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I have just started learning about wireless systems and for some reason I'm hung up on what I feel is a fundamental idea.

Consider some transmitter-receiver pair with isotropic antennas. The receiver needs some minimum power (say, Pr), and knowing the transmit power (Pt) and the frequency, I can determine the maximum working distance R between the transmitter and the receiver via the path loss and link budget equations.

Now knowing R, I decide to set up two of the same receiver as before, each a distance R from the transmitter. Will my system still work, or does the transmit power Pt need to scale up with the number of receivers? What about for an arbitrarily large number of receivers?

I'm torn between thinking that the system couldn't possibly work because it does not seem to obey conservation of energy, and that it should work because the EM waves are radiating in all directions, so I was not "using" all of the power in the first place. Any clarifications would be welcome, especially if you can link sources. Thanks!

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When an isotropic antenna transmits power it does so in all directions. At some distance R all that power is passing thru the surface of an imaginary sphere of radius R. At distance 2R, the same amount of power is passing thru the surface of a sphere of twice the radius etc etc..

An isotropic receive antenna placed at some distance to the transmit antenna can only collect a small fraction of that power. It has, what is called, an effective area (or antenna aperture) and this is measured in sq metres.

This means that two isotropic antennas (that don't overlap) can each collect their own power and the transmit antenna doesn't know - it believes (if it had the power to reason) that all the power transmitted is going to reach the far ends of the universe.

The same is basically true of any antenna - providing the effective apertures don't overlap they'll each collect the "theoretical" power transmitted by that sort of antenna.

All this falls down when you get to the near field because in the near field you can effect the transmit antenna by loading.

Think of it like a light-bulb - several people in the room can each see the light but if one person stands in front of another then somebody misses out.

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