three-layer neural network with 15 neurons in the first layer and 11 neurons in the hidden layer reaches an E s 9.31 и rms 10 y3 , and it is able to synthesize filters which satisfy the Ž . requirements of the test set filters. In Figure 2 b , for the sake of brevity, we have only shown the FE analysis of three Ž . filters synthesized by the neural network continuous line Ž . and the original ones coming from the test set dotted line . As is apparent, the synthesized filters and the desired masks match well.It is worth pointing out that the reduced size of both learning and test sets can be allowed because of the extreme simplicity of the chosen filter. A larger learning set and a more sophisticated neural-network structure are required when dealing with more complex filtering devices; nevertheless, the features of this technique remain the same. IV. CONCLUSIONSIn this communication, a quick approach to microwave filter design is presented. This methodology has been applied to a low-order filtering device, giving good results and costing very little computational time in the neural-network learning process. It is worth mentioning that the versatility of the FE may be very useful to generate training sets for more involved microwave filtering devices. In these latter cases, the combined FErneural-network methodology becomes suitable for saving time during the microwave filter design procedure. Future work will be devoted to the use of this procedure in the case of more complex and different order waveguide and planar technology filtering structures as are required in practical applications.

A unique approach for applying neurocomputing technology for accurate CAD of microwave circuits is described. In our proposed method, a multilayer perceptron neural network (MLPNN) is trained to predict the scattering parameters of MMIC passive elements based on the element's physical dimensions. The sparameters were obtained by performing a fullwave electromagnetic (EM) analysis of these elements. An X-band MLPNN spiral inductor model is developed. The MLPNN computed sparameter values are in excellent agreement with those obtained from E M simulations with correlations greater than 0.99 for all modeled parameters.

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