Field and Wave Electromagnetics 2nd Edition by David Cheng

Exercise 17

Do Problem for a uniform-phased cosinusoidal amplitude distribution

and compare your results with those obtained in Example 11-13 for a uniform field distribution.
Problem:
Assume that the field in an a × b rectangular aperture in an xy -plane is linearly polarized in the y-direction and that the aperture excitation has a uniform phase and a triangular amplitude distribution

Find (a) the pattern function in the xz -plane, (b) the half-power beamwidth, (c) the location of the first nulls, and (d) the level of the first sidelobes. Compare the results with those obtained in Example 11-13 for uniform field distribution.