11.3.1 Transmit Power And Effective Isotropic Radiated Power
After that brief introduction, let us now look at the problem a little more rigorously. If the transmitter amplifier provides power Pamp at its output, the power provided into the antenna terminals is:
where Lt is the coupling loss between the transmitter and the antenna due to connector and transmission-line losses or impedance mismatch. Lt is a fractional quantity between 0 and 1, representing the proportion of amplifier power reaching the antenna terminals.
The power Pt is the power transmitted by the antenna. Earlier we considered a perfect isotropic radiator. Radiating spherically is wasteful, however, as we normally want to transmit to a target receiver and we normally want to increase the power radiated in that direction. We therefore need to modify our isotropic radiated power by taking into account the gain of the transmit antenna in the direction of the receiver. The result is called the effective isotropic radiated power (EIRP). The EIRP of the transmitter in the direction of the receiver is:
where Gt is the transmitting gain in the direction of the receiving antenna. The EIRP represents the power that would have to be radiated isotropically to achieve the same field strength in that direction as the actual directional antenna. Note that antenna gain is dimensionless in Equation 11.5—when we convert it to dB for use in logarithmic equations we will couch gain in dBi in decibel form.
If the propagation medium were perfect, the power density at a distance d from the transmitter would be:
In practice, the medium is not lossless, and attenuation occurs due to absorption, scattering, and other atmospheric effects. Grouping these losses into a single factor La (a fractional value ≤ 1) gives
where La is the total of the atmospheric losses between the transmitting and receiving antennas. These losses are due to a number of reasons that we discuss shortly.
Substituting from Equation (11.5):