RadHaz Analysis

0273-EX-ST-2009 Text Documents

ViaSat, Inc.

2009-06-04ELS_98807

Analysis of Non-Ionizing Radiation for an 13 m Earth Station Antenna System This report analyzes the non-ionizing radiation levels for a 13 m earth station antenna system. This antenna system is operated at two different frequencies and power levels. Both are examined in this document. The FCC’s Office of Engineering Technology’s Bulletin No. 65 specifies that there are two separate tiers of exposure limits that are dependant upon the situation in which the exposure takes place and/or the status of the individuals who are subject to the exposure. The two tiers are General Population / Uncontrolled environment, and an Occupational / Controlled environment. The applicable exposure limit for the General Population / Uncontrolled environment, i.e., areas that people may enter freely, at this frequency of operation is 1 mW/cm^2 average power density over a 30 minute period. The applicable exposure limit for the Occupational / Controlled environment, i.e., areas that only authorized / trained personnel have access to, at this frequency of operation is 5 mW/cm^2 average power density over a 6 minute period. Summary of expected radiation levels for an Uncontrolled environment when operating at 7.075 GHz and 243 W of input power Region Maximum Power Density Hazard Assessment Far field (Rff) = 2393 m 0.176 mW/cm2 Satisfies FCC MPE Near field (Rnf) = 997.1 m 0.411 mW/cm2 Satisfies FCC MPE Transition region (Rt) (Rt) = Rnf < Rt < Rff 0.411 mW/cm2 Satisfies FCC MPE Main Reflector Surface (Ssurface) 0.735 mW/cm2 Satisfies FCC MPE Note, power density level in the area between the feed and the reflector surface is greater than the reflector surface and is assumed to be a potential hazard.

Because expected radiation levels satisfy MPE for an Uncontrolled environment when operating at 7.075 GHz, the levels for a controlled environment are therefore also satisfied and not shown. Summary of expected radiation levels for an Uncontrolled environment when operating at 1.842 GHz and 1321 W of input power Region Maximum Power Density Hazard Assessment Far field (Rff) = 623 m 0.875 mW/cm2 Satisfies FCC MPE Near field (Rnf) = 260 m 2.043 mW/cm2 Potential Hazard Transition region (Rt) (Rt) = Rnf < Rt < Rff 2.043 mW/cm2 Potential Hazard Main Reflector Surface (Ssurface) 3.982 mW/cm2 Potential Hazard Note, power density level in the area between the feed and the reflector surface is greater than the reflector surface and is assumed to be a potential hazard. Summary of expected radiation levels for a Controlled environment Region Maximum Power Density Hazard Assessment Far field (Rff) = 623 m 0.875 mW/cm2 Satisfies FCC MPE Near field (Rnf) = 260 m 2.043 mW/cm2 Satisfies FCC MPE Transition region (Rt) (Rt) = Rnf < Rt < Rff 2.043 mW/cm2 Satisfies FCC MPE Main Reflector Surface (Ssurface) 3.982 mW/cm2 Satisfies FCC MPE Note, power density level in the area between the feed and the reflector surface is greater than the reflector surface and is assumed to be a potential hazard. Conclusions The proposed earth station system will be located in an environment with controlled access and will be serviced by trained personnel. Only trained personnel will operate the transmitting system during testing. No access to the reflector/feed area will be permitted when the transmitter is turned on. Based on the above analysis it is concluded that no hazard exists for the public when the system is operated at either 7.075 GHz or 1.842 GHz

Analysis for operation at 7.075 GHz The analysis and calculations that follow in this report are performed in compliance with the methods described in the OET Bulletin No. 65. Definition of terms The terms are used in the formulas here are defined as follows: Ssurface = maximum power density at the antenna surface Snf = maximum near-field power density St = power density in the transition region Sff = power density (on axis) Rnf = extent of near-field Rff = distance to the beginning of the far-field R = distance to point of interest Pa = 300 W maximum power amplifier output Lfs = 0.9 dB loss between power amplifier and antenna feed P = 243 W power fed to the antenna in Watts A = 132.732 m2 physical area of the aperture antenna G = 520218 power gain relative to an isotropic radiator D = 13 m diameter of antenna in meters F = 7075 frequency in MHz λ = 0.042 m wavelength in meters (300/FMHz) η = 0.56 aperture efficiency Antenna Surface. The maximum power density directly in front of an antenna (e.g., at the antenna surface) can be approximated by the following equation: Ssurface = (4 * P) / A (1.1) = (4 * 243 W) / 132.732 m2 = 0.735 mW/cm2 Near Field Region. In the near-field or Fresnel region, of the main beam, the power density can reach a maximum before it begins to decrease with distance. The extent of the near field can be described by the following equation (D and λ in same units): Rnf = D2 / (4 * λ) (1.2) = (13 m)2 / (4 * 0.042 m) = 997.086 m

The magnitude of the on-axis (main beam) power density varies according to location in the near field. However, the maximum value of the near-field, on-axis, power density can be expressed by the following equation: Snf = (16 * η * P) / (π * D2) (1.3) = (16 * 0.6 * 243 W) / (π * (13 m)2) = 0.412 mW/cm2 Transition Region. Power density in the transition region decreases inversely with distance from the antenna, while power density in the far field (Fraunhofer region) of the antenna decreases inversely with the square of the distance. The transition region will then be the region extending from Rnf to Rff. If the location of interest falls within this transition region, the on-axis power density can be determined from the following equation: St = (Snf * Rnf) / R (1.4) = (0.412 mW/cm2 * 997.086 m) / R = (410.332 m * mW/cm2) / R where R is the location of interest in meters Far-Field Region. The power density in the far-field or Fraunhofer region of the antenna pattern decreases inversely as the square of the distance. The distance to the start of the far field can be calculated by the following equation: Rff = (0.6 * D2) / λ (1.5) = (0.6 * (13 m)2) / 0.042 m = 2393 m The power density at the start of the far-field region of the radiation pattern can be estimated by the equation: Sff = (P * G) / (4 * π * Rff2) (1.6) = (243 W * 520218) / (4 * π * (2393 m)2) = 0.176 mW/cm2


Analysis for operation at 1.842 GHz The analysis and calculations that follow in this report are performed in compliance with the methods described in the OET Bulletin No. 65. Definition of terms The terms are used in the formulas here are defined as follows: Ssurface = maximum power density at the antenna surface Snf = maximum near-field power density St = power density in the transition region Sff = power density (on axis) Rnf = extent of near-field Rff = distance to the beginning of the far-field R = distance to point of interest Pa = 2000 W maximum power amplifier output Lfs = 1.8 dB loss between power amplifier and antenna feed P = 1321 W power fed to the antenna in Watts A = 132.732 m2 physical area of the aperture antenna G = 32302.9 power gain relative to an isotropic radiator D = 13 m diameter of antenna in meters F = 1842 frequency in MHz λ = 0.163 m wavelength in meters (300/FMHz) η = 0.513 aperture efficiency Antenna Surface. The maximum power density directly in front of an antenna (e.g., at the antenna surface) can be approximated by the following equation: Ssurface = (4 * P) / A (1.1) = (4 * 1321 W) / 132.732 m2 = 3.982 mW/cm2 Near Field Region. In the near-field or Fresnel region, of the main beam, the power density can reach a maximum before it begins to decrease with distance. The extent of the near field can be described by the following equation (D and λ in same units): Rnf = D2 / (4 * λ) (1.2) = (13 m)2 / (4 * 0.163 m) = 259.595 m

The magnitude of the on-axis (main beam) power density varies according to location in the near field. However, the maximum value of the near-field, on-axis, power density can be expressed by the following equation: Snf = (16 * η * P) / (π * D2) (1.3) = (16 * 0.6 * 1321 W) / (π * (13 m)2) = 2.043 mW/cm2 Transition Region. Power density in the transition region decreases inversely with distance from the antenna, while power density in the far field (Fraunhofer region) of the antenna decreases inversely with the square of the distance. The transition region will then be the region extending from Rnf to Rff. If the location of interest falls within this transition region, the on-axis power density can be determined from the following equation: St = (Snf * Rnf) / R (1.4) = (2.043 mW/cm2 * 259.595 m) / R = (530.306 m * mW/cm2) / R where R is the location of interest in meters Far-Field Region. The power density in the far-field or Fraunhofer region of the antenna pattern decreases inversely as the square of the distance. The distance to the start of the far field can be calculated by the following equation: Rff = (0.6 * D2) / λ (1.5) = (0.6 * (13 m)2) / 0.163 m = 623.027 m The power density at the start of the far-field region of the radiation pattern can be estimated by the equation: Sff = (P * G) / (4 * π * Rff2) (1.6) = (1321 W * 32302.911) / (4 * π * (623.027 m)2) = 0.875 mW/cm2


Document Created: 2009-06-04 15:45:37
Document Modified: 2009-06-04 15:45:37
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