Datasheet
LTC3861-1
27
38611fa
For more information www.linear.com/LTC3861-1
applicaTions inFormaTion
The RC network across the error amplifier and the feed-
forward components R3 and C3 introduce two pole-zero
pairs to obtain a phase boost at the system unity-gain
frequency, f
C
. In theory, the zeros and poles are placed
symmetrically around f
C
, and the spread between the zeros
and the poles is adjusted to give the desired phase boost
at f
C
. However, in practice, if the crossover frequency
is much higher than the LC double-pole frequency, this
method of frequency compensation normally generates
a phase dip within the unity bandwidth and creates some
concern regarding conditional stability.
If conditional stability is a concern, move the error ampli
-
fier’s zero to a lower frequency to avoid excessive phase
dip. The following equations can be used to compute the
feedback compensation components value:
f Switching frequency
f
LC
f
R
SW
LC
OUT
ESR
=
=
π
=
π
1
2
1
2
EESR OUT
C
choose:
f Crossover freq uency
f
ff
C
SW
Z ERR LC
==
==
π
10
1
2
1( )
RRC
f
f
R RC
ff
Z RES
C
P ERR ESR
21
5
1
2 1 33
2
1
()
()
==
π+
()
= ==
π
==
π
1
2 21 2
5
1
2 33
2
RC C
ff
RC
P RES C
( // )
()
Required error amplifier gain at frequency f
C
:
A ≈ 40log 1+
f
C
f
LC
⎛
⎝
⎜
⎞
⎠
⎟
2
– 20log 1+
f
C
f
ESR
⎛
⎝
⎜
⎞
⎠
⎟
2
– 20log A
MOD
( )
≈20log
R2
R1
•
1+
f
LC
f
C
⎛
⎝
⎜
⎞
⎠
⎟
1+
f
P2(RES)
f
C
+
f
P2(RES)
– f
Z2(RES)
f
Z2(RES)
⎛
⎝
⎜
⎞
⎠
⎟
1+
f
C
f
ESR
+
f
LC
f
ESR
– f
LC
⎛
⎝
⎜
⎞
⎠
⎟
1+
f
P2(RES)
f
C
⎛
⎝
⎜
⎞
⎠
⎟
where AMOD is the modulator and line feedforward gain
and is equal to:
A
MOD
≈
V
IN(MAX)
• DC
MAX
V
RAMP
≈ 12V/ V
where DC
MAX
is the maximum duty cycle and V
RAMP
is
the line feedforward compensated PWM ramp voltage.
Once the value of resistor R1, poles and zeros location
have been decided, the value of R2, C1, C2, R3 and C3
can be obtained from the previous equations.
Compensating a switching power supply feedback loop
is a complex task. The applications shown in this data
sheet show typical values, optimized for the power
components shown. Though similar power compon-
ents should suffice, substantially changing even one
major power component may degrade performance
significantly. Stability also may depend on circuit board
layout. To verify the calculated component values, all
new circuit designs should be prototyped and tested
for stability.