On the Simultaneous Conjugate Match of N-Port Networks

Some advancements are proposed to the theory of simultaneous conjugate match (SCM) of $N$ -ports. It is shown that, if a network qualifies for geometrical unconditional stability (g-US), then it can be matched simultaneously at all ports. The proof serves as the basis for constructing an iterative algorithm (AlgG) which is guaranteed to converge to the SCM condition for all $N$ -ports exhibiting g-US. In addition to the main results above mentioned, two more iterative algorithms are presented (AlgS and AlsA), which are conjectured to work for all networks satisfying g-US. AlgS can be shown to converge globally for $N = 2$ and AlgA to converge locally for all $N$ . Besides their theoretical interest, these results find a natural application in the matching of passive networks, and in particular of $N$ -element phased arrays. However, they can be applied to any (i.e., also active) $N$ -port as long as this is known to exhibit g-US.