CS51312 datasheet(12/18 Pages) CHERRY

12 / 18 page

Application Information: continued

where

∆IL = inductor ripple current;

VOUT = output voltage;

TOFF = switch Off-Time;

L = inductor value.

The designer can now verify if the number of output

capacitors from step 2 will provide an acceptable output

voltage ripple (1% of output voltage is common). The for-

mula below is used:

∆IL =

Rearranging we have:

ESRMAX =

where

ESRMAX = maximum allowable ESR;

∆VOUT = 1% × VOUT = maximum allowable output volt-

age ripple ( budgeted by the designer );

∆IL = inductor ripple current;

VOUT = output voltage.

The number of output capacitors is determined by:

Number of capacitors =

where ESRCAP = maximum ESR per capacitor (specified in

manufacturer’s data sheet).

The designer must also verify that the inductor value

yields reasonable inductor peak and valley currents (the

inductor current is a triangular waveform):

IL(PEAK) = IOUT +

where

IL(PEAK) = inductor peak current;

IOUT = load current;

∆IL = inductor ripple current.

IL(VALLEY) = IOUT −

where IL(VALLEY) = inductor valley current.

Step 5: Selection of the Input Capacitors

These components must be selected and placed carefully to

yield optimal results. Capacitors should be chosen to pro-

vide acceptable ripple on the input supply lines. A key

specification for input capacitors is their ripple current rat-

ing. The input capacitor should also be able to handle the

input RMS current IIN(RMS).

The combination of the input capacitors CIN discharges

during the on-time.

The input capacitor discharge current is given by:

ICINDIS(RMS) =

where

ICINDIS(RMS) = input capacitor discharge current;

IL(PEAK) = inductor peak current;

IL(VALLEY) = inductor valley current.

CIN charges during the off-time, the average current

through the capacitor over one switching cycle is zero:

ICIN(CH) = ICIN(DIS) ×

where

ICIN(CH) = input capacitor charge current;

ICIN(DIS) = input capacitor discharge current;

D = Duty Cycle.

The total Input RMS current is:

ICIN(RMS) = (ICIN(DIS)2 × D) + (ICIN(CH)2 × (1 − D))

The number of input capacitors required is then deter-

mined by:

NCIN =

where

NCIN = number of input capacitors;

ICIN(RMS) = total input RMS current;

IRIPPLE = input capacitor ripple current rating (specified

in manufacturer’s data sheets).

The total input capacitor ESR needs to be determined in

order to calculate the power dissipation of the input capac-

itors:

ESRCIN =

where

ESRCIN = total input capacitor ESR;

ESRCAP = maximum ESR per capacitor (specified in

manufacturer’s data sheets);

NCIN = number of input capacitors.

Once the total ESR of the input capacitors is known, the

input capacitor ripple voltage can be determined using the

formula:

VCIN(RMS) = ICIN(RMS) × ESRCIN,

where

VCIN(RMS) = input capacitor RMS voltage;

ICIN(RMS) = total input RMS current;

ESRCIN = total input capacitor ESR.

The designer must determine the input capacitor power

loss in order to ensure there isn’t excessive power dissipa-

tion through these components. The following formula is

used:

PCIN(RMS) = ICIN(RMS)2 × ESRCIN

ESRCAP

NCIN

ICIN(RMS)

IRIPPLE

1 − D

(IL(PEAK)2 + (IL(PEAK) × IL(VALLEY)) + IL(VALLEY)2 × D

∆IL

ESRCAP

ESRMAX

∆VOUT

∆IL

∆VOUT

ESRMAX

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