# Antenna factor

In telecommunications, the antenna factor is defined as the ratio of the electric field strength to the voltage V (units: V or µV) induced across the terminals of a antenna.

For an electric field antenna, the field strength is in units of V/m or µV/m and the resulting antenna factor AF is in units of 1/m:

$AF = \frac EV$

If all quantities are expressed logarithmically in decibels instead of SI units, the above equation becomes

$AF_{\mathrm{dBm}^{-1}} = E_\mathrm{\mathrm{dBV/m}} - V_{\mathrm{dBV}} = E_\mathrm{\mathrm{dB}\mu\mathrm{V/m}} - V_{\mathrm{dB}\mu\mathrm{V}}$

For a magnetic field antenna, the field strength is in units of A/m and the resulting antenna factor is in units of A/(Vm). For the relationship between the electric and magnetic fields, see the impedance of free space.

In a 50 Ω system, the antenna factor is related to the antenna gain G and the wavelength λ via:

$AF = \frac{9.73}{\lambda \sqrt{G} }$

The variable G means antenna gain (dimensionless) and it can be written in terms of effective aperture A to obtain the final expression considering the impedance of free space (376.7Ω) and the load as 50Ω. The antenna effective aperture can be written as A = (λ2G)/4π.