RF Exposure Safety with Three
Multi-Band Inverted-L Antennas
Peter DeNeef, AE7PD
Published in QEX, November/December 2017, pp 3-5.
Reprinted with the permission of the ARRL. Copyright ARRL.
Formatted for electronic devices.
In RF Exposure and You, Ed Hare observes that “End-fed wires worked against earth ground almost always result in more exposure in the shack or nearby rooms than would an antenna located farther away.” [1] You can find safety compliance distances for many antennas in the General Purpose Tables in Section 4 of Supplement B to FCC OET Bulletin 65. [2] The General Purpose Tables are based on a formula that depends on the frequency, power, and antenna gain. [The formula is given in Section 2 of Supplement B to FCC OET Bulletin 65 along with an EPA-recommended power factor of 2.56 that is used to account for ground reflections—Ed.] The Paul Evans, VP9KF, online calculator uses this same formula. [3] ARRL Lab comparisons with numerical electromagnetic code (NEC) simulations showed that predictions from the general purpose formula give conservative compliance distances for a number of resonant antennas—dipoles, ground planes, and Yagis.
In 2007, Kai Siwiak, KE4PT, reported a similar comparison for a non-resonant end-fed inverted L antenna. [4] The KE4PT attic-mounted antenna comprises a pair of 48 ft long parallel horizontal wires separated 1 m apart and shorted at each end, with a 14 ft vertical section fed at the bottom against a ground rod connected to a 21 ft high vertical mast. Predictions from the general purpose formula were useful at 7 MHz and above, but they are too low for the lower frequency bands. Strong RF magnetic fields near the wires result in compliance distances greater than even the conservative tables predict.
I calculated FCC compliance distances using NEC models for three end-fed inverted L antennas, and compared them with predictions from the OET Bulletin tables. My NEC models [5,6] are available on the QEX files web page.
Figure 1(A) shows my NEC model of a 13 ft high inverted-L. It comprises a a 61 ft length of #14 copper wire with a 48 ft horizontal section, and is similar in overall size to the KE4PT antenna. To be conservative the model includes a very good radial ground system that is described in the NEC Model section below. To avoid problems with wire-to-earth connections in NEC2 the buried radials are represented by slightly elevated wires.
Figure 2 shows FCC compliance distances for Controlled areas at 100 watts average power. Distances are measured from the closest part of the antenna to the point of exposure. Figure 3 shows distances for Uncontrolled/Public areas. The diagonal lines are predictions from the general purpose formula when the gain is 0 dBi. They are too low in the 40 – 80 meter bands.
The open circles are from the ARRL NEC Tables (from Note 1) for resonant quarter-wave ground-mounted verticals. W1RFI notes that the compliance distances from this NEC model can be used for end-fed random wires longer than a quarter-wave. Accordingly, the NEC Table predictions above the quarter-wave resonance at 4.09 MHz are close to or above the simulation results. (At 25.1 MHz the two Public area distances are within 0.5 ft, a difference that is not significant when the predictions are used conservatively.) There is no NEC table for the 60 meter band.
At 25.1 MHz the feed point impedance is nearly 2000 ohms—beyond the range of a typical tuner—because the wire length is close to three half-wavelengths.
A Higher Wire
Figure 1-B (above) shows my NEC model for a 30 ft high inverted-L with the same wire length and radial system as Figure 1 (A). Figures 4 & 5 show the 100 watt compliance distances for controlled and for public areas respectively. The general purpose formula predictions are again too low in the lower frequency bands, and the ARRL NEC Table predictions are close to or above the simulation results.
A Lower Wire
Figure 6 shows my NEC model for an inverted-L mounted along the top of a 6 ft high fence. A grounded counterpoise runs parallel to the wire at a height of 1 ft. Figures 7 & 8 show that the 100 watt compliance distances for this antenna are longer than for the previous examples for both uncontrolled and public areas respectively. For instance, at 14.3 MHz the distance in controlled areas is 3.9 ft, compared with 1.8 ft for the 13 ft high wire and 1.3 ft for the 30 ft high wire. Both types of prediction fail for many of the bands in both controlled and uncontrolled/public areas.
The fields near this antenna are more intense because the wire is coupled more closely to the ground system. Figure 9 shows contour plots from the simulation, showing two magnetic field strengths at 14.3 MHz and 100 watts. HC = 0.34 A/m and HU =0.15 A/m are the maximum permitted exposure in controlled areas and uncontrolled/public areas respectively. Arrows indicate the horizontal compliance distances, 3.9 ft and 8.3 ft. The cross-section view in Figure 9 is at a peak of the standing wave current, 12 ft. from the feed point end of the wire. At a peak of the standing wave voltage—17 ft farther along the wire—the contours of the electric field are similar to Figure 9. The compliance distances for electric field exposure are 3.6 ft and 7.5 ft, so the magnetic field determines the results in this case. Figure 10 shows 14.3 MHz compliance distances vs. average power. Decreasing the power from 100 W to 50 W reduces the distances by about 30%.
NEC Models
I used NEC2 models to compute electric and magnetic field strengths, and compared them to FCC maximum permitted exposures [2]. Each reported compliance distance is the longer of two calculated distances, one for the electric field and another for the magnetic field.
All wires are #14 AWG copper. To be conservative each model includes a very good ground system. NEC2-based programs do not calculate wire-to-earth connections accurately, so buried radials are represented by wires that are slightly elevated—between 0.001 and 0.01 wavelength above earth ground. For example, at 14 MHz the
elevation d = 0.5 ft. The ground systems for the 13 ft and 30 ft high inverted-L antennas are thirty-two 48 ft radials over NEC average ground. The segment lengths are smaller near the central junction, gradually increasing at greater distances from the junction to reduce computation time. [5]
The counterpoise for the 6 ft high inverted-L is connected to earth ground. To avoid problems with the wire-to-earth connection I used NEC perfect ground in the model. KE4PT compared his NEC2 simulations (including wire-to-ground connections) vs. spot calculations with an NEC3 engine, which can model buried ground rods. The relative field strengths away from the ground post connection were typically within 10%. Ground-level field values were only similar if he used a perfect ground in the NEC2 model.
Incidental Radiation
W1RFI lists end-fed wires with one end in the shack as a problem that can cause excessive incidental radiation. Incidental RF fields are from sources not included in the NEC simulation, such as cables, equipment, and longer wires to an RF ground system. They can create unexpected hot spots.
Conclusions
If you use a fixed or portable end-fed antenna, a remote tuner is more than just a good idea for convenience. It enables you to locate the antenna a safe distance away. These compliance distances are important if the wire is located close to people in controlled or public areas. Neither the general purpose formula nor the ARRL NEC Tables work for all bands in all three examples. For the two classic inverted-L antennas the predictions from the ARRL NEC tables are useful when the wire is longer than a quarter-wavelength.
For the lowest inverted-L, ground coupling increases the calculated compliance distances to the point that ARRL NEC table predictions are often too low. In the analysis of his end-fed antenna, KE4PT concludes that unusual antennas require careful evaluation, especially if a ground or ground post is part of the system.
References
1. E. Hare, W1RFI, RF Exposure and You, ARRL. (Currently out of print), use OET Bullletin 65b (1997).
Note added 4/29/2020: Archived at http://www.arrl.org/rf-safety-publications.
2. Evaluating Compliance with FCC Guidelines For Human Exposure to Radiofrequency Fields, OET Bulletin 65b (1997),
https://www.fcc.gov/bureaus/oet/info/documents/bulletins/oet65/oet65b.pdf
3. P. Evans, VP9KF, Amateur Radio RF Safety Calculator.
http://hintlink.com/power_density.htm
4. K. Siwiak, “KE4PT, An All-Band Attic Antenna,” QST, Oct 2007, pp. 33-37.
5. Several versions of EZNEC antenna modeling software are available from developer Roy Lewallen, W7EL, at https://www.eznec.com
6. Arie Voors, 4n3c2 NEC based antenna modeler and optimizer
https://www.qsl.net/4nec2/