RF Exposure Analysis

0123-EX-ST-2018 Text Documents

ViaSat, Inc.


Analysis of Non-Ionizing Radiation for a 13.5 m Earth Station Antenna System

This report analyzes the non-ionizing radiation levels for a 13.5 m earth station antenna

The FCC’s Office of Engineering Technology’s Bulletin No. 65 specifies that there are
two separate tiers of exposure limits that are dependent 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.

The antenna will not be operated in an uncontrolled environment so only the controlled
environment values are summarized.

Summary of expected radiation levels for a Controlled environment

Region                         Maximum Power Density                 Hazard Assessment

Far field (Rff) = 3063.92 m           0.96 mW/cm2                    Satisfies FCC MPE

Near field (Rnf) = 1276.63 m          1.36 mW/cm2                    Satisfies FCC MPE

Transition region (Rt)
(Rt) = Rnf < Rt < Rff                 1.745 mW/cm2                   Satisfies FCC MPE

Main Reflector Surface (Ssurface)     2.84 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.


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.


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 = 1310W                     maximum power amplifier output
Lfs = 1.1 dB                   loss between power amplifier and antenna feed
P = 1016.88 W                  power fed to the antenna in Watts
A = 143.14 m                   physical area of the aperture antenna
G = 677837.65                  power gain relative to an isotropic radiator
D = 13.5 m                     diameter of antenna in meters
F = 8400                       frequency in MHz
l = 0.036 m                    wavelength in meters (300/FMHz)
h = 0.48                       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 * 1016.88 W) / 143.14 m2

        = 2.84 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 l in same units):

Rnf     = D2 / (4 * l)                                                     (1.2)

        = (13.5 m)2 / (4 * 0.036 m)

        = 1276.64 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 * h * P) / (p * D2)                                              (1.3)

       = (16 * 0.48 * 1016.88 W) / (p * (13.5 m)2)

       = 1.364 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

St     = (Snf * Rnf) / R                                                      (1.4)

       = (1.364 mW/cm2 * 1276.63 m) / R

       = (1741.33 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) / l                                                       (1.5)

       = (0.6 * (13.5 m)2) / 0.036 m

       = 3063.92 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 * p * Rff2)                                             (1.6)

       = (1016.88 W * 677837.65) / (4 * p * (3063.92 m)2)

       = 0.96 mW/cm2

Document Created: 0430-12-08 00:00:00
Document Modified: 0430-12-08 00:00:00

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