Nodal equations for sensitivity analysis

This paper introduces a new modification of the nodal equations for sensitivity analysis, based on circuit partitioning into 12 branch groups. This modification is highly suitable for both frequency and time domain circuit sensitivity analyses, because the entire adjoint coefficient matrix is obtainable by transposition only. Hence the formulation of the adjoint circuit equations does not require the construction of the adjoint circuit. Even more, if LU factorization is used in the solution process of the original circuit equations, the factor matrices of the adjoint circuit equations are obtained by transposition of the factor matrices of the original circuit, and the solution of the adjoint circuit equations is computed by forward and backward substitutions only.