This paper introduces a novel neural-network-based approach for extracting some eigenpairs of real normal matrices of ordern. Based on the proposed algorithm, the eigenvalues that have the largest and smallest modulus, real parts, or absolute values of imaginary parts can be extracted, respectively, as well as the corresponding eigenvectors. Although the ordinary differential equation on which our proposed algorithm is built is onlyn-dimensional, it can succeed to extractn-dimensional complex eigenvectors that are indeed 2n-dimensional real vectors. Moreover, we show that extracting eigen-pairs of general real matrices can be reduced to those of real normal matrices by employing the norm-reducing skill. Numerical experiments verified the computational capability of the proposed algorithm.
A novel compact microstrip Wilkinson power divider with an easy design and fabrication is proposed in this paper. Through capacitive or inductive loading of both of the quarter-wave transmission lines and the isolated resistor employed in conventional Wilkinson power dividers, reduction of the transmission line segments from g/4 to g/30 is obtained. Therefore, the proposed structure can distinctly save the occupied area. Furthermore, some useful design equations based on odd-even mode analysis for the proposed circuit model are introduced to provide an accurate method to design compact Wilkinson power dividers. The fabricated power divider designed for the frequency of 800MHz is 84% smaller than conventional ones, and has a 120MHz bandwidth for which the input return loss is better than 20-dB. Within this bandwidth, the insertion loss is less than 0.3-dB and the isolation between the outputs more than 20-dB.Index Terms-Wilkinson power divider, compact size, capacitive or inductive loading, quarter-wave transmission lines.
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