MDA (Matrix Decomposition Algorithm)-combined novel SVD (Singular Value Decomposition) method for complex circuit

Abstract

The invention discloses a method for quick electromagnetic simulation of a complex circuit, comprising the following steps of efficiently simulating the complex circuit based on MDA (Matrix Decomposition Algorithm)-combined novel SVD (Singular Value Decomposition); precisely simulating a model by utilizing a triangle; and carrying out low rank compression on a far field group by utilizing a favorable low rank characteristic principle of the far field group in a tree structure to obtain a relatively sparse matrix representation form. The invention provides an MDA-based novel singular value compression method which is independent of an expansion form of a green function so as to shorten internal memory and computation time. The method disclosed by the invention is a pure mathematical method, can reduce computation complexity to O (NlogN) and internal memory consumption to O (NlogN), is particularly suitable for electromagnetic simulation analysis of the large scale complex circuit and can also provide effective condition for simulation of more complex circuit structure of the green function.

Description

technical field [0001] The invention relates to an electromagnetic simulation technology, in particular to a new singular value decomposition method based on matrix decomposition, which can provide an important analysis approach for the analysis of electromagnetic characteristics of complex integrated circuits. Background technique [0002] With the development of science and technology, the operating frequency of existing integrated circuits is continuously increasing rapidly, and the integration level can be doubled in a few years, but then, the distortion and time delay of integrated circuits due to dispersion, discontinuity and packaging , and problems such as crosstalk noise due to coupling have also become very serious. The traditional quasi-static design method can no longer meet the design requirements, but the accurate electromagnetic field full-wave simulation analysis method can better solve these problems. At present, complex integrated circuits such as microwave...

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Problems solved by technology

[0002] With the development of science and technology, the operating frequency of existing integrated circuits is continuously increasing rapidly, and the integration level can be doubled in a few years, but then, integrated circuits Distortion and delay due to dispersion, discontinuity and packaging, and crosstalk noise due to coupling also become very serious

The traditional quasi-static design method can no longer meet the design requirements, but the accurate electromagnetic field full-wave simulation analysis method can better solve these problems. At present, complex integrated circuits such as microwave integrated circuits, microstrip antennas, and microstrip scatterers The full-wave analysis can be divided into two categories: one is the analysis method based on the differential equation model, and the other is the analysis method based on the integral equation model

The analysis method of differential equation model is mainly based on volume division, therefore, this method will lead to very large unknowns and require a lot of computing resources, so it is difficult to apply

Based on the analysis method of the integral equation model, a variety of integral methods are disclosed in the existing literature for analyzing the structure of complex circuits, such as W.C.Chew, J.M.Jin, E.Michielssen, and J.Song, Fast efficient algorithms in computational electromagnetics, Boston, MA: Artech House, 2001 disclosed a multi-layer fast multipole algorithm (MLFMA). This method mainly uses the addition theorem to expand the Green's function. Its memory and computational complexity are very low, but this method is excessive. Relying on the expression of Green's function, the application of this method is greatly restricted in complex circuit problems

Literature Kapur, S.; Long, D.E., "IES3: efficient electrostatic and electromagnetic simulation," IEEE Computational Science & Engineering, Vol.5, pp.60-67, May 1998. and literature Fang-Shun Deng; Si-Yuan He; Hai-Tao Chen; Wei-Dong Hu; Wen-Xian Yu; Guo-Qiang Zhu, "Numerical Simulation of Vector WaveScattering From the Target and Rough Surface Composite Model With 3-D Multilevel UVMethod," IEEE Trans. Antennas Propagat., Vol. .AP-58, pp.1625-16348, 2010. Proposed a purely mathematical method. These methods have nothing to do with the expansion of the Green's function. They are more complex than the multi-layer fast multipole algorithm, and their computational complexity and storage capacity are obvious. Reduced, but the memory and computing time are still relatively large, so the problem is still not fundamentally solved

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