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NX2415

TWO PHASE SYNCHRONOUS PWM CONTROLLER WITH INTEGRATED FET DRIVER AND DIFFERENTIAL CURRENT SENSE

Microsemi Corporation 

NX2415

Based On Transient Requirement

Typically, the output voltage droop during transient

is specified as:

∆VDROOP <∆VTRAN @ step load DISTEP

During the transient, the voltage droop during the

transient is composed of two sections. One Section is

dependent on the ESR of capacitor, the other section is

a function of the inductor, output capacitance as well as

input, output voltage. For example, overshoot caused by

DISTEP transient load which is from high load to low load,

can be estimated as the following equation,if assuming

the bandwidth of system is high enough.

∆Vovershoot

=

ESR × ∆Istep

+

VOUT

2 × L × COUT

× τ2

...(6)

where τ is the a function of capacitor, etc.

τ

=

0LEFVF ×iOfU∆TIsLtepEF−F

≤ Lcrit

ESR ×

COUT

where

if LEFF ≥ Lcrit

...(7)

LEFF

=

LOUT

N

=

0.68uH

2

= 0.34uH

Lcrit

=

ESR × COUT × VOUT

∆Istep

=

ESR E × CE × VOUT

∆Istep

...(8)

where ESRE and CE represents ESR and capaci-

tance of each capacitor if multiple capacitors are used

in parallel.

The above equation shows that if the selected out-

put inductor is smaller than the critical inductance, the

voltage droop or overshoot is only dependent on the ESR

of output capacitor. For low frequency capacitor such

as electrolytic capacitor, the product of ESR and ca-

pacitance is high and L ≤ Lcrit is true. In that case, the

transient spec is dependent on the ESR of capacitor.

In most cases, the output capacitors are multiple

capacitors in parallel. The number of capacitors can be

calculated by the following

N = ESR E × ∆Istep +

VOUT

× τ2

∆Vtran

2 × L × CE × ∆Vtran

where

...(9)

τ

=

0LEFFV×iOfU∆TIsLtepEF−F

≤ Lcrit

ESRE

×

CE

if LEFF ≥ Lcrit ...(10)

For example, assume voltage droop during transient

is 120mV for 30A load step.

If the OS-CON capacitors (1000uF, 7mΩ ) is used,

the critical inductance is given as

Lcrit

=

ESR E × CE × VOUT

∆Istep

=

7mΩ ×1000µF×1.2V = 0.28µH

30A

The effective inductor value is 0.34uH which is big-

ger than critical inductance. In that case, the output volt-

age transient not only dependent on the ESR, but also

capacitance.

number of capacitors is

τ

=

LEFF × ∆Istep

VOUT

− ESRE

× CE

= 0.34µH × 30A − 7mΩ ×1000µF = 1.5us

1.2V

N = ESRE × ∆Istep +

VOUT

× τ2

∆Vtran

2× LEFF × CE × ∆Vtran

= 7mΩ×30A +

120mV

1.2V

× (1.5us)2

2 × 0.34µH×1000µF ×120mV

= 1.78

The number of capacitors has to satisfied both ripple

and transient requirement. Overall, we can choose N=2.

It should be considered that the proposed equa-

tion is based on ideal case, in reality, the droop or over-

shoot is typically more than the calculation. The equa-

tion gives a good start. For more margin, more capaci-

tors have to be chosen after the test. Typically, for high

frequency capacitor such as high quality POSCAP es-

pecially ceramic capacitor, 20% to 100% (for ceramic)

more capacitors have to be chosen since the ESR of

capacitors is so low that the PCB parasitic can affect

the results tremendously. More capacitors have to be

selected to compensate these parasitic parameters.

Rev.4.8

9

05/06/08

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