Datasheet
f
PC2
=
2S x C
C2
x (R
C
// R
O
)
1
GAIN (dB)
fpc
fzc
0
RHPz
COMP
LOOP
FREQUENCY (kHz)
R
C
=
B
EA
gm
x ILIM
gm
x R4
B =
f
CROSS
f
P1
x A
cm
A
cm
=
R3 x I
OUT
x KD
V
IN
LM3431
SNVS547G –NOVEMBER 2007–REVISED MAY 2013
www.ti.com
Where
• B is the mid-frequency compensation gain (in v/v)
• R4 is the current limit setting resistor
• Acm is the control-output DC gain
• the gm values are given in the ELECTRICAL CHARACTERISTICS table (25)
Fcross is the maximum allowable crossover frequency, based on the calculated values of f
pn
and RHPz. Any Rc
value lower than the value calculated above can be used and will ensure a low enough crossover frequency. Rc
should set the B value typically between 0.01v/v and 0.1v/v (-20db to -40db). Larger values of R
C
will give a
higher loop bandwidth.
However, because the dynamic response of the LM3431 is enhanced by the FF pin (See Setting FF section) the
R
C
value can be set conservatively. The typical range for R
C
is between 300ohm and 3 kΩ. Next, select a value
for Cc to set the compensation zero, f
zc
, to a frequency greater or equal to the maximum calculated value of f
p1
(f
zc
cancels the power pole, f
p1
). Since an fzc value of up to a half decade above fp1 is acceptable, choose a
standard capacitor value smaller than calculated. Confirm that fpc, the dominant low frequency pole in the control
loop, is less than 100 Hz and below f
p1
. The typical range for C
C
is between 10 nF and 100 nF. The
compensation zero-pole pair is shown graphically below, along with the total control loop, which is the sum of the
compensation and output-control response. Since the calculated crossover frequency is an approximation,
stability should always be verified on the bench.
Figure 20. Typical Compensation and Total Loop Bode Plots
When using an output capacitor with a high ESR value, another pole, f
pc2
, may be introduced to cancel the zero
created by the ESR. This is accomplished by adding another capacitor, C
C2
, shown as C13 in the Figure 14. The
pole should be placed at the same frequency as f
z1
. This pole can be calculated as:
(26)
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