A plane wave propagating in air is normally incident on a lossy non-magnetic dielectric material
with $\gamma$ = 0.5 + j3.0 (1/m). The dielectric material occupies the half-space y ≥ 0. The magnetic
field of the incident wave is given by
$\vec{H} = -0.1 \hat{a_x} \sin(2\pi \times 10^8 t - 2y)$ (A/m)
a) Write the phasor expression of the reflected electric field.
b) Write the instantaneous expression of the transmitted electric field.
c) Calculate the incident, reflected and transmitted power densities.
A radome protecting a microwave transmitter has $\epsilon_r$=4 and is designed as a half-wavelength
reflectionless slab at the operating frequency of 10 GHz.
a) Find the smallest radome thickness.
b) Because of manufacturing imperfections, suppose that the actual constructed thickness of
the above radome is 5% off the desired half-wavelength thickness. Determine the
percentage of reflected power in this case.
A plane wave propagating in a lossless non-magnetic dielectric material with $\epsilon_{r1}$ = 2.25 is incident
upon the planar surface of another lossless non-magnetic dielectric material with $\epsilon_{r2}$= 4
occupying the half-space x ≥ 0. The electric field of the incident wave is given by
$\vec{E} = 20 \hat{a_y} e^{-j(3x+4z)}$ (V/m)
a) Produce a sketch of the problem.
b) What is the polarization of the wave (TE/TM)?
c) Find the angle of incidence.
d) Find the frequency of the wave.
e) Write the phasor expression of the reflected electric field.
f) Write the instantaneous expression of the transmitted magnetic field.
A submarine at a depth z = 50 m below the sea surface uses a wire antenna to receive signals at
frequency f = 1 kHz. Seawater has $\epsilon_r$ = 80, $\mu_r$ = 1 and $\sigma$ = 1.1 S/m at this frequency. Calculate
the time-average power density that reaches the submarine if the magnetic field of the plane wave
just inside the sea surface (z= 0) is
$\vec{H} = (100 \hat{a_y})$ (mA/m)