Friis formulas for noise
Friis formula or Friis's formula (sometimes Friis' formula), named after Danish-American electrical engineer Harald T. Friis, refers to either of two formulas used in telecommunications engineering to calculate the signal-to-noise ratio of a multistage amplifier. One relates to noise factor while the other relates to noise temperature.
Contents |
The Friis formula for noise factor
Friis's formula is used to calculate the total noise factor of a cascade of stages, each with its own noise factor and gain. The total noise factor can then be used to calculate the total noise figure. The total noise factor is given as
where 
and 
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.
An important consequence of this formula is that the overall noise figure of a radio receiver is primarily established by the noise figure of its first amplifying stage. Subsequent stages have a diminishing effect on signal-to-noise ratio. For this reason, the first stage amplifier in a receiver is often called the low-noise amplifier (LNA). The overall receiver noise figure is then
where 
is the overall noise factor of the subsequent stages. According to the equation, the overall noise figure, 
, is dominated by the noise figure of the LNA, 
, if the gain is sufficiently high.
The Friis formula for noise temperature
Friis's formula can be equivalently expressed in terms of noise temperature:
Printed references
- J.D.Kraus, Radio Astronomy, McGraw-Hill, 1966.