I
OM
=
I
(SW)(min)(lim)
+
I
(L1)(PP)
2
V
I(min)
V
I(min)
+ V
F
± V
O
(
)(
)
I
(SW)M
=
(I
OM
×
V
I(min)
+ V
F
± V
O
V
I(min)
+
I
(L1)(PP)
2
)
)
(
D
=
±V
O
+ V
F
±V
O
+ V
F
+ V
I(min)
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Check the Internal Switch S1
3
SLVA721A–February 2017–Revised August 2017
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Copyright © 2017, Texas Instruments Incorporated
Basic Calculation of an Inverting Buck-Boost Power Stage
In order to design each external component and to analyze the IC capabilities, the following parameters
must be prepared:
Table 1. Design Parameters
Description Parameter Unit
Input voltage range V
I(min)
to V
IM
V
Output voltage V
O
V
Maximum average output current I
OM
A
Forward voltage drop of the rectifier diode V
F
V
Allowed inductor current ripple I
(L1)(PP)
mA
Recommended Inductance Range (data sheet) L1 µH
Minimum switching current limit of internal switch S1 (data sheet) I
(SW)(min)(lim)
A
Switching frequency of the internal switch S1 (data sheet) f
(SW)
MHz
As for all inductive converters one of the essential formulas is the steady state duty cycle. This can be
derived from the inductor volt-second balance and the capacitor charge balance. For a robust design it is
recommended to calculate the worst-case scenario. For the inverting buck-boost this means the
maximum duty cycle D present at the minimum input voltage. It is specified as:
(1)
Rearranging Equation 1 provides the DC conversion ratio V
O
/ V
I
:
(2)
2 Check the Internal Switch S1
In the first step it is important to evaluate if the internal switch S1 can withstand the output current
requirement of the application. The minimum switching current limit I
(SW)(min)(lim)
of the internal switch S1 of
the chosen converter must be higher or equal to the maximum switching current I
(SW)M
that is defined as:
(3)
It is also possible to calculate the maximum output current I
OM
that the converter can achieve by
rearranging Equation 3, as:
(4)
The maximum voltage stress that the switch must withstand is V
(SW)M
and can be calculated with:
(5)
3 Select the Inductor
The next step is to select the required inductance. If the inductance range is not limited by the IC you can
estimate the required inductance based on the well-known differential equation:
(6)
The average inductor current I
(L1)(AV)
is calculated by:
(7)
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