ECE 442 Power Electronics 1

DC-DC Converters

• Convert a fixed DC Source into a Variable DC Source

• DC equivalent to an AC transformer with variable turns ratio

• Step-up and Step-down versions

• Applications– Motor Control– Voltage Regulators

ECE 442 Power Electronics 2

Step-down Operation

• Switch SW is known as a “Chopper”

• Use BJT, MOSFET, or IGBT

• Close for time t1

– VS appears across R

• Open for time t2

– Voltage across R = 0

• Repeat • Period T = t1 + t2

ECE 442 Power Electronics 3

Waveforms for the Step-Down Converter

ECE 442 Power Electronics 4

Average Value of the Output Voltage

1

1

0

0

11

1

1

t

a O

t

a S

a S S

a S

V v dtT

V V dtT

tV V ft V

TV kV

ECE 442 Power Electronics 5

Average Value of the Load Current

1

a Sa

V kVI

R RT period

tk dutycycleT

f frequency

ECE 442 Power Electronics 6

rms Value of the output voltage

1

22

0

1

22

0

1

1

kT

O O

kT

O S

O S

V v dtT

V V dtT

V kV

ECE 442 Power Electronics 7

If the converter is “lossless”, Pin = Pout

0

2

0

2

2

1

1

1

kT

in O

kTO

in

Sin

Sin

P v idtT

vP dt

T R

VP kT

T R

VP k

R

ECE 442 Power Electronics 8

Effective Input Resistance seen by VS

S Si

Sa

i

V VR

VI kR

RR

k

ECE 442 Power Electronics 9

Modes of Operation

• Constant – frequency operation– Period T held constant, t1 varied

– Width of the pulse changes – “Pulse-width modulation”, PWM

• Variable -- frequency operation– Change the chopping frequency (period T)

– Either t1 or t2 is kept constant

– “Frequency modulation”

ECE 442 Power Electronics 10

Generation of Duty Cycle

• Compare a dc reference signal with a saw-tooth carrier signal

DC Reference Signal Carrier Signal

ECE 442 Power Electronics 11

rr

Vv k

T

@r cr

rcr

cr

r

v V t kT

VV kT

TV

k MV

kT

ECE 442 Power Electronics 12

To generate the gating signal

• Generate the triangular waveform of period T, vr, and the dc carrier signal, vcr

• Compare to generate the difference vc - vcr

• Apply to a “hard limiter” to “square off”

ECE 442 Power Electronics 13

Step-Down Converter with RL Load

ECE 442 Power Electronics 14

Mode 1: Switch Closed

1

1S

diV Ri L E

dt

1 1( ) 1

R Rt t

L LSV E

i t I e eR

1( )t t kT

1 ( 0) 1( )

ti t I

1

1 2( )

t t kT

i kT I

ECE 442 Power Electronics 15

Mode 2: Switch Open

2

2

2 2

2 2

0

( 0)

( ) 1R Rt t

L L

diRi L E

dti t I

Ei t I e e

R

2

2

2 2 3 1

0 (1 )

@ (1 )

( )

t t kT

t t K T

i t I I

ECE 442 Power Electronics 16

Current for “Continuous” Mode

ECE 442 Power Electronics 17

1

2

(1 )

max

1111

11

4

kz

S

z

kz

S

z

kz z k z

S

z

S

V e EI

R e RV e E

IR e RTR

zLV e e e

IR eV

IfL

ECE 442 Power Electronics 18

10

10

1

kz

z

S

I

e Ee V

For Continuous Current

ECE 442 Power Electronics 19

Define the load emf ratio

11

S

kz

z

S

Ex

VE e

xV e

ECE 442 Power Electronics 20

Vs220V

J1

1V 0V

XFG1

L7.5mH

R5ohm

D2DIODE_VIRTUAL

Example 5.2

ECE 442 Power Electronics 21

ECE 442 Power Electronics 22

SPICE Results