Electronic circuit analysis using transformation matrices in conjunction with the multi-node method

The representation of a network by its indefinite admittance matrix and the subsequent reduction to a nodal matrix is easily achieved. Any set of linear equations can be reduced by matrix partitioning to a 2×2 matrix; however, it is important to realize that if the easy-to-set-up nodal matrix is reduced, the resultant two-port representation has a node common to the input and output ports. The reduction procedure can also be applied to two-ports such as lattice networks and difference amplifiers that do not have a node common to the ports of interest. The lack of the common node means that reduction of the nodal matrix is no longer applicable and the nodal equations must therefore be transformed into the required form before the reduction procedure is used. Transformation matrices are used to transform the nodal equations into a new set of equations that contains voltage and current vectors related to the two ports of interest.