Calculation of Antenna Parameters in Reception
The gain in any given direction and the impedance at a given frequency are the same when the antenna is used in transmission or in reception.
The electric field of an electromagnetic wave induces a small voltage in each small segment in all electric conductors. The induced voltage depends on the electrical field and the conductor length. The voltage depends also on the relative orientation of the segment and the electrical field.
Each small voltage induces a current and these currents circulate through a small part of the antenna impedance. The result of all those currents and tensions is far from immediate. However, using the reciprocity theorem, it is possible to prove that the Thévenin equivalent circuit of a receiving antenna is:
- is the Thévenin equivalent circuit tension.
- is the Thévenin equivalent circuit impedance and is the same as the antenna impedance.
- is the series resistive part of the antenna impedance .
- is the directive gain of the antenna (the same as in emission) in the direction of arrival of electromagnetic waves.
- is the wavelength.
- is the magnitude of the electrical field of the incoming electromagnetic wave.
- is the angle of misalignment of the electrical field of the incoming wave with the antenna. For a dipole antenna, the maximum induced voltage is obtained when the electrical field is parallel to the dipole. If this is not the case and they are misaligned by an angle, the induced voltage will be multiplied by .
- is a universal constant called vacuum impedance or impedance of free space.
The equivalent circuit and the formula at right are valid for any type of antenna. It can be as well a dipole antenna, a loop antenna, a parabolic antenna, or an antenna array.
From this formula, it is easy to prove the following definitions:
-
- Antenna effective length
is the length which, multiplied by the electrical field of the received wave, give the voltage of the Thévenin equivalent antenna circuit.
-
- Maximum available power
is the maximum power that an antenna can extract from the incoming electromagnetic wave.
-
- Cross section or effective capture surface
is the surface which multiplied by the power per unit surface of the incoming wave, gives the maximum available power.
The maximum power that an antenna can extract from the electromagnetic field depends only on the gain of the antenna and the squared wavelength . It does not depend on the antenna dimensions.
Using the equivalent circuit, it can be shown that the maximum power is absorbed by the antenna when it is terminated with a load matched to the antenna input impedance. This also implies that under matched conditions, the amount of power re-radiated by the receiving antenna is equal to that absorbed.
Read more about this topic: Antenna Measurement
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