A fully recursive approach to the computation of higher order sensitivities of linear active circuits

This paper presents a new recursive method to compute the higher order sensitivities of any node voltage, as well as of the circuit performances (gain, input/output impedance, or reflection coefficients) with respect to all circuit parameters. The starting point is the adjoint system approach and the expressions obtained for the first-order sensitivities when using nodal analysis. Instead of further differentiating them, the images of the higher order derivatives are generated by recursion up to any given order. The procedure is illustrated with three examples.