Friis formula

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The terms the Friis formula and Friis's formula (sometimes Friis' formula), named after Harald T. Friis, can refer to either of two formulas used in telecommunications engineering. The first, discussed here, is used to compute the noise figure or noise temperature of a system composed of a number of cascaded stages. The second, called the Friis transmission equation, is used in computing transmission of signals between two antennas using electromagnetic waves, and is discussed in a separate article.

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[edit] The Friis formula for noise figure

Friis's formula is used to calculate the total noise figure of a cascade of stages, each with its own noise figure and gain. It is given as

F_{total} = F_1 + \frac{F_2-1}{G_1} + \frac{F_3-1}{G_1 G_2} + \frac{F_4-1}{G_1 G_2 G_3} + ...

where Fn and Gn are the noise factor and available power gain, respectively, of the n-th stage. Note that both magnitudes are expressed as ratios, not in decibels.

As an example, consider the cascaded system to be a receiver with the first stage being a low-noise amplifier (LNA). The overall receiver noise figure is then

F_{receiver} = F_{LNA} + \frac{(F_{rest}-1)}{G_{LNA}}

where Frest is the overall noise factor of the subsequent stages. According to the equation, the overall noise figure, Freceiver, is dominated by the noise figure of the LNA, FLNA, if the gain is sufficiently high.

[edit] The Friis formula for noise temperature

Friis's formula can be equivalently expressed in terms of noise temperature:

T_{total} = T_1 + \frac{T_2}{G_1} + \frac{T_3}{G_1 G_2} + ...

[edit] Printed references

  • J.D.Kraus, Radio Astronomy, McGraw-Hill, 1966.

[edit] Online references

  • RF Cafe [1]
  • Microwave Encyclopedia [2]
  • Friis biography at IEEE [3]
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