(

)

OPPMAX

max

LPP

SW

O

D

0.5

V

ESR

=

I

4

F

C

-

-

´

´

(13)

(

)

12

OUT

IN(MAX)

OUT

COUT(RMS)

IN(MAX)

OUT

SW

C

V

× V

V

1

I

=

×

V

× L

× F

× N

æ

ö

-

ç

÷

ç

÷

è

ø

(14)

COMPENSATION COMPONENTS

ggm

REF

DC

O

V

V

G

=

V

´

(15)

(

)

PO

OO

Z

V

= 1/ 2

R

C

p

´

´

´

(16)

(

)

Z1

Z

Z

F

= 1/ 2

R

C

p

´

´

´

(17)

(

)

P1

Z

P

F

= 1/ 2

R

C

p

´

´

´

(18)

TPS54331

The maximum ESR of the output capacitor can be determined from the amount of allowable output ripple as

specified in the initial design parameters. The contribution to the output ripple voltage due to ESR is the inductor

ripple current times the ESR of the output filter, so the maximum specified ESR as listed in the capacitor data

sheet is given by Equation 13

output capacitor is given by Equation 14.

For this design example, two 47-

µF ceramic output capacitors are chosen for C8 and C9. These are TDK

C3216X5R0J476MT, rated at 6.3 V with a maximum ESR of 2 m

Ω and a ripple current rating in excess of 3 A.

The calculated total RMS ripple current is 161 mA ( 80.6 mA each) and the maximum total ESR required is 43

m

Ω. These output capacitors exceed the requirements by a wide margin and will result in a reliable,

high-performance design. it is important to note that the actual capacitance in circuit may be less than the

catalog value when the output is operating at the desired output of 3.3 V The selected output capacitor must be

rated for a voltage greater than the desired output voltage plus ½ the ripple voltage. Any derating amount must

also be included. Other capacitor types work well with the TPS54331, depending on the needs of the application.

The external compensation used with the TPS54331 allows for a wide range of output filter configurations. A

large range of capacitor values and types of dielectric are supported. The design example uses ceramic X5R

dielectric output capacitors, but other types are supported.

A Type II compensation scheme is recommended for the TPS54331. The compensation components are chosen

to set the desired closed loop cross over frequency and phase margin for output filter components. The type II

compensation has the following characteristics; a dc gain component, a low frequency pole, and a mid frequency

zero / pole pair.

The dc gain is determined by Equation 15:

Where:

The low-frequency pole is determined by Equation 16:

The mid-frequency zero is determined by Equation 17:

And, the mid-frequency pole is given by Equation 18:

The first step is to choose the closed loop crossover frequency. In general, the closed-loop crossover frequency

should be less than 1/8 of the minimum operating frequency, but for the TPS54331it is recommended that the

maximum closed loop crossover frequency be not greater than 25 kHz. Next, the required gain and phase boost

of the crossover network needs to be calculated. By definition, the gain of the compensation network must be the

inverse of the gain of the modulator and output filter. For this design example, where the ESR zero is much

higher than the closed loop crossover frequency, the gain of the modulator and output filter can be approximated

by Equation 19:

Copyright © 2008, Texas Instruments Incorporated

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