DC-DC converters can step up or step down a DC voltage level. They operate by rapidly switching a transistor, such as a MOSFET or IGBT, to chop the input voltage into a pulsed waveform. The average value of the output voltage is determined by the duty cycle of the pulses. Applications include motor control and voltage regulation. The converter can operate in continuous or discontinuous conduction mode depending on the load current and duty cycle settings.

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