Datasheet

LTC3122
16
3122fa
For more information www.linear.com/LTC3122
The compensation will force the converter gain G
BOOST
to unity at ƒ
C
by using the following expression for C
C
:
C
C
=
10
3
• g
ma
• R2 • G
ƒC
a
1
− 1
( )
a
2
2π • ƒ
C
• R1+ R2
( )
a
1
pF
(g
ma
in µS, ƒ
C
in kHz, G
ƒC
in V/V)
Once C
C
is calculated, R
C
and C
F
are determined by:
R
C
=
10
6
• a
1
2π • ƒ
C
• C
C
kΩ (ƒ
C
in kHz, C
C
in pF)
C
F
=
C
C
a
1
− 1
The values of the phase lead components are given by
the expressions:
R
PL
=
R1− a
2
•
R1•R2
R1+R2
⎛
⎝
⎜
⎞
⎠
⎟
a
2
−1
kΩ and
C
PL
=
10
6
a
2
−1
( )
R1+R2
( )
2π • ƒ
C
•R1
2
a
2
pF
where R1, R2, and R
PL
are in kΩ and ƒ
C
is in kHz.
Note that selecting Φ
2
= 0° forces a
2
= 1, and so the
converter will have Type II compensation and therefore
no feedforward: R
PL
is open (infinite impedance) and C
PL
= 0pF. If a
2
= 0.833 • V
OUT
(its maximum), feedforward is
maximized; R
PL
= 0 and C
PL
is maximized for this com-
pensation method.
Once the compensation values have been calculated, ob-
taining a converter bode plot is strongly recommended to
verify calculations and adjust values as required.
Using the circuit in Figure 5 as an example, Table 3 shows
the parameters used to generate the bode plot shown in
Figure 6.
Table 3. Bode Plot Parameters for Type II Compensation
PARAMETER VALUE UNITS COMMENT
V
IN
5 V App Specific
V
OUT
12 V App Specific
R
L
15 Ω App Specific
C
OUT
22 µF App Specific
R
ESR
5 mΩ App Specific
L 3.3 µH App Specific
ƒ
OSC
1 MHz Adjustable
R1 1020 kΩ Adjustable
R2 113 kΩ Adjustable
g
ma
95 µS Fixed
R
O
10 MΩ Fixed
g
mp
3.4 S Fixed
η
80 % App Specific
R
C
210 kΩ Adjustable
C
C
390 pF Adjustable
C
F
10 pF Adjustable
R
PL
0 kΩ Optional
C
PL
0 pF Optional
From Figure 6, the phase is 60° when the gain reaches
0dB, so the phase margin of the converter is 60°. The
crossover frequency is 15kHz, which is more than three
times lower than the 108.4kHz frequency of the RHP zero
to achieve adequate phase margin.
applicaTions inForMaTion