Datasheet

1
2SR
FB1
C
ff
f
pff
=
R
FB2
R
FB1
R
FB2
+
= f
zff
V
OUT
V
FB
(Hz)
1
2SR
FB1
C
ff
(Hz)
f
zff
=
40
MAGNITUDE (dB)
10
2
10
3
10
4
10
5
10
6
FREQUENCY (Hz)
-120
-80
-40
0
10
7
-300
-250
-200
-150
-100
-50
0
PHASE (°)
Plotted Q values: 0.01, 0.05, 0.1, 0.2, 0.5, 1, 2, 10
Q = 0.01
Q = 0.01
Q = 10
Q = 10
LM3477
www.ti.com SNVS141K –OCTOBER 2000–REVISED MARCH 2013
SAMPLING POLE QUALITY FACTOR
In a current mode control architecture, there is an inherent resonace at half the switching frequency. The
LM3477/A internally compensates for this by adding a negative slope to the PWM control waveform (see
DEFAULT/ADJUSTABLE SLOPE COMPENSATION). The factor in the power stage equations above, Q,
describes how much resonance will be observed. Q is a function of duty cycle and m
c
. Figure 35 shows how the
power stage bode plot is affected as Q is varied from 0.01 to 10. The resonance is caused by two complex poles
at half the switching frequency. If m
c
is too low, the resonant peaking could become severe coinciding with
subharmonic oscillations in the inductor current. If m
c
is too high, the two complex poles split and the converter
begins to act like a voltage mode converter and the compensation scheme used above should be changed.
The Quality Factor Q of the Two Complex Poles is used to qualify how much resonant peaking is observed in the
Power Stage Bode Plot
Figure 35.
If Q>2, the sampling poles are imaginary and are approaching the right half of the imaginary plane (the system is
becoming unstable). In this case, Q must be decreased by either increasing the inductance, or more preferably,
adding more slope compensation through the R
SL
resistor (see DEFAULT/ADJUSTABLE SLOPE
COMPENSATION).
If Q<0.15, it means that one of the sampling poles is decreasing in frequency towards the dominant power pole,
f
p1
. There are three ways to compensate for this. Decrease the crossover frequency, add a phase lead network,
or use the output capacitor's ESR to cancel out the low frequency sampling pole.
One option is to decrease the crossover frequency so that the phase margin is not as severely decreased by the
sampling pole. Decreasing the crossover frequency to between 1kHz to 10kHz is advisable here. As a result,
there will be a decrease in transient response performance.
Another option is the use of the feed-forward capacitor, Cff. This will provide a positive phase shift (lead) which
can be used to increase phase margin. However, it is important to note that the effectiveness of Cff decreases
with output voltage. This is due to the fact that the frequencies of the zero f
zff
and pole f
pff
get closer together as
the output voltage is reduced.
The frequency of the feed-forward zero and pole are:
(61)
(62)
A third option is to strategically place the ESR zero f
ESR
of the output capacitor to cancel out the sampling pole.
In this case, the capacitor C
C2
will not be used to cancel out f
ESR
. f
ESR
should be placed around the crossover
frequency f
c
, but this will depend on how low Q is.
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