Application details

L6731B

18/24

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

maximum output current. The inductance value can be calculated with the following

relationship:

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

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

I

Fsw

Vout

Vin

L

L

⋅

∆

⋅

−

≅

(2)

ESR

Iout

Vout

ESR

⋅

∆

=

∆

(3)

)

max

min

,

(

2

2

Vout

D

Vin

Cout

L

Iout

Vout

COUT

−

⋅

⋅

⋅

⋅

∆

=

∆

(4)

Vout

Cout

L

Iout

Vout

COUT

⋅

⋅

⋅

∆

=

∆

2

2

(5)

)

8

1

(

Fsw

Cout

ESR

I

Vout

L

⋅

⋅

+

⋅

∆

=

∆

(6)