Datasheet

kFF
COP
´=
1
O OA
Z
COMP ggm REF ESR
V R 0.98
R =
GM V V R
´ ´
´ ´ ´
zZ
Z
RF
C
´´´
=
1
2
1
p
zP
P
RF
C
´´´
=
1
2
1
p
6
2.5 8.696 10 0.98
Rz = = 30.5 k
9 800 0.8 0.160
´ ´ ´
W
´ ´ ´
1
= = 237 pF
2 22000 30500´ ´ ´
Cz
p
1
= = 237 pF
2 22000 30500´ ´ ´
Cp
p
TPS54233
www.ti.com SLUS859B –OCTOBER 2008– REVISED FEBRUARY 2011
(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 established by the pole and zero relationships, the value of
R
Z
can be derived directly by Equation 25 :
(25)
Where:
V
O
= Output voltage
R
OA
= 8.696 MΩ
GM
COMP
= 9 A/V
V
ggm
= 800
V
REF
= 0.8 V
R
ESR
= Equivalent series resistance of the output capacitor
With R
Z
known, C
Z
and C
P
can be calculated using Equation 26 and Equation 27:
(26)
(27)
For this design, a singe 470 μF output capacitor is used. The ESR is approximately .160 Ω. The desired closed
loop crossover frequency is 22000 Hz.
Using Equation 19 and Equation 20, the output stage gain and phase loss are equivalent as:
Gain = –3.114 dB
and
PL = –4.96 degrees
For 60 degrees of phase margin, Equation 21 requires no additional phase boost, so K can be set equal to 1.
Equation 22, Equation 23, and Equation 24 are used to find the zero and pole frequencies of:
F
Z1
= 22000 Hz
And
F
P1
= 22000 Hz
R
Z
, C
Z
, and C
P
are calculated using Equation 25, Equation 26, and Equation 27:
(28)
(29)
(30)
Using standard values for R3, C6, and C7 in the application schematic of Figure 12:
R3 = 30.9 kΩ
C6 = 220 pF
© 2008–2011, Texas Instruments Incorporated Submit Documentation Feedback 15
Product Folder Link(s): TPS54233