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 dtTtV V ft VT

V kV

ECE 442 Power Electronics 5

Average Value of the Load Current

1

a SaV kVIR R

T periodtk dutycycleT

f frequency

ECE 442 Power Electronics 6

rms Value of the output voltage

12

2

0

12

2

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 dtT R

VP kTT RV

P kR

ECE 442 Power Electronics 8

Effective Input Resistance seen by VS

S Si

Sa

i

V VRVI kR

RRk

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

rrVv kT

@r cr

rcr

cr

r

v V t kTVV kTTV

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

11S

diV Ri L Edt

1 1( ) 1R Rt tL LS

V Ei t I e eR

1( )t t kT

1 ( 0) 1( )t

i t I

1

1 2( )t t kTi kT I

ECE 442 Power Electronics 15

Mode 2: Switch Open

22

2 2

2 2

0( 0)

( ) 1R Rt tL L

diRi L Edt

i t IEi t I e eR

2

2

2 2 3 1

0 (1 )@ (1 )( )

t t kTt t K T

i t I I

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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 EIR e RV e EIR e RTRzLV e e eIR eVIfL

ECE 442 Power Electronics 18

1 01 01

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

ExVE exV 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

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