On the Simultaneous Conjugate Match of N-Port Networks

• Published in: IEEE transactions on microwave theory and techniques Vol. 72; no. 9; pp. 5285 - 5296
• Main Authors: Colangeli, Sergio, Serino, Antonio, Ciccognani, Walter, Longhi, Patrick E., Limiti, Ernesto
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic stability; Conjugates; Iterative algorithms; Linear networks; Microwave theory and techniques; Networks; Optimization; Phased arrays; Scattering; Scattering parameters; simultaneous conjugate match (SCM); Transmission line matrix methods; unconditional stability; United States > US
• ISSN: 0018-9480; 1557-9670; 1557-9670
• DOI: 10.1109/TMTT.2024.3372332

Some advancements are proposed to the theory of simultaneous conjugate match (SCM) of <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula>-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 <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula>-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 <inline-formula> <tex-math notation="LaTeX">N = 2 </tex-math></inline-formula> and AlgA to converge locally for all <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula>. Besides their theoretical interest, these results find a natural application in the matching of passive networks, and in particular of <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula>-element phased arrays. However, they can be applied to any (i.e., also active) <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula>-port as long as this is known to exhibit g-US.