Page 91 - Maxwell House

NEOCLASSICAL THEORY OF INTERACTION 71

Since all terms in (2.69) and the following, similar harmonic equities have the same complex
exponential factor exp() that factor to be hidden. Note that the polarization and conductive
loss is basically indistinguishable and the practically measured conductivity is the effective
conductivity () defined from (2.67) as
(ω) = + ω ′′ () [S/m] (2.70)
0
In the reference literature, you can usually find two values, () and the electric loss tangent
′

defined as
′′
() (ω)
tan = = (2.71)

′ () ω 0 ′ ()
The loss tangent represents a measure of the dielectric loss and for high-quality modern
−6
dielectrics is in the range of 10 −3 − 10 . It is clear that analyzing, in the same way, the
movement of magnetic moments, we can come to conclusion that the relative magnetic
permeability is frequency dependable and can be split into its real and imaginary part in the
form
() = () − () (2.72)
′′
′

If so, the measure of the magnetic loss can be defined by the magnetic loss tangent as
′′
()
tan = (2.73)

′ ()
st
Then the 1 Maxwell’s equation and the constitutive relation in Table 1.9 can be rewritten in
the form
(, ) = ()(, ) � (2.74)
0
x (, ) = (, ) + (, )

2.4.2 Classification of Materials Based on Their Electrical Property
Table 2.3

Current conduction Field propagation

0 perfect dielectric, lossless
di
≪ 1 low-conductivity material, poor low-loss medium, good dielectric
dt
≈ 1 lossy conducting material, semiconductor lossy propagation medium

≫ 1 high-conductivity material, good high-loss medium, poor
dt di l t i
∞ perfect conductor

Materials are classified based on their electrical properties as conductors, semiconductors, and
′′
()
insulators. The material with tan = ≪ 1 is considered as a good insulator. It means
′
()