Design sensitivities for scattering-matrix calculation with tetrahedral edge elements

The rates of change of the scattering matrix of a microwave dvice with resp ect to geometric or material parameters are of interest to designers, and u seful in automatic optimization. They are most efficiently calculated by th e adjoint variable method, but this usually entails the additional cost of finding the adjoint solutions, In the finite-element formulation presented here, no new solutions are needed beyond those required to calculate the co mplete scattering matrix. Explicit expressions are given for the calculatio n of the required matrix for a tetrahedral edge element. Results are presen ted for three rectangular waveguide problems: a uniform length terminated i n a short-circuit; an H-plane miter bend; and a two-step waveguide impedanc e transformer.