Datasheet

( )
SENSE CO O
Gain = 20 log 2 R F Cp- ´ ´ ´ ´
( ) ( )
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
kFF
COP
´=
1
CO O O OA
Z
ICOMP ggm REF
2 × × F × V × C × R
R =
GM × V × V
p
TPS54331
www.ti.com SLVS839D –JULY 2008– REVISED JANUARY 2012
(19)
Where:
R
SENSE
= 1Ω/12
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
The measured overall loop response for the circuit is given in Figure 20. Note that the actual closed loop
crossover frequency is higher than intended at about 25 kHz. This is primarily due to variation in the actual
values of the output filter components and tolerance variation of the internal feed-forward gain circuitry. Overall
the design has greater than 60 degrees of phase margin and will be completely stable over all combinations of
line and load variability.
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)
(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
C
O
= Output capacitance
F
CO
= Desired crossover frequency
R
OA
= 8 MΩ
GM
COMP
= 12 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:
Copyright © 2008–2012, Texas Instruments Incorporated 15