Agilent 5990-9185EN Revisiting Mismatch Uncertainty with the Rayleigh Distribution - White Paper c20140728 [ free download

File name 5990-9185EN Revisiting Mismatch Uncertainty with the Rayleigh Distribution - White Paper c20140728 [

Keysight Technologies Revisiting Mismatch Uncertainty with the Rayleigh Distribution White Paper 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 correspond- ing 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 reflec- tion 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. 2011 NCSL International Workshop and Symposium Introduction Speaker/Author: Michael Dobbert Keysight Technologies Santa Rosa, CA Co-Author: Joe Gorin Keysight Technologies Santa Rosa, CA Mismatch affects the accuracy of measurements made using RF and microwave equipment such as power meters, signal analyzers, noise figure meters, network analyzers, high frequency oscilloscopes, signal generators, attenuators, couplers, cables and adapters. The measurement uncertainty due to mismatch is often a major component of the total uncertainty for RF and microwave measurements. For RF and microwave systems, knowledge of the complex-valued quantities of source and load reflection coefficients allows for correcting for mismatch with a corresponding uncertainty. However, for many measurements, only reflection coefficient magnitude is known. The lack of phase informa- tion precludes the ability to correct for mismatch and is a source of measurement error when making power measurements. The distribution of errors due to mismatch when dealing with unknown phase is often associated with the well-known U-shaped probability distribution. However, this component of uncertainty is only part of the picture. The total mismatch uncertainty must also consider the errors associated with reflection coefficient magnitude. The total uncertainty may be determined by using an estimate and an associated uncertainty, or by assigning a probability density function (PDF) to the reflection coefficient magnitude. This paper demonstrates