Passive Repeater Calculations
Q: How do I compute fade margin and reliability for a passive repeater link?
A: You must first
determine if the passive repeater is in the “near-field” of
one of the terminal antennas. If the passive
repeater is in the far-field of both antennas, you must treat the two paths as two
independent links. If either the transmitting
antenna or the receiving antenna is in the near-field of
the passive radiator you treat the
entire system as one link.
The calculated field factor needed for this determination is defined as 1/k
1/k = __pld___
4 A cos(α
where:
1/k
= Field factor (unitless)
d = Distance from the
near terminal antenna to the passive reflector in feet
A =
Passive reflector area in square feet
l
= Wavelength in feet
α
= One-half the horizontal angle include between the two terminals in degrees
If the field factor (1/k) is 2.5 or less, then the
If 1/k is greater than 2.5, the passive is in the far field.
The antenna is in the near-field of the passive repeater
If
the antenna is in the near-field of the passive repeater, the entire circuit
encompassing the antenna and passive repeater may be considered as an antenna
system. An example of this is the
typical “fly-swatter
passive” with a reflector (acting as a mirror in a periscope fashion) mounted at 45° to
the ground at the top of a tower. It is
illuminated by an antenna near ground level looking directly up.
In this case it is necessary to determine the gain of that system. The gain is proportional to the projected area of the passive repeater
and the efficiency of illumination, and is usually greater than that of the illuminating
antenna.
A book entitled “Passive
Repeater Engineering-Manual
161A” showing the equations is available for download here. For
more information go to
To use the Microwave Data Base Manager, you consider the system as a single path with the path length equal to the distance from the far terminal to the passive repeater. The antenna gain at the passive end is equal to that of the antenna/passive system gain. A detailed methodology for this calculation can be found in the above referenced text on page 40 in Manual 161A. All other program entries are the same as those of a normal microwave link.
The passive repeater is in the far-field of both terminals
If the passive repeater is in the far-field of both terminals (1/k> 2.5), it is necessary to assume that there are two independent paths. The gain of the passive (Gp) is again dependent upon the projected area of the passive and the illumination efficiency. The formula for the gain in dBi is:
Gp = 20 log [(4pA
cosα) /
l2 ]
Using the SoftWright TAP Microwave Data Base Manager, this case is treated as two paths. At the passive repeater end of each path, the gain used is that determined from the above equation. There are no additional losses at the passive end of the circuits since no waveguide or other transmission elements are involved. The transmitted power (EIRP) used for the second path (passive to far end) is equal to the “Received Signal Level” determined in the calculation for the first path (near end to passive). All other parameters entered are those you would normally enter for a two link system.
[Thanks
to Jim Hart of Hartech, Inc., a