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RF Equations

Free Space Loss

Free Space Loss = 32.5 + 20log(d) + 20log(f) dB, Where D is the distance in km and f

is the frequency in MHz

Free Space Loss = 92.5 + 20log(d) + 20log(f) dB, Where D is the distance in km and f

is the frequency in GHz

Dish Antennas

Gain

G = 4 Ae / 2 where Ae is the effective area Ae = x A

= illumination efficiency and A = D2/4 where D = dish diameter.

Beamwidth

This is related to the gain. For a circular dish, the half power beamwidth in the

Electrical plane is E = 73 / D. A useful approximation where the half power

beamwidth is expressed in degrees gives the gain in dB:

Gain (dB) ~ 10 log10 [31,000 / (Elevation Beamwidth) x (Azimuth Beamwidth)]

Focal length of parabolic dish

This only works for prime focus dishes but can be useful. Measure the diameter of thedish, call this value D. Then measure the depth of the dish, the distance from from the

plane of the rim to the centre and call this value d. Then:

FL = D2 / 16d

Focal point of a parabolic satellite dish

Focal point inside horn = dFL / D dD / 16 FL

D = dish diameter

d = feed waveguide aperture diameter (without scalar ring)FL = dish focal length (prime focus)

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Far Field / Near Field

An antenna is not a point source of radiation and this has to be taken into account whencalculating the field strength at a distance from the antenna. At large distances, a dish

may be considered as effectively equivalent to a point source, this is the far field. In the

far field, the wavefront can be considered to be planar with E and H field vectors

normal to the direction of propagation. Close to the dish is the near field region, where

evaluating the E and H fields is more complex. The transition from near field to far

field is not sharp, however the near field for a parabolic antenna is generally considered

to extend out to the distance:

dnearfield < D2/8

The far field distance is given by:

dfarfield >2D2/

Where D is the dish diameter and the wavelength.

Some figures may be of interest, at 10GHz with a 1m dish, the far field distance is 70m.

RF Exposure

At the inner edge of the far field region of a dish, the power flux density (PFD) for a

transmitted power P may be calculated as:

PFD = 3 P/64D2 watts/m2

The situation in the near field is more complex. For a dish antenna with a tapered feed

the variation in near field power density with distance and normalised to unity at the

edge of the far field (2D2/ ) can be modelled as:

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where

R = Distance from aperture.

To calculate the field, increase the power density at the edge of the far field by the ratio

calculated from the equation above.

When working out exposure limits the maximum value of the above function has been

taken as a worst case. This occurs near X = 0.1, which is 10% of the far field distance.

The correction factor at this point is 41.3.

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