Datasheet
Z
ZEA
=
1
C
COMP
x R
COMP
Z
O
=
1
(C
HF
+ C
COMP
) x R
FB2
Z
HF
=
C
HF
x C
COMP
x R
COMP
(C
HF
+ C
COMP
)
x
G
EA(S)
=
1 +
s
s
Z
ZEA
1 +
s
Z
O
Z
HF
K
FB
=
R
FB1
R
FB1
+ R
FB2
x
1
-G
EA(S)
x
=
V
COMP
1 +
+
1
A
OL
s
Z
BW
V
OUT(FB)
1 +
G
EA(S)
K
FB
S
e
=
(V
IN
± V
OUT
) x K
SL
+ V
SL
T
S
n
=
V
IN
x A x R
S
L
m
C
=
S
e
S
n
1
S x (m
C
± 0.5)
Q
=
Z
Z
=
1
C
OUT
x ESR
Z
n
=
S
T
Z
P
=
1
C
OUT
x
1
R
LOAD
+
1
K
m
x A x R
S
V
SL
=
I
OS
x T
C
RAMP
K
SL
=
g
m
x T
C
RAMP
K
m
=
(D ± 0.5) x A x R
S
x T
L
+ (1 - 2 x D) x K
SL
+
1
V
SL
V
IN
R
LOAD
A x R
S
x
x
1 +
s
Z
Z
x
=
V
OUT
V
COMP
1 +
s
Z
P
+
1 +
s
Z
n
x Q
s
2
Z
n
2
1 +
R
LOAD
K
m
x A x R
S
1
LM25116
www.ti.com
SNVS509D –APRIL 2007–REVISED FEBRUARY 2013
(44)
(45)
(46)
(47)
(48)
K
m
is the effective DC gain of the modulating comparator. The duty cycle D = V
OUT
/ V
IN
. K
SL
is the proportional
slope compensation term. V
SL
is the fixed slope compensation term. Slope compensation is set by m
c
, which is
the ratio of the external ramp to the natural ramp. The switching frequency sampling gain is characterized by ω
n
and Q, which accounts for the high frequency inductor pole.
For V
SL
without R
RAMP
, use I
OS
= 25 µA
For V
SL
with R
RAMP
to V
CC
, use I
OS
= 25 µA + V
CC
/R
RAMP
For V
SL
with R
RAMP
to -V
CC
, use I
OS
= 25 µA - V
CC
/R
RAMP
ERROR AMPLIFIER TRANSFER FUNCTION
The following equations are used to calculate the error amplifier transfer function:
(49)
(50)
where
• A
OL
= 10,000 (80 dB) and
• ω
BW
= 2π x f
BW
. G
EA(S)
is the ideal error amplifier gain, which is modified at DC and high frequency by the open
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