Datasheet

ADP2441 Data Sheet
Rev. A | Page 22 of 32
Correspondingly, there are three transfer functions:
)(
)(
)(
sZg
V
V
sV
sV
COMP
m
OUT
REF
OUT
COMP

(14)
CS
COMP
L
G
sV
sI

)(
)(
(15)
)(
)(
)(
sZ
sI
sV
FILT
L
OUT
 (16)
where:
g
m
is the transconductance of the error amplifier and equals
250 µA/V.
G
CS
is the current sense gain and equals 2 A/V.
V
OUT
is the output voltage of the regulator.
V
REF
is the internal reference voltage and equals 0.6 V.
Z
COMP
(s) is the impedance of the RC compensation network that
forms a pole at the origin and a zero as expressed in Equation 17.
COM
P
COMPCOMP
COMP
Cs
C
Rs
sZ



1
)(
(17)
Z
FILT
(s) is the impedance of the output filter and is expressed as
OUT
LOAD
LOAD
FILT
CRs
R
sZ


1
)(
(18)
where s is the angular frequency, which can be written as s = 2πf.
The overall loop gain, H(s), is obtained by multiplying the three
transfer functions previously mentioned as follows:
)()()( sZsZ
V
V
GgsH
FILT
COMP
OUT
REF
CS
m
 (19)
When the switching frequency (f
SW
), output voltage (V
OUT
),
output inductor (L), and output capacitor (C
OUT
) values are
selected, the unity crossover frequency can be set to 1/12 of the
switching frequency.
At the crossover frequency, the gain of the open-loop transfer
function is unity.
H(f
CROSSOVER
) = 1 (20)
This yields Equation 21 for the RC compensation network
impedance at the crossover frequency.
REF
OUT
CS
m
OUT
CROSSOVER
CROSSOVERCOMP
V
V
Gg
Cf
fZ







2
)(
(21)
Placing s = f
CROSSOVER
in Equation 17,
COMP
COMPCOMP
Cf
CRf
fZ
CROSSOVER
CROSSOVER
CROSSOVERCOMP








2
21
)( (22)
To ensure that there is sufficient phase margin at the crossover
frequency, place the compensator zero at 1/8 of the crossover
frequency, as shown in the following equation:
82
1
CROSSOVER
COMP
ZERO
f
CR
f
COMP


 (23)
Solving Equation 21, Equation 22, and Equation 23 yields the
value for the resistor and capacitor in the RC compensation
network, as shown in Equation 24 and Equation 25.
REF
OUTOUT
CS
m
CROSSOVER
COMP
V
VC
Gg
f
R





2
9.0
(24)
COMP
ZERO
COMP
Rf
C


2
1
(25)
Using these equations allows calculating the compensations for
the voltage loop.