Datasheet

f
S
2
<
f
ESR
3.16
2Sf
C
R
C
d
d
C
C1
1
2Sf
p1
R
C
R
C
=
f
C
x R
GM
A
DC
x GM x R
GM
x H x f
P1
- f
C
:
Q =
1
Sm
c
x D' - 0.5)
f
ESR
=
2SC
OUT
R
ESR
1
(Hz)
1
C
OUT
R
f
p1
=
+
(m
c
x D' - 0.5)
1
f
s
LC
OUT
1
2S
(Hz)
V
IN
D' x 1.8R
SN
L
S
n
=
m
c
= 1+
S
e
S
n
R
1.8R
SN
R
f
S
L
m
c
x D' - 0.5
A
DC
=
1
1+
LM3477
SNVS141K –OCTOBER 2000–REVISED MARCH 2013 www.ti.com
(37)
(38)
S
e
= f
S
(V
SL
+ 50x10
−6
R
SL
) (39)
(40)
(41)
(42)
(43)
With the power stage known, a compensator can be designed to achieve improved performance and stability.
The LM3477/A will typically require only a single resistor and capacitor for compensation, but depending on the
power stage it could require three or four external components.
It is a good idea to check that Q is between 0.15 and 2, if it was not already done when selecting the inductor. If
Q is less than 0.15 or greater than 2, skip to SAMPLING POLE QUALITY FACTOR before continuing with the
compensator design.
First, a target crossover frequency (f
c
) for the loop gain must be selected. The crossover frequency is the
bandwidth of the converter. A higher bandwidth generally corresponds to faster response times and lower
overshoots to load transients. However, the bandwidth should not be much higher than 1/10 the switching
frequency. The LM3477/A operates with a 500kHz switching frequency, so it is recommended to choose a
crossover frequency between 10kHz - 50kHz.
The schematic of the LM3477/A compensator is shown in Figure 32. The default design uses R
c
and C
C1
to form
a lag (type 2) compensator. The C
C2
capacitor can be added to form an additional pole that is typically used to
cancel out the esr zero of the output capacitor. Finally, if extra phase margin is needed, the Cff capacitor can be
added (this does not help at low output voltages, see below).
The strategy taken here for choosing R
c
and C
C1
is to set the crossover frequency with R
c
, and set the
compensator zero with C
C1
. Using the selected target crossover frequency, f
C
, set R
C
to:
(44)
f
C
= Crossover frequency in Hertz (20kHz - 50kHz is recommended)
R
GM
= 50x10
3
Ω
GM = 1000x10
−6
A/V
The compensator zero, f
Z1
, is set with C
C1
. When fast transient responses are desired, f
Z1
should be placed as
high as possible, however it should not be higher than the selected crossover frequency f
C
. The guideline
proposed here is to choose C
C1
such that f
Z1
falls somewhere between the power pole f
P1
and ½ decade before
the selected crossover frequency fc:
(45)
In this compensation scheme, the pole created by C
C2
is used to cancel out the zero created by the ESR of the
output capacitor. In other schemes such as the methods discussed in SAMPLING POLE QUALITY FACTOR, the
ESR zero is used. For the typical case, use C
C2
if:
(46)
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