Correction to Friis Noise Factors

TL;DR

This paper clarifies the correct formulas for calculating noise factors in multistage networks, correcting previous Friis formulas by defining the total noise factor as the product of stage-wise factors.

Contribution

The paper derives the accurate formulas for stage-wise and total noise factors, correcting the traditional Friis formulas for multistage cascade networks.

Findings

Derived correct formulas for noise factors in cascade networks.

Compared new formulas with Friis's formulas and highlighted differences.

Defined total noise factor as the product of stage-wise noise factors.

Abstract

The signal-to-noise ratio of a multistage cascade network is often estimated using Friis formulas for noise factors (or the noise figures in decibel). In this letter, the correct formulas to calculate the stage-wise noise factors and the total noise factor in terms of the stage-wise noise factors of an n-stage cascade network are derived. A comparison of our derived formulas for noise factors with Friis's formulas is presented. Contrary to Friis's total noise factor in terms of the stage-wise noise factors, we define the actual total noise factor of the n-stage cascade network as the product of its stage-wise noise factors.