Probability Distribution of the Quality Factor of a Mode-Stirred Reverberation Chamber

TL;DR

This paper derives the probability distribution and statistical properties of the quality factor in mode-stirred reverberation chambers, showing it follows a Fisher-Snedecor F-distribution influenced by the number of excited modes.

Contribution

It introduces a novel statistical model for the Q factor in reverberation chambers, linking it to the F-distribution and cavity mode excitation levels.

Findings

Q follows a Fisher-Snedecor F-distribution

Most probable Q is between 2/9 and 1 of its mean

Mean Q exceeds other centrality metrics

Abstract

We derive a probability distribution, confidence intervals and statistics of the quality (Q) factor of an arbitrarily shaped mode-stirred reverberation chamber, based on ensemble distributions of the idealized random cavity field with assumed perfect stir efficiency. It is shown that Q exhibits a Fisher-Snedecor F-distribution whose degrees of freedom are governed by the number of simultaneously excited cavity modes per stir state. The most probable value of Q is between a fraction 2/9 and 1 of its mean value, and between a fraction 4/9 and 1 of its asymptotic (composite Q) value. The arithmetic mean value is found to always exceed the values of all other theoretical metrics for centrality of Q. For a rectangular cavity, we retrieve the known asymptotic Q in the limit of highly overmoded regime.