Proper Spatially Averaged Value of RF Fields

Maximum permissible exposure (MPE) limits promulgated by the Federal Communications Commission (FCC) and those recommended by the IEEE (C95.1-1999) are stated in terms of spatially averaged values, averaged over the body size. In practice, measures of the spatial average of RF fields are generally made along a vertical line extending from the ground to head height. The issue of simple vertical line linear field averaging vs. averaging over the projected area (shadow cross section) of the body is discussed at this site elsewhere. This discussion provides insight gained during a measurement project at the World Trade Center to study the RF field levels on the public walkway on the roof of the south tower of the WTC complex.

Because the MPE limits are intended to control the whole-body average specific absorption rate (SAR) in the exposed subject, and because the limits were derived with the assumption that the incident RF fields were uniform, plane electromagnetic waves, the most appropriate measure of field would be one that is devoid of any particular perturbations the might be caused by the exposed subject. For this reason, RF exposure assessments are often performed in the absence of the person normally being exposed. In this fashion, a more meaningful assessment of the exposure fields that could lead to a given SAR value can be made. For example, in evaluating RF field exposures associated with RF heat sealers, it is common practice to remove the operator from their normal position and attempt to perform the measurements with a minimum of observer introduced field perturbation.

Ironically, the very requirement to assess the magnitude of spatially averaged RF fields carries with it an inherent potential for inaccurately determining the proper value. Observer introduced field reflections can significantly alter the field that the measurement probe senses, leading to erroneous field survey results and, sometimes, questionable regulatory compliance assessments. The impact of the interaction of the incident field with the body can be envisioned in this figure.


This figure shows the spatially averaged power density along a vertical 1.8 meter line illustrating the effects of field interaction with a 20-cm radius conductive cylinder, also 1.8 m in height, placed at 1 m radially from the vertical line axis. The cylinder, used as an approximation of the human body standing near a point at which the RF field is being spatially averaged during field measurements, is positioned at eight different locations, each 45 degrees away from the other. The effects of field reflections from the cylinder are illustrated by expressing the 1.8 meter spatial average power density relative to that obtained during unperturbed field conditions (with the cylinder absent). The incident field location was illuminated by a two element, 100 MHz tilted dipole transmitting antenna positioned 30 meters above the height of the roof surface and 100 meters laterally from the point. The spatial resolution of the field calculations was 1 cm and a total of 183 such calculated fields were used in obtaining the spatial average. The unperturbed field is shown in curve 1. The results illustrate the substantial variation in spatially averaged power density values depending on the position of the cylinder. The average of eight spatial averages was found to be 132% of the unperturbed spatial average, indicating that operator interaction with the fields is expected to be substantial in the VHF band similar to the RF environment found on the roof of the south tower of the WTC. The ratio of the maximum spatial average to the unperturbed spatial average was found to be 1.92. These results will be affected by exact location of the reflective body relative to the measurement point and body size and orientation relative to the incident RF field.

While the above results are based on theoretical analysis, using a method of moments technique for computing fields of wire antennas, the figure below provides representative results from an intensive set of measurements taken on the roof of the World Trade Center south tower walkway. In this case, measurements of the spatially averaged fields were obtained at many locations along the walkway for a wide range of broadcast station operating scenarios. At each measurement point, eight measurements of the spatially averaged field were made, each from a different direction relative to the point and equally spaced about the point every 45 degrees, and for the set of eight values, the overall mean and standard deviation were calculated.


Measured spatially averaged RF fields at point 5 on the WTC south tower walkway are expressed as a percentage of the FCC general public/uncontrolled exposure MPE limit. Measured values are displayed as two joined vertical bars with the midpoint equal to the mean value of the spatially averaged fields. The upper and lower extent of the vertical bars corresponds to one standard deviation above and below the mean value.

Based on measurement results obtained in the study, several conclusions were able to be drawn relative to the issue of determining spatially averaged fields.