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applied. In general, therefore, the frequency of application for a coil
becomes important at increasing frequencies. Inductors lose their ideal
characteristics and in fact begin to act as capacitive elements with
increasing losses at very high frequencies.
The capacitor, like the inductor, is not ideal at higher frequencies. In
fact, a transition point can be defined where the characteristics of the
capacitor will actually be inductive. The complete equivalent model for
a capacitor is provided in Fig. 14.26. The resistance R s, defined by the
resistivity of the dielectric (typically 10 12 �·m or better) and the case
resistance, will determine the level of leakage current to expect during
the discharge cycle. In other words, a charged capacitor can discharge
both through the case and through the dielectric at a rate determined by
the resistance of each path. Depending on the capacitor, the discharge
time can extend from a few seconds for some electrolytic capacitors to
hours (paper) or perhaps days (polystyrene). Inversely, therefore, electrolytics
obviously have much lower levels of R s than paper or polystyrene.
The resistance R p reflects the energy lost as the atoms continually
realign themselves in the dielectric due to the applied alternating ac
voltage. Molecular friction is present due to the motion of the atoms as
they respond to the alternating applied electric field. Interestingly
enough, however, the relative permittivity will decrease with increasing
frequencies but will eventually take a complete turnaround and begin to
increase at very high frequencies. The inductance L s includes the inductance
of the capacitor leads and any inductive effects introduced by
the design of the capacitor. Be aware that the inductance of the leads
is about 0.05 mH per centimeter or 0.2 mH for a capacitor with two
2-cm leads—a level that can be important at high frequencies. As for
the inductor, the capacitor will behave quite ideally for the low- and
mid-frequency range, as shown by the plot of Fig. 14.27 for a 0.01-mF
20
10
Z (�)
XC ≅
1
2 �fC
0.01 �F �
Inductive characteristics
due to L s
1 2 3 4 5 6 78910 20 f (MHz–
log scale)
FIG. 14.27
Impedance characteristics of a 0.01-mF metalized film capacitor versus
frequency.
metalized film capacitor with 2-cm leads. As the frequency increases,
however, and the reactance X s becomes larger, a frequency will eventually
be reached where the reactance of the coil equals that of the capacitor
(a resonant condition to be described in Chapter 20). Any additional
increase in frequency will simply result in X s being greater than X C, and
the element will behave like an inductor. In general, therefore, the frequency
of application is important for capacitive elements because
FREQUENCY RESPONSE OF THE BASIC ELEMENTS ⏐⏐⏐ 591
L s (leads)
R s (dielectric loss)
C
R p (leakage)
FIG. 14.26
Practical equivalent for a capacitor.