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What is the direction of first null of broadside 4-element isotropic antenna having a separation of λ/2?(a) 60°(b) 30°(c) 180°(d) 0°The question was posed to me in exam.Enquiry is from Radiation Pattern for 4-Isotropic Elements topic in portion Antenna Array of Antennas

Answer»

The correct ANSWER is (a) 60°

To elaborate: The nulls of the N- ELEMENT array is given by

\(θ_n=cos^{-1}⁡(\frac{λ}{2πd} \LEFT[-β±\frac{2πn}{N}\right])=cos^{-1}⁡(\frac{λ}{2πd} \left[±\frac{2πn}{N}\right])\)

⇨ \(θ_n=cos^{-1}⁡(\frac{λ}{2π(λ/2)} \left[±\frac{2πn}{N}\right])=cos^{-1} (±\frac{2n}{4})=cos^{-1}(±\frac{n}{2})\)

⇨ \(n=1 (first \,NULL) cos^{-1} (±\frac{n}{2})=cos^{-1} (±\frac{1}{2})=60° or 120°. \)



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