A neural network method for the analysis of multilayered shielded microwave circuits

Abstract

Abstract-In this paper, a neural-network-based method for the analysis of practical multilayered shielded microwave circuits is presented. Using this idea, a radial basis function neural network (RBFNN) is trained to approximate the space-domain multilayered media boxed Green's functions used in the integral-equation (IE) method. Once the RBFNN has been trained, the outputs of the neural network (NN) replace the exact Green's functions, during the numerical solution of the IE. The computation of the RBFNN output values is very fast in comparison with the numerical methods used to calculate the exact Green's functions. This paper describes two novel strategies for efficiently training the RBFNN. In the first strategy, the input space of the RBFNN is divided into several spatial and frequency regions. The spatial subdivision is extended for the first time to both observation and source regions. In addition, the subdivision of the observation points regions is applied in a novel manner to the whole cross section of the metallic box. The second strategy combines the above region subdivision with an adaptive selection of the neurons variances in each region. The accuracy and the computational gain achieved with the NN method proposed makes possible the implementation of computer-aided-design tools that can be used for the analysis and design of integrated shielded microwave circuits (e.g., monolithic microwave integrated circuit devices) on a real-time basis.Index Terms-Computer-aided design (CAD), multilayered circuits, multilayered Green's functions, neural networks (NNs), printed circuits, radial basis function neural network (RBFNN), shielded microwave circuits.

A neural-network method for the analysis of multilayered shielded microwave circuits

“…1, there is no region subdivision in the input space. Similar distributions were used in [22] and [21]. Due to problem symmetries, the source points are distributed along a spatial net belonging to the first quadrant of a rectangular box of dimensions ( , ) ( , ); see Fig.…”

“…In [21] and [22], a study of some appropriate variance values, associated with the OLS training algorithm, was presented. Although a range of variance values exists that permits a correct training, a norm weighting matrix filled with inappropriate values will increase both the training and the testing errors.…”

“…On the other hand, far from the singularity, the variations are smoother, and thus higher values of variance would be more convenient. In the previous strategy, a fixed initial variance is selected within a reasonable range of variances as reported in [22]. However, this value is not the optimum for all source-observation distances.…”

“…This initial value must be selected within some variance limits [22]. If the training and testing threshold error is not reached, the variance is decreased at each step.…”

“…More recently, NNs have been used in the estimation of the spatial-domain Green's functions of a shielded multilayered structure [21], [22]. In these works, the Green's functions were directly approximated by an NN for the case of a source and observation points placed inside the corresponding box, and for a specific fixed frequency.…”