LTC3861-1 Datasheet, PDF (27/36 Pages) Linear Technology – Dual, Multiphase Step-Down Voltage Mode DC/DC Controller with Accurate Current Sharing

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_SW = Switching frequency
f_LC = _2π
1
LC_OUT
f_ESR
=
2π
1
R_ESR
C_OUT
choose:
f_C
=
Crossover
frequency
=
f_SW
10
f_Z1(ERR)
=
f_LC
=
1
2πR2C1
f_Z2(RES)
=
f_C
5
=
2π
1
(R1+ R3)C3
f_P1(ERR)
=
f_ESR
=
1
2πR2(C1//
C2)
f_P2(RES)
=
5f_C
=
1
2πR3C3
Required error amplifier gain at frequency f_C:
A
( ) ^{≈ 40log}
1+
⎛
⎝⎜
f_C
f_LC
⎞
⎠⎟
2
–
20log
1+
⎛
⎝⎜
f_C ⎞ ²
f_{ESR ⎠⎟}
– 20log
A_MOD
≈
20
log
R2
R1
•
⎛
⎝⎜
1+
⎛
⎝⎜
f_LC
f_C
1+
⎞
⎠⎟
⎛
⎜ ¹⁺
⎝
f_P2(RES)
f_C
+
f_C
f_ESR
+
f_LC
f_ESR –
f_LC
f_P2(RES) – f_Z2(RES)
f_Z2(RES)
⎞
⎠⎟
⎛
⎝⎜
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.
38611f
27