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Project Compliance to Radiation Exposure Limits.

 

This report was rendered after after being asked to study the safety issues in a project involving power transmission

Introduction

 

The nature to the RF radiation involved in this project is of the pulsed type with a duty cycle less than 1%. Though reported RF radiation threats, as local heating of lightly blood irrigated organs and cardiac pace maker interference could logically relate to peak more than to average RF power densities, every RF radiation regulatory code in the frequency range of interest refers only to average power density and not peak.  Also, no papers in relation to peak v/s average RF radiation could be found, just some comments that the issue has not been properly researched and that there are concerns with the broadcast of DTV, which will have five times more the peak to average ratio than the old NTSC.

 

The criterion to be used for evaluating human exposure to RF radiation will be that of table 1 in document 47 CFR Ch. (10-1-07 edition), which specifies that maximum power densities at different frequency bands. According to that source, at 1030 MHz the power density must average less than 3 mw/cm2 in 6 minutes. It also specifies power density limits for uncontrolled exposures at less than 0.6 mw/cm2 in 30 minutes. These specifications are tighter than those from OSHA (1910.97(a)(2)(1), that allow up 10 mw/cm2.

 

For these frequencies, the electric and magnetic field limits are not specified in the mentioned documents. No wonder, since for such short wave lengths (30 cm), exposures can be assumed to happen already in the radiation zone where the relation between the fields is already determined by the permittivity and permeability of the air and not by particularities of antenna geometries.

 

Considering a perfect omni directional radiator, the power density at a distance r can be expressed as:

 

P = W / (4p r2)                                                                        eq 1

 

Where W is the average power being radiated. For this project, the power would be no more than 560 W at 1% duty cycle, but since interrogations sequences are not likely to be continuous, the real average power can be a lot less that this value. Yet, we will use a 1% duty cycled at 1KW as a worst case figure or 10000 mw of average power.

 

The distances at which the safety conditions for maximum exposure are no longer met for an isotropic antenna is:

 

r = (W / (4p P)) = (10000 / (4p 3)) < 16 cm                       eq 2

 

Case of a Rod Dipole Antenna

The isotropic antenna is just an abstract concept, since an isotropic radiator would violate the basic laws of electromagnetism. The nearest to that is the omni-directional antenna made out of a rod conductor, which has a gain of 2.2 dBi in the plane perpendicular to the rod; this means that the power density there would be 1.66 that of the isotropic radiator, bringing the safety distance to 20 cm.

 

Considering now the above gain, that we can call G, the distances at which the safety conditions for uncontrolled exposure are no longer met satisfy the following inequality:

 

r = (W G (4p P)) = (10000*1.66 / (4p 0.6)) < 46 cm         eq 3

 

These distances compare closely of the wavelength (~30 cm) and so, the 1/ r2 dependency can not be assumed to hold. A rod antenna has roughly a 1/r dependency for distances much smaller than its size and far from the rod extreme, but it could render a good worst case criterion. For points in the mentioned vicinity, the power density can be expressed as:

 

P = W / (2p L r)                                                                      eq 4

 

Where L is the length of the rod antenna. For a 1/4l dipole at 1030 MHz, L is 7.28 cm. Complying distance limit now would be:

 

r = (W / (2p LP)) = (10000 * 1.66 / (4p 7.28*3)) = 60 cm     eq 5

 

It would be safe to say that for distances greater than 60 cm from the rod antenna, radiation is below the rated controlled exposures values.

 

The distance for uncontrolled exposure will then be five times the above or 300 cm. This distance, however, can be considered much greater than 30 cm, so it is already in the 1/ r2 zone that would render 45 cm.  Even if the complying distance could be nearer to this last figure than 300 cm, we should take 150 cm as the compliant distance.

 

Normally antennas are installed in high places for range improvement, rod antennas radiate poorly for directions paralleling the rods, so power densities in the vicinity below a vertically polarized antenna (as happens to be the case) can be expected to be even less.

 

The case of a Directional antenna with a 7dBi gain

 

This antenna also specifies a vertical beam width of 57.  Since the antenna is oriented towards the horizon the (7dBi 3 dB) = 4 dBi radius vector will hit the ground at ~3 h, where h is the height. The power density for points nearer to the antennas pole will increase due to the 1/r2, but will decrease for its pattern.

 

For a worst case calculation, we can do one that considers only the increasing effect of the 1/r2, so we can use eq3 with a G = 2.5 (4dB), the distance r will we minimal height of the pole that, even for uncontrolled exposure, need not be greater than 94 cm for compliance to the CFR safety specification.

 

Considering that any point within the beam sees the full 7dBi gain, the controlled exposure safety distance (from eq3) is only 80 cm, which is less than, not only 3 h, but less than h = 94 cm itself. The uncontrolled exposure safety distance, need not be estimated from beneath the antenna, but within the beam and that brings it up to 180 cm.

 

Peak Power Safety Distance Consideration

 

Though the specifications referenced in the 47 CFR Ch. (10-1-07 edition) consider only average power densities, even without any experimental evidence being reported yet, pulsed RF radiation may have different effects than CW on human tissue. Also the chance of strong pulses interfering with pace makers is obviously greater than that of softly modulated radiation with same average power.

 

If we had considered the instantaneous power instead of the average, the calculated safe distances for maximum exposure would go up ten fold, making the pole ~30 ft. tall to comply to such a requirement or if on the top of a two story building the pole may be 12 ft. This last figure for distance still satisfies the controlled exposure safety limit for a 1000 watt continuous transmission. .

 

The OSHA web site has a link to a radiation safety calculator from University of Texas Amateur Radio Club N5XU. (http://n5xu.ece.utexas.edu/rfsafety/). This calculator is also referenced in the FCC document: Supplement B (Edition 97-01 )to OET Bulletin 65 (Edition 97-01).

 

Results, using this calculator, are less demanding than the ones obtained here. The difference may stem from our worst-case considerations. Below a table comparing results, distances are expressed in feet.

 

Type of antenna

CE (ours)

CE (UTex)

UE (ours)

UE (Utex)

Rod Dipole (avg)

2

1

5

2.3

Directional (avg)

3

1.3

5

3.9

Directional (peak)

30

13

50

39

 

CE and UE stand for Controlled and Uncontrolled Exposure respectively

 

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