 | The frequency dependent current density j flowing through a
dielectric is easily obtained. Þ | |
j(w) = | dD dt | = e(w) · | dE dt | = w · e'' ·
E(w) | + | i · w · e' · E(w) | | | | | in phase | | out of phase |
|
|
|  | The in-phase part generates active power
and thus heats up the dielectric, the out-of-phase part just produces reactive power | |
|  | The power losses
caused by a dielectric are thus directly proportional to the imaginary component of the dielectric function | |
| |
LA | = | power turned
into heat | = w · |e''| ·
E2 |
|
| |
| | | | |
 | The relation between active and
reactive power is called "tangens Delta" (tg(d)); this is clear by looking
at the usual pointer diagram of the current | |
|
| |
LA LR | := | tg d | = |
IA IR | = | e'' e' |
|
| |
| | | |
|  | The pointer diagram for an
ideal dielectric s(w = 0) = 0can always be
obtained form an (ideal) resistor R(w) in parallel to an (ideal) capacitor
C(w). | |
|  | R(w)
expresses the apparent conductivity sDK(w) of
the dielectric, it follows that | |
| |
| |
| | | | |
 | For a real dielectric with a non-vanishing conductivity at zero (or small) frequencies, we now
just add another resistor in parallel. This allows to express all conductivity
effects of a real dielectric in the imaginary part of its (usually measured) dielectric function via | |
|
|  | We have no all materials covered with respect to their dielectric behavior - in principle even metals,
but then resorting to a dielectric function would be overkill. | |
| | | | |
 | A
good example for using the dielectric function is "dirty" water with a not-too-small (ionic) conductivity,
commonly encountered in food. | |
|
|  | The polarization mechanism is orientation
polarization, we expect large imaginary parts of the dielectric function in the GHz region. | |
|  | It follows that
food can be heated by microwave (ovens)! | |
| |
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© H. Föll (Electronic Materials - Script)