Datasheet

ADP1821
Rev. C | Page 17 of 24
Solving for C
I
in Equation 33 yields
LCZ
I
fR
C
π
1
=
(35)
Use the larger value of C
I
from Equation 34 or Equation 35.
Because of the finite output current drive of the error amplifier,
C
I
needs to be less than 10 nF. If it is larger than 10 nF, choose a
larger R
TOP
and recalculate R
Z
and C
I
until C
I
is less than 10 nF.
Next, choose the high frequency pole
f
P1
to be ½ of f
SW
.
SWP
ff
2
1
1
=
(36)
Since
C
HF
<< C
I
, Equation 29 is simplified to
HFZ
P
CR
f
π 2
1
1
=
(37)
Solving for C
HF
in Equation 36 and Equation 37 yields
ZSW
HF
Rf
C
π
1
=
(38)
Type III Compensator
0V
VRAMP
G
(dB)
PHASE
–270°
–90°
f
Z
f
P
C
HF
C
I
R
Z
C
FF
R
TOP
R
BOT
FROM
V
OUT
VREF
EA
COMP
TO PWM
R
FF
–
1
S
L
O
P
E
–
1
S
L
O
P
E
+
1
S
LO
P
E
0
5310-018
Figure 19. Type III Compensation
If the output capacitor ESR zero frequency is greater than ½ of
the crossover frequency, use Type III compensator as shown in
Figure 19. Set the poles and zeros as follows:
SWPP
fff
2
1
21
==
(39)
IZ
SWCO
ZZ
CR
ff
ff
π 2
1
404
21
====
(40)
or
IZ
LC
ZZ
CR
f
ff
π 2
1
2
2
1
===
(41)
Use the lower zero frequency from Equation 40 or Equation 41.
Calculate the compensator resistor, R
Z
, by
2
1
LCIN
COZRAMPTOP
Z
fV
ffVR
R =
(42)
Next calculate C
I
1
2
1
ZZ
I
fR
C
π
=
(43)
Because of the finite output current drive of the error amplifier,
C
I
needs to be less than 10 nF. If it is larger than 10 nF, choose a
larger R
TOP
and recalculate R
Z
and C
I
until C
I
is less than 10 nF.
Since
C
HF
<< C
I
, combining Equation 29 and Equation 39 yields
ZSW
HF
Rf
C
π
1
=
(44)
Next calculate the feedforward capacitor C
FF.
Assume R
FF
<< R
TOP
,
then Equation 28 is simplified to
TOPFF
Z
RC
f
π 2
1
2
=
(45)
Solving
C
FF
in Equation 45 yields
2
2
1
ZTOP
FF
fR
C
π
=
(46)
where
f
Z2
is obtained from Equation 40 or Equation 41.
The feedforward resistor,
R
FF
, can be calculated by combining
Equation 30 and Equation 39
SWFF
FF
fC
R
π
1
=
(47)
Check that the calculated component values are reasonable.
For instance, capacitors smaller than about 10 pF should be
avoided. In addition, the ADP1821 error amplifier has finite
output current drive, so R
Z
values less than 3 kΩ and C
I
values
greater than 10 nF should be avoided. If necessary, recalculate
the compensation network with a different starting value of R
TOP
. If
C
HF
is too small, start with a smaller value of R
TOP
. If R
Z
is too
small and C
I
is too big, start with a larger value of R
TOP
.
In general, aluminum electrolytic capacitors have high ESR,
therefore, a Type II compensation is adequate. However, if
several aluminum electrolytic capacitors are connected in
parallel, producing a low effective ESR, then Type III compensation
is needed. In addition, ceramic capacitors have very low ESR, on
the order of a few milliohms, requiring Type III compensation for
ceramic output capacitors. Type III compensation offers better
performance than Type II in terms of more low frequency gain,
more phase margin, and less high frequency gain at the
crossover frequency.