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EAS487: Radar Remote Sensing Spring 2014

HOMEWORK 3: Antenna arrays

Reference: Lectures 13-16 Due: 2014 February 26

Problem 1. Fill in the details leading to the ex-pression for the half-power beamwidth of an endrearray given in class. This should be a fairly shortderivation.

Problem 2. Consider a three-element array of antennas spaced by a distance d on the x axis. Findvalues of and d such that there is no radiationin the x direction but maximum radiation in the+ x direction. Sketch the radiation pattern in thex y plane. You can consider the antenna elementsthemselves to be isotropic radiators for this problem.If there is more than one solution to the problem,give the general rule, and sketch a few representativesolutions.

Problem 3. In class, we used the example of a21 element array of dipole antennas spaced by 0.9 to estimate the performance of broadside antennaarrays. Lets do the calculations exactly here usingnumerical analysis.

a) Calculate the HPWB in the E and H planes.Show plots for both planes (in dB so that thesidelobes show).

b) Estimate the gain of the array on the basisof what you found in (a).

c) Now, make an exact calculation of the gain.This will require 2-D numerical integration overthe entire pattern to nd the total radiatedpower. Compare the result with (b) and alsowith the estimate from class.

Problem 4. Suppose we have a 12 by 15 rect-angular array of half-wave dipole antennas in thex y plane. The separation between dipole elementsis a quarter wavelength in both directions, and thedipoles are oriented parallel to the x axis. The arrayis situated a quarter wavelength above a perfectlyconducting ground, and all the dipoles are excited inphase with a current I .

a) Derive a complete expression for the normal-ized radiation pattern versus and for thisarray. Be sure to include the correct elementfactor and the effects of the ground plane. Wehave here essentially a 3-D array (12x15x2).

b) Find the HPBW in the x z (=0) and y z(= / 2) planes.

c) Plot the radiation patterns in these twoplanes, and make sure they are consistent withthe HPBW you found in (b).

c) How would you phase the array to shift the

main beam to = 15

, =90

.d) Plot the pattern for (c) in the y z planeand recompute the HPBW. Compare the resultswith those from (b) and (c). Are they consis-tent?

CORNELL UNIVERSITY c DAVE HYSELL (02/11/14)HW 31