In a radio receiver composed of two stages, the total noise factor \(F\) can be computed using Friis’s formula as\[F = F_1 + \frac{F_2 – 1}{G_1},\]where \(F_1\) is the noise factor of the first block, \(G_1\) is the gain of the first stage and \(F_2\) is the noise factor of the second stage. If \(G_1\) is large enough, then the contribution of the second factor is small and the total noise factor of the whole system is essentially the same as the noise factor of the first stage. This is the reason why a low noise amplifier is useful as a frontend, because it has a low noise factor \(F_1\) and high gain \(G_1\).

If \(F_2\) and \(G_1\) are known (perhaps only approximately), then it is easy to check if the contribution of the frontend to the total noise figure is large enough so that the total noise figure is determined by the noise figure such frontend alone. However, it may happen that one or both of \(F_2\) and \(G_1\) are not known. In email communication, Leif Åsbrink mentioned that there is an easy way of checking the contribution of the frontend without knowing these parameters. The method is to switch off the frontend and note the drop in the noise floor. He gave the following estimates: if the noise floor drops by more than 10dB, then the total noise figure is the same as the noise figure of the frontend up to 1dB; if the noise floor drops by more than 17dB, then the total noise figure is the same as the noise figure of the frontend up to 0.1dB. Here I present the maths behind these kind of estimates.

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