LTC3882_15 Datasheet, PDF (45/104 Pages) Linear Technology – Dual Output PolyPhase Step-Down DC/DC Voltage Mode Controller with Digital Power System Management

LTC3882
APPLICATIONS INFORMATION
also provides flexibility in choosing pole and zero loca-
tions. In particular, it allows the use of Type 3 compensa-
tion to provide phase boost at the LC pole frequency for
significantly improving the control loop phase margin,
as shown in Figure 23.
–1
GAIN
0
PHASE
+1
–1
BOOST
FREQ
–90
–180
–270
–380
3882 F23
Figure 23. Type 3 Compensation Frequency Response
In a typical LTC3882 circuit, the feedback loop closed around
this control amplifier and compensation network consists
of the line feedforward circuit, the modulator, the external
inductor and the output capacitor. All these components
affect loop behavior and need to be accounted for in the
frequency compensation.
The modulator consists of the PWM generator, the output
MOSFET drivers and the external MOSFETs themselves.
Step-down modulator gain varies linearly with the input
voltage. The line feedforward circuit compensates for this
change in gain, and provides a constant gain A_MOD of 4V/V
from the error amplifier output COMP to the inductor input
(average DC voltage) regardless of V_IN. The combination
of the line feedforward circuit and the modulator looks
like a linear voltage transfer function from COMP to the
inductor input with a fairly benign AC behavior at typical
loop compensation frequencies. Significant phase shift
will not begin to occur in this transfer function until half
the switching frequency.
The external inductor/output capacitor combination makes
a more significant contribution to loop behavior. These
components cause a 2nd order amplitude roll-off that filters
the PWM waveform, resulting in the desired DC output
voltage. But the additional 180° phase shift produced by
this filter causes stability issues in the feedback loop and
must be frequency compensated. At higher frequencies,
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.
The transfer function of the Type 3 circuit shown in Figure 25
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
(crossover) 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 zero to a lower frequency to avoid excessive phase
dip. The following equations can be used to compute the
feedback compensation component values:
f_LC = _2π
1
LC_OUT
f_ESR
=
1
2πR_ESRC_OUT
choose:
f_C
=
crossover
frequency
=
f_PWM
10
f_Z1(ERR)
=
f_LC
=
1
2πR2C1
f_{Z 2(RES )}
=
f_C
5
=
1
2π(R1+ R3)C3
f_P1(ERR) = f_ESR =
1
2πR2(C1//C2)
f_P2(RES)
= 5f_C
=
1
2πR3C3
For more information www.linear.com/LTC3882
3882f
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