Reducing the Number of Measurements of a Multiport Circuit Using Covering Designs and Turán Systems

Abstract

A theory of arrangements of measurements for obtaining the scattering matrix of a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$v$ </tex-math></inline-formula> -port circuit using a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -port vector network analyzer (VNA) is developed based on covering designs and Turán systems, which are two kinds of structures in combinatorial design theory. The results of this letter provide a general strategy for reducing the number of multiport measurements of microwave circuits.