Datasheet
f
p
=
1
2SC
OUT
(m
c
D' - 0.5))
R
OUT
1
1
f
s
( +
L
V
IN
- V
OUT
4 x f
S
x L
m
c
= 1 +
C
c1
8
2
3
SR
c
f
c
0 dB
f
c
f
zcomp
f
p
f
ESR
(f
pcomp
)
f
s
/2
Gain
0
/sC
c1
LM21305
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SNVS639F –DECEMBER 2009–REVISED MARCH 2013
Figure 31. LM21305 Loop Gain Asymptotic Approximation
The loop gain determines both static and dynamic performance of the converter. The power stage response is
fixed by the selection of the power components and the compensator is therefore designed around the power
stage response to achieve the desired loop response. The goal is to design a control loop characteristic with high
crossover frequency (or loop bandwidth) and adequate gain and phase margins under all operation conditions.
COMPENSATION COMPONENTS SELECTION
To select the compensation components, a desired crossover frequency needs to be selected. It is
recommended to select f
c
equal to or lower than 1/6 of the switching frequency. The effect of F
h
(s) can be
ignored to simplify the design. The capacitor ESR zero is also assumed to be at least 3 times higher than f
c
. The
compensation resistor can be found by:
(20)
C
c1
does not affect the crossover frequency f
c
, but it sets the compensator zero f
Zcomp
and affects the phase
margin of the loop. For a fast design, C
c1
= 4.7 nF gives adequate performance in most LM21305 applications.
Larger C
c1
capacitance gives higher phase margin but at the expense of longer transient response settling time.
It is recommended to set the compensation zero no higher than f
c
/3 to ensure enough phase margin, implying:
(21)
PLOTTING THE LOOP GAIN
To include the effect of F
h
(s) and the ESR zero, the complete loop gain can be plotted using a software tool such
as MATLAB, Mathcad, or Excel. The components in the loop gain can be determined as follows. The DC gain of
the power stage can be found by:
(22)
where f
s
is the switching frequency,
(23)
and D' = 1 − D.
Minimum R
OUT
should be used in the calculation R
OUT
= V
OUT
/I
OUT
. F
p
(s) can be expressed by:
(24)
where the power stage pole considering the slope compensation effect is:
(25)
The high frequency behavior F
h
(s) can be expressed by:
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