Datasheet

LTC3536
15
3536fa
Figure 4. Small-Signal Model
variety of output voltages, switching frequencies, and
external component values supported by the LTC3536.
V
IN
is the input supply voltage, V
OUT
the programmed
output voltage, L is the external buck-boost inductor, C
OUT
the output capacitor, R
S
the series resistance in the power
path (it can be approximated as twice the average power
switch resistance plus the DC resistance of the inductor)
and R
C
is the output capacitor ESR.
Buck Mode
The small-signal transfer function of the buck-boost
converter is different in the buck and boost modes of op-
eration and care must be taken to ensure stability in both
operating regions. When stepping down from a higher
input voltage to a lower output voltage, the converter
will operate in buck mode and the small-signal transfer
function from the error amplifier output, V
C
, to the con-
verter output voltage is given by the following equation:
V
OUT
V
C
s
( )
Buck Mode
= 2.64 • V
IN
•
1+ sR
C
C
OUT
1+
s
ω
O
Q
+
s
ω
O






2
This transfer function has a single zero created by the
output capacitor ESR and a resonant pair of poles. In most
applications, an output capacitor with a very low ESR is
utilized in order to reduce the output voltage ripple to ac-
ceptable levels. Such low values of capacitor ESR result
in a very high frequency zero and as a result the zero is
commonly too high in frequency to significantly impact
compensation of the feedback loop.
The denominator of the buck mode transfer function
exhibits a pair of resonant poles generated by the LC
OUT
filtering of the power stage. The resonant frequency of
the power stage, f
O
, is given by the following expression
where L is the value of the inductor in henries.
ω
O
=
1
LC
OUT
, f
O
=
1
2π LC
OUT
The quality factor, Q, has a significant impact on compensa-
tion of the voltage loop since a higher Q factor produces
a sharper loss of phase near the resonant frequency. The
quality factor is inversely related to the amount of damping
in the power stage and is substantially influenced by the
average series resistance of the power stage, R
S
. Lower
values of R
S
will increase the Q and result in a sharper
loss of phase near the resonant frequency and will require
more phase boost or lower bandwidth to maintain an
adequate phase margin.
Q =
LC
OUT
C
OUT
R
C
+R
S
( )
+
L
R
LOAD
Boost Mode
When stepping up from a lower input voltage to a higher
output voltage, the buck-boost converter will operate in
boost mode where 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
( )
Boost Mode
= 2.64 • G
1+sR
C
C
OUT
( )
1–
s
ω
Z






1+
s
ω
O
Q
+
s
ω
O






2
In boost mode operation, the transfer function is character-
ized by a pair of resonant poles and a zero generated by
the ESR of the output capacitor as in buck mode. However,
in addition there is a right-half plane zero which generates
applicaTions inForMaTion
PWMV
C
V
IN
V
OUT
C
OUT
R
C
R
LOAD
3536 F04
A D
B C
L
R
S