Passive Networks – Proof that Only Reciprocal Circuits are Passive Circuits

AS photon describes the 2 port parameters are determined by the Laplace parameters S11 thru S22.

There also exists an inverse relationship called y parameters.

Both have determinates D in the matrix calculations and may be used to convert from s to y and visa versa.

s parameters are more useful for cascaded networks.

y parameters are more useful for parallel networks.

Full explanation are in the links above.

This doesn't quite answer the same question as how to resolve Norton Equivalent current/resistance using a computer, but it does offer an alternative route to handling voltage sources (which was the original goal): Modified Nodal Analysis

The basic idea is to treat the currents as additional unknowns. We can then add a few extra linear equations describing the current, and by adding in "trivial" equations we can continue to use known voltages as "unknown quantities". This makes combining the elemental matrices still a trivial task, and we just end up with a slightly larger matrix to solve.