Analytical $S$-Parameter Sensitivity Formula for the Shape Parameters of Dielectric Objects

An exact sensitivity expression is proposed for the computation of $S$-parameter derivatives with respect to the shape parameters of isotropic dielectric objects. While an exact expression has already been developed for the shape parameters of volumetric metallic objects, to our knowledge, the case of dielectric objects has only been treated with approximations. The proposed expression integrates the field solution on the surfaces of the objects of interest. This solution is already available from the simulation computing the $S$-parameters. Therefore, it features negligible computational overhead compared with the full-wave simulation. At the same time, it provides the best accuracy for the given numerical field solution. It is validated through the sensitivity analysis of microwave structures simulated by a commercial electromagnetic solver based on the finite-element method.