CS51313 datasheet(12/20 Pages) CHERRY

12 / 20 page

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

rent transient can be verified by the following formula:

∆VOUT = ∆VESR + ∆VESL + ∆VCAP

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 =

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 =

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 fre-

quency 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 =

− TON,

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

the Off-Time, TOFF, above:

COFF =

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 induc-

tor 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 satu-

rating, 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 com-

monly 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 =

where

VIN = input voltage;

VOUT = output voltage;

tTR = output voltage transient response time (assigned

by the designer);

∆I = load transient.

The inductor ripple current can then be determined:

∆IL =

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).

ESRCAP

ESRMAX

∆VOUT

∆IL

∆VOUT

ESRMAX

VOUT × TOFF

(VIN − VOUT) × tTR

∆Ι

Period × (1 − D)

3980

FSW

Duty Cycle

FSW

VOUT + (VHFET + VL + VDROOP)

VIN + VLFET − VHFET − VL

Application Information: continued

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