JPL's Wireless Communication Reference WebsiteChapter: Wireless Channels |
For propagation distances d much larger than the antenna size, the far field of the electromagnetic wave dominates all other components. That is, we are allowed to model the radiating antenna as a point source with negligible physical dimensions. In such case, the energy radiated by an omni-directional antenna is spread over the surface of a sphere. This allows us to analyse the effect of distance on the received signal power.
Figure: Transmit antenna modelled as a point source. Transmit power is spread over the surface area of a hypothetical sphere. The receiver antenna has an aperture A, illustrated in orange. |
The surface area of a sphere of radius d is 4pd^{2}. The power density w at distance d from a transmitter with power p_{T} and antenna gain G_{t} is
w = p_{T} G_{t}/ (4 p d^{2}).
The available power p_{R} at a receive antenna with gain G_{R} is
where A is the effective area or `aperture' of the antenna, with G_{R} = 4p A / l^{2}. The wavelength l is c / f_{c} with c the velocity of light and f_{c} the carrier frequency. The product G_{t} p_{T} is called the effectively radiated power (ERP) of the transmitter.
Engineers speak about a "20 log d" path loss law.
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