LTC3112_15 Datasheet, PDF (18/32 Pages) Linear Technology – 15V, 2.5A Synchronous Buck-Boost DC/DC Converter

LTC3112
Applications Information
Buck Mode Small Signal Model
The LTC3112 uses a voltage mode control loop to main-
tain regulation of the output voltage. An externally com-
pensated error amplifier drives the COMP pin to generate
the appropriate duty cycle of the power switches. Use of
an external compensation network provides the flexibility
for optimization of closed loop performance over the wide
variety of output voltages, switching frequencies, and
external component values supported by the LTC3112.
The small signal transfer function of the buck-boost con-
verter is different in the buck and boost modes of opera-
tion 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_COMP, to the
converter output voltage is given by the following equation.
V_O
V_COMP
BUCK
MODE
= G_BUCK
1+

¹⁺

s
2πf_Z



s
2πf_OQ
+


s
2πf_O
²

The gain term, G_BUCK, is comprised of two different com-
ponents: the gain of the pulse width modulator and the gain
of the power stage as given by the following expressions
where V_IN is the input voltage to the converter in volts, f
is the switching frequency in Hz, R is the load resistance
in ohms, and t_LOW is the switch pin minimum low time.
A curve showing the switch pin minimum low time can
be found in the Typical Performance Characteristics sec-
tion of this data sheet. The parameter R_S represents the
average series resistance of the power stage and can be
approximated as twice the average power switch resistance
plus the DC resistance of the inductor.
G_BUCK = G_PWMG_POWER
G_PWM = 2₍1– t_LOW f₎
G_POWER
=
(^1–
V_INR
t_LOW f₎₍R
+ R_S
)
The buck mode gain is well approximated by the follow-
ing equation.
G_BUCK
=
2• V_IN •R
R +R_S
≅
2• V_IN
The buck mode transfer function has a single zero which
is generated by the ESR of the output capacitor. The zero
frequency, f_Z, is given by the following expression where
R_C and C_O are the ESR (in ohms) and value (in farads) of
the output filter capacitor respectively.
f_Z
=
1
2π R_C C_O
In most applications, an output capacitor with a very low
ESR is utilized in order to reduce the output voltage rip-
ple to acceptable 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 ex-
hibits a pair of resonant poles generated by the LC 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.
f_O
=
1
2π
R +R_S
LC_{O (}R +R_{C )}
≅
1
2π
1
LC_O
The quality factor, Q, has a significant impact on com-
pensation 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_{O (}R +R_{C )(}R +R_{S )}
RR_CC_O +L + C_OR_{S (}R +R_C
)
≅
L
R
LC_O
+ C_OR_S
3112fc
18
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