The Zero Voltage Switching(ZVS) Critical Conduction Mode(CRM) Buck
Converter with Tapped-inductor
Jong-Hu Park and B. H. Cho
Department of Electrical Engineering
Seoul National University, Seoul, Korea
E-mail: whoishe@snu.ac.kr
Abstract – This paper proposes a critical conduction mode buck
converter that has soft-switching operation by tapped-inductor. In
this converter, both the active switch and the diode have soft
switching operation by the resonance between the switch parasitic
capacitors and the filter inductor. And, the turn-off switching loss
of the active switch is reduced by the decrease of the turn-off
current. In addition, tapped-inductor changes the conduction
operation, which makes some advantageous conditions that
diminish the conduction loss and device stresses. Therefore, this
topology, ultimately, achieves both the power and cost efficiency
by the simple variation of the classical structure. For the proposed
converter evaluation, this paper provides the operation analysis of
the converter and the hardware verification by 50W prototype
operating at maximum 70kHz.
I. INTRODUCTION
Critical conduction mode(CRM) control is a control
strategy in which the active switch turns on when the inductor
current falls into zero point to remove the freewheeling diode
reverse recovery. This control operates on the boundary
condition between continuous conduction mode(CCM) and
discontinuous conduction mode(DCM) with variable
switching frequency [1-2]. Even though this CRM control has
some merits, the usage is restricted by the increasing
switching loss of the active switch as the power capacity or
the switching frequency goes up. The relatively small filter
inductance of CRM converter, compared with CCM, leads to
the high peak current of the active switch that augments the
switching and conduction losses. For a low voltage, high
current applications, the high switching current problem
becomes more serious. Moreover, the high current rating
semiconductor switch has a large parasitic junction capacitor
in general, the discharging loss of the parasitic junction
capacitor becomes significant at high switching frequency.
In order to overcome these problems, this paper presents
the tapped-inductor scheme for the CRM buck converter.
Tapped inductor configurations have been applied to the
conventional DC-DC converter in the previous researches [37]. Most non-isolated DC-DC converter circuits are based on
the three basic topologies – the buck converter, the boost
converter, and the buck-boost converter, and, the tappedinductor versions of these circuits have the benefits that the
duty cycle of the converter can be adjusted to a desirable
value by controlling the tapped winding ratio to prevent the
extreme duty cycle at the high step-up or low step-down ratio
[8]. This extra degree of design freedom enables the
semiconductor devices to avoid a high-peak current, and,
contributes to the reduction of switching loss and conduction
loss of the CRM converters.
In this paper, the ZVS CRM buck converter with the
tapped-inductor is proposed. The converter alleviates the
drawbacks of the conventional CRM buck converters. The
proposed scheme also provides the ZVS operation for the
switching devices. And, by optimal design of the winding
ratio of the tapped-inductor, both the switching loss and the
conduction loss can be minimized. The voltage stress of the
diode is also reduced according to the tapped winding ratio.
Hence, this converter is suitable for low step-down ratio
applications employing MOSFETs. The following sections
explain the principle of the proposed scheme and the
operating parameter analysis mainly about the efficiency and
device stress. And, finally, the results of the 50W prototype
converter will be given for hardware verification.
II. THE PRINCIPLE OF THE CRITICAL CONDUCTION
MODE(CRM) OPERATION WITH SOFT-SWITCHING
A. Idea
The proposed tapped-inductor buck converter is shown in
Fig. 1. The tapped winding ratio is: N=N1/N2 (N≥1), and N=1
is the conventional untapped buck converter case. Figure 2(a)
and (b) show the Vs in Fig. 1 waveforms of the conventional
and the proposed ZVS buck converter in CRM operation,
respectively. As shown in the shaded area in Fig.2, there
exists a resonant mode between the parasitic capacitances of
the switching devices and the filter inductor in CRM
operation. However, the resonant capacitor voltage of the
untapped converter, Vs in Fig. 2(a), cannot exceed 2Vo, thus,
the soft switching condition cannot be achieved in the
untapped CRM buck for the input-output voltage conversion
ratio lower than 0.5. Moreover, many emerging applications,
such as the high intensity discharging lamp ballast and the
battery charger, call for an extreme step-down ratio which
makes the CRM circuit far from the optimal operating
0-7803-7769-9/03/$17.00 (C) 2003 IEEE
Cd1
N1
Vs
+
Vin
N2
Sw
+
Vs
ZVS
Vin
RL
2Vo
Vo
Vdiode
Cd2
-
-
Vs
+
-
t
Fig. 1
Proposed tapped-inductor buck converter
condition[9]. In this paper, the idea to enhance the resonant
voltage of the active switch into the input voltage level Vin by
the tapped-inductor is suggested to satisfy the soft switching
condition even when a step-down ratio below 0.5 as shown in
Fig. 2(b). For the detail description, the equivalent circuit of
the resonant mode is shown in Fig. 2(c) with assumption that
the output filter capacitance is large enough to be considered
as a voltage source, and the parasitic resistance of the
resonant network is negligible. The resonant capacitor Cr
accounts for the parallel of Cd2 and the reflected Cd1 in Fig. 1,
and Lr refers to the inductance of N2. If the initial condition
of the resonant mode is:
(1)
V C ( 0 ) = 0, I L ( 0 ) = 0
where Vc is Vdiode, and IL is the current flow of winding
N2 in Fig.1. From this condition (1), the equations of Vc(t)
and IL(t) in the resonant mode are derived as follows:
V
(2)
V ( t ) = V − V cos ωt , I (t ) = O sin ωt
C
O
O
where, Z = Lr , ω =
n
Cr
L
1
Zn
.
(3)
LrCr
For ZVS operation, the winding ratio N of the tappedinductor which steps up the secondary voltage Vc into
primary voltage Vs, must satisfy the following condition:
(4)
max (V S ( t )) = V O + N ⋅ V O ≥ Vin .
Thus, the soft switching condition expressed with voltage
gain M and turn ratio N is established as:
N
≥
1
−1 .
M
(5)
B. Operation mode analysis
The proposed ZVS CRM converter in Fig. 1 has very
similar operation to a conventional CRM buck circuit except
for the resonant interval at the end of each switching period.
The proposed circuit has 3 operation stages – active switch
conduction stage, diode conduction stage, and resonant mode
stage. The key waveforms of the converter are shown in Fig.
3. The resonant mode starts when the inductor current reaches
zero. The time span of the diode conduction mode is the rest
period of the active switch turn-off interval except the
resonant mode. The resonant interval, Tr is derived from the
t
(a)
(b)
IL
+
Vc
-
Lr
Vo
Cr
(c)
Fig. 2. The voltage waveforms of Vs in Fig. 1, and the
equivalent circuit of the resonant mode (Vin > 2Vo)
(a) The CRM waveform with untapped inductor
(b) The proposed ZVS CRM waveform
(c) The equivalent circuit of the resonant mode
following condition:
V S (Tr ) = V O − N ⋅ V O cos( ω ⋅ Tr ) = Vin .
(6)
Then, the resonant interval time span, Tr, is:
Tr =
1
ω
 M −1 
cos −1 

M ⋅N 
.
(7)
And, from the voltage-second balance, the voltage gain of
the circuit is implicitly established as:
fS
Tr 

D (1 − M ) − M ⋅ N 1 −
+ M ⋅N ⋅D=
2
π
T
fn


where,
N
≥
1
.
−1
M
( N ⋅ M )2 − ( M
− 1) 2
(8)
And also the switching frequency can be derived
implicitly using (8). However, the filter inductance Lr is
relatively larger than resonant parasitic capacitance, thus IL(t)
during the resonant period is negligible as in the
discontinuous conduction mode. With this assumption IL(t)=0
(0≤ t ≤ Tr), we can obtain the following simple switching
frequency equation:
 Tr 
(1 − M ) ⋅ 1 − 
 RL 
T 

 ⋅
f = 
L
2
(
−
+
1) 2
MN
M
 2
2
(9)
where, the L2 is the inductance of N2.
From the inductor current waveform in Fig. 3, the instant
the active switch turns off, the magnetic flux in the inductor
keeps steady and the inductor turn ratio changes from N1+N2
into N2. Thus, the diode turn-on current jumps into N times of
the switch turn-off current. This means that, for the same
power transfer, the duty cycle of the switch should be wider
than the untapped-case. And, consequently, the peak current
0-7803-7769-9/03/$17.00 (C) 2003 IEEE
of the switch becomes lowered. This reduced peak current
contributes to the decrease of the switching and the
conduction losses of the active switch. In the next section, a
qualitative analysis is performed with the aim of forecasting
the converter behavior such as the efficiency and the device
stress through the voltage conversion ratios.
Sw
On
Off
t
Vin
V
s
t
N I sw,off
III. OPERATION PARAMETER ANALYSIS
t
DTs
(1-D)Ts-Tr
Tr
Fig. 3 Key waveforms of the proposed scheme
sw : the gate signal of the active switch,
Vs : the buck switch source port voltage,
IL : the tapped inductor current
A. Voltage gain: Fig. 4(a)
Figure 4(a) shows the relation between voltage gain M
and duty ratio D according to the various tapped inductor
turns ratios. The Figure is derived from Eq. (10). At an
extremely low M, the duty cycle of the operating point is
increasing as N is increasing, which gives some benefits such
as loss reduction and insensitivity of the voltage gain, M, to
the duty cycle variation.
M vs D
I sw,off
IL
Using the operation parameter formulas derived in
previous section, Fig. 4 shows the normalized parameter
curves which are derived from dividing the proposed
converter parameters by the conventional case(N=1).
M =
D
D + (1 − D ) N
( N ≥ 1, D : duty cycle )
(10)
B. Turn-off current of the active switch: Fig. 4(b)
The turn-off switching current of the active switch, Isw,off ,
is derived as:
M vs Ioff,norm
1
.
M vs Isw,norm
1
2
1
N=1
N=1
0.9
0.9
0.9
0.8
0.8
N=1
0.7
0.5
N=3
0.4
N=4
0.6
0.5
0.6
N=3
0.5
N=4
0.3
0.4
0.4
0.3
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
D
0.6
0.7
0.8
N=2
0.7
N=3
2
Ioff,norm
M
N=2
Isw,norm
0.6
0.8
N=2
0.7
0.9
0.2
0
1
(a) Duty cycle vs. Gain
0.1
0.2
0.3
0.4
0.5
M
0.6
0.7
0.8
0.9
(b) Gain vs. switching current
M vs Vdiode,norm
0.2
0
1
N=4
0.1
0.2
0.3
0.5
M
0.6
0.7
0.8
0.9
1
(c) Gain vs. active switch conduction loss
M vs Vsw,norm
1
0.4
M vs Ploss,sw,norm
4
4
N=1
0.9
3.5
N=4
3.5
N=4
0.8
0.6
N=3
0.5
Ploss,sw,norm
Vsw,norm
Vdiode,norm
3
N=2
0.7
3
N=3
2.5
N=3
2.5
2
N=2
1.5
2
N=2
0.4
1
N=4
N=1
1.5
0.3
0.2
0
0.5
0.1
0.2
0.3
0.4
0.5
M
0.6
0.7
0.8
0.9
1
(d) Gain vs. diode voltage stress
Fig. 4
1
0
N=1
0.1
0.2
0.3
0.4
0.5
M
0.6
0.7
0.8
0.9
1
(e) Gain vs. active switch voltage stress
0
0
0.1
0.2
0.3
0.4
0.6
0.7
0.8
0.9
(f) Gain vs. switching loss
Operation parameter curves of the tapped-inductor CRM converter
0-7803-7769-9/03/$17.00 (C) 2003 IEEE
0.5
M
1
(11)
1− M 

I sw , off = 2 ⋅ I LOAD ⋅  M +
 ( N ≥ 1)
N 

Vsw , norm
And, the normalized parameter, Isw,off, norm is:
= M+
1− M
N
.
(12)
Figure 4(b) shows the result of Eq. (12). The drop of the
turn-off switching current results in the reduction of the
conduction loss as well as the switching loss.
C. Conduction loss of the active switch: Fig. 4(c)
The active switch conduction loss is proportional to the
square of the rms conduction current, Isw,rms , which is:
2
2
I sw
, rms
M ( MN − M + 1) 4 I LOAD
⋅
N
3
=
.
(13)
And, the normalized parameter Isw,rms, norm is :
2
I sw
, rms , norm
=
( MN − M + 1) .
N
(14)
From the Fig. 4(c), the reduction of the rms value of the
active switch current by the higher duty cycle lowers
conduction loss in spite of the same average current as the
untapped case. It is also shown that the higher N also effects
on the reduction of the conduction loss.
D.
Conduction loss of the diode
The diode conduction loss is approximately proportional
to the average conduction current of the diode, Idiode,ave , which
is in the tapped CRM converter:
I diode, ave
= I LOAD (1 − M ) .
(15)
Idiode,ave is independent of turns ratio N, thus the diode
conduction loss is expected the same as that of the untapped
CRM converter.
E.
Device stress: Fig. 4(d), Fig. 4(e)
Tapped inductor also affects on the device stresses such
as the diode voltage stress, Vdiode , and the active switch
voltage stress, Vsw . The diode voltage stress drops by the
voltage dividing of the tapped inductor, thus it is dependent
on N as the following equation:
1
(16)
V
= V + (V − V ) .
diode
O
N
in
O
The normalized parameter Vdiode, norm is:
Vdiode , norm
=
M+
1
(1 − M ) .
N
= Vin + ( N − 1) ⋅ VO .
(18)
And, the normalized parameter Vsw, norm is:
where ILOAD is the average load current.
I sw , off , norm
Vsw
(17)
And, the curve is shown in Fig. 4(d).
On the other hand, the active switch stress is increasing as
turns ratio N goes up. The relation with N is expressed in (18).
= 1 + ( N − 1) M .
(19)
However, the Figure 4(e) shows that the voltage stress
increase is not severe in low M range where the proposed
tapped circuits are concerned in.
F.
Switching loss: Fig. 4(f)
The switching loss of the ZVS CRM buck converter takes
place in all the switching devices. The diode loss, however, is
much minor than the active device loss because of the
preclusion of the reverse recovery. On the active switch loss,
the turn-off loss is dominant due to the ZVS operation of the
switch. For the analysis, we approximate that the loss is
proportional to the product of Isw,off and Vsw . Then, the
normalized switching loss Psw,loss, norm is established as
follows:
Psw , loss , norm = I sw , off , norm × Vsw , norm =
(1 − M + M ⋅ N )2 .
(20)
N
And Fig. 4(f) displays the result. From the Figure, we
know that in a viewpoint of the switching loss, the tapped
converter with high N is advantageous to the low gain
application. However, notice that the loss is increasing rapidly
with voltage gain, thus there is some restriction to the voltage
gain range applicable.
IV. EXPERIMENTAL RESULTS
The proposed ZVS CRM buck converter is implemented to
the 50W high-intensity discharge(HID) lamp ballast
application for the hardware experiment. The input voltage
range of the ballast system is 220VDC ~ 320VDC, and the
output voltage is 86VDC. The step-down ratio of the system is
about 0.27~0.39. The switching frequency is maximum
70kHz. For these design considerations, the major
components used for the hardware prototype are determined
as table 1 presents.
Table 1. The major components used for the hardware prototype
Components
Tapped L
MOSFET
Diode
Parameters
EI3329, N = 3.4, L1 = 2.3mH, L2 = 196uH
IRFBC40 (600V, 6.2A)
MUR820 (200V, 8A)
Figure 5 and Fig. 6 show the experimental results. In Fig.
5, it is shown that the ZVS operation is achieved in the diode
as well as in the MOSFET at the end of the resonant mode.
There is no parasitic voltage ringing across the diode of the
converter, Vdiode in Fig. 5, by the isolation of the tapped
inductor from the turn-off oscillation of the MOSFET. A
capacitive snubber parallel connected with the MOSFET can
attenuate the ringing voltage of the MOSFET with no
dissipation due to the ZVS operation. In Fig. 6, the previous
untapped CRM buck converter shows the efficiency decreases
0-7803-7769-9/03/$17.00 (C) 2003 IEEE
lower than 96% as the conversion ratio goes down, since a
high input voltage drives the operating point into a low duty
cycle and a high switching frequency. In contrast, the
proposed converter keeps about 97% efficiency level with
small variation through the input range. When the experiment
was done in the ambient temperature, the temperature of the
MOSFET that is TO-220 package in the proposed circuit rises
up to 60 °C with no heat sink at the worst condition of
efficiency, and in the previous case, the temperature rises up
to 70 °C at the same condition. Thus, It is concluded that the
efficiency gap between two converter prototypes comes
mainly from difference in the active switch operation as
shown in the result of the loss analysis in previous section.
V. CONCLUSION
In this paper, the ZVS CRM buck converter with the
tapped-inductor is proposed. By adjusting the tapped winding
ratio, the soft switching condition is satisfied, and the turn-off
current of the active switch is reduced. Hence, the decrease of
the total switching loss in the CRM scheme is achieved. In
addition to the improvement of the switching loss, the
increase of operating duty cycle at the same low voltage
conversion as the conventional untapped version reduces the
conduction loss, as well. In this paper, the operation principle
of the converter, and the parameter analysis about the
efficiency and device stress are included. The experimental
verification with 50W hardware prototype is performed to
evaluate the proposed topology and the result shows that the
proposed converter has higher efficiency than the
conventional hard-switching CRM buck type.
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Fig. 5 The major waveforms of the hardware prototype
Measured efficiency (%)
99
98
97
96
95
Tapped - CRM
94
Previous CRM
93
92
220
240
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Input Voltage(V)
Fig. 6 The measured efficiency comparison between the
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