TLM-based time domain adjoint sensitivities: State of the art and outlook

Over the years, Transmission Line Modeling (TLM) of high frequency structures has seen great advances. The pioneering work of Johns, Hoefer, Vahdlieck, and others have helped in making TLM a robust modeling approach. This paved the way for the most recent developments in TLM-based adjoint sensitivity analysis which is reviewed in this work. We show that using at most one extra TLM simulation, the first order sensitivities of an arbitrary objective function are obtained with respect to all parameters regardless of their number. The extra simulation can be eliminated for S-parameter sensitivity analysis. We also show that the sensitivities of complete transient responses can be estimated using also one adjoint simulation. TLM-based adjoint sensitivity analysis is illustrated through two examples.