Antenna Factor: Definition and Formulas

The figure depicts a transmitting antenna and a receiving antenna in a wireless communication chain.

It’s a very useful parameter for EMC (Electromagnetic Compatibility) and EMI (Electromagnetic Interference) testing as it defines the relationship between the electric field around the antenna and the voltage produced by it.

Antenna Factor definition: The ratio of the incident electric field to the generated voltage output from the antenna is known as the antenna factor. This is expressed in the following antenna factor formula.

Antenna factor can also be defined as the ratio of magnetic field to received voltage. It can be expressed as follows:

AF_Magnetic = H_incident / V_received

The power density of the wave (watts per unit area) in free space can be expressed as the product of the E and H fields. Hence, we will have:

P_FS = E * H = |E|² / η

where η is the intrinsic impedance of free space.

The power captured by the antenna from free space can be expressed as follows:

P_received = P_FS * A_e

Where A_e is the antenna aperture, which can be expressed as:

A_e = (λ² *G) / (4 *π)

At the antenna receiver, the received power can be expressed as follows:

P_r = V² / Z_load

From above, the antenna factor can be expressed in different formulas or equations as below:

The following formula is used for antenna factor to gain conversion as well as for gain to antenna factor conversion.