1

1

8

f

>

×

×

Co

Voripple

sw

Iripple

<

Voripple

Resr

Iripple

(

)

12

f

×

-

=

×

×

×

Vout

Vinmax

Vout

Icorms

Vinmax L1

sw

(

)

-

=

×

×

Vinmin

Vout

Vout

Icirms

Iout

Vinmin

Vinmin

0.25

f

×

D

=

×

Ioutmax

Vin

Cin

sw

TPS54821

SLVSB14

– OCTOBER 2011

www.ti.com

Where

ΔIout is the change in output current, Fsw is the regulators switching frequency and ΔVout is the

allowable change in the output voltage. For this example, the transient load response is specified as a 7%

change in Vout for a load step of 4 A. For this example,

ΔIout = 4 A and ΔVout = 0.07 x 3.3 = 0.231 V. Using

these numbers gives a minimum capacitance of 72.2

μF. This value does not take the ESR of the output

capacitor into account in the output voltage change. For ceramic capacitors, the ESR is usually small enough to

ignore in this calculation.

Equation 23 calculates the minimum output capacitance needed to meet the output voltage ripple specification.

Where fsw is the switching frequency, Vripple is the maximum allowable output voltage ripple, and Iripple is the

inductor ripple current. In this case, the maximum output voltage ripple is 33mV. Under this requirement,

Equation 23 yields 14.6

µF.

(23)

Equation 24 calculates the maximum ESR an output capacitor can have to meet the output voltage ripple

specification. Equation 24 indicates the ESR should be less than 17.9 m

Ω. In this case, the ceramic caps’ ESR is

much smaller than 17.9 m

Ω.

(24)

Additional capacitance de-ratings for aging, temperature and DC bias should be factored in which increases this

minimum value. For this example, 2 x 47

μF 10 V X5R ceramic capacitor with 3 mΩ of ESR are used. Capacitors

generally have limits to the amount of ripple current they can handle without failing or producing excess 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 25 can be used to calculate

the RMS ripple current the output capacitor needs to support. For this application, Equation 25 yields 485mA.

(25)

Input Capacitor Selection

The TPS54821 requires a high quality ceramic, type X5R or X7R, input decoupling capacitor of at least 4.7

µF of

effective capacitance on the PVIN input voltage pins and 4.7

µF on the Vin input voltage pin. In some

applications additional bulk capacitance may also be required for the PVIN input. The effective capacitance

includes any DC bias effects. The voltage rating of the input capacitor must be greater than the maximum input

voltage. The capacitor must also have a ripple current rating greater than the maximum input current ripple of the

TPS54821. The input ripple current can be calculated using Equation 26.

(26)

The value of a ceramic capacitor varies significantly over temperature and the amount of DC bias applied to the

capacitor. The capacitance variations due to temperature can be minimized by selecting a dielectric material that

is stable over temperature. X5R and X7R ceramic dielectrics are usually selected for power regulator capacitors

because they have a high capacitance to volume ratio and are fairly stable over temperature. The output

capacitor must also be selected with the DC bias taken into account. The capacitance value of a capacitor

decreases as the DC bias across a capacitor increases. For this example design, a ceramic capacitor with at

least a 25 V voltage rating is required to support the maximum input voltage. For this example, one 10

μF and

one 4.7

µF 25 V capacitors in parallel have been selected as the VIN and PVIN inputs are tied together so the

TPS54821 may operate from a single supply. The input capacitance value determines the input ripple voltage of

the regulator. The input voltage ripple can be calculated using Equation 27. Using the design example values,

Ioutmax = 8 A, Cin = 14.7

μF, Fsw=480 kHz, yields an input voltage ripple of 417 mV and a RMS input ripple

current of 3.94 A.

(27)

22

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