Datasheet

LTC3122
15
3122fa
For more information www.linear.com/LTC3122
G
EA
= g
ma
•R
O
≈ 950V/V
(Not Adjustable; g
ma
= 95µS, R
O
≈ 10MΩ)
G
MP
= g
mp
=
ΔI
L
ΔV
C
≈ 3.4S (Not Adjustable)
G
POWER
=
ΔV
OUT
ΔI
L
=
η • V
IN
2 •I
OUT
Combining the two equations above yields:
G
DC
= G
MP
• G
POWER
≈
1.7 • η • V
IN
I
OUT
V/V
Converter efficiency η will vary with I
OUT
and switching
frequency ƒ
OSC
as shown in the typical performance
characteristics curves.
Output Pole: P1 =
2
2 • π •R
L
• C
OUT
Hz
Error Amplifier Pole: P2 =
1
2 • π •R
O
•(C
C
+C
F
)
Hz
Error Amplifier Zero: Z1 =
1
2 • π •R
C
• C
C
Hz
ESR Zero: Z2 =
1
2 • π •R
ESR
• C
OUT
Hz
RHP Zero: Z3 =
V
IN
2
•R
L
2 • π • V
OUT
2
•L
Hz
High Frequency Pole: P3 >
ƒ
OSC
3
Phase Lead Zero: Z4 =
1
2 • π •(R1+R
PL
) • C
PL
Hz
Phase Lead Pole: P4 =
1
2 • π •
R1•R2
R1+R2
+R
PL
⎛
⎝
⎜
⎞
⎠
⎟
• C
PL
Hz
Error Amplifier Filter Pole:
P5 =
1
2 • π •R
C
•
C
C
• C
F
C
C
+C
F
⎛
⎝
⎜
⎞
⎠
⎟
Hz
The current mode zero (Z3) is a right half plane zero
which can be an issue in feedback control design, but is
manageable with proper external component selection.
As a general rule, the frequency at which the open-loop
gain of the converter is reduced to unity, known as the
crossover frequency ƒ
C
, should be set to less than one
third of the right half plane zero (Z3), and under one eighth
of the switching frequency ƒ
OSC
. Once ƒ
C
is selected, the
values for the compensation components can be calculated
using a bode plot of the power stage or two generally valid
assumptions: P1 dominates the gain of the power stage
for frequencies lower than ƒ
C
and ƒ
C
is much higher than
P2. First calculate the power stage gain at ƒ
C
, G
ƒC
in V/V.
Assuming the output pole P1 dominates G
ƒC
for this range,
it is expressed by:
G
ƒC
≈
G
DC
1+
ƒ
C
P1
⎛
⎝
⎜
⎞
⎠
⎟
2
V/V
Decide how much phase margin (Φ
m
) is desired. Greater
phase margin can offer more stability while lower phase mar-
gin can yield faster transient response. Typically, Φ
m
≈ 60°
is optimal for minimizing transient response time while
allowing sufficient margin to account for component vari-
ability. Φ
1
is the phase boost of Z1, P2, and P5 while Φ
2
is
the phase boost of Z4 and P4. Select Φ
1
and Φ
2
such that

Φ
1
≤ 74°; Φ
2
≤ 2 • tan
−1
V
OUT
1.2V
⎛
⎝
⎜
⎞
⎠
⎟
− 90° and
Φ
1
+ Φ
2
= Φ
m
+tan
−1
ƒ
C
Z3
⎛
⎝
⎜
⎞
⎠
⎟
where V
OUT
is in V and ƒ
C
and Z3 are in kHz.
Setting Z1, P5, Z4, and P4 such that
Z1=
ƒ
C
a
1
, P5 = ƒ
C
a
1
, Z4 =
ƒ
C
a
2
, P4 = ƒ
C
a
2
allows a
1
and a
2
to be determined using Φ
1
and Φ
2
a
1
= tan
2
Φ
1
+ 90°
2
⎛
⎝
⎜
⎞
⎠
⎟
, a
2
= tan
2
Φ
2
+90°
2
⎛
⎝
⎜
⎞
⎠
⎟
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