Exhibit B

1525-EX-ST-2018 Text Documents

Viasat, Inc.

2018-08-29ELS_215039

Analysis of Non-Ionizing Radiation for a ViaSat, model 3420 Parabolic Antenna
Earth Station

This report analyzes the non-ionizing radiation levels for a ViaSat, model 3420 parabolic
antenna earth station.

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 an operational frequency of 2052 MHz is 1 mW/cm^2
average power density over a 6 minute period.

The applicable exposure limit for the Occupational / Controlled environment, i.e., areas that
only authorized / trained personnel have access to, at an operational frequency of 2052 MHz
is 1 mW/cm^2 average power density over a 30 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⎞⎠ = 219.8             Sff = 0.033 ――
                                                   2
                                                                         Satisfies FCC MPE



Transition region ⎛⎝Rt⎞⎠ = 91.6       St = 0.077 ――
                                                  2
                                                                         Satisfies FCC MPE



Near field ⎛⎝Rnf⎞⎠ = 91.6             Snf = 0.077 ――
                                                   2
                                                                         Satisfies FCC MPE



Main Reflector Surface ⎛⎝Ssurface⎞⎠   SSurface = 0.168 ――
                                                        2
                                                                         Satisfies FCC MPE


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.


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)
λ        = wavelength
η        = 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:

                                                             4P
                                      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 λ in same units):

                                                          D2
                                        fR_nf ((D , λ)) ≔ ――
                                                          4λ

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)) ≔ ―――
                                                            ⋅ D2


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⋅ ⎠
                                    fη (G , D , λ) ≔ ―――
                                                     ⎛ ⋅ 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)) ≔ ――――
                                                          λ2


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:

                                                       0.6 ⋅ D 2
                                     fR_ff ((D , λ)) ≔ ―――
                                                          λ

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:

                                                           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)) ≔ ―――
                                                         4 ⋅ ⋅ R2


Results for 24 ft. Diameter Antenna

The relevant values will be calculated for a 24 ft. antenna operating at 2052 MHz using 17.7 W
nominal power.

Constants
c ≔ 299792458 ―                           ≔ 1 ⋅ 10 −3                  ≔1                       ≔1

Variables
                                               ⎛0   ⎞
                                               ⎜――⎟
                                               ⎝ 10 ⎠
D ≔ 24                              Lfs ≔ 10                       Lfs = 1

F ≔ 2052.0                          η ≔ 0.456                                 Pa ≔ 17.7

Definitions
    c                                      D2                           Pa
λ≔―                                 A ≔ ⋅ ――                       P ≔ ――
   F                                        4                           Lfs
G ≔ fG ((A , λ , η))                GdB ≔ 10 ⋅ log ((G))           SSurface ≔ fS_Surface ((P , A))

Rnf ≔ fR_nf ((D , λ))               Snf ≔ fS_nf ((P , D , η))

Rt ≔ Rnf                            St ≔ fS_t ⎛⎝Snf , Rnf , Rt⎞⎠

Rff ≔ fR_ff ((D , λ))               Rf ≔ Rff                       Sff ≔ fS_ff ⎛⎝P , G , Rf⎞⎠

Calculations

λ = ⎛⎝1.461 ⋅ 10 −1⎞⎠               A = 42.028          2
                                                                   P = 17700


G = 1.128 ⋅ 10 4                    GdB = 40.52                    SSurface = 1684.577 ――
                                                                                        2




Rnf = 91.6                          Rnf = 300.4                    Snf = 768.167 ――
                                                                                  2




Rt = 91.6                           Rt = 300.4                     St = 768.167 ――
                                                                                 2




Rff = 219.8                         Rff = 721                      Sff = 329.058 ――
                                                                                  2



Document Created: 2017-05-25 13:22:46
Document Modified: 2017-05-25 13:22:46

© 2024 FCC.report
This site is not affiliated with or endorsed by the FCC