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7/28/2019 High Gain Switched Coupled Inductor Boost
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High-Gain Switched-Coupled-Inductor Boost
Converter
Ian Laird, Dylan Dah-Chuan Lu and Vassilios G. AgelidisSchool of Electrical and Information Engineering
University of Sydney
NSW 2006
Australia
AbstractWhen a low voltage DC power source is used, aDC-DC converter with a high step-up voltage gain is requiredto raise the voltage to more applicable levels. This is typicallyachieved in classical converters which often have to be drivenby pulse width modulation (PWM) waves with extremely highduty cycles. Although theoretically step-up converters can achievean infinite gain as the duty cycle approaches unity, in realitythe gain will peak due to losses in the converter. Increasingthe duty cycle beyond this point will only degrade the voltagegain. A solution to this problem is to use a converter that willproduce the desired gain at a smaller duty cycle. This paperproposes replacing the inductor in the classical boost converterwith a switched-coupled-inductor (SCL) configuration in orderto achieve high gains with moderate duty cycles. Mathematicalanalysis is presented along with selected experimental results tosupport the theoretical considerations.
I. INTRODUCTION
Small scale distributed power systems are growing in ac-
ceptance and usage every day. This is due to a number of
benefits that distributed power systems provide that centralised
power generation does not. For example they can provide an
end user with backup power in case the grid fails. In remoteareas where it is either too difficult or expensive to connect
to the grid, these systems provide a source of power. They
are also suited for use with renewable technologies that are
cost effective on a small scale such as photovoltaics (PV) and
thermoelectrics (TE).
However due to their small scale, distributed power systems
tend to generate low voltage levels which are unsuitable for
many applications or feeding back into the grid. As such high-
gain, step-up converters are required in order to produce the
desired voltage levels. Classical DC-DC step-up converters
include the boost, buck-boost, Cuk and Sepic. However in
order to achieve this gain, classical converters often have
to be driven by pulse width modulation (PWM) waves with
extremely high duty cycles (D > 0.9).Despite some converters being theoretically able to produce
these high conversion ratios, in reality the maximum ratio is
limited by the commutation times of the transistor and diode.
These times become critical as they constitute a larger portion
This project was sponsored by an Australian Postgraduate Award (APA),the Norman I. Price scholarship and in part by the ARC Discovery Projects(Project Code: DP0985867)
Corresponding author contact: [email protected]
of the total period as the frequency increases. For step-up
operation, the large duty cycles results in a small conduction
time for the diode. Thus if the frequency is increased too
much, the commutation times will take up all of the diodes
conduction [1]. As a result the range of usable duty cycle
values and hence the maximum gain, shrinks with increasing
frequency [2].Designing at lower frequencies will mean larger inductors
and capacitors to achieve the same ripple currents and voltages
as for higher frequencies. Alternately if higher frequencies are
used, the extreme duty cycle will mean the inductor current
will fall rapidly during the diodes conduction and hence
produce a large EMI emission. Also the short conduction time
will mean the diodes current will have a high peak in order
to produce the same average current similar to the step-down
situation for the transistor encountered in [3]. The diode could
also malfunction as there might not be enough time for it to
fully turn off and on during its short conduction period [4].
Several switching blocks, that use either capacitor or in-
ductor switching, are described in [4]. These blocks consistof either 2 capacitors and 2-3 diodes (C-switching) or 2
inductors and 2-3 diodes (L-switching). These blocks are
inserted into classical converters (such as the buck and boost)
in the place of the capacitors or inductors typically used for
energy conversion. The high step-up gain is achieved by using
the diodes to ensure that the capacitors/inductors are charged
in parallel and discharged in series. These blocks store less
energy in their electric/magnetic fields and thus are smaller,
lighter and cheaper than an equivalent transformer.
Coupled-inductors have been used to achieve this high step-
up without using extreme duty cycles. The drawback of this
method though is that the leakage energy can induce high
voltage stresses and large switching losses. Converters havebeen proposed that handle the leakage energy such as in [5].
This paper proposes replacing the inductor in the classical
boost converter with switched-coupled-inductor (SCL) config-
uration in order to achieve high gains with moderate duty
cycles.
The paper is organised as follows. Section II outlines the
circuits operation and switching states. Section III shows the
derivation of various circuit parameters and design equations.
Section IV compares the SCL boost with various other topolo-
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Fig. 1. Switched-coupled-inductor (SCL) boost converter
gies. Section V outlines the experimental verification of the
analysis through the testing of a constructed converter. Finally
conclusions are drawn in Section VI.
I I . PRINCIPLES OF OPERATION
The proposed circuit is shown in Fig. 1. N1 and N2 are
coupled such that N1 < N2. Since this converter is based on
the boost, the output voltage will always be greater than the
input (Vo Vi). For the following discussion and equations,Ton = t1 t0 and Toff = t2 t1.
The converter is able to operate in both the continuous
conduction mode (CCM) and the discontinuous conduction
mode (DCM). Modes 1 and 2 describe the entirety of the
continuous and part of the discontinuous operation of the
converter while mode 3 relates specifically to discontinuous
operation. The equations derived for mode 1 and 2 can be
used for CCM by substituting Toff = T Ton or for DCMby substituting ILmmin = 0. The switching diagrams of thesemodes are shown in Fig. 2.
A. Continuous Conduction Mode (CCM)
As mentioned above, CCM is described by modes 1 and
2 as shown in Fig. 2a and 2b. The switching waveforms for
CCM are shown in Fig. 3.1) Mode 1 [t0 - t1]: At t0 switch S turns on. This puts
DFW in reverse bias so that the load is supplied by only
the energy stored in Co. D1 becomes forward bias allowing
current in the magnetising inductor, Lm, to build up from its
minimum value (i.e. iLm(t0 = 0) = ILmmin). The voltageon N1 is reflected on N2 such that |v1| < |v2|. Thereforeaccording to Kirchhoffs voltage law (KVL), D2 becomes
reverse bias. Therefore the non-zero voltages and currents
during this stage are:
(a) Mode 1
(b) Mode 2
(c) Mode 3
Fig. 2. Proposed converter modes of operation
v1(t) = Vi
v2(t) =N2N1
Vi
iLm(t) =ViLm
t + ILmmin
vD2(t) =
1 N2N1
Vi
vDFW(t) = Vo
iCi(t) = ViLm
t ILmmin + Ii
iCo(t) = Io
for t0 t t1 (1)
2) Mode 2 [t1 - t2]: At t1 switch S turns off and stops
Lm from storing any more energy. N2 reverses its polarity
causing D2 and DFW to become forward bias. Energy stored
in Lm is magnetically transferred to N2 and then released into
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Co and the load, causing the current in N2 to drop from its
maximum value (i.e. i2(t1 = Ton) = IL2max). The voltage onN2 is reflected on N1 and thus again according to KVL, D1becomes reverse biased. Therefore the non-zero voltages and
currents during this stage are:
v2(t) = Vi Vo
i2(t) = ViVoN2N1
2
Lm(t Ton) + IL2max
v1(t) =N1N2
(Vi Vo)
vD1(t) =
1 N1N2
(Vi Vo)
vDS(t) = Vo
iCi(t) = Ii ViVoN2N1
2
Lm(t Ton) IL2max
iCo(t) =ViVoN2N1
2
Lm(t Ton) + IL2max Io
for t1 t t2
(2)
B. Discontinuous Conduction Mode (DCM)
As mentioned above, DCM is described by modes 1, 2 and
3 as shown in Fig. 2a, 2b and 2c. The switching waveforms
for DCM are shown in Fig. 4.
1) Mode 3 [t2 - t3]: If the converter is operating in
continuous conduction mode (CCM) then t2 will mark the end
of the period and the circuit will return to the first switching
state. However if it is operating in discontinuous conduction
mode (DCM) then at t2 the current in N2 will have dropped
to zero and thus the voltage on N1 will also be zero. With no
current flowing in the inductors, all the diodes will turn off.
Therefore the load is supplied by only the energy stored in Coas was the case during stage 1. An analysis of the circuit shows
it is possible for the diodes and switch to take on a range of
values according to the following equations and marked bythe gray sections in Fig. 4.
Vi Vo < vD1(t) < 0
Vi Vo < vD2(t) < 0
Vi Vo < vDFW (t) < 0
Vi < vDS(t) < Vo
for t2 t t3 (3)
The actual voltage of the diodes and switch is based on how
fast the switch voltage can discharge. As this is usually very
quick the equations above become:
vD1(t) 0
vD2(t) 0
vDFW (t) Vi Vo
vDS(t) Vi
for t2 t t3 (4)
III. CONVERTER ANALYSIS
A. Converter gain
Taking the voltage-second balance of Lm we obtain the
following converter gain:
Fig. 3. CCM waveforms (a) Switch voltage (b) D1 voltage (c) D2 voltage(d) DFW voltage (e) Coupled inductor voltage (N1 = dotted, N2 = solid)(f) Coupled inductor current (N1 = dotted, N2 = solid) (g) Output capacitorcurrent (h) Input capacitor current
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Fig. 4. DCM waveforms (a) Switch voltage (b) D1 voltage (c) D2 voltage(d) DFW voltage (e) Coupled inductor voltage (N1 = dotted, N2 = solid)(f) Coupled inductor current (N1 = dotted, N2 = solid) (g) Output capacitorcurrent (h) Input capacitor current
ViTon +N1
N2(Vi Vo) Toff = 0
Vi
Ton +
N1
N2Toff
=
N1
N2VoToff
Vo
Vi=
N2
N1
Ton
Toff+ 1 (5)
B. Inductor ripple current
During t0 - t1 current builds up in N1 such that it reaches a
maximum at t1. Similarly during t1 - t2 current decreases in
N2 to a minimum at t2. Therefore by using i1(t1 = Ton) =ILmmax and i2(t2 = Ton + Toff) = IL2min to evaluatethe inductor current in (1) and (2) respectively we obtain the
following:
I1 =Vi
LmTon (6)
I2 = Vo Vi
N2N1
2Lm
Toff (7)
C. Capacitor ripple voltage
1) Output capacitor: The derivation of the ripple on the
output capacitor is the same as for a regular boost converter.
During t1 - t2 the current in Co decreases in a linear fashion
and thus the voltage across Co follows a parabolic path that
increases to a maximum, VComax . Substituting iCo(t) given in(2) into iC(t) = C
dvCdt
we obtain the following:
vCo(t) =Vi Vo
2N2N1
2LmCo
t2 2Tont
+
IL2max IoCo
t + K
(8)
where K = constant
Since the maximum voltage occurs whendvCo(t)
dt = 0 we
can determine that tComax = Ton +
N2N1
2
Lm(IoIL2max)ViVo
.
Therefore using vCo
tComax
= VComax to evaluate (8) we
obtain:
vCo(t) =
(Vi Vo) (t Ton) +
N2N12
Lm (IL2max Io)2
2N2N1
2LmCo (Vi Vo)
+VComax (9)
Under certain operating conditions the switch will turn on
before the capacitor has reached VComax . For this case the
maximum voltage occurs at t2 i.e. vCo(t2 = Ton + Toff) =
V
Comax. Using this to evaluate (8) we obtain:
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vCo(t) =Vi Vo
2N2N1
2LmCo
(t Ton)
2 T 2off
+IL2max Io
Co(t Ton Toff) + V
Comax(10)
The boundary between these 2 cases occurs whent2 =tComax which after simplifying becomes Io = IL2min. Starting
at t2 and continuing to t1 in the next cycle, the voltage across
Co decreases linearly until it reaches a minimum at t1, thus
vCo(t1 = Ton) = VComin . Using this to evaluate (9) and (10)we obtain:
VCo =
N2N1
2
Lm(IL2maxIo)2
2Co(VoVi)for Io IL2min
IoCo
(T Toff) for Io IL2min(11)
2) Input capacitor: The derivation of the ripple voltage on
the input capacitor proceeds in a similar way as to that for the
output capacitor and thus the process will not be outlined here.Below are the ripple voltage equations for the input capacitor:
VCi =
12Ci
Lm(IiILmmax)
2
Vi
N2N1
2
Lm(IiIL2max)2
ViVo
for ILmmin Ii IL2maxTonCi
12 (ILmmin + ILmmax) Ii
for IL2max < Ii < ILmmin
Lm2CiVi
(ILmmax Ii)2
for Ii ILmmin and Ii > IL2max
ILmmin+ILmmax2 Ii
TonCi
N22Lm(IiIL2max)
2
2N21Ci(ViVo)
for Ii < ILmmin and Ii IL2max(12)
IV. COMPARISON WITH OTHER TOPOLOGIES
Table I shows a comparison of the SCL boost with the
classical boost, switched-inductor (SL) boost [4] and flyback
converters. This comparison covers only CCM since the mag-
nitude ofToff is dependent on the values of inductors used in
the topology. Below is the number of components, the voltage
gain and the switch and primary diode voltages for each of
the topologies.
From Table I it can be seen that the SCL boost has the
greatest voltage gain as long as N2N1
> 2. Compared with theboost and flyback it requires more components to implement
however this is still less than the SL boost. The switch voltage
of the flyback is typically lower than that of the boost-based
converters since Np
< Ns
for step-up mode however the
required blocking voltage of the diode will be much higher.
The boost-based converters also have the advantage of a
natural switch clamping feature created by the output diode
as compared to the flyback. The larger gain of the SCL boost
means that it is less likely to encounter switching problems
(due to extreme duty cycle) than the other converters.
V. EXPERIMENTAL RESULTS
In order to compare the ideal analysis with the actual per-
formance of the proposed converter, two 100 W were designed
and built whose common specifications can be summarised as
follows:
Po = 100W f = 100kHz Maximum voltage gain = 15
Percent VCi = 0.2% Percent VCo = 0.2%
By varying the value of the coupled inductor, one converter
was designed to operate in CCM for 0 < D < 1, and theother to operate in DCM for 0.02 < D < 0.8. The componentvalues and circuit parameters that resulted from these designs,
including where the DCM converter differs from the CCM
converter, and where the calculated values differ for these that
were used, are shown in Table II.
Fig. 5 shows the voltage gain versus duty cycle for the CCMversion of the proposed SCL as well as the standard boost
and flyback converters. The SCL and flyback were compared
to each other using the same turns ratio and the ideal gains
are based on equations from table I. These are compared to
experimental results produced by placing the proposed SCL
converter under different loads. As can be seen the gain drops
off at higher duty cycle values resulting in a maximum gain at
D 0.8. Fig. 6 shows the efficiency versus the output currentfor the DCM version of the proposed converter. Fig. 7 shows
TABLE ITOPOLOGY COMPARISON
Parameter SCL Boost Boost SL Boos t [4] Flyback a
Inductors 2 1 2 2
Cores 1 1 2 1
Diodes 3 1 4 1
Voltage GainN2N1
D1D
+ 11
1D2
D1D
+ 1NsNp
D1D
Switch Voltage Vo Vo Vo Vi +NpNs
Vo
Diode Voltage Vo Vo VoNsNp
Vi + Vo
aNp = Primary winding, Ns = Secondary winding
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TABLE IICONVERTER COMPONENTS AND PARAMETERS
Component Value
f 100 kHz
S MTW32N20E
D1 MUR3040PT
D2, DFW MBR40250N2N1
CCM: 5 DCM: 3.5
Lm CCM: 44.2 H DCM: 4.94 H
Core material 0P-43434-EC
Ci Calculated: 1058 F Used: 1000 F
Co Calculated: 12.5 F Used: 47 F
Fig. 5. Voltage gain versus duty cycle for proposed converter operating in
CCM for 0 < D < 1. The coupled inductor has N2N1
= 5 and Lm = 44.2H.
The ideal gains are based on table I and the experimental gain for variousloads are shown.
the experimental waveforms obtained during the operation of
the DCM version of the converter.
Fig. 6. Efficiency versus output current for proposed converter operating
in DCM for 0.02 < D < 0.8. The coupled inductor hasN2N1
= 3.5 and
Lm = 4.94H. Vi and Vo were fixed at 20 V and 100 V respectively.
Fig. 7. Experimental switching waveforms for DCM converter (a) Gatevoltage, (b) Superposition of current in N1 and N2, (c) Switch voltage
VI . CONCLUSION
This paper has proposed a converter topology that uses an
SCL configuration to modify the classical boost converter.
Analysis has shown that the converter has a higher gain than
the boost and flyback and the results were experimentally
verified.
REFERENCES
[1] B. Axelrod, Y. Berkovich and A. Ioinovici, Hybrid switched-capacitor-Cuk/Zeta/Sepic converters in step-up mode, in Proc. IEEE InternationalSymposium on Circuits and Systems, Kobe, Japan, May 2005, pp. 1310-1313.
[2] D. Maksimovic and S. Cuk, Switching converters with wide DC conver-sion range, IEEE Trans. Power Electronics, vol. 6, no. 1, pp. 151-157,Jan. 1991.
[3] J. Wei and F.C. Lee, Two novel soft-switched, high frequency, high-efficiency, non-isolated voltage regulators - the phase-shift buck converterand the matrix-transformer phase-buck converter, IEEE Trans. Power
Electronics, vol. 20, no. 2, pp. 292-299, Mar. 2005.
[4] B. Axelrod, Y. Berkovich and A. Ioinovici, Switched-capacitor/switched-inductor structures for getting transformerless hybrid DC-DC PWMconverters, IEEE Trans. Circuits and Systems I: Regular Papers, vol.55, no. 2, pp. 687-696, Mar. 2008.
[5] Q. Zhao and F.C. Lee, High performance coupled-inductor DC-DCconverters, in Proc. Applied Power Electronics Conf., Miami, USA, Feb.2003, pp. 109-113.
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