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Revisiting Mismatch Uncertainty with the Rayleigh Distribution

백서

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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