LTC3536_15 Datasheet, PDF (15/28 Pages) Linear Technology – 1A Low Noise, Buck-Boost DC/DC Converter

LTC3536
Applications Information
V_IN
V_C
PWM
A
L
B
C_OUT
V_OUT
D
R_C
R_S
R_LOAD
C
3536 F04
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+
1+ sR_CC_OUT
s
ω_OQ
+


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
=
2π
1
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 =
C_OUT
LC_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:
( ) _VOUT
V_C
(s) _Boost
= 2.64 • G
Mode
1+ sR_CC_OUT


1–
s
ω_Z


1+
s
ω_OQ
+


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
3536fa
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