Matrix analysis of constrained networks

Following a review of nodal analysis of unconstrained lumped linear time-invariant networks it is shown how networks with imposed unilateral constraints, i.e. transmittances and voltage sources, can conveniently be analysed by matrix methods. Their admittance matrix is equal to the product of a submatrix of the admittance matrix before the application of the constraints and a transmittance matrix which describes the constraints. Constraints lower the rank of the original admittance matrix, thus making the method quite attractive in practice. Applications included are a computing network, difference amplifiers, a d.c. amplifier and signal-flow graphs.