SC2542
POWER MANAGEMENT
Applications Information (Cont.)
Aluminum capacitors (e.g. electrolytic) have high capaci-
tances and low ESL. The ESR has the dominant effect
on the output ripple voltage. It is therefore very impor-
tant to minimize the ESR. Other types to choose are
solid OS-CON, POSCAP, and tantalum.
When determining the ESR value, both the steady state
ripple-voltage and the dynamic load transient need to be
considered. To meet the steady state output ripple-volt-
age spec, the ESR should satisfy:
RESR1
<
∆VO
δIO
To limit the dynamic output voltage overshoot/under-
shoot within a (say 3%) of the steady state output volt-
age from no load to full load, the ESR value should sat-
isfy:
RESR2
<
3%VO
IO
Then, the required ESR value of the output capacitors
should be:
Resr = min{Resr1,Resr2 }.
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 10uF, 4mÙ ceramic
capacitor is connected in parallel with 2x1500uF, 90mÙ
electrolytic capacitors, the ripple current in the ceramic
capacitor is only about 42% of the current in the electro-
lytic capacitors at the ripple frequency. If a 100uF, 2mÙ
ceramic capacitor is used, the ripple current in the ce-
ramic capacitor will be about 4.2 times of that in the
electrolytic capacitors. When two 100uF, 2mÙ ceramic
capacitors are used, the current ratio increases to 8.3.
In this case most of the ripple current flows in the ce-
ramic decoupling capacitor. The ESR of the ceramic ca-
pacitors 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 capaci-
tors. The total equivalent ESR is not simply the parallel
combination of all the individual ESR either. Instead they
should be calculated using the following formula.
CEQ(ω )
=
( R1A + R1B )2 ω 2C1A2C1B 2 + (C1A + C 1B )2
( R1A2C1A + R1B 2C1B )ω 2C1AC1B + (C1A + C1B )
The voltage rating of aluminum capacitors should be at
least 1.5Vo. The RMS current ripple rating should also
be greater than: δ IO
23
Usually it is necessary to have several capacitors of the
same type in parallel to satisfy the ESR requirement. The
voltage ripple caused by the capacitor charge/discharge
should be an order of magnitude smaller than the volt-
age ripple caused by the ESR. To guarantee this, the ca-
pacitance should satisfy:
CO
>
2π
10
fs RESR
In many applications, several low ESR ceramic capaci-
tors are added in parallel with the aluminum capacitors
in order to further reduce ESR and improve high fre-
quency decoupling. Because the values of capacitance
and ESR are usually different in ceramic and aluminum
capacitors, the following remarks are made to clarify
some practical issues.
CEQ (ω )
=
R1A R1B ( R1A
( R1 A
+ R1B )ω 2C1A2C1B 2 + ( R 1B C1B2 + R1AC1A2 )
+ R1B )2ω 2C1A2C1B 2 + (C1A + C1B )2
where R1a and C1a are the ESR and capacitance of elec-
trolytic capacitors, and R1b and C1b are the ESR and
capacitance of the ceramic capacitors, respectively (Fig-
ure 13)
C1a
C1b
Ceq
R1a
R1b
Req
Figure 14. Equivalent RC branch.
2005 Semtech Corp.
16
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