Datasheet
POLE2
COMP SW
1
C =
R f p´ ´
C O
POLE1
COMP
R C
C =
R
´
COMP
COMP
1
C =
2 R Kdcm Fmp´ ´ ´ ´
V
CO
O
COMP
V
REF
POLE
gmea
R =
Kdcm Fm
x
f
x
x x f
( )
0.5
CO2 SW POLE
(Hz) =f f f´
( )
0.5
CO1 ZERO POLE
(Hz) =f f f´
ZERO
C O
1
(Hz) =
R C 2
f
p´ ´ ´
O
S
POLE
O O
O
O S
V
2
V
1
(Hz) =
V V
C 2 1
I V
f
p
æ ö
-
ç ÷
ç ÷
´
ç ÷
´ ´ ´ -
ç ÷
è ø
S O
O SW
gmps
Fm =
V V
+ 0.277
L f
æ ö
-
ç ÷
´
è ø
( )
O S O
S O
O
O
V V V
2
Kdcm =
D1
Rdc
V 2 + V
V
I
´ -
´
æ ö
ç ÷
ç ÷
´ -
ç ÷
ç ÷
è ø
ZERO
POLE
s
1 +
2
Gdcm(s) Fm Kdcm
s
1 +
2
f
f
p
p
´ ´
» ´ ´
´ ´
TPS54062
SLVSAV1B –MAY 2011–REVISED AUGUST 2012
www.ti.com
Closing the Feedback Loop
The method presented here is easy to calculate and includes the effect of the slope compensation that is internal
to the device. This method assumes the crossover frequency is between the modulator pole and the esr zero
and the esr zero is at least 10 times greater the modulator pole. Once the output components are determined,
use the equations below to close the feedback loop. A current mode controlled power supply operating in DCM
has a transfer function which has an esr zero and pole as shown in Equation 39. To calculate the current mode
power stage gain, first calculate, Kdcm, DCM gain, and Fm, modulator gain, in Equation 40 and Equation 41.
Kdcm and Fm are 26.3 and 1.34 respectively. The location of the pole and esr zero are calculated using
Equation 42 and Equation 43 . The pole and zero are 67 Hz and 2 MHz, respectively. Use the lower value of
Equation 44 and Equation 45 as a starting point for the crossover frequency. Equation 44 is the geometric mean
of the power stage pole and the esr zero and Equation 45 is the mean of power stage pole and the switching
frequency. The crossover frequency is chosen as 2.5 kHz from Equation 45.
To determine the compensation resistor, R
COMP
, use Equation 46. Assume the power stage transconductance,
gmps, is 0.65 A/V. The output voltage, V
O
, reference voltage, V
REF
, and amplifier transconductance, gmea, are
3.3 V, 0.8 V and 102 µA/V, respectively. R
COMP
is calculated to be 32.7 kΩ, use the nearest standard value of
32.4 kΩ. Use Equation 47 to set the compensation zero to the modulator pole frequency. Equation 47 yields 139
nF for compensating capacitor C
COMP
, a 330 nF is used on the board. Use the larger value of Equation 48 or
Equation 49 to calculate the C
POLE
, to set the compensation pole. Equation 49 yields 98 pF so the nearest
standard of 100 pF is used.
(39)
(40)
(41)
(42)
(43)
(44)
(45)
(46)
(47)
(48)
(49)
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