A two-element dipole array is configured to provide zero radiation in the broadside ( = 90) and end-fire ( = 0, 180) directions, but

A two-element dipole array is configured to provide zero radiation in the broadside (ϕ = ± 90◦) and end-fire (ϕ = 0, 180◦) directions, but with maxima occurring at angles in between. Consider such a set-up with ψ = π at ϕ = 0 and ψ = −3π at ϕ = π, with both values determined in the H-plane.

(a) Verify that these values give zero broadside and end-fire radiation.

(b) Determine the required relative current phase, ξ. b) Determine the required element spacing, d.

(c) Determine the values of ϕ at which maxima in the radiation pattern occur.

(d) Determine the values of φ at which maxima in the radiation pattern occur.