rt9206 Richtek Technology Corporation, rt9206 Datasheet - Page 17

• Manufacturer Part Number: rt9206
• Description: High Efficiency, Synchronous Buck With Dual Linear Controllers
• Manufacturer: Richtek Technology Corporation

V
IN
V
DS9206-11 March 2007
From control system point of view, the block diagram of
Figure 5 is shown in Figure 6.
First, deriving the accurate small-signal models of power
stage, the equation (18) is the transfer function of
v
technique.
REF
G
Figure 5. The simplified diagram for synchronous Buck
O
P(S)
Figure 6. The control block diagram of synchronous
(s)/d(s), which be obtained by space averaging
i
+
S1
-
V
Generator
OUT(S)
PWM
d
d
(S)
S1
Compensator
+
-
converter and control loop.
S2
C(s)
S
2
Buck converter
x
Vc(s)
Sensor Gain
L
i
S2
Ra+Rb
x
Compensator
Rb
C
+ V
1
V
O
L
C
Generator
L
Cc2
rc x
-
PWM
1/Vr
S(
H (s)
V
R
V
C
+
OC
i
L
-
L
+
OR
-
L
O
Rc1
Cc1
d(s)
G(S)
x
rc x
S
r
C
C
i
C
OUT
gm
Converter
Gp(s)
C
BUCK
+
-
R
L
O
V
)
REF
V
1
I
Rb
OUT
OUT
Ra
+
-
x V
(18)
V
Sensor
OUT
IN
Gain
In Figure 7, the resonance of the output LC filter produces
a double pole and 40dB/decade slop. The resonance
frequency is expressed as follows :
Next, deriving the transfer function d(s)/v
duty ratio pulse-width modulator (PWM Generator). The
transfer function T
where, V
in datasheet.
For simplification, the transfer function of PWM generator
and Buck converter can is combined. The resulting is shown
in equation (20)
The transfer function of Equation (20) is a second order
system and Bode plot is shown in Figure 7.
G
(S)
Phase
VIN/Vr
Figure 7. The Bode plot of Buck power stage
V
-180°
-90°
V
OUT(S)
r
0°
is the amplitude of ramp-waveform which is listed
C(S)
Gain
S
f
P
m
T
2
fp
(s) of the modulator is given by
m(S)
x
2
L
x
C
V
1
d
O
C(S)
(S)
1
L
x
rc x
x
S(
fz
C
R
C
O
L
Vr
1
L
O
x
rc x
S
RT9206
C
www.richtek.com
(s) of the direct
C
(Hz)
O
)
1
x
f
f
V
Vr
(21)
(19)
(20)
IN
17