MAX15021
Dual, 4A/2A, 4MHz, Step-Down
DC-DC Regulator withTracking/
Sequencing Capability
Maxim Integrated | 19www.maximintegrated.com
The locations of the zeros and poles should be such
that the phase margin peaks around f
CO
.
Set the ratios of f
CO
-to-f
Z
and f
P
-to-f
CO
equal to one anoth-
er, e.g.,
f
CO
= f
P = 5 is a good number to get approximately
f
Z
f
CO
60° of phase margin at f
CO
. Whichever technique, it is
important to place the two zeros at or below the double
pole to avoid the conditional stability issue.
The following procedure is recommended:
1) Select a crossover frequency, f
CO
, at or below one-
tenth the switching frequency (f
SW
):
2) Calculate the LC double-pole frequency, f
LC
:
where C
OUT
is the output capacitor of the regulator.
3) Select the feedback resistor, R
F
, in the range of
3.3kΩ to 30kΩ.
4) Place the compensator’s first
zero at or below the output filter’s
double-pole, f
LC
, as follows:
5) The gain of the modulator (Gain
MOD
)—comprised of
the regulator’s pulse-width modulator, LC filter,
feedback divider, and associated circuitry—at the
crossover frequency is:
The gain of the error amplifier (Gain
E/A
) in midband fre-
quencies is:
The total loop gain is the product of the modulator gain
and the error amplifier gain at f
CO
should be equal to 1,
as follows:
Gain
MOD
x Gain
E/A
= 1
So:
Solving for C
I
:
6) For those situations where f
LC
< f
CO
< f
ESR
< f
SW
/2,
as with low-ESR tantalum capacitors, the compen-
sator’s second pole (f
P2
) should be used to cancel
f
ESR
. This provides additional phase margin. On the
system Bode plot, the loop gain maintains its
+20dB/decade slope up to
1
/
2
of the switching fre-
quency verses flattening out soon after the 0dB
crossover. Then set:
f
P2
= f
ESR
If a ceramic capacitor is used, then the capacitor ESR
zero, f
ESR
, is likely to be located even above one-half of
the switching frequency, that is f
LC
< f
CO
< f
SW
/2 <
f
ESR
. In this case, the frequency of the second pole
(f
P2
) should be placed high enough not to significantly
erode the phase margin at the crossover frequency.
For example, f
P2
can be set at 5 x f
CO
, so that its con-
tribution to phase loss at the crossover frequency f
CO
is
only about 11°:
f
P2
= 5 x f
CO
Once f
P2
is known, calculate R
I
:
7) Place the second zero (f
Z2
) at 0.2 x f
CO
or at f
LC
,
whichever is lower, and calculate R
1
using the fol-
lowing equation:
8) Place the third pole (f
P3
) at 1/2 the switching fre-
quency and calculate C
CF
from:
9) Calculate R
2
as:
where V
FB
= 0.6V (typ).
