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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 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 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 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 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
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