The interior of a $${{20} \over 3}\,\,cm\,\, \times \,\,{{20} \over 4}\,\,cm$$ rectangular waveguide is completely filled with a dielectric of $${ \in _r} = 4$$. Waves of free space wave-lengths shorter than .........can be propagated in the $$T{E_{11}}$$ mode.

A wave traveling in the $$+Z$$-direction, is the resultant of two linearly polarized components, $${E_x}\,\,\, = \,\,\,\,\,\,3$$ $$\,\,\,\,\cos \omega t$$ and $$\,{E_y}\,\,\,\, = \,\,\,2\,\cos \,\left( {\omega t + {{45}^ \circ }} \right)$$

Determine
(1) The axial ratio
(2) The angle between the major axis of the polarization ellipse and the $$+x$$-axis.

For a dipole antenna

Two spacecrafts are separated by 3000 km. Each has a paraboloidal reflector antenna of 0.85 m diameter operating at a frequency of 2 GHz with an aperture efficiency of 64%. If the space crafts A's receiver requires 1pW for a 20 dB signal-to-noise ratio, what transmitter power is required on the spacecraft B to achieve this signal-to-noise ratio?