# Phased array minimum size

I want to know two things,how big does the phased array needs to be to form proper beam and what is the smallest area the beam can be focused.I learned little bit about lasers and with focal lense,the smallest spot that it can be focused is 1 wavelenght in theory,in practice about double.From loudspeaker theory I know that for driver to exhibit directional radiation it needs to be atleast 1 wavelenght big,significant beaming doesnt happen until the driver is 5 times the wavelenght.

But this isnt optics or acustics,how does this work for microwave phased array transmitters? I want to achieve small spot size,around 1cm and very low divergence,pencil like beam,but I also would like to use relatively lower frequencies like 2.4 GHz which have 12.5 cm wavelenght.If it was like speakers and lasers,smallest spot size would 12.5 cm,and the array would be too large,around 60 cm in diameter.

I know that dielectric materials slow down the speed of electric field,thus shortening the wavelenght without increasing frequency,is it possible to use this property to make small size array that is able to focus to spot size that is below 1 wavelenght in vacuum/air?

• Dielectric materials shorten the wavelength, but it increases right back to the original value when the beam leaves the dielectric and goes back into air or vacuum. I don't think making a spot size smaller than 1/10 wavelength is very likely to be doable. – The Photon Oct 26 '17 at 19:09
• I am aware that is the case,but I am not sure if that prohibits focusing below 1 wavelenght in air if the antena is surrounded by high dielectric material.Even if the beam cant have less diameter or focus below 1 wavelenght,I believe it might help with the beam forming,so instead of large array I can use smaller one,the minimum spot size doesnt change,but maybe the effective array size changes. – wav scientist Oct 26 '17 at 19:21
• Beam width, in the far field, is approximately Wavelength / (Diameter of the array). Same as for optics. So you can decide how small you want your beam. To avoid creating other beams, the so-called grating lobes, you need a filled array, with elements less than 1 wavelength apart. – tomnexus Oct 26 '17 at 19:35
• How wide,and how many elements in row considering rectangular array shape would you recomend for 24 GHz? I want to send a tube like beam at distance of 10 meter,I would like the beam width be as close to 1 wavelenght. – wav scientist Oct 26 '17 at 19:41
• If you're about to design 24 GHz antenna arrays, I'm afraid that I have to be very honest with you: you need to go and read a(better) book on antenna and antenna systems design.Your knowledge about loudspeaker design does help,but not much.Your question indicates you haven't really understood the basic math behind antennas and electromagnetic wave propagation,and 24 GHz is a frequency where a lot of the more subtle kinky details start to show,where even engineers with solid EM education start to wave their hands and leave it to the expert.Building 24GHz array feed system is challenging enough! – Marcus Müller Oct 26 '17 at 21:52