 %
IDD2
0.36 A
0.33 A
−8.33 %
Vo
20.0 V
19.3 V
−3.50 %
η
89.5 %
88.5 %
−1.12 %
θ
2π
circuit, ZVS in the auxiliary circuit, and specified output
vo (V)
00
25
0
f
VDD1
00
π
θ
2π
(b)
voltage simultaneously. The experimental results showed the
good agreement with the numerical predictions, which indicated the validity of the numerical design procedure. In the
Fig. 3 Waveforms of proposed converter. (a) From numerical
predictions. (b) From experimental measurements.
experimental results, the proposed converter achieved 88.5
% power conversion efficiency with 7.5 W output power at 1
MHz operating frequency.
TDS3014 oscilloscope. The current waveforms are measured
It is expected that this converter will be built into many
by Tektronix TCP202 current probe. It is seen from Fig. 3
applications.
and Table 1 that the experimental results agreed with the
(WPT) system is one of the good applications for the pro-
numerical predictions quantitatively, which showed validity
posed converter. When a wireless coupling device is added
of the design procedure. Additionally, the measured power
between the inverter and rectifier, high power-transfer effi-
conversion efficiency is 88.5 % with 7.5 W output power and
ciency WPT system may be realized, which is an important
1 MHz operating frequency.
research problem in the future.
In particular, the wireless power transfer
5. Conclusion
Acknowledgments
This paper has proposed the resonant converter with the
This research was partially supported by Scholarship
class-EM inverter and class-E rectifier. By applying the class-
Foundation and Grant-in-Aid for scientific research (No.
EM inverter in the inverter part, the proposed converter
23760253) of JSPS and Support Center for Advanced
achieves high power added efficiency with low cost compared
Telecommunications Technology Research, Japan.
with the resonant converters with the class-E inverter. By
using the numerical design procedure, accurate component
values for achieving ZVS/ZDVS and ZCS/ZDCS in the main
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