Multiport $S$-Parameter and $T$-Parameter Conversion With Symmetry Extension

Abstract

We propose a generalized <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> -matrix definition that facilitates the conversion between the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> -parameter and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> -parameter for multiport networks based on the well understood and mathematically simple two-port relations. This approach generalizes all multiport networks into two cases: balanced and unbalanced. Balanced networks have the same number of entrance and exit ports and are symmetric to the two-port network. Unbalanced networks generate a nonsquare <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> -matrix and do not have the same number of entrance and exit ports. Through careful selection of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> -matrix, this method extends two-port symmetry to multiport networks and provides an engineering implementable relationship between the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> -parameter and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> -parameter for multiport networks. This symmetry extension allows a practical means to cascade and de-embed such networks.