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SWITCH-MODE POWER
SUPPLIES AND SYSTEMS
Lecture No 5
Silesian University of Technology
Faculty of Automatic Control, Electronics
and Computer Sciences
Ryszard Siurek Ph.D., El. Eng.
Continous/discontinuos current (magnetic flux) flow
in output inductance of step-down regulator
IL
UIN
t
Uwe
D U0
Ro
ΔIL  2I 0cr
U0
U0  U IN
,
U0 >U0
U0
t
C
L
U1
IL
D
T
L
U0
U1
I0
I0cr
critical current
ΔIL
L
L
T
I0
t1
2I0cr
1
U0 (  1)
U -U

 IN 0 t 
t
L
L
I0cr  U0
1
t
T
(1   )  U0
(1   )
2L

2L
T
I0cr
I0<I0cr
I0cr 
U0
U
(1   )  IN  (1   )
2fL
2fL

t
T
Step-down regulator output characteristic
U0
UIN
U IN
U0 
2LI0
1
U INT 2
  0,5
0,5UIN
For output current exceeding critical
value output voltage depends
linearly on duty cycle – stable
feedback loop is easy to accomplish
U0  U IN

I0
For output current below critical
value output characteristic bocomes
significantly nonlinear, which makes
difficult to maintain stable operation
of closed feedback loop
I0cr
Critical current decrease may be obtained:
- by increasing the switching frequency
- by increasing the inductance of the output choke
Step-down regulator
- output voltage is always lower than the input voltage
- output voltage rises to the maximum value of the input voltage
in case of no-load condition
- AC current component is the same for output inductor and capacitor
„Step-up” (boost) switching regulator
L
ID
IL
TU
T
UIN
t
D
Io
IC
C
~
UC
U0
T
UC Ro
U0
Assumptions:
1.
Diode D and transitor T are perfect (ideal) switches
2.
Series resistance of the choke L is negligible (rL = 0)
3.
Capacitance C is very large (DUc << Uo)
EL
I cycle U T
IN
D
EC
T – ON, D – OFF
Io
II cycle
EL
D
UIN T
EC
T – OFF, D – ON
Io
Basic waveforms in step-up switching regulator
I cycle - equivalent circuit
ILmin
rL=~ 0 I‘L L
0<t<t
I0
~
UC
IT
UIN
T0 
Ro
U0
L
rL
,
~
UC << U0
UT
I0 
U0
 iC (t)
R0
i (t)  I Lmine

t
T0
t

U
 IN (1  e T0 )
rL
t
IT
T
ILmin
t
ILmax
IL
Calculation of IL – superposition method
'
L
t
ΔIL'
ILmin
t
ID
ILmin
t
t
t
U
t
i L' (t)  I Lmin (1  .....)  IN (1  1  ...)
T0
rL
T0
<<1
U t
U
i L' (t)  I Lmin  IN
 I Lmin  IN t
L
rL
L
rL
inductor current swing
U
ΔIL'  IN t
L
IC
t
~
UC
Uc(0)
t
t
uC (t) 
I0 t
1
i
(t)
dt

U
(0)

t
C
C
C 0
C 0
II cycle - equivalent circuit
rL=~ 0
UT
U0
„
I L
ILmax
L
UIN
t<t<T
I0
~
UC
UT
Ro
U0
t
t
IT
T
t
L
T0 
rL
I0 
~
UC << U0
inductor current swing
in steady state:
U0
R0
U  U IN
ΔI   0
(T  t )
L
''
L
ΔIL'   ΔIL''
ILmax
IL
ΔI
IINAV
'
L
ILmin
t
ID
U  U IN
U IN
t 0
(T  t )
L
L
Τ
U0 
U IN
T -t
t
IC
t
Step-up regulator transfer function
U0 UIN 1
1 
Uo > UIN
~
UC
t
T
1
uC (t)   iC (t)dt
Cτ
Continous/discontinuos current (magnetic flux) flow
in step-up regulator inductance
U0
IIN
DIL

IINcr
t
T
’ > 

Uwe
from energy balance:
I INAVU IN  I0U 0
I INAV  I0
I INcr 
U0
1
 I0
U IN
1
DI L U IN

t
2
2L
 I INcr 
U IN
 (1   )
2fL
The same as for
step-down
I0cr
Step-up regulator
- output voltage always higher than the input voltage
- can not operate in no-load condition (output voltage rise
out of control)
- high value of RMS output capacitor current
I0
„Step-up-step-down” (flyback) switching regulator
T
IT
ID
IL
t
UL
T
L
~
UC
IC
D
UIN
Io
C
U0
UC Ro
U0
Assumptions:
1.
Diode D and transitor T are perfect (ideal) switches
2.
Series resistance of the choke L is negligible (rL = 0)
3.
Capacitance C is very large (DUc << Uo)
T
D
I cycle U
IN
EC
EL
T – ON, D – OFF
T
Io
II cycle
D
EL EC
Uwe
T – OFF,
D – ON
Io
Basic waveforms in flyback switching regulator
I cycle - equivalent circuit
IT
ILmin
0<t<t
I0
I‘L
UL
L
UIN
T0 
L
rL
~
UC
UIN
Ro
U0
~
UC << U0
I0 
U0
 iC (t)
R0
U
ΔI  IN t
L
'
L
inductor current swing
II cycle - equivalent circuit
„
ILmax
IL
I0
t<t<T
t
t
T
-U0
IT
ILmin
t
ILmax
IL
ΔIL'
ILmin
ID
~
UC
L
UL
t
ILmax
„
I0=ILavr
Ro
t
U0
IC
inductor current swing
in steady state:
Flyback regulator
transfer function
ΔIL''  
U0
(T  t )
L
t
ΔIL'   ΔIL''
U0  UIN 
1 
~
UC
Uc(0)
t
t
1
uC (t)   iC (t)dt
C0
Continous/discontinuos current (magnetic flux) flow
in flyback regulator inductance
IL
(Fm)
continuous current flow
critical current flow
Ilmaxcr=DIL
t
IT
discontinuous current flow
t
t1
T
t
The
value
of
energy
accumulated in the inductor by the end
of I cycle is constant, so current
decreasing
below
critical
value
(beginning of discontinuous current
flow) must result in output voltage rise.
ID
T
I0
UL
I0cr   iD (t)dt  ... 
I0cr I <I
0 0cr
0
U0
(1   2 )
2Lf
U0
I0cr 
(1  2 )
2Lf
UIN
t
U0
I Lmaxcr 
U IN
t
L
(1)
U 2 2
from energy balance we obtain:
2
LI Lmaxcr
2

energy stored in the choke
by the end of I cycle
U02
Τ
R0
-U  IN
0
2LfI
(2)
-U0

energy transfered to the
load during the pulse
repetition period T

LR0
UIN
t
L
2T
t
T
  0,5
Uwe
R0 

 U0  U IN
1 
 > 0,5
from equtions (1) & (2) we obtain:
U0 
0
 < 0,5
U0
I0

2 2
UIN
U0  
2LfI0
I0cr
I0
Flyback regulator
- output voltage of opposite polarity, may be higher or lower
than the input voltage
- can not operate in no-load condition (output voltage rise out of
control)
- high value of RMS output capacitor current