Assignment 3
RAT
November 2023
1] Show that the directions of maxima of the array factor of two element array shown in
fig., with excitations I1 = ejkd/2 and I2 = e−jkd/2 ,are give by ;
θm = cos−1 ( +2 mπ+kd
); m=0,1,2...
kd
and the array has atleast one maximum along θ=0
2]Calculate the directions of the maxima and the nulls of the array factor of an array of two
infinitesimal dipoles oriented along the z-direction, kept at z1 = 0.125λ and z2 = 0.125λ,
and carrying currents I1 = e−jπ/4 and I2 = ejπ/4 , respectively.
3]Show that for a 2-element array with α = kd the condition for the nulls to appear in the
array factor is;
d
=> 2n−1
;n=1,2,3...
λ
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4]Show that the peaks of the array factor of an N-element uniform array are given by the
solution of the equation
N tan( ψ2 ) = tan( N2ψ )
5]For a uniform 7-element array with α= 0, calculate the exact location of the peak of the
first side lobe by solving the transcendental equation [Eqn :-N tan( ψ2 ) = tan( N2ψ )], and
calculate its level (in dB) with respect to the main lobe peak.
6]Design a 4-element, broadside array of isotropic elements spaced
1
λ
2
apart, that has an array
factor with all the side lobes 25 dB below the main lobe.
7]Design an array of 7 elements with element spacing 0.75λ and side lobes 30 dB below the
main lobe pointing along θ = 0o .
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