Multiplexer design is a challenging task due to the high number of variables involved, raising the difficulty as the numbers of filters increase. Numerical computing tools provide a suitable environment to evaluate topologies and technologies before starting the long journey to the device. A direct scattering matrix solution for a star-junction multiplexer, based on the circuit theory, is presented in this work. The resulting star-junction matrix is introduced in a matrix system with the scattering matrix of each filter to evaluate the overall multiplexer response. This approach allows the acquisition of main multiplexer parameters like transmission, reflection, and cross-isolation response in a compact way, achieving a good starting point for the further full-wave optimization procedure. Furthermore, an approach for the design of a star-junction multiplexer is tackled based on the reflection coefficient phase. A triplexer under this interpretation is presented and evaluated using lumped elements.

中文翻译：

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基于梯型滤波器的理想星形结多路复用器的散射矩阵解

由于涉及大量变量，多路复用器设计是一项具有挑战性的任务，随着滤波器数量的增加，难度也随之增加。数值计算工具提供了一个合适的环境来评估拓扑和技术，然后再开始漫长的设备之旅。本文提出了一种基于电路理论的星形结多路复用器的直接散射矩阵解。将得到的星形结矩阵引入矩阵系统中，每个滤波器的散射矩阵用于评估整体多路复用器响应。这种方法允许以紧凑的方式获取主要的多路复用器参数，如传输、反射和交叉隔离响应，为进一步的全波优化过程提供了一个良好的起点。此外，基于反射系数相位解决了星型结多路复用器的设计方法。在这种解释下的三工器被提出并使用集总元件进行评估。