SC2441ITSTRT View Datasheet(PDF) - Semtech Corporation

Part Name

Description

MFG CO.

SC2441ITSTRT

Very Low Input Voltage 2-Phase Synchronous Step-down Controllers with Step-up Converter

Semtech Corporation 

SC2441

POWER MANAGEMENT

Applications Information (Cont.)

∫ vo (t) =

Vo

+

1

Co

t

ib (t)dt + Lesl

0

dib (t)

dt

+

R esr ib

(t).

This basic equation illustrates the effects of ESR, ESL and

Co on the output voltage.

The first term is the DC voltage across Co at time t=0. The

second term is the ripple-voltage caused by the inductor

ripple-current. The third term is the voltage ripple due to

ESL and the fourth term is the voltage ripple due to ESR.

The total output voltage ripple is then a vector sum of the

last three terms.

Since the inductor current is a triangular waveform with

peak-to-peak value δ*Io, the ripple-voltage caused by

inductor current ripples is

∆v C

≈

δIo

8Cofs

.

The ripple-voltage due to ESL is

∆v ESL

= Leslfs

δIo

D

and the ESR ripple-voltage is

∆vESR = Resr δIo.

Aluminum capacitors (e.g. electrolytic, solid OS-CON,

POSCAP, tantalum) have high capacitances and low ESL’s.

The ESR has the dominant effect on the output ripple

voltage. It is therefore very important to minimize the ESR.

When determining the ESR value, both the steady state

ripple-voltage and the dynamic load transient need to be

considered. To keep the steady state output ripple-voltage

< ∆Vo, the ESR should satisfy

R esr1

<

∆Vo

δIo

.

To limit the dynamic output voltage overshoot/undershoot

within α (say 3%) of the steady state output voltage) under

0 to full load current swing, the ESR value should be

R esr 2

<

αVo

Io

.

The required ESR value of the output capacitors should

be

Resr = min{Resr1,Resr2 }.

In the aluminum capacitor selection, the working voltage

rating is normally suggested to be greater than 1.5Vo.

The allowable current ripple (RMS) should be greater than

δIo .

23

Usually it is necessary to have several capacitors of the

same type in parallel to satisfy the ESR requirement. The

voltage ripple cause by the capacitor charge/discharge

should be an order of magnitude smaller than the voltage

ripple caused by the ESR. To guarantee this, the

capacitance should satisfy

Co

>

10

2πfsR esr

.

In many application circuits, several low ESR ceramic

capacitors are added in parallel with the aluminum

capacitors to further reduce ESR and improve high

frequency decoupling. Since the capacitances and the

ESR’s of ceramic and aluminum capacitors are different,

the following remarks are made to clarify some practical

issues.

Remark 1: High frequency ceramic capacitors may not carry

most of the ripple current. It also depends on the capacitor

value. Only when the capacitor value is set properly, the

effect of ceramic capacitor low ESR starts to be significant.

For example, if a 10µF, 4mΩ ceramic capacitor is

connected in parallel with 2x1500µF, 90mΩ electrolytic

capacitors, the ripple current in the ceramic capacitor is

only about 42% of the current in the electrolytic capacitors

at the ripple frequency. If a 100µF, 2mΩ ceramic capacitor

is used, the ripple current in the ceramic capacitor will be

about 4.2 times of that in the electrolytic capacitors. When

two 100µF, 2mΩ ceramic capacitors are used, the current

ratio increases to 8.3. In this case most of the ripple

current flows in the ceramic decoupling capacitor. The ESR

of the ceramic capacitors will then determine the output

ripple-voltage.

Remark 2: The total equivalent capacitance of the filter

bank is not simply the sum of all the paralleled capacitors.

The total equivalent ESR is not simply the parallel

combination of all the individual ESR’s either. Instead they

should be calculated using the following formulae.

Ceq(ω) :=

(R1a + R1b )2 ω2C1a2C1b2 + (C1a + C1b )2

(R1a2C1a + R1b2C1b )ω2C1aC1b + (C1a + C1b )

 2005 Semtech Corp.

15

www.semtech.com

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