
16
2005 Semtech Corp.
www.semtech.com
POWER MANAGEMENT
Applications Information (Cont.)
SC2441
2
b
1
a
1
2
b
1
2
a
1
2
2
b
1
a
1
2
a
1
a
1
2
b
1
+
b
1
2
b
1
2
a
1
2
b
1
a
1
b
1
a
1
eq
)
C
C
(
C
C
)
R
R
(
)
C
R
C
R
(
+
C
C
)
R
R
(
R
R
:
ω
(
R
ω
+
+
+
ω
+
=
where R
and C
are the ESR and capacitance of
electrolytic capacitors, and R
and C
are the ESR and
capacitance of the ceramic capacitors respectively (Figure
7).
C1a
R1a
C1b
R1b
Ceq
Req
Figure 7. Equivalent RC branch.
Req and Ceq are both functions of frequency. For rigorous
design, the equivalent ESR should be evaluated at the
ripple frequency for voltage ripple calculation when both
ceramic and electrolytic capacitors are used. If R
= R
=
R
and C
= C
= C
1
, then R
eq
and C
eq
will be frequency-
independent and
R
eq
= 1/2 R
1
and C
eq
= 2C
1
.
Input Capacitor (C
in
)
The input supply to the converter usually comes from a
pre-regulator. Since the input supply is not ideal, input
capacitors are needed to filter the current pulses at the
switching frequency. A simple buck converter is shown in
Figure 8.
Figure 8. Buck converter input model
In Figure 8 the DC input voltage source has an internal
impedance R
in
and the input capacitor C
has an ESR
denoted as R
. MOSFET and input capacitor current
waveforms, ESR voltage ripple and input voltage ripple
are shown in Figure 9.
Figure 9. Typical waveforms at the input of a buck
converter.
It can be seen that the current in the input capacitor pulses
with high di/dt. Capacitors with low ESL should be used. It
is also important to place the input capacitor close to the
MOSFET’s on the PC board to reduce trace inductances
around the pulse current loop.
The RMS value of the capacitor current is approximately
].
)
D
1
D
η
)
D
η
1
)(
12
1
[(
D
I
I
2
2
2
o
Cin
+
δ
+
=
The power losses at the input capacitors is then
P
Cin
= I
Cin
2
R
esr
.
For reliable operation
,
the maximum power dissipation in
the capacitors should not result in more than 10
o
C of
temperature rise. Many manufacturers specify the
maximum allowable ripple current (ARMS) rating of the
capacitor at a given ripple frequency and ambient
temperature. The input capacitance should be high enough
to handle the ripple current. For higher power applications,
multiple capacitors are placed in parallel to increase the
ripple current handling capability.
Sometimes meeting tight input voltage ripple specifications
may require the use of larger input capacitance. At full
load, the peak-to-peak input voltage ripple due to the ESR
is