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If a specific cell tower contains transmitters with an output power of 120 W along with antennas having 16.5 db of gain, would this not result in an effective radiated power in the kW range? The frequency is 2100 MHz and the antenna height is 105 ft. If a residential community is located less than a quarter of a mile from the tower, would there be cause for concern?

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Almost certainly not an issue, but without knowing the details of the antenna design all you can do is measure or compute worst possible design values...

Consider that a 16.5dBi (I am guessing dBi, but you don't specify) omni directional antenna will have a very 'flat' pattern (It kind of must if it is to have 16.5dB of gain while being an omni), and it is 30m up, so both the pattern and the 30m between you and the bottom of thing thing makes for low field strengths close to the antenna.

At ~500m (Use SI units already, makes the sums easier), with an EIRP of 120W * 10^(16.5/10) = ~5,400W EIRP, what power density do we have if you were right in the radiating plane (Probably a slightly tilted down cone, but whatever)? The area of a sphere is 4*Pi*R^2, so at 500m that energy is spread over 3.14*10^6 m, giving a power density of 1.7mW/m^2, well below any sane exposure limit. In W/square cm that is 170nW/cm^2.

How about a really cack handed design that put 120W out in a isotropic radiator (stupid, and a waste because an isotropic radiator by definition cannot have gain, which is why nobody does it), how much power would someone standing ~30m away (at the base of the tower) be exposed to? 120W / 4 * 3.14 * 30m^2 = ~10mW/m^2 (~1uW/cm^2).

If you are going to worry about this stuff, worry about the 2W transmitter in your pants pocket, at 10cm (0.1m), that thing works out to (assuming isotropic radiator, not a safe assumption), 2W / 4 * 3.14 * 0.1^2 = 16W/m^2 (about 10,000 times what that tower is hitting you with at 500m). Of course it throttles back when it has a good signal from a reasonably nearby tower, so you might see the tower as lowering your exposure in some circumstances....

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  • \$\begingroup\$ The tower information was obtained from an online cell tower map. The antenna gain was shown only as 16.5. The elevation angle is -2. The distance from the antenna to the nearest building is 187M. I expect you are correct in your assessment of the low signal strength. The 120W was not particuarly concering, but along with the 16.5 dB antenna gain I had to wonder. \$\endgroup\$
    – UpNorth
    Jan 28, 2019 at 19:37
  • \$\begingroup\$ That's the nice thing about engineering, no need to wonder, you can just do the sums... But in this case power density is pretty pony even if that building 187M away was in the main lobe. Cell phone towers are a pretty noddy RF source by and large, and generally the system designers know what they are about, the phone in your pocket is a MUCH bigger issue if issue there be. \$\endgroup\$
    – Dan Mills
    Jan 28, 2019 at 23:53

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