Doug Lung /
Calculating RF Power Density and Exposure
The FCC is actively checking broadcast sites for compliance with FCC Rules §1.1310, RF radiation exposure limits. Every broadcaster has had to certify compliance with the rules either in the original application for their facility or in the license renewal. However, sites that met exposure limits in the past may exceed the limits now due to the addition of DTV transmitters. This month I'll look at how the FCC is evaluating compliance, new requirements the FCC is considering, and give you some tools for accurately evaluating RF power density from your analog or DTV facility.


FCC engineers have been making unannounced visits to broadcast sites to see if RF power density exceeds the amount specified in §1.1310 in areas accessible to the public. The power density limit for public exposure is 0.2 mW per cm2 at VHF TV frequencies. The power density at UHF depends on the frequency. The formula used to determine the maximum power density at UHF channels in areas accessible to the public is:

Power Density (mW/cm2) = F(MHz)/1500

FCC Rule §1.1307(b)(3) states: "In general, when the guidelines specified in §1.1310 are exceeded in an accessible area due to the emissions from multiple fixed transmitters, actions necessary to bring the area into compliance are the shared responsibility of all licensees whose transmitters produce, at the area in question, power density levels that exceed 5 percent of the power density exposure limit applicable to their particular transmitter or field strength levels that, when squared, exceed 5 percent of the square of the electric or magnetic field strength limit applicable to their particular transmitter."

One method the FCC has been using to determine the contribution of individual transmitters to the total RF power density in public areas at the site is to measure the power density before and after an individual transmitter is shut off. If the power density drops more than 5 percent of the public exposure limit, then the station is considered to be responsible for bringing the area into compliance and may be fined.

The FCC is proposing new RF exposure regulations. I reported on this Notice of Proposed Rule Making (NPRM) in my June 30 RF Report. Please refer to that article for a complete description of the proposed changes.

The FCC is not planning to change the allowable exposure limits or OET-65 calculation techniques; however they are considering allowing the use of spatial averaging, which should lead to measurements that more closely match absorption by a human in congested areas where there are a lot of reflections or multiple sources contributing RF.

Under the proposed rules, when calculations are used to show RF power density will not exceed FCC limits the licensee would have to provide details on how the power density was calculated. The spreadsheet I'm describing here should meet those requirements when the number of contributors is limited (and thus easily studied) or when the resulting power density in public areas is less than 5 percent of the public exposure limits.

The commission is also proposing to modify §1.1310 with language stating, "Licensees and applicants are generally responsible for compliance with both the occupational/controlled exposure limits and the general population/uncontrolled exposure limits in Table 1 as they apply to transmitters under their jurisdiction. Licensees and applicants should be aware that the occupational/controlled exposure limits apply especially in situations where workers may have access to areas in very close proximity to antennas where access to the general public may be restricted."

Given the difficulty some sites are likely to have bringing power density down to the public exposure levels, broadcasters will be relieved to find that the NPRM states that transient individuals simply need to be made aware of their exposure and says this could be achieved "by means of written and/or verbal information, including, for instance, appropriate signage." The words "exercise control" would be specified as meaning "an exposed individual is able to reduce or avoid exposure by administrative or engineering work practices, such as use of personal protective equipment or time averaging of exposure." The FCC has had a policy of allowing the use of signs, rather than fences or barriers, in areas such as roads or hiking trails. The NPRM would add a note explaining this to the rules.


The definitive guide for calculating the power density is FCC Office of Engineering and Technology Bulletin OET-65, Evaluating Compliance With FCC Guidelines for Human Exposure to Radiofrequency Electromagnetic Fields. Supplement A has additional information for broadcast stations. You can download it from

The formula for determining the power density from an analog TV station is:

(click thumbnail)

I showed how this formula was derived in my RF Technology column in the October 1992 issue of TV Technology. You will find the same information in more detail in OET-65. I haven't posted this on my Web site, but will if there is interest. Note that while the formula hasn't changed since the article was published, the allowed RF power density levels have.

There is no special formula for DTV transmitters. Because DTV effective radiated power is defined as average power, calculation is simplified since there is no need to convert the peak (sync tip) visual effective radiated power to average power. Replace the [0.4 ERPv +ERPA] portion of the equation with [ERPD] where ERPD is the DTV effective radiated power.

While it would be possible to calculate the power density at each critical location individually, unless a large number of points around the tower are evaluated at all various distances, it is easy to miss a hot spot generated by a side lobe peak in the elevation pattern or a public area on higher ground that received excessive RF because it was close to the main beam from the antenna. This can be a problem on mountaintop sites where terrain is irregular and towers tend to be shorter.


After being faced with some complex RF exposure studies, I decided there had to be an easier, more accurate way to determine power density on the ground. I developed a simple spreadsheet application to analyze RF power density at different angles and distances from the antenna. The current result is shown in Fig. 1. You can download the spreadsheet from my site at Look in the FTP (files) area.

(click thumbnail)
Fig. 1

The spreadsheet should be self explanatory, but I'll describe the entries required and walk you through a sample analysis.

Before beginning an analysis, you will need the elevation pattern from the antenna manufacturer. This is usually part of the antenna specification and should be available electronically. Elevation pattern data exported from Dielectric's DASP software or Andrew's ABSP software may be sufficient. I would recommend, however, that if the study shows you are close to the limits you should try to obtain the elevation pattern for your specific antenna from the manufacturer.

If the antenna has mechanical beam tilt, you will need to take that into account by moving the elevation pattern up or down by the amount of tilt at the azimuth studied. As the tilt varies proportionately with azimuth, you can set up another spreadsheet to determine the amount of mechanical tilt at any azimuth angle.

Let's set up the spreadsheet for a hypothetical analysis, starting from the top left corner of the spreadsheet.

Enter the maximum visual ERP (main beam) in cell C5. Enter the aural ERP (usually 10 percent of the visual ERP) in cell C6. If analyzing a DTV station, leave C5 blank or enter zero and put the maximum average main beam DTV ERP in C6. Cell C7 allows you to enter different relative field values (0 to 1) for the azimuth pattern. I recommend leaving this at 1 to see ground power density at the maximum ERP. To analyze exposure at different azimuths, enter the relative field for that radial in C7.

The average ERP is calculated from the numbers in cells C5, C6 and C7 and displayed in cell C8.

As noted earlier, the RF radiation limits in §1.1310 change with frequency. Enter the frequency in C9 in megahertz and the controlled and uncontrolled (public) environment power density allowed will be displayed in C10 and C11, respectively.

Enter the antenna center of radiation height above ground in C12. The 2-meter value in C13 for the height of a person should be left unchanged for most FCC studies. In cell C14 you can enter an adjustment to compensate for terrain changes or to analyze rooftop exposure. Use a positive number if the adjustment moves the point above the tower base or a negative number to lower it.

Once this data is entered, the calculated minimum distances that comply with occupational and public exposure limits is displayed in cells C16 through C19. I added cells C20 and C21 to show the minimum distance to 5 percent of the public exposure limit. Cell C22 is a place to put the antenna model number for reference.

The spreadsheet gets a bit more complicated in row 27. This is where the on ground power density is calculated at each available elevation angle from the antenna. Cell B27 contains the elevation angle from the antenna. For this spreadsheet, 90 degrees is straight down and 0 degrees is horizontal, matching the format used by the major antenna manufacturers in their specifications. The relative field at the angle in cell B27 is in C27. These two columns are the only ones that require input in this part of the spreadsheet. Trigonometry is used to calculate the total distance to the ground at this angle. Note that at 90 degrees, this will be radiation center height in C15. The horizontal distance from the tower to the point on the ground is calculated using the Pythagorean theorem and displayed in E27. Although E27 is not used in the power density calculation, it is needed to determine where the analyzed spot is in relation to the tower.

The calculated power density, using the formula described earlier, is displayed in cell F27. Cells G27 and H27 show the power density as a percent of the occupational and uncontrolled (public) exposure levels in §1.1310. I set up the spreadsheet so that cells with power density in excess of 5 percent of the public limit are displayed in red.

To add the data for your antenna, delete the data below row 27 in columns B and C. Paste the data from the antenna elevation pattern into columns B (angle) and C (relative field) starting at row 27. If you run short of the formulas in columns D through H, simply copy them from the rows above. Note that the formulas don't work for elevation angles of zero degrees to higher, as they never hit the ground. I've found the best way to get data from manufacturer's data sheets or software is to paste or import the data into another spreadsheet, where it can be sorted and easily pasted into the analysis sheet. If you receive the antenna data in a PDF document, it is best to copy the data off the page, paste it into a text document, and import it into a spreadsheet.

Try it out and if you have any questions on the spreadsheet, drop me a note at

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