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You are an antenna engineer and you are asked to design a high directivity/gain antenna for space-borne
communication system operating at 10 GHz. The speci cations of the antenna are such that its pattern
consists basically of one major lobe and, for simplicity, no minor lobes (if there are any minor lobes they are
of such very low intensity and you can assume they are negligible/zero). Also it is desired that the pattern is
symmetrical in the azimuthal plane. In order to meet the desired objectives, the main lobe of the pattern
should have a half-power beamwidth of 10 degrees. In order to expedite the design, it is assumed that the
major lobe of the normalized radiation intensity of the antenna is approximated by U(theta, phi) =
cos^n(theta) and it exists only in the upper hemisphere (0 lessthanorequalto 6 lessthanorequalto pi/2, 0
lessthanorequalto phi lessthanorequalto 2pi). Determine the: Value of n (not necessarily an integer) to meet
the speci cations of the major lobe. Keep 5 signi cant gures in your calculations. Exact maximum directivity
of the antenna (dimensionless and in dB). Approximate maximum directivity of the antenna based on Kraus'
formula (dimension- less and in dB). Approximate maximum directivity of the antenna based on Tai &
Pereira's formula (dimensionless and in dB).
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