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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.

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Free-space path loss

In telecommunication, the free-space path loss (FSPL) (also known as free-space loss, FSL) is the attenuation of radio energy between the feedpoints of two antennas that results from the combination of the receiving antenna's capture area plus the obstacle-free, line-of-sight (LoS) path through free space (usually air). The "Standard Definitions of Terms for Antennas", IEEE Std 145-1993, defines free-space loss as "The loss between two isotropic radiators in free space, expressed as a power ratio.

Path loss

Path loss, or path attenuation, is the reduction in power density (attenuation) of an electromagnetic wave as it propagates through space. Path loss is a major component in the analysis and design of the link budget of a telecommunication system. This term is commonly used in wireless communications and signal propagation. Path loss may be due to many effects, such as free-space loss, refraction, diffraction, reflection, aperture-medium coupling loss, and absorption.

Decibel

The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a power ratio of 101/10 (approximately 1.26) or root-power ratio of 10 (approximately 1.12). The unit expresses a relative change or an absolute value. In the latter case, the numeric value expresses the ratio of a value to a fixed reference value; when used in this way, the unit symbol is often suffixed with letter codes that indicate the reference value.

Friis' Formula: Antenna Gain and Power Density EE-445: Microwaves, the basics of wireless communications

Explores Friis' formula, antenna gain, power density, RADAR, and Doppler RADAR.

Power and Power Density, Friis Formula Considerations EE-345: Radiation and antennas

Discusses power, antennas, Friis formula, and optimizing power transfer in communication systems.

Radiation and Antennas: Ideal Antennas EE-345: Radiation and antennas

Explores radiation at antennas, reciprocity, directivity, and the Friis formula.