where
Ae = effective receiving antenna, m2
Pout = power delivered by antenna, W
Pd = power density of the incident wave, W/m2
Following this, then:
In addition, from the ITT Handbook3
where
Gr = gain of the receiving antenna wavelength, m
The output voltage from the antenna VL and the output power are related by the impedance seen by the antenna.
where
Pout = power delivered at the output of the antenna, W
VL = output voltage, V
Z = load impedance of the device connected to the antenna, Ω
Finally, the relationship between electric field strength and power density of the incident and the electric field strength is
where
Pd = power density of the incident wave, W/m2
E = electric field, V/m
Substituting Equations (4), (5) and (6) into Equation (7), gives, for a plane wave
Solving for the AF gives
In a 50-ohm system this becomes
In dBs, this becomes (in units of inverse meters)
The TAF provides a means of computation of the input voltage to the antenna to provide a given value of electric or electromagnetic field at a stated distance from the antenna. The transmit antenna factor relates the value of the electric or electromagnetic field generated by an antenna as a function of its input. Thus, the fundamental relationship is
The transmit antenna factor is, then, expressed in terms of dB:
or:
Derivation of the TAF proceeds from three standard relationships. The first is a variation of the Friss transmission formula4.
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