where
P t | = | Transmitted Power - Watts |
P r | = | Recieved Power - Watts |
G t | = | Transmitted Antenna Gain - As ratio |
G r | = | Receive Antenna Gain - As ratio |
R t | = | Range from Transmitter to Reflector - Meters |
R r | = | Range from Reflector to Receiver - Meters |
λ | = | Wavelength - Meters |
S | = | Cross section area of reflector |
However this is for reflections off a solid object. We can also simplify this in terms of path loss the follwoing way.
If we look at that equation, and ignore S we see that the loss is minimised when one of the distances in minimised and the other is maximised. The reason for this is that this is the case where most of the transmitted power is reflected.
Another way to think about this - when you have have a couple of antennas connected back to back running as a passive repeater. The passive antenna will only re-transmit the energy that it picks up.
The value for S in the case of two antennas back to back is
beyond the scope of this WWW page. Other
common devices for the reflector that is S are water
towers and steel bridges.
OK. The question becomes what affects S. It is dependant on a number of
factors. These include

 | Capture Area of the antennas
Directivity of the antennas
Efficiency of the antennas
Feedline losses |
Some of these factors are actually used in the calculation for the GAIN
of the antennas. I suspect that S can be computed if you take the ANTILOG
of the antenna gains added, with some constants and multipliers. I think it
might ge something like S = k log -1((Gain 1
Gain2) +n), but that is a guess.
How to build a Passive Antenna

A passive antenna for 802.11 is quite simple. All you need to do is connect two normal antennas together by a SHORT piece of cable. Both antennas and the cable should be 50 Ohms. It is important to get as much gain on both back to back antennas as possible.
It is important there there is NO AMPLIFIER between the antennas. 802.11
is bi-directional. Amplifiers generally only amplify
in one direction leading to problems.
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