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H(s) + H
1
(s) H
2
(s) H
3
(s)
(2)
H
1
(s) +
R
2
ǒ
R
2
) R
1
Ǔ
(3)
H
2
(s) + * Gm
R
O
ǒ
1 ) s C
C
R
C
Ǔ
ǒ
1 ) s C
C
R
O
Ǔ ǒ
1 ) s C
C2
R
C
Ǔ
(4)
H
3
(s) +
(1 ) s C
O
ESR)
ǒ
1 ) s C
O
RL
Ǔ
RL
R
S
(5)
w
P1
+
1
ǒ
C
C
R
O
Ǔ
(6)
w
P2
+
1
ǒ
C
O
RL
Ǔ
(7)
w
P3
+
1
ǒ
C
C2
R
C
Ǔ
(8)
w
Z1
+
1
ǒ
C
C
R
C
Ǔ
(9)
w
Z2
+
1
ǒ
C
O
ESR
Ǔ
(10)
f
0
+
1
2p
R2
R1 ) R2
Gm
C
O
R
C
R
S
+
1
2p
1.0
V
OUT
Gm
C
O
R
C
R
S
(11)
L +
1
I
IND(ripple)
f
ǒ
V
IN(max)
* V
OUT
Ǔ
V
OUT
V
IN(max)
+
2
I
OUT(max)
f
ǒ
V
IN(max)
* V
OUT
Ǔ
V
OUT
V
IN(max)
(12)
I
IND(peak)
+
V
TRIP
R
DS(on)
)
1
L f
ǒ
V
IN(max)
* V
OUT
Ǔ
V
OUT
V
IN(max)
(13)
TPS51120
SLUS670B – JULY 2005 – REVISED FEBRUARY 2007
Here, the inductor is located inside the local feedback loop and its inductance does not appear in the small
signal model. As a result, a modulated current source including the power inductor can be modeled as a current
source with its transconductance of 1/R
S
and the output capacitor represent the modulator portion. This
simplified model is applicable in the frequency space up to approximately a half of the switching frequency. One
note is, although the inductance has no influence to small signal model, it has influence to the large signal model
as it limits slew rate of the current source. This means the buck converter’s load transient response, one of the
large signal behaviors, can be improved by using smaller inductance without affecting the loop stability.
Total open loop transfer function of the whole system is given by Equation 2 .
Assuming RL>>ESR, R
O
>>R
C
and C
C
>>C
C
2, each transfer function of three block is shown in Equation 3
through Equation 5 .
There are three poles and two zeros in H(s). Each pole and zero is given by Equation 6 through Equation 10 .
Usually, each frequency of those poles and zeros is lower than the 0 dB frequency, f
0
. However, the f
0
should be
kept under 1/3 of the switching frequency to avoid effect of switching circuit delay. The f
0
is given by next
equation Equation 11 .
Based on small signal analysis above, the external components can be selected by following manner.
1. Choose the inductor.The inductance value should be determined to give the ripple current of
approximately 1/4 to 1/2 of maximum output current.
The inductor also needs to have low DCR to achieve good efficiency, as well as enough room above
peak inductor current before saturation. The peak inductor current can be estimated in Equation 13 .
19
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