ripple

eq

ripple

V

Z

I

=

2

cap

eff

1

Z

ESR

sw C

=

+

×

×

f

p

elec

eq

cer

elec

eq

Z

×

=

-

Z

Z

Z

Z

(

)

2

cer

eff

cer

cer

1

C

sw

Z

ESR

=

×

×

-

f

p

(

)

(

)

cer

eff

C

Vrating

C

Vrating Vout

×

=

-

(

)

12

f

×

-

=

×

×

×

Vout

Vinmax

Vout

Icorms

Vinmax L1

sw

1

capx

COxRMS

CORMS

sum

Z

I

I

Z

æ

ö

=

×

-

ç

÷

è

ø

TPS54521

SLVS981 – JUNE 2010

www.ti.com

Where

ΔIout is the change in output current, fsw is the regulator's switching frequency and ΔVout is the

allowable change in the output voltage. For this example, the transient load response is specified as a 3%

change in Vout for a load step of 5A. Using these numbers (

ΔIout = 5.0 A and ΔVout= 0.03 x 3.3 = 0.099 V)

gives a minimum capacitance of 210 mF.

The low cost, small size electrolytic capacitor chosen is Chemi-con’s EKZE6R3LL331MF11D (330 mF). This

capacitor has an ESR of 125.2 m

Ω. The ceramic capacitor’s ESR is estimated at 4 mΩ, providing low impedance

at the switching frequency to diminish the output voltage ripple. In order to determine the capacitance needed for

the ceramic capacitor, the required output impedance at the switching frequency must be calculated. Equation 23

yields 39.3 m

Ω for this design.

(23)

For each capacitor, the impedance at the switching frequency is the sum of their ESR and the absolute value of

their reactive impedance. For the electrolytic capacitor, Equation 24 yields an impedance of 126.2 m

Ω.

(24)

maximum impedance for the ceramic capacitor is calculated using Equation 25. For this design, this equation

yields 57 m

Ω.

(25)

Equation 26 can be used to calculate the effective capacitance required for the ceramic capacitor. For this

design, 6.25 uF are needed to meet the impedance requirement, which will meet the output voltage ripple

specification.

(26)

The capacitance of the ceramic capacitor is highly dependent on the DC output voltage. Equation 27 is used to

select the output capacitance required based on its voltage rating. For a 10 V ceramic capacitor, the minimum

standard value that meets the ripple specification is 10 mF. Using Equation 24, the impedance of this capacitor is

53.5 m

Ω at the switching frequency of 480 kHz. This is less (better) than the required maximum of 57 mΩ

needed to meet the output voltage ripple requirement.

(27)

Capacitors generally have limits to the amount of ripple current they can handle without failing or producing

excessive heat. An output capacitor that can support the inductor ripple current must be specified. Some

capacitor data sheets specify the RMS (Root Mean Square) value of the maximum ripple current. Equation 28

can be used to calculate the RMS ripple current the output capacitors need to support. For this application,

Equation 28 yields 485mA.

(28)

Knowing their impedance, the RMS current through each capacitor can be calculated using Equation 29 with

capacitors are 144.4 mA and 340.6 mA, respectively.

This is well within the ripple current rating of each

capacitor.

(29)

24

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