RadHaz

0248-EX-PL-2015 Text Documents

ViaSat, Inc.

2015-04-23ELS_161547

OET 65 Radiation Hazard Analysis 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 P = power fed to the antenna A = physical area of the aperture antenna G = power gain in the direction of interest relative to an isotropic radiator D = maximum dimension of antenna (diameter if circular) l = wavelength h = aperture efficiency, typically 0.65 to 0.75 Formulas 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: 4⋅P fS.surface (P , A) ≔ ―― A 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 l in same units): 2 D fR.nf (D , λ) ≔ ―― 4⋅λ 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: 16 ⋅ η ⋅ P fS.nf (P , D , η) ≔ ――― 2 ⋅D

Aperture efficiency can be estimated, or a reasonable approximation for circular apertures can be obtained from the ratio of the effective aperture area to the physical area as follows: ⎛ G ⋅ λ2 ⎞ ⎜――⎟ ⎝ 4⋅π ⎠ ( ) fη G , D , λ ≔ ――― ⎛ π ⋅ D2 ⎞ ⎜――― ⎟ ⎝ 4 ⎠ If the antenna gain is not known, it can be calculated from the following equation using the actual or estimated value for aperture efficiency: 4⋅ ⋅η⋅A fG (A , λ , η) ≔ ―――― 2 λ 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. For purposes of evaluating RF exposure, the distance to the beginning of the far-field region (farthest extent of the transition region) can be approximated by the following equation: 2 0.6 ⋅ D fR.ff (D , λ) ≔ ――― λ The transition region will then be the region extending from R nf to R ff . If the location of interest falls within this transition region, the on-axis power density can be determined from the following equation: Snf ⋅ Rnf fS.t ⎛⎝Snf , Rnf , R⎞⎠ ≔ ――― R 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 power density in the far-field region of the radiation pattern can be estimated by the general equation discussed earlier: P⋅G fS.ff (P , G , R) ≔ ――― 2 4⋅ ⋅R R lt

Results The relevant values will be calculated for a 12 inch antenna operating at 29.5 GHz using a 20 watt power amplifier. −3 c ≔ 299792458 ⋅ ― mW ≔ 1 ⋅ 10 ⋅ Rt ≔ 2.285 ⋅ Rf ≔ 5.485 ⋅ D ≔ 12 ⋅ D = 0.305 10 1 F ≔ 29.5 ⋅ F = ⎛⎝2.95 ⋅ 10 ⎞⎠ ― Pa ≔ 20 ⋅ Pa = 20 .0 ―― 10 Lfs ≔ 10 Lfs = 1 Pa P ≔ ―― P = 20 Lfs η ≔ 0.57 η = 0.57 c λ≔― λ = 0.01 F 2 D 2 A ≔ ⋅ ―― A = 0.073 4 3 G ≔ fG (A , λ , η) G = 5.061 ⋅ 10 10 ⋅ log (G) = 37.042 Ssurface ≔ fS.surface (P , A) Ssurface = 109.64 ―― 2 ⎛ P⎞ Rnf ≔ fR.nf (D , λ) Rnf = 2.285 10 ⋅ log ⎜G ⋅ ―⎟ = 50.052 ⎝ ⎠ Snf ≔ fS.nf (P , D , η) Snf = 62.495 ―― 2 Rff ≔ fR.ff (D , λ) Rff = 5.485 Rff = 17.996 Snf ⋅ Rnf = 142.829 ⋅ ―― St ≔ fS.t ⎛⎝Snf , Rnf , Rt⎞⎠ St = 62.507 ―― 2 2

Sff ≔ fS.ff ⎛⎝P , G , Rf⎞⎠ Sff = 26.772 ―― 2 ‾‾‾‾‾‾‾‾‾‾‾ (P ⋅ G) R5mW ≔ ――――― R5mW = 12.692 R5mW = 41.64 mW 4 ⋅ ⋅ 5 ⋅ ―― 2


Document Created: 2015-04-23 11:48:33
Document Modified: 2015-04-23 11:48:33
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