Total field of Phased-Array

•Total field = E(y), where phase difference y=(2pd/l)cosfsinq, e.i.
–E(y) = 1+ exp(jy)+ exp(j2y)+ exp(j3y)+ exp(j4y)+ exp(j5y)+ …+ exp[j(N-1)y]
–= [1- exp(jNy)]/ [1- exp(jy)]
–= [exp(jNy/2)/ exp(jy/2)]/ {[exp(jNy/2)- exp(-jNy/2)]/ [exp(jy/2)- exp(-jy/2)]
–= exp[j(N-1)y/2][sin(Ny/2)/ sin(y/2)], refer to the first element, or
–= sin(Ny/2)/ sin(y/2), refer to the center element