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Question: Derivation of equation of uniform linear antenna array directivity pattern

Question:Derivation of equation of uniform linear antenna array directivity pattern

attskijsotona 5
series simplification
November 28 2020
1

Hello community!
Given an equation

R := 1/N*S

where

S:=sum(exp(I*k*(i-1)*varepsilon), i = 1 .. n)

and can be interpreted as geometric series, so if we apply 'simplify' we get

(exp(I*k*n*varepsilon)-1)/(exp(I*k*varepsilon)-1)

The problem is in next steps, i want to obtain the final form using Maple

RR := sin((1/2)*k*n*varepsilon)/(n*sin((1/2)*k*varepsilon))

As known

(exp(I*k*n*varepsilon)-1)/(exp(I*k*varepsilon)-1) = e^(-(1/2)*j*k*n*varepsilon)*sin((1/2)*k*n*varepsilon)/(e^(-(1/2)*j*k*varepsilon)*sin((1/2)*k*varepsilon))

 

 
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