LTC3114-1_15 Datasheet, PDF (26/34 Pages) Linear Technology – 40V, 1A Synchronous Buck-Boost DC/DC Converter with Programmable Output Current

LTC3114-1
APPLICATIONS INFORMATION
where:
G_CS is the inner current loop closed-loop transconduc-
tance = 1.97A/V
R_LOAD is the minimum load resistance in ohms
g_m is the transconductance of the error amplifier, 120µS
R_Z is the compensation zero setting resistor (one of
our design variables)
V_OUT is the output voltage
Our desired closed-loop frequency (f_CC) defined earlier is
29kHz. Assuming that we have a single pole response in
our system, we can express the ratio of the closed-loop
crossover frequency to f_P1 in the buck mode of operation
as follows:
f_{CC =} G_CS •R_LOAD • g_m •R_z
f_P1
V_O
We can now calculate R_Z by rearranging the previous
equation:
R_Z
=
f_CC
•
V_OUT • 2π •C_OUT
G_CS • g_m
It’s important to note that the value of R_Z is proportional
to the overall crossover frequency, f_CC. If we later want to
adjust f_CC lower, for example, R_Z can be lowered in value
and C_P1 increased proportionally to keep the compensa-
tion zero at the same frequency.
As mentioned previously, we will place the zero at fre-
quency P1, yielding:
C_P1
=
2π
1
•R_Z
•
f_P1
or more simply,
R_LOAD • C_OUT
R_Z
where R_l is the minimum load resistance in buck mode,
12Ω in this example.
Quickly substituting our values in the above equations
yields:
R_Z = 407k, C_P1 = 1.3nF,
but please continue reading as this is not the final answer.
If the inner current loop were an ideal V_CCS, then the
previously derived compensation would be sufficient to
stabilize the converter. However, the inner current loop
utilizes an operational amplifier with an integral compen-
sation network, which contributes an additional zero and
pole in the power stage response, the gain peaking, as
described previously. The effect of the additional zero/pole
pair pushes out f_CC, our crossover frequency, beyond what
was predicted by the previous calculations. A simplified
approach to calculating our compensation components
then is to re-use the previous equations but scale f_CC, the
cross over frequency, by a scaling factor (α), which will
account for the gain boost present in the system:
f_CC′
=
f_CC
3
•(α),
where
α
=
0.42
So, in our example, this results in:
f_CC′
=
29kHz
3
•
(0.42)
=
4.06kHz
Using the new value of f_CC′ in the previous equations for
R_Z and C_C yields:
R_Z
=
4.06kHz•12V • 2π • 44µF
1.97A _• 120µA
V
V
R_Z = 56.9kΩ, use 56.2kΩ
C_P1
=
12Ω • 44µF
56.2k
C_P1 = 9.4nF, use 10nF
C_P2 is usually chosen to be a small value around 10pF as
it is meant to filter out high frequency switching frequency
related components.
Keep in mind that this analysis assumes that the zero pro-
vided by the output capacitor and its ESR is at a frequency
much higher than f_CC.
26
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