Capacitors are usually rated in terms of DC voltage.
This rating means that the part can be expected to
operate reli-ably on a long-term basis at that DC
voltage and at the capacitor’s rated temperature.
Since most applications include some AC voltage component,
it is important to understand the factors which determine
how much AC a given DC-rated part can withstand. These
factors include frequency, voltage, power rating (size),
capacitance value and the dielectric characteristics.
The effects of AC on capacitor characteristics and
reliabil-ity depend partly on the type of dielectric
used. For ceramic capacitors, the three primary dielectrics
(NPO, X7R and Z5U) all have different characteristic
changes with respect to applied AC. For example, with
NPO dielectric, the values of capacitance and dissipation
factor will remain rel-atively constant when various
AC signals are applied. X7R, however, will exhibit
small changes with the applied fre-quency and significant
changes with the magnitude of voltage applied. Z5U
will change even more with both fre-quency and voltage.
The particular capacitor designs will affect the amount
of change which will occur in these para-meters, since
they are dependent on both the dielectric used and
on the thickness of that dielectric for a given voltage.
These figures reference only the X7R dielectric. NPO
will show no measurable changes with either voltage
or fre-quency. Z5U will exhibit changes similar to
X7R, but of much greater magnitudes. For this reason,
Z5U is seldom used in AC applications.
While the changes due to frequency can be easily
charted for X7R (see Figure 1), those due to the voltage
level depend upon the dielectric stress (volts per
mil of dielectric thickness) and will be different
for each voltage rating. Typical values for X7R are
shown in Figures 2 through 5.
For a given application, the power dissipated in
a capacitor can be calculated from the formula P=i²
R, where P = the power in watts, i = the rms current
through the capacitor and R = the Equivalent Series
Resistance (ESR) of the capacitor. Then i= 2 pie
fCE, where f = the frequency in Hertz, C= the capacitance
in Farads and E = the rms voltage applied. Finally
R= d/(2 pie fC), where d = the dissi-pation
factor. Combining these three equations, the final
power formula derived is P=2 pie fCE²d.
Now it is necessary to determine the values of capacitance
and dissipation factor, assuming that we know the
applied voltage and frequency. The capacitance can
be determined from Figures 1, 2 and 3 by modifying
the nominal capaci-tance by the changes shown for
the given frequency and voltage stress. Dissipation
factor can similarly be deter-mined from Figures 1,
4 and 5. Note that these values are typical and will
vary from one manufacturer to another. The cap changes
due to voltage can also be modified by the manufacturer
to meet a given application requirement.
After the above corrections to capacitance and dissipation
factor are made based upon the circuit voltage and
fre-quency, the actual power consumption in the capacitor
can be calculated from the formula P=2 pie
fCE²d. Note that both the capacitance value and
the frequency directly affect the power for a given
voltage. This is why it is not possible to assign
a generic AC rating (or a factor to apply to the DC
rating) for capacitors. Only when these values are
known (as in fixed value 60Hz power applications)
can this be done.
Once the power is determined, it is necessary to
find out whether a given capacitor will be able to
withstand it. Johanson Dielectrics has developed a
table of power ratings for various sizes of capacitors
so this can be easily com-pared with the calculated
power (see Table 1).
These power ratings are based upon a 25°C temperature
rise as measured on the surface of the capacitor when
power is applied. The ratings are also based on standard
mounting on a PC board, no nearby heat sources and
with no external coating or potting which could inhibit
heat con-duction.
Here is an example: 0.1µF, 500V, X7R, 2520
size chip to be surface mounted and operated at 30Vrms
and 10kHz. From the Johanson Dielectrics Catalog ,
select Johanson part number 501H47W104KV4. To use
the formula P=2 pie fCE²d, the values
of f (10,000) and E (30) are known, and the values
of C and d must be determined from Figures 1 through
5.
Accordingly, the capacitance due to frequency changes
–2% due to frequency (Figure 1) and +25% due
to the voltage (use the 500VDC curve in Figure 2).
This makes “C” the actual capacitance (.1)(.98)(1.25)=.123µF.
Simi-larly, “d”, the dissipation factor
using the higher of the two values in Figures 1 and
4 is 8%(.08).
The values now are known:
f=10000
C=.123 (e-6)
E=30
d=.08
The calculated power is 0.56 watt. Referring to
Table 1, the rated power for the H47 size is 1.3 watt
so the design is valid for this application.
Applications Engineering assistance is available
from the factory for other specific applications or
questions.
