
AP-523
E
20
Another useful formula for estimating the amount of bulk
capacitance required is shown in Equation 3. This
ignores the ESR of the component but furnishes the
amount of capacitance that would be required from an
ideal component.
Equation 3. Capacitance for an Ideal Capacitor
C
I
v
t
=
D
I
represents the current that the bulk capacitance must
be able to deliver or sink. This is equal to the difference
between high and low current states since the power
supply will initially continue to supply the same current
that it had been prior to the load change.
D
v
is the
allowable voltage change budgeted for bulk capacitive
sag (discharge) over the period
D
t.
D
t
is the reaction time
of the power source.
Assuming some representative numbers for
I
,
D
V
, and
D
t
,
the capacitance required is shown by Equation 4.
Equation 4. Capacitance needed if ESR is 0 ohms
C
A
V
x
s
F
=
=
85
.
0 060
.
30 10
4250
6
μ
Combining the above formulas to remove the resistive
drop from the budget for the bulk capacitance gives
Equation 5.
Equation 5. Capacitance vs. ESR
C
I
×
t
V
I
ESR
=
×
This equation leads to the capacitance vs. ESR graph
shown in Figure 19, when
D
V
is assumed to be 60 mV,
I
is assumed to be 8.5A, and the reaction time (
D
t
) of the
power source is 30
m
s. The shaded area of the graph
covers capacitance types that are insufficient for this
application. Again this provides a figure that can be used
to get a feel for the type of capacitors required. For
example, to satisfy this equation one could use twelve
1000
m
F capacitors if the ESR of each was 53 m
W
. The
parallel resistance of 12 capacitors would be 4.4 m
W
and
the parallel capacitance would be 12,000
m
F, which falls
in the white zone of the graph in Figure 19.
0
5000
10000
15000
20000
25000
30000
0.000
0.001
0.002
0.003
0.004
0.005
0.006
Resistance (
)
Capacitance (
F)
Figure 19. Capacitance Required vs. ESR at 8.5A, 60 mV
D
V and 30
m
s
D
t