Help me with directional antenna design

I am trying to create a directional antenna by using a simple patch antenna and a parabolic dish. i understand about having to guess the possition between the focal point and the dish but i was wondering what is the best for reflection what type of material. currently i can only get it down to 30 degrees using a 200mm wide dish but i want it at 15 degrees.

I have been thinking about using a phased array as well but i am having trouble with that getting it too work. when you have to place them 1/2 wavelenght apart is that from center when using a dipole stripline.

like if i was using a stripline for 2.4ghz 3mm wide and 31.25 1/4 wavelenght long should i go center of that line to the next strip?

Increasing your aperture diameter will decrease the beamwidth. If you are around 30 degrees and want to be at 15 degrees you need to double the parabola diameter to something on the order of 400mm.

You might look into a copy of the SABOR software. It is really inexpensive and will give you a way to estimate the size fo the antenna you want to design.

Kraus "Antennas" is a useful reference to get started.