Foxtrot Radiation Hazard Analysis

0059-EX-ST-2006 Text Documents

ViaSat, Inc.

2006-02-24ELS_74766

Design Analysis Author: Keith Dishman Date: 14 July 2005 Revision: - Subject: Radiation Hazard Analysis of the Foxtrot 7.3M Antenna 1. Introduction This analysis has been prepared to determine the radiation hazard levels for the Foxtrot 7.3M antenna. This analysis is not intended to certify that a safety hazard does or does not exist. It is the responsibility of the organization operating the antenna to evaluate the results of this analysis, along with other sources of data, and determine if a safety hazard exists. 2. Applicable Safety Standards The applicable safety standard for electromagnetic field exposure specified in the Antenna System Requirements Specification is summarized in Table 1. TABLE 1 - ELECTROMAGNETIC FIELD EXPOSURE STANDARDS Power Density Limit General public Occupational Standard Title Issuing Organization exposure exposure Guidelines for Limiting Exposure to Time-Varying Electric, International Commission Magnetic, and Electromagnetic on Non-Ionizing Radiation 1.0 mW/cm2 5.0 mW/cm2 Fields (Up to 300 GHz), issued Protection (ICNIRP) 1998 The power density values given are those that apply to the transmit frequency band of the Foxtrot antenna, 2.000-2.125 GHz. Foxtrot Radiation Hazard Analysis - Rev 1.doc Last Changed: 7/14/05

Radiation Hazard Analysis of the Foxtrot 7.3M Antenna 14-Jul-05 3. Antenna Description The antenna being considered in this analysis utilizes a 7.3-meter diameter axi-symmetric prime-focus design. Some of the antenna dimensions are shown in Figure 1. The antenna is capable of transmitting over the 2.000 to 2.125 GHz frequency band. This analysis will be performed at the mid-band frequency of 2.06 GHz. The antenna is equipped with a high power solid-state amplifier (SSPA) that is capable of producing a saturated output power level of 50 watts. The power delivered to the antenna is 288.0 in determined by subtracting the 62.8° transmission line and diplexer losses from Feed horn the SSPA output power. The loss between 3.32 in square aperture the SSPA output and the antenna feed horn is approximately 3.0 dB. This results in 25.0 watts maximum being radiated by the antenna feed. main reflector FIGURE 1 - ANTENNA GEOMETRY 4. Analysis 4.1 General The power flux densities in the spatial areas surrounding the antenna can be estimated from the geometry of the antenna system and by the use of computer programs capable of computing the near- and far-field radiation patterns of the antenna. The spatial areas around the antenna will be divided into specific regions and an appropriate analysis method will be used for each region. The following regions will be considered: • Region between the feed horn aperture and the main reflector • Region directly in front of the reflector aperture (parallel beam region) • Nearfield region • Far-field region These regions are illustrated in Figure 2. For a large antenna of aperture diameter D, most of the energy in the far-field region, beginning at a distance R=2D2/λ, occurs within a conical volume having a half-angle of λ/D radians. Close to the antenna, the energy is mostly confined to a cylindrical volume of diameter D. This energy is substantially parallel over the first part of the Nearfield region, diverging into a cone of half-angle λ/D at a transition range R0=D2/2λ. The transition from one region to the next is gradual, and the dimensions shown Page 2 of 6

Radiation Hazard Analysis of the Foxtrot 7.3M Antenna 14-Jul-05 indicate the traditional boundaries. Within the region between the feed and main reflector, the energy radiated by the feed is enclosed in a conical shaped volume extending from the feed aperture to the main reflector. λ/D (1.14°) D "parallel" beam region R0=D2/2λ (603 ft) near-field region R=2D2/λ (2,333 ft) far-field region FIGURE 2 - FIELD REGIONS 4.2 Main Reflector – Feed Region The energy radiated from the feed horn is confined to a conically shaped region that extends from the feed aperture to the surface of the main reflector. The energy reflects from the surface of the main reflector and is directed back along the antenna boresite direction. The feed horn is designed such that the energy level at the edge of the main reflector is less than the level at the center of the main reflector. As a first approximation, the energy distribution can be assumed to be uniform over the conical region’s cross-section and the power density can be expressed as: P W = A where A = cross sectional area of the conical region in square centimeters P = radiated power in milliwatts. At the feed aperture (3.32 inches square) we have a power density of: A f = (W f ) = (8.43 cm) = 71.1 cm 2 2 2 P = 25.0 W = 2.5 × 10 4 mW W f = 351.6 mW/cm 2 Page 3 of 6

Radiation Hazard Analysis of the Foxtrot 7.3M Antenna 14-Jul-05 Assuming that total reflection occurs at the main reflector, the power density over the reflector aperture is: 2 ⎛D⎞ Am = π ⎜ ⎟ = π (365.76 cm ) = 420,283.4 cm 2 2 ⎝2⎠ P = 25.0 W = 2.5 × 10 4 mW Wm = 0.06 mW/cm 2 Throughout most of the region between the feed and the main reflector, the actual power density that exists at a particular point is the combination of direct radiation and reflected radiation. For example, over most of the reflector aperture a person would be exposed to direct energy from the feed and to energy reflected from the main reflector. As a result, the electric field in some regions could be twice as strong, resulting in a power density four times as strong (power is proportional to voltage squared). As a conservative estimate, the power densities computed above are multiplied by four, resulting in the following power density values: Feed Aperture Wf = 1,406.2 mW/cm2 Main Reflector Surface Wm = 0.24 mW/cm2 4.3 On-Axis Power Density The radiated power in the region directly in front of the antenna reflector is primarily confined to a cylindrical volume having the same diameter as the reflector and extending out to a distance of approximately R0=D2/2λ. In this region, the power density varies as both a function of distance along the antenna axis and of distance away from the antenna axis. Figure 3 shows the on-axis power density vs. distance for a circular aperture with a 10 dB edge taper, computed using the expression derived by Mumford [3]. Also shown in Figure 3 are approximate formulas by Mumford that can be used to estimate the maximum power density. Page 4 of 6

Radiation Hazard Analysis of the Foxtrot 7.3M Antenna 14-Jul-05 On-Axis Radiation Hazard Analysis 10 1 Power Density (mW/cm^2) 0.1 0.01 1 .10 3 1 .10 1 .10 3 4 10 100 Distance (feet) Exact Expression Approximate Expression FIGURE 3 - ON-AXIS POWER DENSITY VS. DISTANCE FOR A CIRCULAR APERTURE WITH A 6 DB PARABOLIC ON PEDESTAL APERTURE TAPER The simple expression for the maximum on-axis power density in the near-field region is: 4P Wnf = mW/cm 2 Am where P is the transmit power and Am is the reflector aperture area. For the Foxtrot antenna, this is: Am = π (Rm ) = π (365.8 cm ) = 420,283.4 cm 2 2 2 P = 25.0 W = 2.5 × 10 4 mW Wnf = 0.24 mW/cm 2 The simple expression for the maximum on-axis power density in the far-field region is: Page 5 of 6

Radiation Hazard Analysis of the Foxtrot 7.3M Antenna 14-Jul-05 Am P W ff = mW/cm 2 λr 2 2 where λ is the wavelength and r is the distance from the aperture. 4.4 Off-Axis Power Density In order to determine the variation of power density off of the antenna axis, more sophisticated antenna analysis methods must be used. One such tool is the GRASP9 computer code, which permits the near- and far-field patterns of reflector antennas, such as the Foxtrot antenna, to be analyzed. Previous analyses of similar antennas shows that the power density is relatively constant over the angular region corresponding to the cylindrical projection of the main reflector aperture, and that the power drops off rapidly outside the main reflector boundaries. The magnitude of the power density corresponds to the on-axis power density levels predicted by the approximate expression in the previous sections. Because the on-axis power density for the Foxtrot antenna is well below the 1.0 mW/cm2 power density limit of the general public exposure standard, it is not necessary to compute the off-axis power density levels. 5. Summary of Results The results of the analyses are summarized in Table 2. TABLE 2 - SUMMARY OF RESULTS Comparison to Safety Standard Power General public Occupational Density exposure exposure Region mW/cm2 1 mW/cm2 5 mW/cm2 Feed Aperture 1,406.2 Exceeded Exceeded Main Reflector Surface 0.24 Acceptable Acceptable Aperture Plane 0.24 Acceptable Acceptable Near-field at a Radius of 0.05 Acceptable Acceptable 1,000 feet Far-field (beam peak) See Figure 3 Acceptable Acceptable These results indicate that the only region where the referenced safety standards are exceeded is the following: • The conical shaped region between the feed and main reflector. Personnel hazards in this area may be avoided by disabling the transmitter whenever anyone attempts to access the area between the feed and main reflector. 6. References 1. Guidelines for Limiting Exposure to Time-Varying Electric, Magnetic, and Electromagnetic Fields (Up to 300 GHz), International Commission on Non-Ionizing Radiation Protection (ICNIRP), 1998. 2. Mumford, W.W., “Some Technical Aspects of Microwave Radiation Hazards”, Proc. IRE, vol. 49, pp. 427-447, February 1961. Page 6 of 6


Document Created: 2006-02-24 14:24:57
Document Modified: 2006-02-24 14:24:57
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