they are still low. And again, good agreement between the neural model predictions and the rigorous analysis with the SFE method is observed.
CONCLUSIONSA new CAD tool for the design of microwave circuits, which combines segmentation, FEM, and ANNs, was presented. First, a fast and accurate neural model of an arbitrary microwave device is developed, starting from a set of training points computed using the SFE method. Afterwards, this neural model, whose evaluation is very fast, is used together with optimization algorithms for the microwave design.The first step in the neural model development is the division of the microwave device into small regions connected by waveguide segments. Then, the GSM of each region is modeled separately by MLPs. To achieve this, training points are needed, which are obtained in a very efficient way using the SFE method. The use of this analysis method allows us to deal with arbitrarily shaped 3-D regions connected by waveguide segments, also with arbitrarily shaped cross sections, and to easily include a very high number of modes in the connection ports into the computations. Finally, the complete GSM system is computed connecting all of the GSMs modeled in each region.By using segmentation techniques, the number of training points needed for a correct modeling is drastically reduced. Therefore, the development of a neural model is simplified considerably because, in the neural model development for microwave devices, the generation of the training set is usually the largest time-consuming step.This CAD tool is used for the design of a transition between coaxial and rectangular waveguides with good results. The neural model developed in this example shows very good agreement with the SFE method used to generate the training set, but it computes the response of the transition in a much shorter time. 2. J.M. Cid and J. Zapata, CAD of rectangular-waveguide H-plane circuits by segmentation, finite elements and artificial neural net-Ž . works, Electron Lett 37 2001 , 98᎐99. 3.