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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. Thus, it may be

more difficult for the converter to stay within the regulation

limits when the load is removed than when it is applied and

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 four individual phase currents that are 90

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;

η 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 21.

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 4 ) DILo 2

(8)

ILo,MIN is the minimum output inductor current:

ILo,MIN + IO,MAX 4 * DILo 2

(9)

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

inductor of value Lo:

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

(10)

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

current is then:

ICIN,RMS + [4D @ (IC,MIN2 ) IC,MIN @ DIC,IN

) DIC,IN2 3) ) IIN,AVG2 @ (1 * 4D)]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)

For a four−phase converter with perfect efficiency (η = 1),

the worst case input ripple−current will occur when the

converter is operating at a 12.5% duty cycle. At this

operating point, the parallel combination of input capacitors

must support an RMS ripple current equal to 12.5% of the

converter’s DC output current. At other duty cycles, the

ripple−current will be less. For example, at a duty cycle of

either 6% or 19%, the four−phase input ripple−current will

be approximately 10% of the converter’s DC output current.

In general, capacitor manufacturers require derating to the

specified ripple−current based on the ambient temperature.

More capacitors will be required because of the current

derating. The designer should know the ESR of the input

capacitors. The input capacitor power loss can be calculated

from:

PCIN + ICIN,RMS2 @ ESR_per_capacitor NIN (13)

Low ESR capacitors are recommended to minimize losses

and reduce capacitor heating. The life of an electrolytic

capacitor is reduced 50% for every 10°C rise in the

capacitor’s temperature.

IC,MAX

IC,MIN

0 A

−IIN,AVG

FET On,

Caps Discharging

FET Off,

Caps Charging

tON

T/4

ΔIC,IN = IC,MAX − IC,MIN

Figure 21. Input Capacitor Current for a

Four−Phase Converter

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