That's a pretty basic one but for some reason I am stuck now:
Suppose I have a transmitter that transmits Ptx=4W_EIRP with an ideal, omni-directional antenna. The power applied to the antenna terminals is 4W.
Now Frii's equation states that the received power is Prx=Ptx * Gtx * Grx * L (Gtx, Grx antenna gains and L path loss).
Now assume a transmission 1m at 950MHz, the path loss is about 32dB. Assuming lossless components, I would receive 2.5mW ... enough to power a micro controller, sensors etc.
Now I assume I have perfect line-of-sight and create super high gain antennas like Gtx=20dBi, Grx=20dBi. Then the received power would be 4W * 10^((-32+20+20)/10) = 25W ! This is higher than the transmitted power and hence unphysical.
Where is the mistake?