Auxiliary branch method and modified nodal voltage equations

A theorem is presented describing a transformation by means of which it is possible to assign to an elementary multiport with fairly general constitutive equations (including all kinds of controlled sources, nullors, ideal transformers, etc.) a modified multiport with the same all-pole terminal behavior. The branch set of this modified multiport is augmented with so called auxiliary branches whereas its constitutive equations are always in conductance form. Therefore an interconnection of a family of multiports transformed in this manner can always be analyzed by means of a system of nodal voltage equations. It will be shown that this system of equations is equivalent to a system of modified nodal voltage equations set up for the network that is an interconnection of the elementary multiports originally given

On the matrices of capacitance and inductance coefficients for lossless homogeneous multiconductor transmission lines

Using results from the theory of planar fields and complex functions it is shown that for lossless homogeneous multiconductor transmission lines the computation of the matrices of capacitance and inductance coefficients can be reduced to the solution of some special Dirichlet boundary value problems. Additionally, a function theoretic proof is given for the relationship LC = ϵµE between these matrices