ANNs are first trained to learn the device behavior, starting from a few samples which are obtained using SFELP. The device is then designed by using the neural model and overall optimization. The efficiency and accuracy of neural models increase as a result of combining different techniques.With segmentation, the whole device is divided into small regions which are modeled separately. Thus, two main effects are attained: the number of design parameters in each region is smaller, and the behavior to be modeled smoother. It is also not necessary to model the behavior of a region if it can be computed analytically. On the other hand, the GAM decomposition in Eq. (3) allows us to simplify the behavior to be modeled; because matrix J can be computed analytically. Thus, it is only necessary to model the PGAM. If the device to be designed can be considered as lossless, the functional dependence of this matrix with frequency can be expressed through a sum of real poles. In the regions obtained as a result of segmentation, all or nearly all these poles are placed further away, because the dimensions of the regions are so small. This information is then exploited through the use of neural models that emulate the frequency modeling of reduced-order Padé models. The positions and residues of the inner poles are modeled with MLPs, as is the effect of the outer poles with the models in Eq. (8). In both cases, frequency is not an input parameter of the MLPs. Training data are extracted very efficiently from the reduced frequency models computed with SFELP. Finally, the use of many MLPs avoids the use of high complexity MLPs, whose management is largely more difficult.Several examples have been presented. Behavior of a small microwave region is illustrated in Section 7.1. In Sections 7.2 and 7.3, microwave devices are designed by using overall optimization. The CPU time required by these design processes is dramatically reduced as a consequence of using ANNs. The design results illustrate the high degree of accuracy that can be achieved using the proposed neural models.
ACKNOWLEDGMENTThis work was supported by CICYT, Spain, under contract no TEC2004 -00950/TCM. REFERENCES 1. J.E. Rayas-Sánchez, EM-Based optimization of microwave circuits using artificial neural networks: