Antenna factor

Antennas
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In electromagnetics, 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 an antenna. 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 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.

For a 50 Ω load, knowing that P_D A_e = P_r = V²/R and E²=377P_D, 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

A_e = (λ²G)/4π : the antenna effective aperture
G: the antenna gain

For antennas which are not defined by a physical area, such as monopoles and dipoles consisting of thin rod conductors, the effective length is used to measure the ratio between E and V.

Notes

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

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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