Normalized total field of Phased-Array

•Define Array factor f(y) = Normalized total field En(y) = E(y)/Emax, where Emax= N, if y=0, e.i.
–f(y) = (1/N)sin(Ny/2) / sin(y/2);
•Define Array factor f(f,q) = Normalized total field En(f,q) = E(f,q)/Emax, where Emax= N if q= f= p/2, e.i.
–f(f,q) = {sin[(pd/l)Ncosfsinq] / Nsin[(pd/l)cosfsinq], or
–f(f) = {sin[(pd/l)Ncosf] / Nsin[(pd/l)cosf], if q= p/2;
•Define Array factor f(n,r) = Normalized total field En(n,r) = E(n,r)/Emax, where Emax= N if elevation n= (p/2)- q= (p/2)- p/2= 0 and azimuth r= (p/2)- f= (p/2)- p/2= 0, e.i.
–f(n,r) = {sin[(pd/l)Ncosnsinr] / Nsin[(pd/l)cosnsinr], or
–f(r) = {sin[(pd/l)Nsinr] / Nsin[(pd/l)sinr], if n= 0.
•Normalized total field or array factor determine DOA, Direction of Arrival, in general,
–r at any n (or f at any q), or specifically
–r at n= 0 (or f at q= p/2)