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
Pointe diagram for currents flowing 
through a dielectric
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.  
dielectric function water
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)