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Antenna reciprocity: directivity/gain

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amp2:
Hi,

I read in my courses that antennas are reciprocal so they should have the same directivity and gain when transmitting and receiving. So if I have two transceivers (operating at sub-GHz) one with a pcb trace antenna and the other with a commercial stick dipole, and assuming the transmit power is identical in both transceivers and the path loss being same, will the received power rssi in both transceivers be identical? In theory and in practice?
   

indeterminatus:
Interesting question, also keen to learn the answer to this!

rubidium:
For starters, the receive and transmit gains will easily differ simply if the polarization of the arriving wave is not exactly that of what is being transmitted. Think about it.  Let's say I have 2 identical receivers each driven by identical dipole antennas. Off at infinity I have a single transmitter. As I rotate one of the receive dipoles with respect to the other, certainly I am going to experience received signal strength differences between the 2 receivers.

Further differences will depend on the antenna. Certainly if the antenna is comprised of multiple elements that can be independently weighted, then there is the latitude to have independent transmit and receive patterns. Certainly modern radars (my world) do this to impose sidelobe control on receive to suppress intentional interference, while generally just letting the transmit side go without so-called tapering.

fourfathom:
All else being equal?  I can't prove it, but YES.

ejeffrey:

--- Quote from: amp2 on June 15, 2021, 12:55:26 pm ---Hi,

I read in my courses that antennas are reciprocal so they should have the same directivity and gain when transmitting and receiving. So if I have two transceivers (operating at sub-GHz) one with a pcb trace antenna and the other with a commercial stick dipole, and assuming the transmit power is identical in both transceivers and the path loss being same, will the received power rssi in both transceivers be identical? In theory and in practice?
 

--- End quote ---

Loss is non-reciprocal but in a trival way and that can include path loss as well as loss in the antenna itself.  In any case, as long as the antennas are passive, have no ferrites, and everything is time invariant, this is true,  |S21| = |S12|.  This is a single mode analysis, if you have multiple modes you need to consider each pair of modes independently.

This doesn't mean the link works just as well in either direction because it only applies to the transferred signal, the two antennas may have very different susceptibility to third party signals such as interference and noise.  For instance, a satellite dish can have a very good received SNR even with weak received power because the background noise it sees is generally deep space with a noise temperature of 2.725K.  Try to run the link in reverse and the SNR will be worse because the background noise is blackbody radiation of the earth, plus any in-band terrestrial noise sources.

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