?2005 Fairchild Semiconductor Corporation
www.fairchildsemi.com
FAN5069 Rev. 1.1.5
17
Poles and Zeros of Plant Transfer Function:
Plant zero frequency =
(EQ. 28)
Plant 1
st
pole frequency =
(EQ. 29)
Plant 2
nd
pole frequency =
(EQ. 30)
Plant 3
rd
pole frequency =
(EQ. 31)
Plant gain (magnitude) response:
(EQ. 32)
Plant phase response:
(EQ. 33)
Choose R1, R
BIAS
to set the output voltage using EQ.6. Choose the zero crossover frequency F
cross
of the overall
loop. Typically F
cross
should be less than fifth of F
sw
. Choose the desired phase margin; typically between 60?to 90?
Calculate plant gain at F
cross
using EQ.34 by substituting F
cross
in place of f. The gain that the amplifier needs to pro-
vide to get the required crossover is given by:
(EQ. 34)
The phase boost required is calculated as given in (EQ. 35)
(EQ. 35)
where M is the desired phase margin in degrees.
The feedback component values are calculated as given in equations below:
(EQ. 36)
(EQ. 37)
(EQ. 38)
(EQ. 39)
(EQ. 40)
(EQ. 41)
f
z
1
2   ?nbsp  C
o
R
es
?/DIV>
?/DIV>
?/DIV>
-------------- ----------------- ---------- -
=
f
p1
1
2   ?nbsp   C
o
R
p
L
e
R
L
------ -
+
?/DIV>
?/DIV>
?/DIV>
?/DIV>
?/DIV>
?/DIV>
?/DIV>
- ----------------- ----------------- ----------------- ------ -
=
f
p2
1
2   ?/DIV>
?/DIV>
- ---------- -
1
C
o
R
L
?/DIV>
----------------- -- -
R
p
L
e
------ -
+
?/DIV>
?/DIV>
?/DIV>
?/DIV>
?/DIV>
=
f
p3
?/DIV>
n
2
L
e
?/DIV>
2   ?nbsp  R
p
?/DIV>
?/DIV>
- ----------------- ------- -
=
G
p
(f)
20
M
0
log
10
1
f
f
z
--- -
?nbsp ?/DIV>
?nbsp ?/DIV>
2
+
1
f
f
p1
------ -
?nbsp   ?/DIV>
?nbsp   ?/DIV>
2
+
1
f
f
p2
------ -
?nbsp   ?/DIV>
?nbsp   ?/DIV>
2
+
1
f
f
p3
-- ---- -
?nbsp   ?/DIV>
?nbsp   ?/DIV>
2
+
?/DIV>
?/DIV>
------------ ----------------- ----------------- ----------------- ----------------- ----------------- -------- -
log
?/DIV>
+
?/DIV>
=
G
P
(f)
tan
1
    f
f
z
--- -
?nbsp ?/DIV>
?nbsp ?/DIV>
tan
1
    f
f
p1
------ -
?nbsp   ?/DIV>
?nbsp   ?/DIV>
tan
1
    f
f
p2
------ -
?nbsp   ?/DIV>
?nbsp   ?/DIV>
tan
1
    f
f
p3
------ -
?nbsp   ?/DIV>
?nbsp   ?/DIV>
=
G
AMP
1
G
p
(F
cross
)
-------------- ----------------- -
=
Phase Boost    M
G
P
(F
cross
)
90?/DIV>
=
K
Tan
Boost
4
--------------- -
?/DIV>
?/DIV>
?/DIV>
?/DIV>
45
+
?/DIV>
?/DIV>
?/DIV>
?/DIV>
?/DIV>
?/DIV>
2
=
C2
1
2   ?nbsp  F
cross
G
AMP
R1
?/DIV>
?/DIV>
?/DIV>
?/DIV>
------------ ----------------- ----------------- ----------------- -------- -
=
C1
C2    K   1
(
)
?/DIV>
=
C3
1
2   ?nbsp  F
cross
K
?/DIV>
?/DIV>
?/DIV>
R3
?/DIV>
---- ----------------- ----------------- ----------------- -------- -
=
R2
K
2   ?nbsp  F
cross
?/DIV>
?/DIV>
C1
?/DIV>
-------- ----------------- ----------------- ------- -
=
R3
R1
K   1
(
)
---------- ------- -
=
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