LM2746MXAX datasheet(15/24 Pages) NSC

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Application Information (Continued)

Input Capacitor

The input capacitors in a Buck converter are subjected to

high stress due to the input current trapezoidal waveform.

Input capacitors are selected for their ripple current capabil-

ity and their ability to withstand the heat generated since that

ripple current passes through their ESR. Input rms current is

approximately:

The power dissipated by each input capacitor is:

where n is the number of capacitors, and ESR is the equiva-

lent series resistance of each capacitor. The equation above

indicates that power loss in each capacitor decreases rapidly

as the number of input capacitors increases. The worst-case

ripple for a Buck converter occurs during full load and when

the duty cycle (D) is 0.5. For this 3.3V to 1.2V design the

duty cycle is 0.364. For a 4A maximum load the ripple

current is 1.92A.

Output Inductor

The output inductor forms the first half of the power stage in

a Buck converter. It is responsible for smoothing the square

wave created by the switching action and for controlling the

output current ripple (

∆I

OUT). The inductance is chosen by

selecting between tradeoffs in efficiency and response time.

The smaller the output inductor, the more quickly the con-

verter can respond to transients in the load current. How-

ever, as shown in the efficiency calculations, a smaller in-

ductor requires a higher switching frequency to maintain the

same level of output current ripple. An increase in frequency

can mean increasing loss in the MOSFETs due to the charg-

ing and discharging of the gates. Generally the switching

frequency is chosen so that conduction loss outweighs

switching loss. The equation for output inductor selection is:

L = 1.6µH

Here we have plugged in the values for output current ripple,

input voltage, output voltage, switching frequency, and as-

sumed a 40% peak-to-peak output current ripple. This yields

an inductance of 1.6 µH. The output inductor must be rated

to handle the peak current (also equal to the peak switch

current), which is (I

OUT + 0.5*

∆I

OUT) = 4.8A, for a 4A design.

The Coilcraft DO3316P-222P is 2.2 µH, is rated to 7.4A

peak, and has a direct current resistance (DCR) of 12m

Ω.

After selecting an output inductor, inductor current ripple

should be re-calculated with the new inductance value, as

this information is needed to select the output capacitor.

Re-arranging the equation used to select inductance yields

the following:

IN(MAX) is assumed to be 10% above the steady state input

voltage, or 3.6V. The actual current ripple will then be 1.2A.

Peak inductor/switch current will be 4.6A.

Output Capacitor

The output capacitor forms the second half of the power

stage of a Buck switching converter. It is used to control the

output voltage ripple (

∆V

OUT) and to supply load current

during fast load transients.

In this example the output current is 4A and the expected

type of capacitor is an aluminum electrolytic, as with the

input capacitors. Other possibilities include ceramic, tanta-

lum, and solid electrolyte capacitors, however the ceramic

type often do not have the large capacitance needed to

supply current for load transients, and tantalums tend to be

more expensive than aluminum electrolytic. Aluminum ca-

pacitors tend to have very high capacitance and fairly low

ESR, meaning that the ESR zero, which affects system

stability, will be much lower than the switching frequency.

The large capacitance means that at the switching fre-

quency, the ESR is dominant, hence the type and number of

output capacitors is selected on the basis of ESR. One

simple formula to find the maximum ESR based on the

desired output voltage ripple,

∆V

OUT and the designed out-

put current ripple,

∆I

OUT, is:

In this example, in order to maintain a 2% peak-to-peak

output voltage ripple and a 40% peak-to-peak inductor cur-

rent ripple, the required maximum ESR is 20m

Ω. The Sanyo

20147791

FIGURE 11. Maximum Duty Cycle vs V

J = 125˚C

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