A Simple and General method to Perform Large-Scale Series/Parallel Reduction of Proximally Coupled Two-terminal Networks by Employment of the Primitive Impedance/Admittance Matrices

The process of reduction of series/parallel combinations involving an arbitrarily large number of magnetically coupled two-terminal networks containing a diverse combination of circuit elements is a conceptually fundamental task and yet has received only scant attention in relevant literature, the only attempts in this direction being limited to a few ad hoc and laboured developments featuring extremely elementary topologies while furnishing meagre, if any, scope for mathematical extension. This paper proposes a powerful tool wherewith large-scale series/parallel reductions of networks with proximal coupling may be achieved in an efficient and facile manner, without any specific limit on the number of constituents, thereby ensuring the generality of the approach. The primitive impedance/admittance matrices are employed for this purpose in their time-domain operational form, which ensures the retention of the most general form of the interrelationships between the terminal voltages and currents of the individual blocks as well as their combination. The presented method has been demonstrated with numerous examples involving inductor networks and inductor-resistor combinations in series, parallel,and some series/parallel topologies.