# Amplification of the Radiation from Two Collocated Cellular System Antennas by the Ground Wave of an AM Broadcast Station

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3 gument. The double subscripts mean that this is the z component of the field from the third source (the low frequency source). The form of this equation shows clearly that there is an interplay between field terms that fall off as the inverse of the distance from the source and those that fall off as the inverse square root of that distance. This is the hall mark of a mixture of sky waves and ground waves - i.e. waves that travel along the interface between the earth s surface and the atmosphere. In the high frequency limit, the Fresnel integrals each asymptotically approach 1/, and the complex field equation reduces to E 3, 3 = 1 π r i I Z 0 k l e i - ω t () This is the equation for the complex field of a simple dipole, whose electrical size is kl, in the presence of a perfectly conducting boundary surface. Although the most mathematically expedient way to carry out electromagnetic field calculations is in the complex plane, the physically significant part of the field is the real part of the expressions stated above. The current appearing in these expressions is proportional to the output power of the source divided by the radiation resistance of its antenna. An equation relating the radiation resistance to the electrical size of a dipole antenna is given in Balanis book 5 on p The broadcast source is actually a monopole source over a lossy ground plane. The radiation resistance for a monopole over a surface is 1/ the radiation resistance of a dipole that is twice as long as the monopole. Using the parameters stated on the Federal Communications Commission (FCC) web site, I have computed the electric field of radio station WGY as a function of distance from the antenna. At 1 km, the field is calculated to be about 0 V/m, in fairly good agreement with the FCC s stated value of V/m. This calculation assumed a value of the soil refractive index that is consistent with results from both Balanis P. 173 and Kraus 6 P. 851 for dry earth. The refractive index is a function of the wave frequency, the relative permittivity of the soil, and the electrical conductivity. WGY s frequency is 0.81 Mhz. For Balanis set of dry soil parameters: permittivity = 10 and conductivity = 0.01 S/m, the absolute value of the complex refractive index of the soil is?14.905, and this is in good agreement with the value for Kraus parameters for dry midwestern U.S. soil of permittivity = 16 and conductivity = 0.01 S/m. Therefore, the refractive index of 14.9 was used in these calculations for dry earth. The figure on the next page shows the real part of the electric field resulting from the low frequency source at various distances from the source. This field is time dependent, being a sum of two different functions of position multiplied by a sine term in the time and a cosine term, respectively. The results on the next page correspond to time = zero or an integer multiple of the oscillation period. Some of the people on the ridge live between 6 and 6.5 km from the source. Thus, they are subjected to a fluctuating ground wave field whose maximum amplitude is about V/m. More importantly, the microwave sources on the tower are enveloped in this field. 5 C.A. Balanis, Antenna Theory: Analysis and Design, second edition, John Wiley and Sons, New York (1997) 6 J.D. Kraus, Antennas, second edition, McGraw-Hill, Inc., Boston (1988) 66

5 In the approximation that the frequency of the broadcast source is much smaller than either microwave frequency, one can write the power density of the composite field from all three sources as s = N cos - k r + ω t + M sin - k r + ω t + 1 ρ + N 1 cos- k 1 r 1 + ω 1 t + M 1 sin - k 1 r 1 + ω 1 t + 1 ρ A 4 + A 3 + A 4 A 3 sin - k 3 r 3 + ω 3 t Z 0 (3) In this equation,???and?? are power densities in the absence of the low frequency source for each of the microwave fields, the M s and N s are magnification terms for each of the microwave sources, and the last term in the equation represents the power density stored in the fields of the low frequency source. The magnification terms can be written in terms of ratios of field amplitudes, where the amplitude is defined as the coefficient of the sinusoidal time dependent terms that appear in the electric fields. Thus, the magnification terms are M 1 = A 4 cos k 3 r 3 - A 3 sin k 3 r 3, N A 1 = A 3 cos k 3 r 3 - A 4 sin k 3 r 3 (4) 1 A 1 and an analogous pair of terms applies to the second microwave source. The amplitudes of the microwave fields can be written in either of two equivalent forms. A 1 = - 1 Pw 1 R rad 1 Z 0 k 1 l 1 π r 1, A = - 1 Pw Z 0 π r (5) with analogous equations for the amplitude of the fields from the second microwave source. To use the first form of the amplitude, one must know not only the effective isotropic radiated power (EIRP), accounting for the gain characteristics of the antenna, but one must also know the radiation resistance of the antenna. High gain microwave antennas are more complicated structures than simple dipoles - e.g., the antennas for the second microwave source are log periodic antennas, and the formula quoted here for radiation resistance does not apply. Thus, second equation has to be used here. For the first source, the maximum power put into any one horizontal sector is 3800 watts. The distances of these antennas from the most medically stressed people on the ridge varies from 150 m to 500 m. Thus, the maximum power density and field strength (in the absence of the low frequency source) of the first microwave source vary from 1.34 µw / cm and 3.18 V/m, respectively to 0.1 µw / cm and 0.95 V/m at the locations of the most affected people. The second microwave source has total maximum EIRP of 1000 watts, but, to be conservative, only a third of that amount will be assumed to radiate into any one sector. The power density and field strength for the second microwave source at the same distances range from 1.4 µw / cm and 3.7 V/m to 0.17 µw / cm and 0.98 V/m. 68

6 The amplitudes A 3 and A 4 are computed from the equations which follow: A 3 = - S + 1 cos π η 1 η + C - 1 sin π η 1 η π 1 I Z 0 k l π r (6) and A 4 = C - 1 cos 1 η + S - 1 sin 1 η I Z 0 k l 4 r (7) The total time dependent magnification factor for microwave source is N cos - k r + ω t + M sin - k r + ω t + 1 Conventionally, the magnification effect would be ignored on the basis that the average value of this term is 1.0. However, laboratory experiments have demonstrated that sinusoidal RF waves can affect biochemical processes in cells. Thus, it seems likely that these terms should not be averaged out, but the maximum magnification effect should be determined, so that any likely hazard to health can be noted. Fig. 3 shows the total magnification factor for source at a location 500 m from the tower for dry earth conditions and time = 1/8 oscillation period of source. Fig. 3 Total Magnification of Microwave Source versus Distance from Low Frequency Source for Location 500 m from Microwave Tower (time = 1/8 period of source, Dry Soil) Distance from Low Frequency Broadcast Source (km) 69

7 Figure 4 shows the same kind of results, except that the calculation considers the effect of wet soil. Fig. 4 Total Magnification of Microwave Source versus Distance from Low Frequency Source for Location 500 m from Microwave Tower (time = 1/8 period of source, Wet Soil) Distance from Low Frequency Broadcast Source (km) Very similar results are also obtained for the other microwave source (but not shown here). Having two microwave sources, whose electric field strengths are nearly the same, doubles the overall level of the microwave radiation field on the ridge where the radiation sufferers live. Also variation in the local surface terrain and in soil conditions can likely create hot spots in the radiation density, and these occurrences cannot be predicted, but can be measured. These calculations suggest that the microwave tower could have been located in a minimum ground wave region, had some effort been made to survey the radiation field of all RF sources in the area. 70

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ANTENNA THEORY ANALYSIS AND DESIGN THIRD EDITION Constantine A. Balanis T WILEY INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION Contents Preface 1 Antennas 1.1 Introduction 1.2 Types of Antennas 1.3