A discrete adjoint variable method for printed-circuit board computer-aided design

We propose an adjoint-variable method for design sensitivity analysis of printed circuits and antennas where allowable perturbations in the design parameters are of a discrete type. We extend previous work on the sensitivity analysis of waveguide structures, where changes in the design parameters are stepwise, on-grid volumetric perturbations. Here, we explore the feasibility of such an approach in the case of printed-circuit board problems (with open boundaries) where perturbations relate to the shapes elements of infinitesimal thickness. We propose a complex-variable formulation of our approximate sensitivity analysis that improves its computational efficiency. The proposed technique offers significant increases in efficiency, accuracy, and convergence when compared to traditional sensitivity-analysis techniques. Its implementation is straightforward. The response and its gradient with respect to all possible design parameters are computed with at most two full-wave analyses – of the original and the adjoint problems. It operates on a fixed discretization grid where perturbations of grid nodes are not needed. We illustrate our technique through the sensitivity analysis of a microstrip line and a probe-fed printed patch antenna as well as the optimization of a printed Yagi antenna array.