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Application details L6731B
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6 Application details
6.1 Inductor design
The inductance value is defined by a compromise between the transient response time, the
efficiency, the cost and the size. The inductor has to be calculated to sustain the output and the
input voltage variation to maintain the ripple current (∆I
L
) between 20% and 30% of the
maximum output current. The inductance value can be calculated with the following
relationship:
Where F
SW
is the switching frequency, Vin is the input voltage and Vout is the output voltage.
Increasing the value of the inductance reduces the ripple current but, at the same time,
increases the converter response time to a load transient. If the compensation network is well
designed, during a load transient the device is able to set the duty cycle to 100% or to 0%.
When one of these conditions is reached, the response time is limited by the time required to
change the inductor current. During this time the output current is supplied by the output
capacitors. Minimizing the response time can minimize the output capacitor size.
6.2 Output capacitors
The output capacitors are basic components for the fast transient response of the power
supply. They depend on the output voltage ripple requirements, as well as any output voltage
deviation requirement during a load transient. During a load transient, the output capacitors
supply the current to the load or absorb the current stored in the inductor until the converter
reacts. In fact, even if the controller recognizes immediately the load transient and sets the duty
cycle at 100% or 0%, the current slope is limited by the inductor value. The output voltage has
a first drop due to the current variation inside the capacitor (neglecting the effect of the ESL):
Moreover, there is an additional drop due to the effective capacitor discharge or charge that is
given by the following formulas:
Formula (4) is valid in case of positive load transient while the formula (5) is valid in case of
negative load transient. D
MAX
is the maximum duty cycle value that in the L6731D is 100%. For
a given inductor value, minimum input voltage, output voltage and maximum load transient, a
maximum ESR and a minimum Cout value can be set. The ESR and Cout values also affect
the static output voltage ripple. In the worst case the output voltage ripple can be calculated
with the following formula:
Usually the voltage drop due to the ESR is the biggest one while the drop due to the capacitor
discharge is almost negligible.
Vin
Vout
IFsw
VoutVin
L
L
⋅
∆⋅
≅
(2)
ESRIoutVout
ESR
⋅∆=∆
(3)
)maxmin,(2
2
VoutDVinCout
LIout
Vout
COUT
−⋅⋅⋅
⋅∆
=∆
(4)
VoutCout
LIout
Vout
COUT
⋅⋅
⋅∆
=∆
2
2
(5)
)
8
1
(
FswCout
ESRIVout
L
⋅⋅
+⋅∆=∆
(6)
