A generalized multiport conversion between S parameter and ABCD parameter

The two-port ABCD parameter is widely applied to a cascade network. Still, it is hard to utilize the ABCD parameter when the number of ports is more than two. In order to solve this problem, the generalized multiport conversion for complex terminal impedance between
$S$
parameter and ABCD parameter is proposed in this paper, which can be integrated in circuit simulators and vector network analyzer to obtain ABCD parameter directly. Moreover, while several pairs of ports are connected each other, the
$S$
parameter of the remaining ports is derived, which contributes to taking advantage of
$S$
parameter for multi port network analysis, especially for complicated topologies and coupling mechanisms. The conversion between
$S$
and ABCD parameter of a four-port asymmetrical coupled transmission line is verified in this paper, and the good agreement demonstrates the proposed theory well.