Abstract
To maximize the matching between a coaxial cable and rectangular waveguides, we present a computational topology optimisation approach that decides for each point in a given domain whether to hold a good conductor or a good dielectric. The conductivity is determined by a gradient-based optimisation method that relies on finite-difference time-domain solutions to the 3D Maxwell’s equations. Unlike previously reported results in the literature for this kind of problems, our design algorithm can efficiently handle tens of thousands of design variables that can allow novel conceptual waveguide designs. We demonstrate the effectiveness of the approach by presenting optimised transitions with reflection coefficients lower than −15 dB over more than a 60% bandwidth, both for right-angle and end-launcher configurations. The performance of the proposed transitions is cross-verified with a commercial software, and one design case is validated experimentally.
Highlights
Coaxial-to-waveguide transitions have been designed using a variety of techniques
The adjoint-field approach utilises these internally computed field values together with the field values of an additional system of equations, the adjoint equation, to compute sensitivity information for all design variables. (The adjoint equation is here the Maxwell equations, but with a different forcing that depend on the choice of objective function.) Using this approach, it is possible, with only one extra solution of a system of equations per design cycle, to compute sensitivity information for all design variables
A straightforward implementation of standard material distribution methods for topology optimisation along the line developed for mechanics problems will not work; the ohmic barrier will effectively prevent the optimisation algorithm to change from conductor to air or vice versa
Summary
Coaxial-to-waveguide transitions have been designed using a variety of techniques. By trial and error, Wheeler[1] placed metallic blocks close to the transition plane inside the waveguide to obtain a wideband operation. Information on how a change of each pixel individually improves a performance measure is obtained in one sweep (forward plus adjoint equations), independent of the number of design variables. This is in stark contrast to the dominating metaheuristic optimisation methods, such as genetic algorithms and swarm optimisation, routinely used for electromagnetic problems. A straightforward implementation of standard material distribution methods for topology optimisation along the line developed for mechanics problems will not work; the ohmic barrier will effectively prevent the optimisation algorithm to change from conductor to air or vice versa. A Danish group pursues a similar approach for frequency-domain problems[18,19,27], whereas we concentrate on wide-band applications using time domain methods
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