(

)

-

=

×

×

Vinmin

Vout

Vout

Icirms

Iout

Vinmin

Vinmin

(

)

12

f

×

-

=

×

×

×

Vout

Vinmax

Vout

Icorms

Vinmax L1

sw

((

)

)

rated

out

rated

eff

rated

V

V

C

C

V

-

×

=

2

cap

eff

1

Z

ESR

sw C

=

+

×

×

f

p

ripple

eq

ripple

V

Z

I

=

2

f

× D

>

× D

Iout

Co

sw

Vout

TPS54521

SLVS981C – JUNE 2010 – REVISED AUGUST 2013

www.ti.com

change in load current and output voltage and adjust the duty cycle to react to the change. The output capacitor

must be sized to supply the extra current to the load until the control loop responds to the load change. The

output capacitance must be large enough to supply the difference in current for 2 clock cycles while only allowing

a tolerable amount of droop in the output voltage. Equation 22 shows the minimum output capacitance necessary

to accomplish this.

(22)

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 1%

change in Vout for a load step of 3A. Using these numbers (

ΔIout = 3.0 A and ΔVout= 0.01 x 5 = 0.05 V) gives a

minimum capacitance of 171

μF.

The next consideration is the maximum impedance at the switching frequency required to meet the output

voltage ripple specification. The ripple current in the inductor is absorbed by the output capacitor and creates a

ripple voltage across the capacitor's ESR and reactive impedance. Equation 23 calculates the maximum

impedance to meet the ripple voltage specification of 75 mV. Equation 23 yields 49 m

Ω for this design.

(23)

This impedance at the switching frequency is the sum of its ESR and the absolute value of its reactive

impedance. Equation 24 calculates the impedance at the switching frequency for any capacitor and must yield a

resultant Zcap less than the Zeq found in Equation 23 to meet the output voltage ripple specification. The

6TPB220M (220 µF, 40 m

Ω ESR) Poscap from Sanyo meets the impedance requirements of Equation 23 and

the capacitance requirements of Equation 22.

(24)

Ceff in Equation 24 is the effective capacitance of the output capacitor. This capacitance is equal to the rated

capacitance for most capacitor types, except for ceramics. The capacitance of ceramic capacitors is highly

dependent on the DC output voltage due to the DC bias effect, which reduces the effective capacitance as the

DC voltage on the capacitor is increased. Equation 25 is used to estimate the effective capacitance of a ceramic

capacitor, based on its voltage rating, the output voltage, and its nominal capacitance.

(25)

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 26

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

Equation 26 yields 441 mA, which is less than the output capacitor's rating of 2 A.

(26)

Input Capacitor Selection

The TPS54521 requires a high quality ceramic, type X5R or X7R, input decoupling capacitor of roughly 4.7 µF on

each input voltage rail (VIN and PVIN). In some applications, additional bulk capacitance may also be required

for the PVIN input. 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

TPS54521. The input ripple current for this design, using Equation 27, is 2.42 A.

(27)

24

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