Accuracy Criterion for $S$-Matrix Reconstruction Transforms on Multiport Networks

S
-matrix reconstruction transforms are based on two stages of matrix transformation to remove the mismatch-induced errors. Over the years, these transforms are widely used in measurements of multiport devices using a two-port vector network analyzer, especially for noncoaxial applications because high-quality matched loads are hardly accessible. In this paper, analytical error analysis of the
S
-matrix reconstruction transforms is performed to develop the accuracy criterion that is explicitly expressed in matrix form in terms of the
S
-matrix of the multiport device and the reflection coefficient matrix of the auxiliary terminations. The analytical insights in this paper can pave the way for using strongly reflecting auxiliary terminations. For noncoaxial measurements, strongly reflecting termination, such as a short-circuited or an open-circuited transmission line is more repeatable, reliable, and economical than terminations with loss like resistors. Consequently, the use of strongly reflecting auxiliary terminations is speculated to ease noncoaxial multiport measurements.