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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?

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    \$\begingroup\$ 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. \$\endgroup\$ – The Photon Oct 26 '17 at 19:09
  • \$\begingroup\$ 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. \$\endgroup\$ – wav scientist Oct 26 '17 at 19:21
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    \$\begingroup\$ 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. \$\endgroup\$ – tomnexus Oct 26 '17 at 19:35
  • \$\begingroup\$ 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. \$\endgroup\$ – wav scientist Oct 26 '17 at 19:41
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    \$\begingroup\$ 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! \$\endgroup\$ – Marcus Müller Oct 26 '17 at 21:52
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Just like lens apertures and loadspeaker arrays, a phased array antenna needs physical width to be able to focus a tight beam.

The tightest beam you can form is limited by the diffraction limit for that width, in the ballpark of wavelength/array_width. To get a 'reasonably' focussed beam, you will need an array width 'many' wavelengths.

I notice from the comments that you want to use 24GHz, which has a free-space wavelength of 12.5mm, which suggests that on the face of it, the physical width of the array you need is going to be the least of your problems. Then you want 1 wavelength width at 10m, or about 1mradian beam width. That's going to need an array width of the order of 1000 wavelengths or >12m, which is totally impractical (not that 24GHz is practical for an amateur). You may need to rethink your specifications.

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  • \$\begingroup\$ 24 GHz have wavelenght 1.25 cm,not 12.5,you are mistaking it for my earlier mention of 2.4 GHz,the wifi & bluetooth ism band.How many wavelenghts does the array need to be in order to get 2 or 3 wavelenght wide beam at distance of 10 meters? Is there online calculator so I can input frequency,array width and it shows the radiation patern? And what about my dielectric theory,can high permitivity dielectric slow down the waves,shortening their wavelenght so making the array act like bigger array with air dielectric so I can use smaller array for same narrow beam? \$\endgroup\$ – wav scientist Oct 27 '17 at 10:12
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    \$\begingroup\$ @wavscientist in my book, 12.5mm is 1.25cm. If you went for middle ground of perhaps 1ft aperture, that could achieve in the ballpark of a 1ft beam at 10m. If you fill the entire space between your antenna and your target with dielectric, say fill the room with oil, then yes, the reduced wavelength will reduce all the sizes. But if you have to pass through air, that's not much different from vacuum, and any dielectric loading within or on the antenna is not going to help beam-forming in air at all. \$\endgroup\$ – Neil_UK Oct 27 '17 at 10:18

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