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A New Algorithm for Solving of Harmonic Balance Equations by Using the Model Order Reduction Method

机译:用模型降阶法求解谐波平衡方程的新算法

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The harmonic balance method (HB) is widely used for modeling nonlinear radio circuits in electronic CAD systems. The main problems of CAD algorithms and programs based on various modifications of HB methods are significant requirements for computer memory and huge computational costs when modeling complex circuits containing thousands of electronic components and hundreds of thousands of model equations. Methods of model order reduction have become popular in recent years, and can significantly reduce the dimension and memory required for electronic circuit models for dynamic mode analysis. The main problems of low-order methods for modeling electronic circuits are associated with very small reductions in computational costs (with a significant reduction in the dimension of the equations and the required memory for the model). A new method and algorithm of solving the equations of harmonic balance method used in electronic CAD systems is presented. The new algorithm is based on applying the ideas of model order reduction methods to harmonic balance equations. In comparison with previously developed method of usage the ideas of model order reduction for harmonic balance method, the new method replaces the vector (matrix) of equation unknowns by two matrices of small dimensions that are solved by iteratively (as into the standard harmonic balance method). The first system of equations reduces the number of harmonics in balance equations, and the second system of equations reduces the number of circuit nodes. These equations of small dimensions are solved sequentially, so this algorithm allows significantly reduce the size of computer memory for storing of model equations and reduce of computational costs. The simulation program was developed in the Matlab/Simulink system. The results of modeling test circuit with different number of electronic circuit nodes and the number of considered harmonics showed that the gain was obtained only for dimensions of problems more than one hundred (the number of nodes and the number of considered harmonics).
机译:谐波平衡法(HB)被广泛用于对电子CAD系统中的非线性无线电电路进行建模。在对包含数千个电子元件和数十万个模型方程的复杂电路进行建模时,基于HB方法的各种修改的CAD算法和程序的主要问题是对计算机内存的巨大要求和巨大的计算成本。减少模型阶数的方法近年来变得很流行,并且可以显着减小用于动态模式分析的电子电路模型所需的尺寸和内存。用于对电子电路进行建模的低阶方法的主要问题与计算成本的极小降低(与方程式的维数和模型所需的存储量的显着降低)有关。提出了一种求解电子CAD系统中谐波平衡法方程的新方法和新算法。新算法基于将模型阶数减少方法的思想应用于谐波平衡方程。与以前开发的谐波平衡方法模型降阶方法的使用方法相比,新方法用两个小尺寸的矩阵替换了方程未知数的矢量(矩阵),这些矩阵通过迭代求解(如标准谐波平衡方法一样) )。第一个方程式系统减少了平衡方程式中的谐波数量,第二个方程式系统减少了电路节点的数量。这些小尺寸的方程式是顺序求解的,因此该算法可以大大减少用于存储模型方程式的计算机内存的大小,并降低计算成本。该仿真程序是在Matlab / Simulink系统中开发的。对具有不同电子电路节点数和考虑的谐波数的测试电路进行建模的结果表明,仅对超过一百个问题(节点数和考虑的谐波数)的问题获得了增益。

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