Datasheet

LTC3536
16
3536fa
increasing gain and decreasing phase at higher frequen-
cies. As a result, the crossover frequency in boost mode
operation generally must be set lower than in buck mode
in order to maintain sufficient phase margin.
G= V
IN
•
R
LOAD
R
S
•
1–
R
S
R
LOAD
•
V
OUT
V
IN






2
1+
R
LOAD
R
S
•
V
IN
V
OUT






2
ω
O
=
R
S
+R
LOAD
V
IN
V
OUT






2
LC
OUT
R
LOAD
+R
C
( )
In boost mode operation, the frequency of the right-half
plane zero, f
Z
, is given by the following expression. The
frequency of the right half plane zero decreases at higher
loads and with larger inductors.
ω
Z
=
V
IN
V
OUT






2
R
LOAD
–R
S
L
, f
Z
=
V
IN
V
OUT






2
R
LOAD
–R
S
2πL
Finally, the magnitude of the quality factor of the power
stage in boost mode operation is given by the following
expression:
Q =
LC
OUT
R
LOAD
+R
C
( )
R
S
+R
LOAD
V
IN
V
OUT






2
L +C
OUT
R
LOAD
R
C
V
IN
V
OUT






2
+R
S
C
OUT
R
LOAD
+R
C
( )
Buck-Boost Mode
When the converter operates in buck-boost mode and the
small-signal transfer function from control voltage, V
C
, to
the output voltage is given by the following expression:
V
OUT
V
C
s
( )
Buck-Boost Mode
=
17.62 • G
1+sR
C
C
OUT
( )
1–
s
ω
Z






1+
s
ω
O
Q
+
s
ω
O






2
Also in buck-boost mode operation, the transfer function
is characterized by a pair of resonant poles and a zero
generated by the ESR of the output capacitor as in buck
mode and a right half plane zero.
G=
0.15 • V
OUT
R
LOAD
• ε
2
• 1.85 –R
S
• 1.85 – ε
( )
( )
ε • 1.85 – ε
( )
• R
S
+R
LOAD
• ε
2
( )
where the variable ε is defined:
ε =
V
IN
• 1.85
V
OUT
+ V
IN
ω
O
=
R
S
+R
LOAD
• ε
2
LC
OUT
R
LOAD
+R
C
( )
In buck-boost mode operation, the frequency of the right-
half plane zero, f
Z
, is given by the following expression.
The frequency of the right-half plane zero decreases at
higher loads and with larger inductors.
ω
Z
=
1.85 • ε
2
R
LOAD
–R
S
• 1.85 – ε
( )
L • 1.85– ε
( )
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