Revisiting Mismatch Uncertainty with the Rayleigh Distribution

About this Article
This article by Mike Dobbert and Joe Gorin was presented by Mike at the NCSLI 2011 Symposium and published in the Proceedings. It won the "Dr. Allen V. Astin" overall Best Conference Paper award.

Abstract

This paper examines several important aspects of estimating mismatch uncertainty, which is
often a major component of the total uncertainty for RF and microwave measurements.
Expressions for mismatch correction and the corresponding uncertainty are presented for
reflection coefficients with known magnitude and phase. For reflection coefficients with
unknown phase, two scenarios are considered; that is, when estimates exist for the reflection
coefficient magnitude resulting in the well-known U-shaped uncertainty distribution and when
dealing with assumed reflection coefficient magnitude values. For the latter scenario, this paper demonstrates that the reflection coefficient magnitude is best modeled with a Rayleigh
distribution. Measurement data is presented revealing a very good fit to the Rayleigh
distribution. Finally, this paper presents methods for estimating the Rayleigh distribution
parameter from information found in manufacturer’s data sheets. The objective of this paper is to provide comprehensive techniques for estimating realistic mismatch uncertainty, which usually gives a three to six times lower estimate of mismatch uncertainty compared with estimates from commonly used techniques.

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Revisiting Mismatch Uncertainty with the Rayleigh Distribution