I have a question about RSSI and EIRP. When I bring my smartphone very near my antenna wifi router (+20 dBm EIRP) the analyzer wifi application shows me an RSSI level about -20 to -25 dBm (a negative value). I don't understand this value! If I have +20 dBm EIRP (a positive value), why do I get -20 dBm when I bring my phone close to the router antenna? Why don't I get a value of +20dBm?
The energy output by your transmitter radiates in all directions (perhaps more in some depending on antenna design, but still generally true).
Geometrically speaking, only a very tiny fraction of that outgoing energy is intercepted by the receive antenna.
Hence you have substantial path loss, and even more so if you allow for losses in the transmitter and receive circuitry/antennas that may not be calibrated out of your numbers.
Further, your receiver may have a maximum signal level, either due to limiting at some point in the front end, or the taking of the measurement itself may effectively impose a maximum. RSSI measurements on consumer gadgetry tend to be advisory at best, and there's little need for them to work in the kind of extreme circumstances you are trying.
If you want to take a good measurement, couple a similar antenna to a 2.4 GHz RF power meter, or a professional quality spectrum analyzer with a front end that can accept that much power (most tend to have nameplate limits in the 10-20 dBm range, but you can add a calibrated attenuator inline).