Power Electonics

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

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

3. Waveforms for the Step-Down Converter

4. Average Value of the Output Voltage
1
1
0
0
1
1
1
1
t
a O
t
a S
a S S
a S
V v dt
T
V V dt
T
t
V V ft V
T
V kV


 




5. Average Value of the Load Current
1
a S
a
V kV
I
R R
T period
t
k dutycycle
T
f frequency
 

 


6. rms Value of the output voltage
1
2
2
0
1
2
2
0
1
1
kT
O O
kT
O S
O S
V v dt
T
V V dt
T
V kV
 
  
 
 
  
 




7. If the converter is “lossless”, Pin = Pout
0
2
0
2
2
1
1
1
kT
in O
kT
O
in
S
in
S
in
P v idt
T
v
P dt
T R
V
P kT
T R
V
P k
R







8. Effective Input Resistance seen by VS
S S
i
Sa
i
V V
R
VI k
R
R
R
k
 


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”

10. Generation of Duty Cycle
• Compare a dc reference signal with a
saw-tooth carrier signal
DC Reference Signal Carrier Signal

11. r
r
V
v k
T

@r cr
r
cr
cr
r
v V t kT
V
V kT
T
V
k M
V
 

 
kT

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”

13. Step-Down Converter with RL Load

14. Mode 1: Switch Closed
1
1S
di
V Ri L E
dt
  
 1 1
( ) 1
R R
t t
L LS
V E
i t I e e
R
 
   1
( )t t kT
1 ( 0) 1
( ) t
i t I

1
1 2
( )
t t kT
i kT I
 


15. Mode 2: Switch Open
 
2
2
2 2
2 2
0
( 0)
( ) 1
R R
t t
L L
di
Ri L E
dt
i t I
E
i t I e e
R
 
  
 
  
2
2
2 2 3 1
0 (1 )
@ (1 )
( )
t t k T
t t K T
i t I I
   
  
 

16. Current for “Continuous” Mode

17.  
 
1
2
(1 )
max
1
1
1
1
1
1
4
kz
S
z
kz
S
z
kz z k z
S
z
S
V e E
I
R e R
V e E
I
R e R
T R
z
L
V e e e
I
R e
V
I
fL

   


 


 


    
  
 

18. 1
0
1
0
1
kz
z
S
I
e E
e V

 
   
For Continuous Current

19. Define the load emf ratio
1
1
S
kz
z
S
E
x
V
E e
x
V e


 


20. Vs
220V
J1
1V 0V
XFG1
L
7.5mH
R
5ohm
D2
DIODE_VIRTUAL
Example 5.2

22. SPICE Results