Question

The wave and antenna polarizations in XYZ system are given by:

rhow = sin(θ1)cos(φ1)x + sin(θ1)sin(φ1)y + cos(θ1)z
rhoa = sin(θ2)cos(φ2)x + sin(θ2)sin(φ2)y + cos(θ2)z

Find the equation for the polarization loss factor (PLF). Put the antenna at the origin along Z-axis and specify the angles (θ1,φ1) where PLF is minimum and maximum. Draw the picture of the direction of travel of wave toward the antenna in both cases.

Answer 1

The polarization loss factor (PLF) is a measure of the reduction in intensity of a polarized wave when it passes through a polarizing filter. The equation for PLF is derived from Malus's Law, I = Io cos²θ, where I is the transmitted wave intensity, Io is the incident wave intensity, and θ is the angle between the direction of polarization and the filter axis. The minimum PLF occurs when the polarization is aligned with the filter, and the maximum PLF occurs when the polarization is perpendicular to the filter.

Step-by-step explanation:

The polarization loss factor (PLF) is a measure of the reduction in intensity of a polarized wave when it passes through a polarizing filter. In this case, the equation for PLF can be derived from Malus's Law:

I = Io cos²θ

where I is the intensity of the transmitted wave, Io is the intensity of the incident wave, and θ is the angle between the direction of polarization and the axis of the filter.

The minimum PLF occurs when θ = 0°, because the wave is perfectly aligned with the filter and no intensity reduction occurs. The maximum PLF occurs when θ = 90°, because the wave is perpendicular to the filter and all intensity is blocked.

In the case of the XYZ system, the angles (θ1, φ1) can be used to determine the direction of polarization and calculate the PLF. However, without specific values for these angles, it is not possible to provide a numerical value for the PLF or draw the direction of travel of the wave toward the antenna.