Antenna factor

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:

AF={\frac {E}{V}}

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} }

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]

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 P_D A_e = P_r = V²/R and E²= ${\sqrt {\frac {\mu _{0}}{\varepsilon _{0}}}}$ P_D ~ 377P_D (E and V noted here are the RMS values averaged over time), the antenna factor is developed as:

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

Where

A_e = (λ²G)/4π : the antenna effective aperture
P_D is the power density in watts per unit area
P_r 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.

Notes

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

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References

Interpreting Antenna Performance Parameters for EMC Applications
Interpreting Antenna Performance Parameters for EMC Applications An excellent page with summaries of all the relevant equations
Antenna Theory

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