Datasheet


SLUS489 − OCTOBER 2001
15
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APPLICATION INFORMATION
The frequency of the poles and zeros are defined by the following equations:
zeros
f
z1
+
1
(
2p R2 C1
)
f
z2
[
1
(
2p R1 C3
)
, assuming R1 ơ R3
poles
f
p1
+
1
(
2p R3 C3
)
f
p2
[
1
(
2p R2 C2
)
, assuming C1 ơ C2
In voltage mode control, the buck, boost, flyback, and SEPIC toplogies all have a 2
nd
order double-pole LC filter
characteristic when operated in CCM. In the buck topology, the frequency of the LC double pole is straight
forward.
f
LC
+
1
ǒ
2p
(
LC
)
1
ń
2
Ǔ
buck topology
In the boost, flyback, and SEPIC toplogies, the frequency of the LC double pole varies as a function of the duty
cycle.
f
LC
+
(
1 * D
)
ǒ
2p
(
LC
)
1
ń
2
Ǔ
boost, flyback, & SEPIC topologies
In addition, each of the topologies have an ESR zero, which occurs when the output capacitor impedance
transitions from capacitive to resistive. The frequency at which this occurs is the ESR zero frequency, f
ESR
, and
is defined by the equation:
f
ESR
+
1
2p
ǒ
R
ESR
Ǔ
C
In the boost, flyback, and SEPIC topologies operated in CCM, there is also a right half-plane (RHP) zero. The
RHP zero has the same positive gain slope as the conventional zero, but has a 90° phase lag. This combination,
in conjunction with its dependence on line and load, make it nearly impossible to compensate within the control
loop. The frequency at which this RHP zero occurs, f
RHP
, is defined by the equations:
f
RHP
+
R
O
(
1 * D
)
2
(
2 p L
)
boost topology
f
RHP
+
R
O
(
1 * D
)
2
(
2 p LD
)
flyback topology
where R
O
is the equivalent output load resistance.
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)