Transcript Elektroniczne Układy i Systemy Zasilania

SWITCH-MODE POWER
SUPPLIES AND SYSTEMS
Lecture No 4
Silesian University of Technology
Faculty of Automatic Control, Electronics
and Computer Sciences
Ryszard Siurek Ph.D., El. Eng.
Linear regulator versus switching regulator
Basic functional diagrams
Linear regulator
Switching regulator
Uce
Uin
Io
Uout
(Uo)
T1
CC
Uin
amp
e
+
Vr
R1
t
T
fs
U1
fs =
Uo = Uin – Uce = const.
Po = Uo.Io
PLoss = Uce.Io
efficiency:
Po
Uo.Io
Uin - Uce
h=
=
=
Pin
Uin.Io
Uin
Uout
(Uo)
Ku
RL
R2
Io
T1
1
T
RL
fc
Cross-over frequency
U1
Uin
t
t
U1av U1av = T Uin = gUin
T

g – duty cycle
U1= U1av + SUisin(2iPfpt)
i=1
Uce > Ucemin (~2,5V)
0,3 < h < 0,5 typical values
Power loss in T1
-
high
eliminated by low-pass filter
Power losses in T1 = 0
Filter power losses (LC) = 0
h=1
(100%)
STEP-DOWN (BUCK) SWITCHING REGULATOR
T
L
IT
IL
ID
Uin
t
U1
T
Io
IC
D
C
~
UC
U0
UC RL
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
T
I cycle U D
in
EC
T – closed, D – open
EL
T
Io
II cycle
Uin D
EC
T – open, D – closed
Io
Basic waveforms in step-down switching regulator
I cycle - equivalent circuit 0 < t < t
,
rL=~ 0 IL L
ILmin I0
~
UC
U0
U1 = Uin
T0 
I0 
U0
I0
Calculation of IL – superposition method
i (t)  I Lmine
'
L

t
T0
t
t
IT
T
ILmin
~
UC << U0
,
L
rL
Ro
U1
t

U  U0
 IN
(1  e T0 )
rL
t
ILmax
IL
ΔIL'
ILmin
t
ID
ILmax
t
t
i L' (t)  I Lmin (1 
U  U0
t
t
.....)  IN
(1  1  ...)
T0
rL
T0
<<1
U
 U0 t
U  U0
i L' (t)  I Lmin  IN
 I Lmin  IN
t
L
rL
L
rL
inductor current swing
U -U
ΔIL'  IN 0 t
L
IC
t
~
UC
t
Uc(0)
t
uC (t)   iC (t)dt  UC (0) 
0
Uwe  U0 2 t
t
2LC
0
II cycle - equivalent circuit
„
IL L
rL=~ 0
ILmax
L
rL
„
Ro
U0
Calculating IL - superposition method
i (t)  I Lmax e
''
L

t -t
T0
t -t

U
 0 (1  e T0 )
rL
t
IT
T
t
ILmax
IL
ILmin
ΔI
I0
'
L
t
ID
Similarly as before:
i L'' (t)  I Lmax 
t
ILmin
U
I0  0
R0
~
UC << U0
U1
I0
~
UC
U0
T0 
t<t<T
ILmax
U0
(t - t )
L
ILmin
t
U
ΔIL''   0 (T  t )
L
inductor current swing
IC
ICsr  0
in steady state: ΔIL'   ΔIL''
U IN - U 0
U
t  0 (T  t )
L
L
U0 
t
T
U IN
~
UC
Uc(t)
t
Step-down regulator transfer function
U0  gUIN
t -t
uC (t) 
t
Τ
U0
1
2
i
(t
t
)
dt

U
(
t
)

(t
t
)
C
C
C t
2LC
t
Inductor & capacitor selection
exemplary calculations for step-down regulator
Design specification: UIN = 10 – 15V, Uo = 5V, Io = 10A, f = 100kHz
Inductor current amplitude (general rule):
we assume:
DIL 
U0
L
(T - t)  L 
U0
DIL
DIL < 0,1 – 0,2 I0max
DIL < 1A
U
U
0
0 
g
hence:
U
U
INmax
INmin
for tmin
(T - t) 
for tmax
L
0,33  g  0,5
Τ  10s
3,3s  t  5s
5[V]
(10[s]- 0,33[s])  3,35 [H]
1[A]
L
5[V]
(10[s]- 0,5[s])  2,5 [H]
1[A]
selected L = 3 H – 4 H
The AC voltage component across the capacitor is approximately described by the
equation:

t
1
2
Δ UC  2  UINmax  U0 tdt  2 UINmax  U0 tmax
L
C 0
C 2L

2
Przyjmijmy:
Δ UC  0,1V
C  2 UINmax  U0 tmax
 625 [F]
2L
Δ UC
max
Selected C = 1000 F