Corrections to Friis noise factor formulas for cascade networks

TL;DR

This paper identifies errors in Friis' noise factor formulas for multistage networks, derives corrected formulas, and validates them against avalanche photodiode models, improving noise estimation accuracy.

Contribution

It corrects and re-derives the formulas for noise factors in cascade networks, addressing errors in Friis' original formulas and providing validated alternatives.

Findings

Corrected formulas for stage-wise noise factors.

Validated formulas against avalanche photodiode models.

Showed differences from traditional Friis' formulas.

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.