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CAD/CAE for Power

Electronics

Course no. 2

Design and modelling aspects of the

main DC-DC converters

Content

1. DC, RMS

2. Main unidirectional single-stage DC-DC Converters (Design Aspects)

3. Chopper with R load

4. Chopper with RLE load

5. Step-down (buck) converter6. Step-up converter (Boost)

7. Buck-Boost converter (inverted voltage)

8. Flyback converter (isolated buck-boost converter)

9. Buck-Boost uk converter

10.Comparison of switch utilizations

11.Effects of parasitics

12.References

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DC, RMS

DC value (average) of a signal (voltage, current):

T1 T1

- -

DCT 0

DCT 0

,

0

21RMS dtvV

021

RMS dtiI

If a waveform can be divided into n harmonics:

2)(

2)2(

2)1(

2 ... nRMSRMSRMSDCRMS VVVVV

2)(

2)2(

2)1(

2 ... nRMSRMSRMSDCRMS IIIII

Problems

Determine the DC and RMS values of the following signals:

a) b) c)

d) e) f)

g)

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Answers

a) ;2 m

RMSm

DC

II

II

b)TTII

TTII mRMS

mDC

00 ;2

c)T

TUU

T

TUU mRMSmDC

00 ;

d)T

TUU

T

TUU mRMS

mDC

00

3;

2

e)3

;2

m

RMS

m

DC

II

II

f)3

;2

mRMS

mDC

UU

UU

g) AIAI RMSDC 18.143;17.8

Problem

Calculate the power losses of an IGBT during conduction,

on CE0iC

M

Im

t

on

CE0

TM

m

0

Solution: IC(DC)=3.8A; IC(RMS)=6A; Pd=5.22W

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Chopper with RLE load

Voltage transfer function, for CCM:

DVV

The PWM switching period:

o

io

i o

o

oDC

Step-down (buck) converter

L

io DVV i o

Current transfer function (CCM):L

oDC

o

DII io /S

S

D

LC

o

+

i o

C

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LC design basics*

Boundary between CCM and DCM (L-design 1):

fRDLb

2)1(

Maximum current ripple through L (L-design 2):

fL

DDVI iL

)1(

Voltage output ripple (C-design):

2min8

)1(

LfV

VDC

o

o

* with ideal components (neglecting the voltage drops on the components)

Problem

Design L and C for a buck converter with the following

specifications: Vi=2025V, Vo=10V, Pn=100W, Pmin=10W,

f=25kHz.

, m n

L-current ripple condition: IL0.5A

C-voltage ripple condition: Vo10mV

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Step-up converter (Boost)

L

VV 1 i o

Current transfer function CCM :

D1 LiDC

io IDI )1( S

C

o

LC design basics*

Boundary between CCM and DCM (L-design 1):

DRDLb

2

)1( 2

Maximum current ripple through L (L-design 2):

fL

DVI iL

Voltage output ripple (C-design)

RfV

DVC

o

o

min

*with ideal components

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Problem

Design L and C for a boost converter with the following

specifications: Vi=1218V, Vo=24V, Pn=120W, Pmin=12W,

= .

The converter must operate in CCM, for PPmin

L-current ripple condition: IL0.5A

C-voltage ripple condition: Vo50mV

Buck-Boost converter (inverted voltage)

L

i

VD

V o

Current transfer function CCM :D1

L

io ID

I

1S

S

D Io

Vi Vo RL C

iLC C

+ o

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LC design basics*

Boundary between CCM and DCM (L-design 1):

RDLb)1( 2

Maximum current ripple through L (L-design 2):

DVI iL

Voltage output ripple (C-design)

DVC omin

o

*with ideal components

Problem

Design L and C for a buck-boost converter with the following

specifications: Vi =1636V, Vo= -24 V, Pn=120W, Pmin=12W,

f=25kHz.

The converter must operate in CCM, for PPmin

L-current ripple condition: IL0.8A

C-voltage ripple condition: Vo50mV

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Flyback converter (isolated buck-boost converter)

Voltage transfer function, for CCM:

1 VnDD

V it

o

21/NNnt

L (magnetizing inductance) design:

RDn )1( 22

fmb

2

C design:

DV

RfVomin

Buck-Boost converter (uk)

Voltage transfer function (CCM): iC1

io VD

DV

1

IL1

S-on S-off 0

Current transfer function (CCM):tvC1

- L2

io ID

I 0 t

iS

L1 iL1 IoC1iC1

+

L2 iL2

t0

L1 L2

Vi S Vo RCD

S D

0

Vi

t

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LC design basics*

Boundary between CCM and DCM (L1, L2-design 1):

RDLb)1(

1 RDLb )1(2

Maximum current ripple through L (L1, L2-design 2):

1

DVI iL 2

DVI iL

Voltage output ripple (C-design)

1 2

2min

)1( VDC o

DVC imin1

2o

*with ideal components

C1

Problem

Design L and C for a uk converter with the following

specifications: Vi =1636V, Vo= - 24V, Pn=120W, Pmin=12W,

f=25kHz.

, m n

L-current ripple condition: IL1,20.8A

C-voltage ripple condition: Vo10mV, VC12V

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Comparison of switch utilizations

Assumptions:

-The converters operate in CCM;

- e components are ea an the converter losses are neglected;

-The current ripple in the inductor is negligible, iL(t)=IL;

=- o o

1Buck

PSUR o

SUR 0.8 (1-D) (D)

switch

utilization

0.4

.Buck-Boost

(D(1-D))ratio

0

0.2pkpk

. . . .D

Effects of parasitics

The output capacitor includes a series resistance, rC, known as

equivalent series resistance (ESR) and is due to the dielectric

losses and physical resistances of leads and connections;

The high-frequency current ripple that flows through capacitor

produces additional voltage drop on ESR;

o u ons o re uce vo age r pp e on :

reducing the current ripple => higher L;

- ,

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L-design aspects

L acts as energy storage element in switched-mode converters and

as filter to smooth out the current harmonics;

same values of ripple current and filtering requirement;

The magnetic core losses depends with the square of frequency;

The coil stray capacitance will cancel the inductor effect above a

certain frequency (i.e. the coil starts to behave as a capacitor);

Therefore L-desi n is a tradeoff between switchin fre uenc and

inductor size.

References

1. N. Mohan, T.M. Undeland, W.P. Robbins, Power Electronics

Converters A lication and Desi n John Wile & Sons 2003

2. M. H. Rashid, Power Electronics. Circuits, Devices and Applications

3rd edition, Pearson Education, 2004, USA.

3. M.H. Rashid, Power Electronics Handbook 3rd edition, Butterworth-Heinemann, 2010, USA.

4. R. W. Erickson, Fundamentals of Power Electronics, Springer, 2001.

5. S. M. Sharkh, M.A. Abu-Sara, Power Electronics converters for

Microgrids, Wiley, 2010, USA.

6. M.C. Brown, Practical Switching Power Supply Design, Academic

ress, , .

7. H. More, Matlab for Engineers, Prentice Hall, 2008.. . ,

(Romanian version), Transilvania University Press, 2008.