Hybrid formulation of explicit formulae for higher order network sensitivities

In the case of linear time-invariant networks, a set of simple recursive formulae are deduced for the first- and higher order sensitivity coefficients of the network voltages and currents with respect to the component values. These formulae are based on Branin´s hybrid formulation method but include terms corresponding to dependent drivers. It is shown that the chief computational effort in using these formulae involves a single matrix inversion or LU factorization carried out once.