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17
FN9214.0
March 9, 2006
A small capacitor,
C
SEN
in Figure 10, can be added to filter
out noise, typically
C
SEN
is chosen so the corresponding
time constant does not reduce the overall phase margin
of the design, typically this is 2x to 10x switching
frequency of the regulator.
As the ISL6540 supports
100% duty cycle, d
MAX
equals 1. The ISL6540 also uses
feedforward compensation, as such V
OSC
is equal to
0.16 multiplied by the voltage at the VFF pin. When tieing
VFF to V
IN
the above equation simplifies to:
0.16 R
F
0
LC
2. Calculate C
1
such that F
Z1
is placed at a fraction of the F
LC
,
at 0.1 to 0.75 of F
LC
(to adjust, change the 0.5 factor to
desired number). The higher the quality factor of the output
filter and/or the higher the ratio F
CE
/F
LC
, the lower the F
Z1
frequency (to maximize phase boost at F
LC
).
2
R
2
0.5 F
LC
3. Calculate C
2
such that F
P1
is placed at F
CE
.
C
2
π
R
2
C
1
F
CE
4. Calculate R
3
such that F
Z2
is placed at F
LC
. Calculate C
3
such that F
P2
is placed below F
SW
(typically, 0.5 to 1.0
times F
SW
). F
SW
represents the regulator’s switching
frequency. Change the numerical factor to reflect desired
placement of this pole. Placement of F
P2
lower in frequency
helps reduce the gain of the compensation network at high
frequency, in turn reducing the HF ripple component at the
COMP pin and minimizing resultant duty cycle jitter.
R
LC
2
π
R
3
0.7 F
SW
It is recommended that a mathematical model is used to plot
the loop response. Check the loop gain against the error
amplifier’s open-loop gain. Verify phase margin results and
adjust as necessary. The following equations describe the
frequency response of the modulator (G
MOD
), feedback
compensation (G
FB
) and closed-loop response (G
CL
):
V
OSC
1
s f
( )
+
As before when tieing VFF to VIN terms in the above
equations can be simplified as follows:
COMPENSATION BREAK FREQUENCY EQUATIONS
Figure 11 shows an asymptotic plot of the DC/DC converter’s
gain vs. frequency. The actual modulator gain has a high gain
peak dependent on the quality factor (Q) of the output filter,
which is not shown. Using the above guidelines should yield a
compensation gain similar to the curve plotted. The open loop
error amplifier gain bounds the compensation gain. Check the
compensation gain at F
P2
against the capabilities of the error
amplifier. The closed loop gain, G
CL
, is constructed on the
log-log graph of Figure 11 by adding the modulator gain,
G
MOD
(in dB), to the feedback compensation gain, G
FB
(in
dB). This is equivalent to multiplying the modulator transfer
function and the compensation transfer function and then
plotting the resulting gain.
R
2
V
R
F
MAX
IN
LC
---------------------------------------------
=
R
2
----------------------------------
=
C
1
----------------------------------------------
=
C
2
1
–
-------------------------------------------------------
=
R
3
------------
1
–
---------------------
=
C
3
------------------------------------------------
=
G
MOD
f
( )
-----------------------------
ESR
DCR
+
(
)
C
s
2
f
( )
L C
+
----------------------------------+
=
G
FB
f
( )
1
s f
( )
R
C
s f
( )
R
1
+
C
1
C
2
(
)
--------+
=
1
s f
( )
R
R
+
(
)
C
+
1
s f
( )
R
3
C
3
+
(
)
1
s f
( )
R
2
2
1
C
2
---------+
+
-------------------------------------------------------------------------------------------------------------------------
G
CL
f
( )
G
MOD
f
( )
G
FB
f
( )
=
where s f
( )
2
π
=
d
V
V
OSC
-----------------------------
1 V
0.16 V
IN
--------------------------
6.25
=
=
F
Z1
2
1
------------------------------
=
F
Z2
1
R
3
)
C
3
-----------------------+
=
F
P1
2
π
R
2
2
C
1
+
C
2
--------------------
--------------------------------------------
=
F
P2
3
3
------------------------------
=
0
F
P1
F
Z2
OPEN LOOP E/A GAIN
F
Z1
F
P2
F
LC
F
CE
COMPENSATION GAIN
CLOSED LOOP GAIN
G
FREQUENCY
MODULATOR GAIN
FIGURE 11. ASYMPTOTIC BODE PLOT OF CONVERTER GAIN
20
d
OSC
V
IN
----V
log
20
R1
log
LOG
L
F
0
G
MOD
G
FB
G
CL
ISL6540