Array factor phased array beam steering problem

[yefj]

Hello, I have created exactly the array factor formula in matlab .
But when i add the beam steering delta member it does nothing to the main lobe.
Why it stays the same?
Thanks.

theta_0=pi*((20)/180);
amplitude_norm_V=[0.05,0.3,0.75,1,0.75,0.3,0.05];
delta=k*d*cos(theta_0);
x=sqrt(1/(sum(amplitude_norm_V.^2)));
real_voltage=amplitude_norm_V.*x;
real_power=(real_voltage.^2);
sum(real_power);
phases=[0,0,0,0,0,0,0]
theta=linspace(0,pi,1000);

f=5.6;

N=6;

lambda=300/f;
k=(2*pi)/lambda;
d=0.8*lambda;
total=0;
tot=0;
for z=1:6
AF=real_voltage(z)*exp(1i*(phases(z)/180*pi))*exp(-1i*(z-1)*k*d*cos(theta)+delta);
total=total+AF;
tot=tot+AF.^2;
end
plot((theta/pi)*180,20*log10(total));