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 sens itivities of any node voltage, as well as of the circuit performances (gain , input/output impedance, or reflection coefficients) with respect to all c ircuit parameters, The starting point is the adjoint system approach and th e expressions obtained for the first-order sensitivities when using nodal a nalysis. Instead of further differentiating them, the images of the higher order derivatives are generated by recursion up to any given order. The pro cedure is illustrated with three examples.