Datasheet

ggm REF
DC
O
V V
G =
V
´
( )
PO OO Z
V = 1/ 2 R Cp´ ´ ´
( )
Z1 Z Z
F = 1/ 2 R Cp´ ´ ´
( )
P1 Z P
F = 1/ 2 R Cp´ ´ ´
O O
SENSE ESR
R R
Gain = 20 log 20 log
R R
æ ö æ ö
-
ç ÷ ç ÷
è ø è ø
( ) ( )
CO ESR O CO O O
PL = tan 2 F R C tan 2 F R Ca ap p´ ´ ´ ´ - ´ ´ ´ ´
( )
90degPB = PM PL- -
÷
ø
ö
ç
è
æ
+= deg45
2
tan
PB
k
k
F
F
CO
Z
=
1
TPS54233
SLUS859B –OCTOBER 2008– REVISED FEBRUARY 2011 www.ti.com
The dc gain is determined by Equation 15:
(15)
Where:
V
ggm
= 800
V
REF
= 0.8 V
The low-frequency pole is determined by Equation 16:
(16)
The mid-frequency zero is determined by Equation 17:
(17)
And, the mid-frequency pole is given by Equation 18:
(18)
The first step is to choose the closed loop crossover frequency. In general, the closed-loop crossover frequency
should be less than 1/8 of the minimum operating frequency, but for the TPS54233it is recommended that the
maximum closed loop crossover frequency be not greater than 25 kHz. Next, the required gain and phase boost
of the crossover network needs to be calculated. By definition, the gain of the compensation network must be the
inverse of the gain of the modulator and output filter. For this design example, where the ESR zero is less than
the closed loop crossover frequency, the gain of the modulator and output filter can be approximated by
Equation 19:
(19)
Where:
R
SENSE
= 1Ω/9
R
O
= V
O
/I
O
R
ESR
= Equivalent series resistance of the output capacitor
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.
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)
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