Antenna factor

In electromagnetics, the antenna factor (AF, units: m−1, reciprocal meter) is defined as the ratio of the electric field E (units: V/m or μV/m) to the voltage V (units: V or μV) induced across the terminals of an antenna:

: AF = \frac{E}{V}

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

: AF_{\mathrm{dB/m}} = E_\mathrm{\mathrm{dBV/m}} - V_{\mathrm{dBV}}

The voltage measured at the output terminals of an antenna is not the actual field intensity due to actual antenna gain, aperture characteristics, and loading effects.

For a magnetic field, with units of A/m, the corresponding antenna factor is in units of A/(V⋅m). For the relationship between the electric and magnetic fields, see the impedance of free space.

For a 50 Ω load, knowing that PD Ae = Pr = V2/R and E2= \sqrt{\frac{\mu_0}{\varepsilon_0}}PD ~ 377PD (E and V noted here are the RMS values averaged over time), the antenna factor is developed as:

: AF = \frac{\sqrt{377 P_D}}{\sqrt{50 P_D A_e}} = \frac{2.75}{\sqrt{A_e}} = \frac{9.73}{\lambda \sqrt{G} }

Where

• Ae = (λ2G)/4π : the antenna effective aperture
• PD is the power density in watts per unit area
• Pr is the power delivered into the load resistance presented by the receiver (normally 50 ohms)
• G: the antenna gain
• \mu_0 is the magnetic constant
• \varepsilon_0 is the electric constant

For antennas which are not defined by a physical area, such as monopoles and dipoles consisting of thin rod conductors, the effective length (units: meter) is used to measure the ratio between voltage and electric field.