Output Capacitor Selection
(Continued)
How the output voltage recovers after that initial excursion
depends on how fast the inductor current falls and how large
the output capacitance is. See
Figure 10
.
The ESR and the capacitance of the output capacitor must
be carefully chosen so that the output voltage overshoot is
within the design’s specification V
. If the total com-
bined ESR of the output capacitors is not low enough, the
initial output voltage excursion will violate the specification,
see
V
. If the ESR is low enough, but there is not enough
output capacitance, the output voltage will travel outside the
specification window due to the extra charge being dumped
into the capacitor, see
V
C2
. The LM3477/A has output over
voltage protection (OVP) which could trigger if the transient
overshoot is high enough. If this happens, the controller will
operate in hysteretic mode (see
OVER VOLTAGE PROTEC-
TION
section) for a few cycles before the output voltage
settles to its steady state. If this behavior is not desired,
substitute V
OVP
(referred to the output) for V
OS(MAX)
(V
OVP
is
found in the
ELECTRICAL CHARACTERISTICS
table) to
find the minimum capacitance and maximum ESR of the
output capacitor.
Calculations for the Output Capacitor
During a loading transient, the delta output voltage
V
has
two changing components. One is the voltage difference
across the ESR (
V
), the other is the voltage difference
caused by the gained charge (
V
q
). This gives:
V
c
=
V
r
+
V
q
The design objective is to keep
V
c
lower than some maxi-
mum overshoot (V
). V
OS(MAX)
is chosen based on
the output load requirements.
Both voltages
V
r
and
V
q
will change with time. For
V
r
the
equation is:
where,
R
ESR
= the output capacitor ESR
I
OUT
= the difference between the load current change
I
OUT(MAX)
I
OUT(MIN)
D
MIN
= Minimum duty cycle of device (0.165 typical)
Evaluating this equation at t = 0 gives
V
r(max)
. Substituting
V
OS(MAX)
for
V
r(MAX)
and solving for R
ESR
The expression for
V
q
is:
From
Figure 11
it can be told that
V
will reach its peak
value at some point in time and then decrease. The larger
the output capacitance is, the earlier the peak will occur. To
find the peak position, let the derivative of
V
C
go to zero,
and the result is:
The intention is to find the capacitance value that will yield, at
t
, a
V
C
that equals V
OS(max)
. Substituting tpeak for t and
equating
V
C
to V
OS(max)
C
OUT(MIN)
:
The chosen output capacitance should not be less than
47μF, even if the solution for C
is less than 47μF.
Notice it is already assumed that the total ESR is no greater
than R
, otherwise the term under the square root
will be a negative number.
Power MOSFET Selection
The drive pin of LM3477/A must be connected to the gate of
an external MOSFET. In a buck topology, the drain of the
external N-Channel MOSFET is connected to the input and
the source is connected to the inductor. The C
pin voltage
provides the gate drive needed for an external N-Channel
MOSFET. The gate drive voltage depends on the input volt-
age (see
TYPICAL PERFORMANCE CHARACTERISTICS
).
In most applications, a logic level MOSFET can be used. For
very low input voltages, a sub-logic level MOSFET should be
used.
The selected MOSFET directly controls the efficiency. The
critical parameters for selection of a MOSFET are:
1.
Minimum threshold voltage, V
TH
(MIN)
2.
On-resistance, R
DS
(ON)
200033B5
FIGURE 10. Output Voltage Overshoot Violation
200033B6
FIGURE 11. Output Voltage Overshoot Peak
L
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