LTC3860_15 Datasheet, PDF (23/36 Pages) Linear Technology – Dual, Multiphase Step-Down Voltage Mode DC/DC Controller with Current Sharing

LTC3860
APPLICATIONS INFORMATION
In a typical LTC3860 circuit, the feedback loop consists
of the line feedforward circuit, the modulator, the external
inductor, the output capacitor and the feedback amplifier
with its compensation network. All these components
affect loop behavior and need to be accounted for in the
loop compensation. The modulator consists of the PWM
generator, the output MOSFET drivers and the external
MOSFETs themselves. The modulator gain varies linearily
with the input voltage. The line feedforward circuit com-
pensates for this change in gain, and provides a constant
gain from the error amplifier output to the inductor input
regardless of input voltage. From a feedback loop point of
view, the combination of the line feedforward circuit and
the modulator looks like a linear voltage transfer function
from COMP to the inductor input. It has fairly benign AC
behavior at typical loop compensation frequencies with
significant phase shift appearing at half the switching
frequency.
The external inductor/output capacitor combination makes
a more significant contribution to loop behavior. These
components cause a second order LC roll-off at the output
with 180° phase shift. This roll-off is what filters the PWM
waveform, resulting in the desired DC output voltage, but
this phase shift causes stability issues in the feedback loop
and must be frequency compensated. At higher frequen-
cies, the reactance of the output capacitor will approach
its ESR, and the roll-off due to the capacitor will stop,
leaving –20dB/decade and 90° of phase shift.
Figure 12 shows a Type 3 amplifier. The transfer function
of this amplifier is given by the following equation:
V_COMP
V_OUT
=
–₍1+ sC1R2_)[1+ s(R1+ R3)C3_]
sR1(C1+ C2)⎡⎣1+ s(C1//C2)R2⎤⎦ ₍1+ sC3R3₎
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
=
1
2π R_ESR
C_OUT
choose:
f_C
=
Crossover
frequency
=
f_SW
10
1
f_Z1(ERR) = f_LC = _2πR2C1
f_{Z 2(RES )}
=
f_C
5
=
1
2π (R1+ R3)C3
1
f_P1(ERR) = f_ESR = _{2πR2(C1// C2)}
1
f_P2(RES) = 5f_C = _2πR3C3
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
•
⎛
⎝⎜ ¹⁺
f_LC
f_C
⎞
⎠⎟
⎛
⎜ ¹⁺
⎝
f_P2(RES)
f_C
+
f_P2(RES) – f_Z2(RES) ⎞
f_Z2(RES)
⎟
⎠
R1
⎛
⎝⎜
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_SAW
≈ 12V/V
3860fc
23