Formulas for RF Exposure

Python implementation of the FCC's formulas for human exposure to radiofrequency electromagnetic fields. FCC rule changes go into effect on May 3, 2021.

If you prefer web-based you can't do better than VP9KF: http://hintlink.com/power_density.htm

Main examples

Is it compliant?

import fcc

dipole_ssb_phone = fcc.PoweredAntenna(watts=100, t_average=50, duty=20, dbi=2.2)
fcc.is_compliant(dipole_ssb_phone, ft=300, mhz=29, ground_reflections=True, controlled=False)  # very far
# (True, 'MPE')
fcc.is_compliant(dipole_ssb_phone, ft=3, mhz=29, ground_reflections=True, controlled=True)  # closer
# (True, 'evaluation')
fcc.is_compliant(dipole_ssb_phone, ft=1, mhz=29, ground_reflections=True, controlled=True)  # too close
# (False, 'evaluation')

little_source = fcc.PoweredAntenna(watts=0.031, t_average=100, duty=100, dbi=0)
fcc.is_compliant(little_source, ft=1/12/2.54, mhz=300, ground_reflections=True, controlled=False)  # quite nearby
# (True, 'SAR')

The arguments to the first example mean (in order): 100 W at feedpoint, 50% usage, a mode with 20% duty (like SSB), 2.2 dBi gain (like a dipole), distance of 300 feet from antenna, 29 MHz, with ground reflection, and uncontrolled environment. The return value tells you whether you are in compliance (True/False), and the means by which compliance was determined (SAR exemption, MPE exemption, or full evaluation).

Do an RF evaluation

print(fcc.RFEvaluationReport(dipole_ssb_phone, ft=6, mhz=29, ground_reflections=True))
# Power density (mW/cm^2): 0.1010875509909991
# MPE controlled (mW/cm^2): 1.070154577883472
# MPE uncontrolled (mW/cm^2): 0.2140309155766944
# Distance controlled (ft): 1.84406757341948
# Distance uncontrolled (ft): 4.123460449269042
# Compliant controlled: True
# Compliant uncontrolled: True

This RFEvaluationReport class takes very similar parameters to the is_compliant() function above, but it does only evaluation (not trying for exemptions) and also gives you more details. It covers both controlled & uncontrolled environments, so there is no parameter to specify this.

Less common examples

What power is exempt by SAR?

fcc.exempt_milliwatts_sar(cm=1, ghz=0.45)
# 44.372516027834514

This calculates threshold power (P_th) for SAR-based exemption (FCC 19-126, page 23). This example says that if you have a 0.45 GHz (450 MHz) source, which is 1 cm away, you get a SAR-based exemption if "each of the maximum time-averaged power or maximum time-averaged ERP is no more than" 44.4 milliwatts. This method of exemption only applies to UHF or higher, not VHF or HF.

What power is exempt by MPE?

fcc.exempt_watts_mpe(meters=1, mhz=444)
# 5.6832

This calculates effective radiated power threshold for MPE-based exemption (FCC report p. 26). This example means that a 444 MHz source which is 1 meter away is exempt if its ERP is no more than 5.7 watts. If the radiator is closer than a certain cutoff distance, "evaluation is required" (p. 25, footnote 143). This method of exemption works over a much broader range of frequencies.

What power is exempt, generally?

fcc.exempt_watts_generic(meters=0.01, mhz=450)
# (0.04437251602783451, 'SAR')
fcc.exempt_watts_generic(meters=1, mhz=444)
# (5.6832, 'MPE')
fcc.exempt_watts_generic(meters=0.16, mhz=310)
# (0.5327389333009732, 'SAR wins')

This calculates a power threshold by the most favorable method available.

Mind your units! They may be different between some function arguments and return values.

Conclusion

Context

FCC released a report in 2019. The rule changes go into effect on May 3, 2021, hence the flurry of discussion of this topical matter. Amateur (ham) radio is no longer categorically excluded from parts of these rules. The report puts in place some "formula-based" exemptions. They are not too complicated but have lots of piecewise function definitions, "magic number" constants, etc. I have not seen any computer code implementations so far.

Links/references

VP9KF! Best Web calculator: http://hintlink.com/power_density.htm

https://docs.fcc.gov/public/attachments/FCC-19-126A1.pdf

http://www.arrl.org/news/updated-radio-frequency-exposure-rules-become-effective-on-may-3

Hare, Ed (W1RFI). RF Exposure and You. 1st ed., American Radio Relay League, 1998-2003. This is a perfectly lovely book. http://www.arrl.org/files/file/Technology/RFsafetyCommittee/RF+Exposure+and+You.pdf

https://transition.fcc.gov/Bureaus/Engineering_Technology/Documents/bulletins/oet65/oet65.pdf

http://n6nb.com/rfsafetybasic.PDF

Abbreviations/definitions

• FCC: Federal Communications Commission (in the United States)

• SAR: specific absorption rate. Limits are specified in W/kg. Limits are set for whole-body, arbitrary tissue volumes, and certain body parts. Generally the less restrictive exemption.

• RF: radio frequency

• ERP: effective radiated power

• MPE: maximum permissible exposure. Limits are specified in V/m, A/m, and/or mW/cm^2. Limits sometimes derived from SAR limits. Different limits for controlled/uncontrolled areas.

• Exemption: when you don't have to do an RF exposure evaluation. There are 3 ways to be exempt (1 mW, SAR-based, and MPE-based).

• Evaluation: means ensuring "that the exposure limits are not exceeded in places that are accessible to people. In the great majority of cases, such an evaluation is simple and generic and does not require a determination of the precise exposure level..." (FCC p. 34). Per Ed Hare, "A routine evaluation is not nearly as onerous as it sounds!" "Most evaluations will not involve measurements," but will use charts, "straightforward calculations or computer modeling..." (Hare, p. 4.8).

• mobile: normally 20cm or more from a person, e.g. desktop PC wifi

• portable: generally used within 20cm of the body