Measurement Uncertainty in Network Analyzers: Differential Error DE Analysis of Error Models Part 5: Step-by-Step Graphical Construction of Complex DE Regions and Real DE Intervals

16 30, N. I. Yannopoulou, P. E. Zimourtopoulos

Abstract


This paper demonstrates the way of how the value of any quantity used in Microwaves and RF and defined, either directly or indirectly, by one ore more complex differentiable functions of one or more Vector Network Analyzer VNA measurements, is affected by its ubiquitous Differential Errors DEs, when these DEs are expressed in terms of the manufacturers' data for both the unavoidable uncertainties of the calibration standards and the inescapable inaccuracies of the VNA indications. This is illustrated by a step-by-step graphical construction of the complex DE Regions DERs and their real rectangular and polar DE Intervals DEIs, which the authors introduced and used in all previous parts of this series. As it is geometrically shown, in order to build the composite figure of any complex DER and then of its DEIs only three basic types of simple figures are needed. These figures result by using combinations of appropriate complex transformations, which are well-known from Complex Analysis, that is: translation, scaling (stretching or shrinking), and rotation. A number of selected applications are presented and some useful, general conclusions are drawn.


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