Global convergence of a blind iterative algorithm for simultaneous conjugate match of N-ports

In a recent paper, it has been shown that, if an N-port network fulfills the condition of (geometrical) unconditional stability at a given frequency, then it can be conjugately matched simultaneous at all ports through lossless matching 2-ports. The proof was based on the construction of a guided iterative algorithm (AlgG) which was shown to converge to the desired result. Two other iterative algorithms were presented (AlgS and AlgA), which are simpler to implement but whose global convergence had not been proven. The present contribution aims at proving the global convergence of the AlgA algorithm, which is notable for being totally independent of the user (unlike AlgG) and of the port numbering (unlike AlgS). As such, this algorithm captures the inherent characteristics only of the network to which it is applied. Several examples of using AlgA to achieve the Simultaneous Conjugate Match (SCM) condition are presented and validated on fabricated circuits. More interestingly, AlgA has a useful role in the framework of stability analysis, i.e., in determining upper and lower bounds on the stability radius of N-port networks. This latter application will be further delved into in a future publication.