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Concept
Friis transmission equation
Summary
The Friis transmission formula is used in telecommunications engineering, equating the power at the terminals of a receive antenna as the product of power density of the incident wave and the effective aperture of the receiving antenna under idealized conditions given another antenna some distance away transmitting a known amount of power. The formula was presented first by Danish-American radio engineer Harald T. Friis in 1946. The formula is sometimes referenced as the Friis transmission equation.
Friis' original idea behind his transmission formula was to dispense with the usage of directivity or gain when describing antenna performance. In their place is the descriptor of antenna capture area as one of two important parts of the transmission formula that characterizes the behavior of a free-space radio circuit.
This leads to his published form of his transmission formula:
where:
is the power fed into the transmitting antenna input terminals;
is the power available at receiving antenna output terminals;
is the effective aperture area of the receiving antenna;
is the effective aperture area of the transmitting antenna;
is the distance between antennas;
is the wavelength of the radio frequency;
and are in the same units of power;
, , and are in the same units.
Distance large enough to ensure a plane wave front at the receive antenna sufficiently approximated by where is the largest linear dimension of either of the antennas.
Friis stated the advantage of this formula over other formulations is the lack of numerical coefficients to remember, but does require the expression of transmitting antenna performance in terms of power flow per unit area instead of field strength and the expression of receiving antenna performance by its effective area rather than by its power gain or radiation resistance.
Few follow Friis' advice on using antenna effective area to characterize antenna performance over the contemporary use of directivity and gain metrics.
Official source
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