# How to find the phase values for the desired steering angle?

The picture attached is self-explanatory.

The antenna system system 24 antenna elements with inter antenna element spacing of wavelength/2.

There are two types of arrangements.

The first one is conventional one, where each antenna element can have its one phase shifter.

While for the second arrangement, 6 antenna elements share a single phase shifter. So, all these antenna elements in a group/subarray will have same phase shifting value.

I want to find the phase shift value for both of these arrangements for a beam steered at 30 degree.

Also, how can I plot the array pattern where I can see that the beam gain is maximum at 30 degree?

For the left example, you have the equations for $$\\delta\$$$$\\phi\$$, the element to element phase difference. You then pick one of your 24 elements as the reference, $$\\phi\$$=0, and the phase shifts for the other 23 elements just fall out from that.

For example, number the elements 1-24, top to bottom. Let the top most element be the reference, so $$\\phi\$$1=0 deg. Then $$\\phi\$$2=1*$$\\delta\$$$$\\phi\$$, $$\\phi\$$3=2*$$\\delta\$$$$\\phi\$$, etc.

For the right example, what you have is a 4-element array with the element spacing being 3 lambda. Call these 4 elements a super-element. So the super-element to super-element phase difference (delta) would be 6 times that of the example on the left.

• thanks a lot. I think, for the first case, phi2=delta_theta and phi3=2*delta_theta, not phi. For the second case lets say we take the first super element as reference and we set $\psi_1=0$. Then for the second super element, is it $\psi_2=6\Delta_{theta}$, $\psi_3=12\Delta_{theta}$ and $\psi_4=18\Delta_{theta}$?
– MGM
Feb 12 at 21:23
• You're right. Delta theta, not delta phi in your example. Note that as you have sketched it out, theta is being used for both the steering angle and the element to element phase setting. I would use phi/delta phi for the latter to reduce confusion between the two phase variables. Feb 12 at 21:30
• thanks. Also I wanted to plot the radiation pattern over an angle range for (assuming from -90 to 90 degrees). theta = linspace(-90, 90, 361); How can I do it with above phase values. Do you have any routine for that? I saw somewhere that they used DFT sort of matrix and then do some operations.
– MGM
Feb 12 at 21:42
• Simplistically, for each angle across your scan volume, you need to calculate the complex signal (phase, amplitude) at each element, then just sum them up. You can do this with a DFT approach as you mentioned since the array is a spacial sampling of the incoming signal. I had MLAB code to do that, but have lost access to the tool since I retired. Their is also Python code out there to do the same thing. Feb 13 at 11:27
• thanks. I did the simulation. For steering angle at 0 and 10 degrees, it works fine. Once I set the steering angle to 20 degree, I get two equal strength beams one pointing at 20 degree and the other one at -20 degree. If the set the steering angle to 30 degree, I get the been steering at -10 degree. Why is is happening like that?
– MGM
Feb 13 at 13:47