Corrections to Friis noise factor formulas for cascade networks

Abstract

The signal-to-noise ratio of a multistage cascade network is often estimated using the well-known Friis' formulas for noise factors (or the noise figures in decibels). However, this article addresses the major errors in Friis' noise factor formulas for higher stages. Additionally, we re-derive the correct formulas to calculate the stage-wise noise factors for cascade networks from the basic definition of noise factors. We then present a comparison of our derived formulas with Friis' noise factor formulas. Contrary to Friis' formula, we define the total noise factor of an n-stage cascade network as the product of its stage-wise noise factors. We further validate our derived formulas for a cascade network by correlating them with the expressions for a staircase avalanche photodiode.

arXiv commentFriis' noise factor formulas for cascade networks are often used to derive other related formulas for devices involving cascade mechanism (eg. staircase APDs). However, Friis' equations for higher stages are themselves incorrect. This article points out the existing mistakes and re-derives the correct formulas for a cascade network's noise factor (10 pages, 3 figures, preprint under submission)