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Electric Field Strength Limit Calculation

Jul 30th 2017, 14:24

kj4saf

Joined: Oct 1st 2015, 01:47
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FCC sets transmit power limits by electric field strength. Field strength is related to TX power, of course, but how are conversion calculations done?

This site: https://www.craf.eu/useful-equations/conversion-formulae/

provides and explains this equation:

(PG)/(4 π d^2) = (E^2)/(120 π),

which can be simplified under certain assumptions (such as antenna gain = 1 and cable loss = 0, eg) to

P = 0.3 E^2.

( P is TX power in watts, and E is electric field strength in volts/meter at 3 meters)

It seems simple enough, but using it yields incorrect results. The error is more likely mine than the site.

Does anyone have any insights into calculating TX power limits based on mandated field strength limits?
Jul 31st 2017, 08:55

aa6e

Joined: Apr 4th 1998, 00:00
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Which FCC rules are you referring to?

The basic rule has to do with PEP output power level with no reference to field strength or antenna gain.

If you are referring to the RF exposure (safety) rules, the considerations are different, and rather more complicated. I recommend you consult http://www.arrl.org/rf-exposure, if you haven't already done so.

Your calculation seems to be on the right track -- You are looking at the field strength in the far field of an isotropic radiator. But we are rarely in the far field (certainly not for common frequencies at 3 meters separation), and our radiators are never isotropic!

Actual electric field strength depends on many things - distance from radiator, antenna radiation pattern and gain (including transmission lines), polarization, as well as power level and environmental details. It's hard to make an accurate calculation from first principles. Mostly, amateurs are well advised (IMO) to use the broad "safe harbor" rules that say that for a certain frequency, separation distance, and power level you are OK without doing a precise measurement. (And the level is different if you're talking about yourself or your family vs the general public.) If you come close to the "danger" level, then you are supposed to do a real measurement to show that you're OK -- or else reduce power.

73 Martin AA6E
Jul 31st 2017, 10:19

W1VT

Super Moderator

Joined: Apr 4th 1998, 00:00
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This paper has a derivation and example.
50mV/m at 3 meters works out to 0.75 mW

Zack W1VT
ARRL Senior Lab Engineer
Jul 31st 2017, 12:08

kj4saf

Joined: Oct 1st 2015, 01:47
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Zack, W1VT, and Martin, AA6E. Thank you both for your replies.

The FCC rule that I am working out is:
47 CFR 15.249 - (This is not the Amateur service, I'm doing the calculation for the ISM 2.4 GHz band.)

Zack, you and I got the same result from the calculation, that's the value that seems can't be right.

I guess my error is not the calculation, but failing to understand the apparently conflicting information of paragraphs ~15.247 b) 3), and the table in section ~15.249. The former gives a 1 watt limit (for digital modulation summed across all antennas and elements, with other caveats), which we "know" to be the case from work in WIFI, and the later gives 50mV/meter at 3 meters, which, calculates to 750 uW TX power (at 0 dB antenna gain).

It's clear that ~15.247 is the operational regulation being followed; I don't understand what ~15.249 a) is conveying.

Thank you again for your responses.
73
ScottD
KJ4SAF

Jul 31st 2017, 14:39

W1VT

Super Moderator

Joined: Apr 4th 1998, 00:00
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The FCC allows much higher power if you meet the spread spectrum rules in 15.247. But, you can you use any modulation technique you want if you reduce power to the level specified in 15.249.

Zack W1VT
ARRL Senior Lab Engineer