Datasheet

MAX16993 Step-Down Controller with
Dual 2.1MHz Step-Down DC-DC Converters
www.maximintegrated.com
Maxim Integrated │ 19
A dominant pole (f
dpEA
) is set by the compensation capac-
itor (C
C
) and the amplifier output resistance (R
OUT,EA
). A
zero (f
ZEA
) is set by the compensation resistor (R
C
) and
the compensation capacitor (C
C
). There is an optional
pole (f
PEA
) set by C
F
and R
C
to cancel the output capaci-
tor ESR zero if it occurs near the crossover frequency
(f
C
, where the loop gain equals 1 (0dB)).
Thus:
dpEA
C OUT,EA C
zEA
CC
pEA
FC
1
f
2 C (R R )
1
f
2C R
1
f
2C R
=
π× × +
=
π× ×
=
π× ×
The loop-gain crossover frequency (f
C
) should be set
below 1/5 of the switching frequency and much higher
than the power-modulator pole (f
pMOD
). Select a value
for f
C
in the range:
SW
pMOD C
f
ff
5
<< ≤
At the crossover frequency, the total loop gain must be
equal to 1.
Thus:
CC
C
C
FB
MOD ( f ) EA ( R )
OUT
EA (f ) m,EA C
pMOD
MOD ( f ) MOD ( dc )
C
V
GAIN GAIN 1
V
GAIN g f
f
GAIN GAIN
f
×× =
= ×
= ×
Therefore:
C
FB
MOD (f ) m,EA C
OUT
V
GAIN g R 1
V
× × ×=
Solving for R
C
:
C
OUT
C
m,EA FB MOD (f )
V
R
g V GAIN
=
××
Set the error-amplifier compensation zero formed by
R
C
and C
C
at the f
pMOD
. Calculate the value of C
C
as
follows:
C
C
1
C
2f R
pMOD
=
π× ×
If f
zMOD
is less than 5 x f
C
, add a second capacitor C
F
from COMP1 to GND. The value of C
F
is:
F
C
1
C
2f R
zMOD
=
π× ×
As the load current decreases, the modulator pole also
decreases; however, the modulator gain increases accord-
ingly and the crossover frequency remains the same.
Below is a numerical example to calculate the compensa-
tion network component values of Figure 4:
A
V_CS
= 8V/V
R
DCR
=22mΩ
g
mc
= 1/(A
V_CS
x R
DC
) = 1/(8 x 0.022) = 5.68
V
OUT
= 5V
I
OUT(MAX)
= 5A
R
LOAD
= V
OUT/
I
OUT(MAX)
=5V/6A=0.833Ω
C
OUT
= 4 x 47µF = 188µF
ESR=9mΩ/4=2.25mΩ
f
SW
= 0.420MHz
GAIN
MOD(dc)
= 5.68 x 0.833 = 4.73
pMOD
SW
pMOD C
CC
zMOD
1
f 1kHz
2 188 F 0.833
f
ff
5
1kHz f 80.6 kHz , Select f 20 kHz
1
f 376 kHz
2 2.25 m 188 F
= ≈
π× µ ×
<< ≤
<< ≤ =
= ≈
π× Ω× µ
Since f
zMOD
> f
C
:
R
C
≈33kΩ
C
C
≈4.7nF
C
F
≈12pF