ECE 442 Power Electronics1 DC-DC Converters Convert a fixed DC Source into a Variable DC Source DC...
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![Page 1: ECE 442 Power Electronics1 DC-DC Converters Convert a fixed DC Source into a Variable DC Source DC equivalent to an AC transformer with variable turns.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6a5503460f94a482ec/html5/thumbnails/1.jpg)
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
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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
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ECE 442 Power Electronics 3
Waveforms for the Step-Down Converter
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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
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ECE 442 Power Electronics 5
Average Value of the Load Current
1
a Sa
V kVI
R RT period
tk dutycycleT
f frequency
![Page 6: ECE 442 Power Electronics1 DC-DC Converters Convert a fixed DC Source into a Variable DC Source DC equivalent to an AC transformer with variable turns.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6a5503460f94a482ec/html5/thumbnails/6.jpg)
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
![Page 7: ECE 442 Power Electronics1 DC-DC Converters Convert a fixed DC Source into a Variable DC Source DC equivalent to an AC transformer with variable turns.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6a5503460f94a482ec/html5/thumbnails/7.jpg)
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
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ECE 442 Power Electronics 8
Effective Input Resistance seen by VS
S Si
Sa
i
V VR
VI kR
RR
k
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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”
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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
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ECE 442 Power Electronics 11
rr
Vv k
T
@r cr
rcr
cr
r
v V t kT
VV kT
TV
k MV
kT
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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”
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ECE 442 Power Electronics 13
Step-Down Converter with RL Load
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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
![Page 15: ECE 442 Power Electronics1 DC-DC Converters Convert a fixed DC Source into a Variable DC Source DC equivalent to an AC transformer with variable turns.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6a5503460f94a482ec/html5/thumbnails/15.jpg)
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
![Page 16: ECE 442 Power Electronics1 DC-DC Converters Convert a fixed DC Source into a Variable DC Source DC equivalent to an AC transformer with variable turns.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6a5503460f94a482ec/html5/thumbnails/16.jpg)
ECE 442 Power Electronics 16
Current for “Continuous” Mode
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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
![Page 18: ECE 442 Power Electronics1 DC-DC Converters Convert a fixed DC Source into a Variable DC Source DC equivalent to an AC transformer with variable turns.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6a5503460f94a482ec/html5/thumbnails/18.jpg)
ECE 442 Power Electronics 18
10
10
1
kz
z
S
I
e Ee V
For Continuous Current
![Page 19: ECE 442 Power Electronics1 DC-DC Converters Convert a fixed DC Source into a Variable DC Source DC equivalent to an AC transformer with variable turns.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6a5503460f94a482ec/html5/thumbnails/19.jpg)
ECE 442 Power Electronics 19
Define the load emf ratio
11
S
kz
z
S
Ex
VE e
xV e
![Page 20: ECE 442 Power Electronics1 DC-DC Converters Convert a fixed DC Source into a Variable DC Source DC equivalent to an AC transformer with variable turns.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6a5503460f94a482ec/html5/thumbnails/20.jpg)
ECE 442 Power Electronics 20
Vs220V
J1
1V 0V
XFG1
L7.5mH
R5ohm
D2DIODE_VIRTUAL
Example 5.2
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ECE 442 Power Electronics 21
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ECE 442 Power Electronics 22
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