Self-adjointS-parameter sensitivities for lossless homogeneous TLM problems

We present a novel efficient algorithm for the estimation of S-parameter sensitivities in homogeneous and lossless transmission line modelling (TLM) problems. Our approach estimates S-parameter adjoint-based sensitivities without actually carrying out any adjoint simulation. By applying a transformation to the original TLM simulation we establish an isomorphism between the original and the adjoint problem. The unique properties of the TLM node in a lossless and homogeneous problem are also exploited in establishing the isomorphism. For an electromagnetic structure with Np ports, only the Np original simulations utilized in evaluating the S-parameters are required to estimate their sensitivities as well. Our novel approach is illustrated through estimating S-parameter sensitivities with respect to waveguide discontinuities. Good match is obtained between our sensitivity estimates and those calculated using finite differences at the response level.