high gain switched coupled inductor boost

7/28/2019 High Gain Switched Coupled Inductor Boost

1/6

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-

PEDS2009

423


2/6

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

PEDS2009

424


3/6

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

PEDS2009

425


4/6

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:

PEDS2009

426


5/6

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

PEDS2009

427


6/6

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.

PEDS2009

428

high gain switched coupled inductor boost

Documents