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ADD8754
To stabilize the regulator, make sure that the regulator crossover
frequency is less than or equal to one-fifth of the right-half
plane zero and less than or equal to one-fifteenth of the
switching frequency.
Rev. 0 | Page 15 of 28
For V
The regulator loop gain is
OUT
CS
COMP
MEA
OUT
IN
OUT
FB
VL
Z
G
Z
G
V
V
V
V
A
×
×
×
×
×
=
(14)
where:
A
VL
is the loop gain.
V
FB
is the feedback regulation voltage, 1.210 V.
V
OUT
is the regulated output voltage.
V
IN
is the input voltage.
G
MEA
is the error amplifier transconductance gain.
Z
COMP
is the impedance of the series RC network from COMP to
GND.
G
CS
is the current sense transconductance gain (the inductor
current divided by the voltage at COMP), which is internally set
by the ADD8754.
Z
OUT
is the impedance of the load and output capacitor.
To determine the crossover frequency, it is important to note
that at that frequency the compensation impedance (
Z
COMP
) is
dominated by the resistor and the output impedance (
Z
OUT
) is
dominated by the impedance of the output capacitor. Therefore,
when solving for the crossover frequency, (by definition of the
crossover frequency) the equation is simplified to
1
2
1
=
×
×
π
×
×
×
×
×
=
OUT
C
C
CS
C
MEA
OUT
V
IN
OUT
V
FB
VL
f
G
R
G
V
V
A
(15)
where:
f
C
is the crossover frequency.
R
C
is the compensation resistor.
Solving for R
C
,
CS
MEA
IN
FB
OUT
OUT
OUT
C
C
G
G
V
V
V
V
C
f
R
×
×
×
×
×
×
×
π
=
2
(16)
FB
= 1.21 V, G
MEA
= 100 μs, and G = 2 sec,
CS
IN
OUT
OUT
OUT
C
C
V
V
V
C
f
R
×
×
×
×
×
=
4
10
55
.
(17)
Once the compensation resistor is known, set the zero formed
by the compensation capacitor and resistor to one-fourth of the
crossover frequency, or
C
C
C
R
f
C
×
×
π
=
2
(18)
where
C
C
is the compensation capacitor.
REF
FB
C2
C
C
R
C
ERROR AMP
0
G
MEA
Figure 19. Compensation Components
The capacitor C2 is chosen to cancel the zero introduced by
output capacitance ESR.
Solving for C2,
C
OUT
R
C
ESR
C2
×
=
(19)
For low ESR output capacitance, such as with a ceramic capaci-
tor, C2 is optional. For optimal transient performance, the R
C
and C
C
might need to be adjusted by observing the load
transient response of the ADD8754. For most applications, the
compensation resistor should be in the range of 30 kΩ to
400 kΩ, and the compensation capacitor should be in the range
of 100 pF to 1.2 nF. Table 12 shows external component values
for several applications.
Table 12. Recommended External Components for Various Input/Output Voltage Conditions
V
IN
(V)
5
5
5
5
3.3
3.3
3.3
3.3
V
OUT
(V)
9
9
12
12
9
9
12
12
f
SW
650 kHz
1.2 MHz
650 kHz
1.2 MHz
650 kHz
1.2 MHz
650 kHz
1.2 MHz
L (μH)
10
4.7
10
4.7
10
4.7
10
4.7
C
OUT
(μF)
10
10
10
10
10
10
10
10
C
IN
(μF)
10
10
10
10
10
10
10
10
R
1
(kΩ)
63.4
63.4
88.7
88.7
63.4
63.4
88.7
88.7
R
2
(kΩ)
10
10
10
10
10
10
10
10
R
C
(kΩ)
84.5
178
140
300
71.5
150
130
280
C
c
(pF)
390
100
220
100
820
180
420
100
I
OUT_MAX
(mA)
450
450
350
350
350
350
250
250