In electromagnetics, the antenna factor (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.

For an electric field antenna, the resulting antenna factor AF is:

${\displaystyle AF={\frac {E}{V))}$

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

${\displaystyle AF_{\mathrm {dB/m} }=E_{\mathrm {\mathrm {dBV/m} } }-V_{\mathrm {dBV} ))$

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.[1][clarification needed]

For a magnetic field antenna, the field 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.

For a 50 Ω load, knowing that PD Ae = Pr = V2/R and E2= ${\displaystyle {\sqrt {\frac {\mu _{0)){\varepsilon _{0))))}$PD ~ 377PD (E and V noted here are the RMS values averaged over time), the antenna factor is developed as:

${\displaystyle AF={\frac {\sqrt {377P_{D))}{\sqrt {50P_{D}A_{e))))={\frac {2.75}{\sqrt {A_{e))))={\frac {9.73}{\lambda {\sqrt {G))))}$

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
• ${\displaystyle \mu _{0))$ is the magnetic constant
• ${\displaystyle \varepsilon _{0))$ 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.

## Notes

1. ^ Electronic Warfare and Radar Systems - Engineering Handbook (4th ed.). US Naval Air Warfare Center Weapons Division. 2013. p. 192.