Datasheet

zP
P
RF
C
´´´
=
1
2
1
p
zZ
Z
RF
C
´´´
=
1
2
1
p
CO O O OA
Z
COMP ggm REF
2 × × F × V × C × R × 0.91
R =
GM × V × V
p
kFF
COP
´=
1
k
F
F
CO
Z
=
1
÷
ø
ö
ç
è
æ
+= deg45
2
tan
PB
k
( )
90 degPB = PM + PL-
( ) ( )
10
CO ESR O CO O O
PL = tan 2 F R C tan 2 F R C´ ´ ´ ´ - ´ ´ ´ ´ -a ap p
TPS54231
www.ti.com SLUS851C –OCTOBER 2008–REVISED JULY 2012
Where:
R
SENSE
= 1Ω/9
F
CO
= Closed-loop crossover frequency
C
O
= Output capacitance
The phase loss is given by Equation 20:
(20)
Where:
R
ESR
= Equivalent series resistance of the output capacitor
R
O
= V
O
/I
O
Now that the phase loss is known the required amount of phase boost to meet the phase margin requirement
can be determined. The required phase boost is given by Equation 21:
(21)
Where PM = the desired phase margin and PL = the phase loss calculated in Equation 20.
A zero / pole pair of the compensation network will be placed symmetrically around the intended closed loop
frequency to provide maximum phase boost at the crossover point. The amount of separation can be determined
by Equation 22 and the resultant zero and pole frequencies are given by Equation 23 and Equation 24
(22)
(23)
(24)
The low-frequency pole is set so that the gain at the crossover frequency is equal to the inverse of the gain of the
modulator and output filter. Due to the relationships of the pole and zero frequencies, the value of R
Z
can be
derived directly by Equation 25 :
(25)
Where:
V
O
= Output voltage
C
O
= Output capacitance
F
CO
= Desired crossover frequency
R
OA
= 8.696 MΩ
GM
COMP
= 9 A/V
V
ggm
= 800
V
REF
= 0.8 V
With R
Z
known, C
Z
and C
P
can be calculated using Equation 26 and Equation 27:
(26)
(27)
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