Point‐by‐point Pareto front exploration and adjoint sensitivities for rapid multi‐objective optimization of compact impedance matching transformers

摘要

This paper proposes a technique for rapid multi-objective optimization of miniaturized impedance matching transformers. The key component of our methodology is direct exploration of the Pareto front in the search for a set of alternative designs that represent the best possible trade-offs between conflicting objectives (here, the maximum reflection level within a frequency band of interest and the circuit size). In particular, starting from the design corresponding to the best electrical performance of the circuit, the subsequent Pareto-optimal designs are obtained by a series of local optimizations with respect to one of the objectives, using the previously found solution as a starting point. The optimization is constrained not to degrade the other objective beyond a certain threshold (determining the spread of the solutions along the Pareto front). Low cost of the design process is ensured by exploiting cheap adjoint sensitivities. Our technique is demonstrated using an example of a compact 3-section impedance transformer matching the 50-Ohm source to the 130-Ohm load and working in 3.1-to-10.6 GHz and range. For this example, 16-element representation of the Pareto set is obtained at the cost of just 60 evaluations of the full-wave EM simulation model of the transformer structure.