LTC3112_15 Datasheet, PDF (19/32 Pages) Linear Technology – 15V, 2.5A Synchronous Buck-Boost DC/DC Converter

LTC3112
Applications Information
Boost Mode Small Signal Model
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_COMP, to the output voltage is given by
the following expression.
V_O
V_COMP
BOOST
MODE
= G_BOOST

¹⁺

s
2πf_Z

^1–

s
2πf_RHPZ
1+
s
2πf_O
Q
+



s
2πf_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
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.
The boost mode gain, G_BOOST, is comprised of two com-
ponents: the pulse width modulator and the power stage.
The gain of the power stage in boost mode is given by the
following equation.
G_POWER
≅
(^1–
V_OUT2
t_LOW f₎ V_IN
By combining the individual terms, the total gain in boost
mode can be reduced to the following expression. Notice
that unlike in buck mode, the gain in boost mode is a
function of both the input and output voltage.
G_BOOST
≅
2 •V_OUT ²
V_IN
In boost mode, the resonant frequency of the power stage
has a dependence on the input and output voltage as shown
by the following equation.
f_O
=
1
2π
R_S
+
RV_IN2
V_OUT2
LC_{O (}R +R_{C )}
≅
1
2π
•
V_IN
V_OUT
1
LC
Finally, the magnitude of the quality factor of the power
stage in boost mode operation is given by the following
expression.
Q=

LC_OR_R_S
+
RV_IN2
V_OUT2



L + C_OR_SR
Compensation of the Voltage Loop
The small signal models of the LTC3112 reveal that the
transfer function from the error amplifier output, V_COMP,
to the output voltage is characterized by a set of resonant
poles and a possible zero generated by the ESR of the
output capacitor as shown in the Bode plot of Figure 4.
In boost mode operation, there is an additional right half
plane zero that produces phase lag and increasing gain at
higher freq­uencies. Typically, the compensation network is
designed to ensure that the loop crossover frequency is low
enough that the phase loss from the right half plane zero
is minimized. The low frequency gain in buck mode is a
constant, but varies with both V_IN and V_OUT in boost mode.
GAIN
–40dB/DEC
–20dB/DEC
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.
f_RHPZ
=
R₍1– t_LOW f₎² V_IN2
2πL V_OUT2
0°
–90°
–180°
–270°
PHASE
BUCK MODE
BOOST MODE
f
f_O
f_RHPZ
3112 F06
Figure 4. Buck-Boost Converter Bode Plot
3112fc
For more information www.linear.com/LTC3112
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