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首页> 外文期刊>IEEE Transactions on Microwave Theory and Techniques >Application of Belevitch Theorem for Pole-Zero Analysis of Microwave Filters With Transmission Lines and Lumped Elements
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Application of Belevitch Theorem for Pole-Zero Analysis of Microwave Filters With Transmission Lines and Lumped Elements

机译：Belevitch定理在带有传输线和集总元件的微波滤波器的零点分析中的应用

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摘要

This paper presents the application of Belevitch theorem for pole-zero analysis of microwave filters synthesized with transmission lines and lumped elements. The scattering (S) matrix determinant (Δ) based on the Belevitch theorem, aptly called Belevitch determinant, comprises poles and zeros that are separated in different half-plane regions. Using the Belevitch determinant, the poles and zeros of filter transfer functions can be determined separately with certainty, e.g., by applying the contour integration method based on argument principle. Note that the contour integration can be evaluated numerically without requiring complicated overall analytical expressions. The proposed method is able to solve the poles and zeros for filters synthesized with noncommensurate transmission lines and lumped elements, where the transform method and the eigenvalue approach are inapplicable. Several applications are discussed to demonstrate the use of Belevitch theorem and the contour integration method to determine the poles and zeros of various microwave filters on the complex plane.
机译：本文介绍了Belevitch定理在利用传输线和集总元件合成的微波滤波器零极点分析中的应用。基于Belevitch定理的散射（S）矩阵行列式（Δ），适当地称为Belevitch行列式，包括在不同半平面区域中分隔的极点和零点。使用Belevitch行列式，可以确定性地分别确定滤波器传递函数的极点和零点，例如，通过应用基于论点原理的轮廓积分方法。注意，轮廓积分可以通过数值进行评估，而无需复杂的整体分析表达式。所提出的方法能够解决由不相称的传输线和集总元件合成的滤波器的零点和零点，而变换方法和特征值方法都不适用。讨论了几个应用程序，以演示Belevitch定理和轮廓积分方法的使用，以确定复杂平面上各种微波滤波器的极点和零点。

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