Traceable Correction Method for Complex Reflection Coefficient Using Calculable Air Line Impedance Standards

Abstract

A correction method for the measurement of complex reflection coefficients using vector network analyzers is presented. The method is based on the invariance property of the cross ratio of the bilinear transformation and is traceable to calculable air line impedance standards. The application of an accurate diameter measurement system (laser micrometer and air gauge system) allows the treatment of air lines as inhomogeneous transmission lines consisting of a cascade connection of a number of equally spaced line sections. Each line section is assumed to be homogeneous and characterized by the characteristic impedance and the propagation constant, which are traceable to the measured diameter values. The presented procedure is an extension and improvement of prior work using the same principle of correction, whereas the air lines were specified by nominal diameter and length values. The aim of this work is to enhance the accuracy of the correction or to reduce the requirements of the manufacturing tolerances of air lines. The derived theory is accompanied by a brief uncertainty consideration and by measurement results obtained by PC-7 air lines at frequencies up to 18 GHz and by numerical simulation results for a hypothetical air line.