Virtual Auxiliary Termination for Multiport Scattering Matrix Measurement Using Two-Port Network Analyzer

Almost all methods for measuring the scattering matrix of an $n$-port device with the use of a two-port vector network analyzer (VNA) require one to terminate the other $n-2$ ports in the fully characterized auxiliary terminations and prefer auxiliary terminations with small or moderate reflection coefficients. In this paper, a technique is presented to measure the auxiliary terminations indirectly. It not only eases the measurement of auxiliary terminations, but also makes the concept of virtual auxiliary termination realizable. In practice, examples of virtual auxiliary terminations can be the inherent connectors or bonding pads of the test device. Also studied is the remedy for the numerical pitfall possibly coexisting with the use of strongly reflecting auxiliary terminations such as virtual auxiliary terminations. The scattering matrix of a four-port circulator is then acquired accordingly from measurements using a two-port VNA and virtual auxiliary terminations.