Accuracy Improvement of the S-parameter Adjoint Sensitivity Analysis for Shape Parameters

The electromagnetic adjoint-based sensitivity analysis uses an exact formula in the case of material parameters, which yields sensitivity accuracy comparable to that of the numerical field solution. For shape parameters, however, the nonanalytical adjoint approaches rely on a field approximation – the adjoint-field mapping, which may affect the accuracy of the computed sensitivity. We show that in the self-adjoint S-parameter sensitivity analysis, this approximation affects the accuracy of the transmission coefficients only (i.e., $S_{kj}, k\neq j$(. We show that the averaging of the sensitivity estimates for the assumed forward and backward perturbations improves significantly the accuracy making it comparable to that of the exact sensitivities. Examples include a waveguide dielectric-resonator filter and a waveguide impedance transformer. The field analysis is performed with a commercial finite-element solver while the sensitivity analysis is performed in MATLAB®.