Friis' formula

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The term Friis' formula 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 receiver 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.

[edit] Friis' formula for noise figure

Friis' formula is used to calculate the overall noise figure of a receiver, which is in turn composed of a number of stages, each with its own noise figure and gain. It is given by

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

Where $F n$ and $G n$ are the noise factor and available gain, respectively, of the n-th stage. Note that both magnitudes are expresed as ratios, instead of decibels. We can express the overall noise figure again in decibels by converting the resulting ratio.

In the case of a receiver with the first stage being a low-noise amplifier (LNA),

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

where $F r e s t$ is the overall noise factor of the subsequent stages. According to the equation, the LNA can reduce the overall noise figure of the receiver, but only if the gain is sufficiently high.