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higher inductor values will result in less than the maximum

ripple current.

LoMIN +

(VIN * VOUT) @ VOUT

(a @ IO,MAX @ VIN @ fSW)

(3)

a is the ripple current as a percentage of the maximum

output current per phase (

a = 0.15 for ±15%, a = 0.25 for

±25%, etc.). If the minimum inductor value is used, the

inductor current will swing ±

a% about its value at the center

(1/2 the DC output current for a two−phase converter).

Therefore, for a two−phase converter, the inductor must be

designed or selected such that it will not saturate with a peak

current of (1 +

a) • IO,MAX/2.

The maximum inductor value is limited by the transient

response of the converter. If the converter is to have a fast

transient response then the inductor should be made as small

as possible. If the inductor is too large its current will change

too slowly, the output voltage will droop excessively, more

bulk capacitors will be required, and the converter cost will

be increased. For a given inductor value, its interesting to

determine the times required to increase or decrease the

current.

For increasing current:

DtINC + Lo @ DIO (VIN * VOUT)

(3.1)

For decreasing current:

DtDEC + Lo @ DIO (VOUT)

(3.2)

For typical processor applications with output voltages

less than half the input voltage, the current will be increased

much more quickly than it can be decreased. It may be more

difficult for the converter to stay within the regulation limits

when the load is removed than when it is applied − excessive

overshoot may result.

The output voltage ripple can be calculated using the

output inductor value derived in this Section (LoMIN), the

number of output capacitors (NOUT,MIN) and the per

capacitor ESR determined in the previous Section:

VOUT,P−P + (ESR per cap NOUT,MIN) @

(VIN * #Phases @ VOUT) @ D (LoMIN @ fSW)

(4)

This formula assumes steady−state conditions with no

more than one phase on at any time. The second term in

Equation 4 is the total ripple current seen by the output

capacitors. The total output ripple current is the “time

summation” of the two individual phase currents that are

180 degrees out−of−phase. As the inductor current in one

phase ramps upward, current in the other phase ramps

downward and provides a canceling of currents during part

of the switching cycle. Therefore, the total output ripple

current and voltage are reduced in a multi−phase converter.

3. Input Capacitor Selection

The choice and number of input capacitors is primarily

determined by their voltage and ripple current ratings. The

designer must choose capacitors that will support the worst

case input voltage with adequate margin. To calculate the

number of input capacitors one must first determine the total

RMS input ripple current. To this end, begin by calculating

the average input current to the converter:

IIN,AVG + IO,MAX @ D h

(5)

where:

D is the duty cycle of the converter, D = VOUT/VIN;

h is the specified minimum efficiency;

IO,MAX is the maximum converter output current.

The input capacitors will discharge when the control FET

is ON and charge when the control FET is OFF as shown in

Figure 14.

IC,MAX

IC,MIN

0 A

−IIN,AVG

FET On,

Caps Discharging

FET Off,

Caps Charging

tON

T/2

DIC,IN = IC,MAX − IC,MIN

Figure 14. Input Capacitor Current for a

Two−Phase Converter

The following equations will determine the maximum and

minimum currents delivered by the input capacitors:

IC,MAX + ILo,MAX h * IIN,AVG

(6)

IC,MIN + ILo,MIN h * IIN,AVG

(7)

ILo,MAX is the maximum output inductor current:

ILo,MAX + IO,MAX 2 ) DILo 2

(8)

ILo,MIN is the minimum output inductor current:

ILo,MIN + IO,MAX 2 * DILo 2

(9)

DILo is the peak−to−peak ripple current in the output

inductor of value Lo:

DILo + (VIN * VOUT) @ D (Lo @ fSW)

(10)

For the two−phase converter, the input capacitor(s) RMS

current is then:

ICIN,RMS + [2D @ (IC,MIN2 ) IC,MIN @ DIC,IN

) DIC,IN2 3) ) IIN,AVG2 @ (1 * 2D)]1 2

(11)

Select the number of input capacitors (NIN) to provide the

RMS input current (ICIN,RMS) based on the RMS ripple

current rating per capacitor (IRMS,RATED):

NIN + ICIN,RMS IRMS,RATED

(12)

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