### 3.4.2 Summary to: Dynamic Properties - Dielectric Losses

| 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 |
sDK(w) | = | w · e''(w)
--- | --- | ---
| 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 |  |
e'' | = | stotal w
--- | --- | ---
|  | 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)! |
Questionaire
Multiple Choice questions to all of 3.4

© H. Föll (Advanced Materials B, part 1 - script)