Page 214 - Satellite Communications, Fourth Edition

194 Chapter Six

6.13. What is the effective aperture of an isotropic antenna operating at a
wavelength of 1 cm?

6.14. Determine the half-power beamwidth of a half-wave dipole.

6.15. A uniformly illuminated rectangular aperture has dimensions a 4l,
b 3l. Plot the radiation patterns in the principal planes.

6.16. Determine the half-power beamwidths in the principal planes for the
uniformly illuminated aperture of Prob. 6.15. Hence determine the gain. State
any assumptions made.

6.17. Explain why the smooth-walled conical horn radiates copolar and cross-
polar field components. Why is it desirable to reduce the cross-polar field as far
as practical, and state what steps can be taken to achieve this.

6.18. When the rectangular aperture shown in Fig. 6.9 is fed from a waveguide
operating in the TE 10 mode, the far-field components (normalized to unity) are
given by

p cos X sin Y
E u su, fd 52 sin f 2
2 p Y
X 2 a b
2
2
E (
, ) E
(
, ) cos
cot
where X and Y are given by Eqs. (6.19) and (6.20). The aperture dimensions are
a 3l, b 2l. Plot the radiation patterns in the principal planes.

6.19. Determine the half-power beamwidths in the principal planes for the
aperture specified in Prob. 6.18, and hence determine the directivity.

6.20. A pyramidal horn antenna has dimensions a 4l, b 2.5l, and an
illumination efficiency of 70 percent. Determine the gain.
6.21. What are the main characteristics of a parabolic reflector that make it
highly suitable for use as an antenna reflector?

6.22. Explain what is meant by the space attenuation function in connection
with the paraboloidal reflector antenna.

6.23. Figure 6.17b can be referred to xy rectangular coordinates with A at the
origin and the x axis directed from A to S. The equation of the parabola is then
2
y 4fx. Given that y max 2.5 m at x max 0.9 m, plot the space attenuation
function.
6.24. What is the f/D ratio for the antenna of Prob. 6.23? Sketch the position
of the focal point in relation to the reflector.