Page 213 - Satellite Communications, Fourth Edition

Antennas 193

6.22 Problems and Exercises
6.1. The power output from a transmitter amplifier is 600 W. The feeder losses
amount to 1 dB, and the voltage reflection coefficient at the antenna is 0.01.
Calculate the radiated power.

6.2. Explain what is meant by the reciprocity theorem as applied to antennas.
A voltage of 100 V applied at the terminals of a transmitting dipole antenna
results in an induced current of 3 mA in a receiving dipole antenna. Calculate
the current induced in the first antenna when a voltage of 350 V is applied to
the terminals of the second antenna.

6.3. The position of a point in the coordinate system of Sec. 6.3 is given
generally as r(
, ). Determine the x, y, and z coordinates of a point 3(30°, 20°).

6.4. What are the main characteristics of a radiated wave in the far-field
region? The components of a wave in the far field region are E
3 mV/m,
E 4 mV/m. Calculate the magnitude of the total electric field. Calculate
also the magnitude of the magnetic field.

6.5. The k vector for the wave specified in Prob. 6.4 is directed along the x
axis. Determine the direction of the resultant electric field in the yz plane.
6.6. The k vector for the wave specified in Prob. 6.4 is directed along the z
axis. Is there sufficient information given to determine the direction of the
resultant electric field in the xy plane? Give reason for your answer.

6.7. The rms value of the electric field of a wave in the far-field region is 3 V/m.
Calculate the power flux density.

6.8. Explain what is meant by the isotropic power gain of an antenna. The gain
of a reflector antenna relative to a 1/2l-dipole feed is 49 dB. What is the isotropic
gain of the antenna?
6.9. The directivity of an antenna is 52 dB, and the antenna efficiency is 0.95.
What is the power gain of the antenna?

6.10. The radiation pattern of an antenna is given by g(
, ) Z sin
sin Z .
Plot the resulting patterns for (a) the xz plane and (b) the yz plane.

6.11. For the antenna in Prob. 6.10, determine the half-power beamwidths, and
hence determine the directivity.

6.12. Explain what is meant by the effective aperture of an antenna. A
paraboloidal reflector antenna has a diameter of 3 m and an illumination
efficiency of 70 percent. Determine (a) its effective aperture and (b) its gain at
a frequency of 4 GHz.