Lossy media Feb. 19, 2007
+
Wave equation for lossy media in phasor form (pp. 287-295):
where
and
is the complex
permittivity with the imaginary part involving conductivity
that denotes Ohmic loss.
,
i.e. attenuation coefficient
(
)
and
phase factor
(rad/m).
Note --
is equal to 8.69 dB/m (p.289 footnote).
+
Plane wave in lossy media:
e.g.
(
,
)
time varying form
Note --
equiv. to
in lossless medium
.
- In terms of phasors, it is best to use exponential form.
Consistently, convert all imaginary terms inside the argument of the exponent
to radian (avoid degrees), e.g.
.
- For conversion into time varying form, group all the
phases (exponent with j) into one group and group all the real amplitudes into
another group.
- To identify a plane wave, group all (real
and imaginary)
exponents with spatial dependency into one group as
propagation factor (e.g.
)
and remaining terms make up the complex
amplitude.
+
TEM wave in lossy media (Sect. 7.3):
&
are
valid but
wave impedance
is complex.
+
Determine of material properties:
insulator or good dielectric
good conductor
Otherwise, semi-conductor or lossy dielectric.
Recall
.
Generally,
where
accounts for conductor and dielectric losses.
Loss tangent
.
______________________________________
HW #9 Due 3/1/07
for a plane wave.
Find frequency in Hz,
, polarization direction, propagation direction, phase
velocity, wavelength inside the medium and
if
. Also find phasor
in
exponential form.
(plane wave or
Maxwell's eqn) and what coordinates is used in this problem (r in the
text book is my
).
Use the formula for k to compute k.
, b)
,
c) 2
for initial input
. Comment on the plots
(see http://scylla.ceas.uwm.edu/361/maple.html)