Accelerated Gradient-Based Optimization of Planar Circuits

We demonstrate, for the first time, the integration of adjoint variable method (AVM) sensitivities and the method of moments (MoM) within an optimization framework, where the $S$-parameters are used to define the cost function. The AVM efficiently estimates the sensitivities of the $S$-parameters using only one MoM simulation with some additional overhead. Two possible approaches are used: the adjoint finite-difference approach and the adjoint Broyden-update approach. The AVM $S$-parameter sensitivities are successfully utilized to optimize a band-stop filter, a band-pass filter, and an electromagnetically coupled microstrip Yagi antenna. The results show that the optimizers supported by AVM sensitivities are capable of reaching feasible designs satisfying the specifications.