Page 154 - Satellite Communications, Fourth Edition

134 Chapter Five

5.4. Two electric field vectors of equal amplitude are 90° out of time phase with
one another. On a set of x-y axes draw the path traced by the tip of the resultant
vector.
5.5. Two electric field vectors of amplitude ratio 3:1, are 90° out of time phase
with one another. On a set of x-y axes draw the path traced by the tip of the
resultant vector. If the peak voltages are 3 V and 1 V determine the average
power developed in a 10 Ω load.
5.6. With reference to a right-hand set of rectangular coordinates, and given
that Eq. (5.4) applies to a plane TEM wave, the horizontal component being
directed along the x axis and the vertical component along the y axis, determine
the sense of polarization of the wave.
5.7. With d 45° and equal amplitude components, determine the sense of
polarization of a wave represented by Eq. (5.6).
5.8. A plane TEM wave has a horizontal ( x directed) component of electric
field of amplitude 3 V/m and a vertical ( y directed) component of electric field
of amplitude 5 V/m. The horizontal component leads the vertical component by
a phase angle of 20°. Determine the sense of polarization.

5.9. A plane TEM wave has a horizontal ( x directed) component of electric
field of amplitude 3 V/m and a vertical ( y directed) component of electric field
of amplitude 5 V/m. The horizontal component lags the vertical component by
a phase angle of 20°. Determine the sense of polarization.

5.10. Given that the plane TEM wave of Prob. 5.8 propagates in free space,
determine the magnitude of the magnetic field.
5.11. Explain what is meant by orthogonal polarization and the importance
of this in satellite communications.
5.12. The TEM wave represented by Eq. (5.4) is received by a linearly polarized
antenna. Determine the reduction in emf induced in the antenna compared to
what would be obtained with polarization matching.

5.13. A plane TEM wave has a horizontal ( x-directed) component of electric
field of amplitude 3 V/m and a vertical ( y-directed) component of electric field
of amplitude 5 V/m. The components are in time phase with one another.
Determine the angle a linearly polarized antenna must be at with reference to
the x axis to receive maximum signal.

5.14. For Prob. 5.13, what would be the reduction in decibels of the received
signal if the antenna is placed along the x axis?
5.15. Explain what is meant by vertical polarization of a satellite signal. A
vertically polarized wave is transmitted from a geostationary satellite and is