Datasheet

Data Sheet ADP2114
Rev. B | Page 29 of 40
The control loop can be broken down into the following three
sections:
• V
OUT
to V
COMP
• V
COMP
to I
L
• I
L
to V
OUT
Correspondingly, there are three transfer functions:
(s)
Zg
V
V
(s)V
(s)V
COMP
m
OUT
REF
OUT
COMP
××
=
(10)
CS
COMP
L
G
(s)
V
(s)
I
=
(11)
(s)Z
(s)I
(s)V
FILT
L
OUT
=
(12)
where:
g
m
is the transconductance of the error amplifier, 550 µs.
G
CS
is the current sense gain, 4 A/V.
V
OUT
is the output voltage of the converter.
V
REF
is the internal reference voltage of 0.6 V.
Z
COMP
(s) is the impedance of the RC compensation network that
forms a pole at origin and a zero as expressed in Equation 13.
COMP
COMPCOMP
COMP
C
s
CRs
(s)
Z
×
××+
=
1
(13)
Z
FILT
(s) is the impedance of the output filter and is expressed as
OUT
LOAD
LOAD
FILT
C
Rs
R
(s)
Z
××+
=
1
(14)
where s is angular frequency that can be written as s = 2πf.
The overall loop gain, H(s), is obtained by multiplying the three
transfer functions previously mentioned as follows:
H(s) = g
M
× G
CS
×
OUT
REF
V
V
× Z
COMP
(s) × Z
FILT
(s) (15)
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 of 1/12 (approximately) the
switching frequency can be targeted.
At the crossover frequency, the gain of the open-loop transfer
function is unity. This yields Equation 16 for the compensation
network impedance at the crossover frequency.
REF
OUT
CS
m
OUT
CROSS
CROSSCOMP
V
V
Gg
Cf
fZ ×
×
×××
=
π2
)(
(16)
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 Equation 17.
8π2
1
CROSS
COMPCOMP
ZERO
f
CR
f ≈
×××
=
(17)
Solving Equation 16 and Equation 17 simultaneously yields the
value for the compensation resistor and compensation
capacitor, as shown in Equation 18 and Equation 19.








×








×=
REF
OUT
OUT
CS
m
CROSS
COMP
V
V
C
GG
F
R
)
π2
(
9
.
0
(18)
COMP
ZERO
COMP
Rf
C
×××
=
π2
1
(19)
The capacitor C
C2
(as shown in Figure 77) forms a pole with the
compensation resistor, R
COMP
, in the feedback loop to ensure
that the loop gain keeps rolling off well beyond the unity-gain
crossover frequency. The value of C
C2
, if used, is typically set to
1/40 of the compensation capacitor, C
COMP
.