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

A theory of arrangements of measurements for obtaining the scattering matrix of a $v$ -port circuit using a $k$ -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.