The majority of potential RF hazard zones at a site occur in the near field, resulting in the necessity to predict both the near and the far field power density of an antenna array.

In August 1996, the FCC issued a new report and order on human exposure to radio frequency radiation (1) . According to the FCC, changes to the rules mean that over 12,000 antenna installations per year will require evaluation to determine their compliance with the new regulations.

In the past, operators of low-power services, such as cellular, paging, private land mobile and PCS, were not required to address the issue of potential human exposure to radio frequency emissions at their radio sites. The low potential for exposure at such sites had been considered sufficient grounds by the FCC to "categorically exclude" most operators from considering human exposure hazards.

Based on new data, the FCC revised the rules to consider the height of sites above ground and the cumulative operating power at sites. Now, most wireless operators are no longer categorically excluded from analyzing their sites, particularly at shared rooftop sites where the cumulative operating power exceeds the threshold. Furthermore, low-powered systems are not necessarily exempt from safety considerations. According to the new rules, operators with transmitters contributing more than 1% of power density share the responsibility to ensure compliance in areas that exceed the exposure limit.

To meet the FCC enforcement deadline of Sept. 1, 1997, operators across the country are developing programs to ensure that their sites are in compliance with the new FCC guidelines. According to many safety experts, including OSHA (2) , the most important way to ensure compliance with FCC RF health and safety rules is for operators to implement their own comprehensive health and safety program.

To help wireless operators implement their own programs, industry associations such as the CTIA and the PCIA have, or are working on, RF safety manuals (3) . Practical steps involved in the implementation of a health and safety program include:

* Developing written RF health and safety policies and procedures. * Implementing policies and procedures, including training of staff and contractors. * Surveying new and existing sites to gather antenna and radio data. * Determining which sites are not categorically excluded. * Determining site compliance by analyzing or measuring its power density.

Methods describing how to measure RF power density are published in a report by the Institute of Electrical and Electronic Engineers (IEEE) (4) . The FCC provides guidelines on how to analyze or predict power density at a radio site (5) . In most cases, it is more cost-effective to determine compliance by predicting power density at a site than it is to take measurements.

Predicting RF power density FCC guidelines provide approximate models that may be used to calculate power density at AM, FM and television broadcast stations, as well as near aperture antennas (5). According to the FCC, cellular and PCS operators will perform 47% of new RF exposure evaluations. So-called omnidirectional and panel antennas are most commonly used by cellular, PCS and paging operators, but the existing FCC guidelines do not provide methods of predicting power density near these type of antennas.

The power density surrounding an antenna varies as a function of location and is dependent on distance and orientation. The fields around an antenna may be divided into two principal regions, one near the antenna called the near field and one at a large distance from the antenna called the far field (6) . The boundary between the two is often taken to be at the radius

R = 2L(squared)/(lambda)

where L is the maximum dimension of the antenna and (lambda) is the wavelength. In the far field, the shape of the antenna pattern is independent of distance. In the near field, the shape of the field pattern depends on the distance, R. Antenna patterns published by manufacturers are typically only applicable in the far field and therefore are only applicable for power density calculations in the far field of the antenna.

For high-gain arrays at broadband PCS frequencies, this boundary can be at a significant distance from the antenna. At broadband PCS frequencies (~1,900MHz) the boundary between the near and the far field is 50m for a 2m antenna. The majority of potential RF hazard zones at a site occur in the near field, resulting in the necessity to predict both the near and the far field power density of an antenna array.

Rigorous analytical techniques and software methods are available that predict fields surrounding antennas (7) . These techniques typically model antennas as small wire elements and metal plates, with some of the elements fed by signal sources. These methods have a practical limitation, however, because they require detailed information on the physical structure of the antenna that is typically not available. Other less rigorous techniques have been developed to obtain adequate estimates of power density near antennas. These techniques make use of available information, including the physical dimensions and the published gain patterns of the antennas.

Far field model In the case of a single radiating antenna, as described by the FCC (5), a prediction for power density in the far field of the antenna can be made by using the following general equation:

S=PG(sub-i)/4(pi)R(squared)

where S is the power density, P is the power input to the antenna, G(sub-i) is the gain of the antenna relative to an isotropic radiator and R is the distance to the center of radiation. An alternative expression is:

S=EIRP/4(pi)R(squared)

where EIRP is the effective isotropically radiated power.

This model can be modified to consider both ground reflection, G, and the gain of the antenna or EIRP in a particular direction as:

S=(gamma)EIRP(theta,phi)/4(pi)R(squared)

where EIRP(theta,phi) is the antenna EIRP at a particular azimuth, (theta), and elevation, (phi), is found by extrapolating the published horizontal and vertical gain patterns of the antenna to form a three-dimensional antenna gain pattern.

Near field models A method of estimating the power density in the near field of a collinear omnidirectional array is described in a technical report prepared for the FCC (8) . This cylindrical method describes a technique of predicting power density in the near field of collinear arrays, commonly used by wireless operators, which is useful only in the main beam of the antenna. To overcome this limitation, a new method has been developed that models collinear antennas as an array of elements. This collinear method is useful anywhere in the near field of a collinear array.

Cylindrical method A cylindrical radiation model involves computing the average power density on the surface of a cylinder, with a height equal to the antenna's aperture, and a radius equal to the distance of interest. This is illustrated in Figure 1 on page 40.

This model is useful in the near field within the aperture of the antenna. Measurement of collinear arrays (8) show that the power density at a fixed height above the surface falls off exponentially as the antenna's height is raised above the surface. The cylindrical model does not reflect this exponential decrease in power density.

Collinear method modeling collinear antennas as an array of elements with a length of one- half wavelength, it is possible to estimate the power density of the array in both the near and far field to within approximately one wavelength of the array. The accuracy of this technique is dependent on how well an array of linear elements, fed in phase, represents the real antenna. In practice, the elements in an array are not necessarily fed in phase. The error introduced by assuming linear phase is, however, small, if the power is averaged spatially over a number of wavelengths. At cellular or broadband PCS frequencies, a human body is about 5 wavelengths or 10 wavelengths long, respectively. Averaging the predicted power density over the height of a human body at cellular and broadband PCS frequencies provides a reasonable estimate of exposure.

The near field power density of a collinear array is modeled by treating the vertical collinear antenna as an array of N elements spaced one wavelength apart, as shown in Figure 2 on page 42.

The collinear method estimates the number of elements in the array and in the gain pattern of each element. The power density near the antenna is calculated by combining the contributions from each element in the array.

(The collinear method is described in detail in the sidebar article, which follows on pages 50-54.)

Predicted vs. measured results The collinear model has been compared against published measured data. A report prepared for the FCC shows measured power density as a function of distance along the main beam of three collinear antennas (8). Some of the data have been published in an earlier paper (9) . These published measured data are compared against the so-called cylindrical (1/R) model and the collinear method described in the previous section.

Along the main beam Measurements performed on a Swedcom model ALP-9209 directional collinear antenna, mounted with its center of radiation 1.75m above the floor, were taken along the main beam of the antenna to a distance of 4m from the antenna. The antenna has a physical height of 70cm and a gain of 8.2dBd. The power input to the antenna was 25W. A comparison between measured data in predicted results, using the cylindrical and the collinear array model, is shown in Figure 3 on page 42.

Similar measurements were taken from two other antennas. The relevant test parameters are shown in Table 1 at the right.

Figures 4 and 5 on page 44 show the comparison between the measured data and predicted results using both the cylindrical and the collinear models.

These results illustrate that both theoretical methods track the measured results, although the predicted results tend, on average, to be conservative. The data are insufficient to draw statistically significant conclusions, but the results indicate that the average error between predicted and measured values appears to be less than 3dB for measured data that is not spatially averaged, and less than 1dB for spatially averaged measured data.

Below the antenna >From these results, it is clear that both models are adequate for predicting power density in the near field within the main beam of the antenna. In many cases, predicting the decrease in power density as a function of height below the antenna is also a requirement. This situation is particularly important on rooftop sites, where antennas are elevated to reduce exposure on the rooftop. The paper prepared for the FCC (8) provides some normalized measured data that shows the decrease in power density below the antenna at a distance of 4 feet from the antennas. These data have been compared with the collinear method and the results are shown in Figures 6 and 7 on page 46.

The correlation of the predictions to the measured data varies. For the short Swedcom antenna, the predicted results are conservative, while the predictions for the longer Decibel antenna, that is more representative of a collinear array, correlate more closely. Assuming one wavelength spacing between elements, the Swedcom antenna dimensions appear to provide only sufficient spacing for a single element. For a single-element "array," the array pattern is the same as the element pattern. The Swedcom manufacturer's data sheet describes the antenna as a log-periodic reflector antenna. This is not a low-gain element, and the collinear method will simply predict a conservative near field approximation using the far-field gain pattern.

Power density prediction software Power density prediction software may be used to engineer and manage radiated power density on rooftop and tower sites. The software can generate a three-dimensional picture of a site showing the location of antennas, with power density levels superimposed on the rooftop. These levels may be predicted using software tools.

As shown in Figure 8 on page 48, a graphical-user interface (GUI) allows a user to specify the structure of a site, to place antennas at the site and to specify the power and frequency of each antenna.

Using the prediction methods described in the previous section, prediction software is used to predict power density as a function of location. As shown in Figure 9 on page 48, the results are displayed graphically as a color plot showing percentage of maximum permissible exposure as a function of location at the site.

Large wireless operators typically operate thousands of sites across the country that are managed by regional divisions. To ensure uniform compliance with FCC regulations and to coordinate the work of multiple divisions, an operator must keep copies of the analysis and site data at headquarters_typically on file in its regulatory department. A convenient way to do this is to store and to manage the data and analysis results in an electronic database, preferably in a client-server environment that enables geographically separated groups to work on a centralized database. A software tool may also provide the user with a database that may be viewed and manipulated.

Existing sites should be re-evaluated for compliance as new tenants are added. A software tool that stores the existing site information and analysis results in a database, and which allows the user to add new tenant information and reanalyze the site, simplifies the compliance determination process.

Conclusion Ensuring compliance with new FCC health and safety rules must be a critical initiative in any wireless operational strategy. While this may present a new challenge for many operators, advanced tools are available to simplify the process. As part of implementing health and safety policies that comply with FCC rules, operators will be required to measure or to predict the power density at their radio sites. In most cases, predicting power density is a more cost-effective method. A method of predicting power density near collinear arrays has been presented and compared with measured results. This method is accomplished easily by using software tools that analyze, store and interpret relevant information about the sites.

References 1. Guidelines for Evaluating the Environmental Effects of Radiofrequency Radiation, FCC Report and Order, ET Docket No. 93-62, August 1, 1996. 2. Curtis, Robert A. "Measurements for OSHA RF Protection Programs," Symposium on Current Issues in RFR and UWB Measurements and Safety, US DOL/OSHA, San Antonio, TX, Feb. 14, 1995. 3. EME Design and Operation Considerations for Wireless Antenna Sites, Cellular Telecommunications Industry Association. 4. IEEE Recommended Practice for the Measurement of Potentially Hazardous Electromagnetic Fields - RF and Microwave, IEEE C95.3-1991. 5. Evaluating Compliance with FCC-Specified Guidelines for Human Exposure to Radiofrequency Radiation," OST/OET Bulletin Number 65, FCC. 6. Kraus, John D. Antennas, McGraw-Hill, 2nd ed., 1988. 7. Burke, G.J. and A.J. Pogio, Numerical Electromagnetics Code (NEC) - Methods of Moments, Lawrence Livermore Laboratory, January 1981. 8. Tell, Richard. Engineering Services for Measurement and Analysis of Radiofrequency (RF) Fields, Office of Engineering and Technology, FCC. 9. Peterson, R.C. and P.A. Testagrossa, "Radio-frequency electromagnetic fields associated with cellular-radio cell-site antennas", Bioelectromagnetics, Vol. 13, pp. 527-542, 1992.

Estimating the pattern of an element in the array The following approximation is used to estimate the gain of an individual element in any direction. Data supplied by antenna manufacturers typically includes the far field horizontal and vertical gain pattern and the physical length of the antenna, L. Assuming that the collinear array comprises elements with a spacing of one wavelength, l, then the number of elements in the array, N, may be estimated as

N=[(L/lambda)-(1/2)]+1

The maximum gain of each element in the array, G(sub-El,sub-sub-Max) , is

G(sub-El,sub-sub Max)=G(sub-A,sub-sub Max)/N

where G(sub-A, sub-sub Max) is the maximum gain of the array. Given the coordinate system shown in Figure 1 at the right, the normalized horizontal gain pattern of each element in the vertical collinear array is estimated to be the same as the normalized horizontal gain pattern of the array G(sub-A)(phi). In contrast, the vertical gain pattern of each element is not readily extracted from the vertical gain pattern of the array because the shape of the array pattern is highly dependent on the phasing and spacing of the array elements. It is possible, however, to make a reasonable approximation, if the gain of each element is less than about 3dB. The normalized vertical gain pattern of the main lobe of the element is approximated as GEl(theta)5cos3(theta), where theta is the elevation angle. This pattern corresponds to a vertical half-power beamwidth of 758.

The gain of each element in any direction is limited to a minimum of 20dB less than the maximum gain of an element. This has the effect of filling in the nulls of the element pattern and is a conservative approximation used to ensure that the gain of the element is not underestimated in any direction. The gain of an element in any direction is thus calculated as

(See manuscript)

As an example, consider a directional collinear array with the vertical and horizontal gain patterns as shown in Figure 2 below. The normalized horizontal array pattern is the same as the normalized horizontal element pattern. Note that the vertical array pattern is not used. The vertical pattern is approximated using a cos3(theta) function, and the element pattern is limited to a minimum gain of 20dB less than the maximum gain. This is illustrated in Figure 3 on page 52.

Calculating power density The time rate of energy flow per unit area is the Poynting vector (1) , or power density (watts per square meter) in the far field of an antenna is

(see manuscript)

where EIRP(theta,phi) is the effective isotropic radiated power.

The effective isotropic radiated power from a single element is:

(see manuscript)

where P is the power fed to the array. The relationship between EIRP, ERP, and P is:

EIRP=1.64ERP=PG(sub-A)

where GA is the power gain of the array relative to an isotropic source.

The relationship between the Poynting vector and the amplitude of the total electric field intensity, E, at a point in the far field is:

S(sub-r)=1/2*E(squared)/Z

where Z is the intrinsic impedance of the medium (Z5377V in free space). The peak electric field from any element at the location of measurement is

(see manuscript)

where R is the distance from the center of antenna to the location of measurement. The signals from the elements have a different amplitude and a different phase when arriving at the point of measurement. The signals can be added vectorially (or as phasors). Using the center of the array as a phase reference, the relative phase of the ith element is:

(see manuscript)

where RRef is the distance to the center of the array with phase zero and is the distance to the ith element. The contribution from each element is broken into its components,

(see manuscript)

The X and Y components of each phasor are added and the equivalent root mean square voltage is calculated as

(see manuscript)

The root mean square electric field is

(see manuscript)

It may be shown that the average power density is

(see manuscript)

Reference 1. John D. Kraus, "Antennas," McGraw-Hill, 2nd edition, 1988.

Mawrey is director of RF engineering, Riley is staff RF engineer, Higgins is software scientist and Slayden is staff software scientist for the UniSite RF engineering firm, Richardson, TX.