SC411 datasheet(13/27 Pages) SEMTECH

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SC411

POWER MANAGEMENT

Application Information (Cont.)

and,

From these values of tON we can calculate the nominal

switching frequency as follows:

and,

ON is generated by a one-shot comparator that samples

BAT via RtON, converting this to a current. This current is

used to charge an internal 3.3pF capacitor to V

OUT. The

equations above reﬂect this along with any internal com-

ponents or delays that inﬂuence t

ON. For our example we

select R

tON = 1MΩ:

ON_VBAT(MIN) = 563ns and tON_VBAT(MAX) = 255ns

fSW_VBAT(MIN) = 266kHz and fSW_VBAT(MAX) = 235kHz

Now that we know t

ON we can calculate suitable values for

the inductor. To do this we select an acceptable inductor

ripple current. The calculations below assume 50% of I

OUT

which will give us a starting place.

and,

For our example:

VBAT(MIN) = 1.3μH and LVBAT(MAX) = 1.6μH

We will select an inductor value of 2.2μH to reduce the

ripple current, which can be calculated as follows:

()Hz

)

MIN

(

VBAT

)

MIN

(

BAT

OUT

)

MIN

(

VBAT

•

()Hz

)

MAX

(

VBAT

)

MAX

(

BAT

OUT

)

MAX

(

VBAT

•

and,

For our example:

RIPPLE_VBAT(MIN) = 1.74AP-P and IRIPPLE_VBAT(MAX) = 2.18AP-P

From this we can calculate the minimum inductor current

rating for normal operation:

For our example:

INDUCTOR(MIN) = 7.1A(MIN)

Next we will calculate the maximum output capacitor

equivalent series resistance (ESR). This is determined by

calculating the remaining static and transient tolerance

allowances. Then the maximum ESR is the smaller of the

calculated static ESR (R

ESR_ST(MAX)) and transient ESR

ESR_TR(MAX)):

Where ERR

ST is the static output tolerance and ERRDC is

the DC error. The DC error will be 1.2% plus the tolerance

of the feedback resistors, thus 2.2% total for 1% feedback

resistors.

For our example:

ERR

ST = 48mV and ERRDC = 26.4mV, therefore,

ESR_ST(MAX) = 19.8mΩ

Where ERR

TR is the transient output tolerance. Note that

this calculation assumes that the worst case load tran-

sient is full load. For half of full load, divide the I

OUT term

by 2.

)

MIN

(

)

MAX

(

VBAT

RIPPLE

)

MAX

(

OUT

)

MIN

(

INDUCT OR

()

Ohms

ERR

)

MAX

(

VBAT

RIPPLE

)

MAX

(

ESR

•

−

()

Ohms

ERR

)

MAX

(

VBAT

RIPPLE

OUT

)

MAX

(

ESR

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−

tON_VBAT(MAX) = 3.3 10

-12

RtON + 37 103

VOUT

VBAT(MAX) + 50 10

-9

LVBAT(MIN) = VBAT(MIN) VOUT

tON_VBAT(MIN)

0.5 IOUT

LVBAT(MAX) = VBAT(MAX) VOUT

tON_VBAT(MAX)

0.5 IOUT

tON_VBAT(MIN)

AP-P

IRIPPLE_VBAT(MIN) = VBAT(MIN) VOUT

AP-P

IRIPPLE_VBAT(MAX) = VBAT(MAX) VOUT

tON_VBAT(MAX)

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