CS51313 datasheet(15/23 Pages) ONSEMI

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CS51313

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where:

ΔtTR = the output voltage transient response time

(assigned by the designer);

ΔVCAP = output voltage deviation due to output capacitor

discharge;

ΔI = Load step.

The total change in output voltage as a result of a load

current transient can be verified by the following formula:

DVOUT + DVESR ) DVESL ) DVCAP

Step 3: Selection of the Duty Cycle,

Switching Frequency, Switch On−Time (TON)

and Switch Off−Time (TOFF)

The duty cycle of a buck converter (including parasitic

losses) is given by the formula:

Duty Cycle + D +

VOUT ) (VHFET ) VL ) VDROOP)

VIN ) VLFET * VHFET * VL

where:

VOUT = buck regulator output voltage;

VHFET = high side FET voltage drop due to RDS(ON);

VL = output inductor voltage drop due to inductor wire DC

resistance;

VDROOP = droop (current sense) resistor voltage drop;

VIN = buck regulator input voltage;

VLFET = low side FET voltage drop due to RDS(ON).

Step3a: Calculation of Switch On−Time

The Switch On−Time (time during which the switching

MOSFET in a synchronous buck topology is conducting) is

determined by:

TON +

Duty Cycle

FSW

where FSW = regulator switching frequency selected by the

designer.

Higher operating frequencies allow the use of smaller

inductor and capacitor values. Nevertheless, it is common to

select lower frequency operation because a higher frequency

results in lower efficiency due to MOSFET gate charge

losses. Additionally, the use of smaller inductors at higher

frequencies results in higher ripple current, higher output

voltage ripple, and lower efficiency at light load currents.

Step 3b: Calculation of Switch Off−Time

The Switch Off−Time (time during which the switching

MOSFET is not conducting) can be determined by:

TOFF + 1.0

FSW

* TON

The COFF capacitor value has to be selected in order to set

the Off−Time, TOFF, above:

COFF +

Period

(1.0 * D)

3980

where:

3980 is a characteristic factor of the CS51313;

D = Duty Cycle.

Step 4: Selection of the Output Inductor

The inductor should be selected based on its inductance,

current capability, and DC resistance. Increasing the

inductor value will decrease output voltage ripple, but

degrade transient response. There are many factors to

consider in selecting the inductor including cost, efficiency,

EMI and ease of manufacture. The inductor must be able to

handle the peak current at the switching frequency without

saturating, and the copper resistance in the winding should

be kept as low as possible to minimize resistive power loss.

There are a variety of materials and types of magnetic cores

that could be used for this application. Among them are

ferrites, molypermalloy cores (MPP), amorphous and

powdered iron cores. Powdered iron cores are very

commonly used. Powdered iron cores are very suitable due

to their high saturation flux density and have low loss at high

frequencies, a distributed gap and exhibit very low EMI.

The inductor value can be determined by:

L +

(VIN * VOUT)

tTR

where:

VIN = input voltage;

VOUT = output voltage;

tTR = output voltage transient response time (assigned by

the designer);

ΔI = load transient.

The inductor ripple current can then be determined:

DIL +

VOUT

TOFF

where:

ΔIL = 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 (1.0% of output voltage is common). The

formula below is used:

DIL + D

VOUT

ESRMAX

Rearranging we have:

ESRMAX + D

VOUT

DIL

where

ESRMAX = maximum allowable ESR;

ΔVOUT = 1.0% × VOUT = maximum allowable output

voltage ripple ( budgeted by the designer );

ΔIL = inductor ripple current;

VOUT = output voltage.

The number of output capacitors is determined by:

Number of capacitors +

ESRCAP

ESRMAX

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