Friis formulas for noise

The Friis formula is used in communications technology to calculate the noise figure of a chain of amplifiers or attenuators, which are composed of stages of which, ... are known to the individual noise figures F1, 2, ... and the gains G1, 2. The formula is named after Harald Friis, who coined this term in 1944.

Definition

The Friis formula for determining the noise figure of an amplifier chain with n elements is given by:

With Fn and Gn as noise figure and gain of the nth stage. Attenuators, as represented, for example, cables having a gain G which is less than one. The gains G are referred to in this context as a profit.

The Friis formula expresses that the noise of the following amplifier stages each for the gain G of the preceding amplifier stages decreases in the total noise figure of the chain is received. Thus, for identical noise figures of the amplifier stages provide a total of one amplifier is the chain better noise properties, has a higher gain and is positioned at the beginning of the chain possible.

For the special case of a low noise preamplifier (LNA ) as the first stage and with respect to the noise figure of dominant summands to a first approximation:

With Frest as total noise figure of the following steps. According to this formula, a low-noise preamplifier reduce the noise figure of an amplifier chain, where the gain is sufficiently high.

Friis formula for noise temperature

The Friis formula can also be expressed with the noise temperature: