多頻濾波器耦合矩陣之合成及其實現於微帶線平行耦合濾波器結構之研究

Abstract

本論文研究主題為一個完整設計雙頻與多頻濾波器的流程，並實現於微帶線平行耦合濾波器架構上。首先提出一種新的全解析式的多頻濾波器耦合矩陣合成技術，透過簡單的操作，將廣為人知的單頻濾波器耦合矩陣合成技術推廣至多頻應用。此提出的技術可以保證其產生之響應遵守廣義柴比雪夫特性，亦即在多頻濾波器各通帶保持等漣波特性。接著，將此合成技術所生成之耦合矩陣轉換到可實現的耦合架構上。本文提出單路徑式與雙路徑式耦合架構，並且對於其在雙頻濾波器應用上進行比較與分析。透過對應其耦合矩陣之耦合係數與平行耦合濾波器的設計參數，可以分別設計出每個路徑所對應的平行耦合濾波器。對於雙路徑式架構，需要兩個同向雙工器將兩路徑連接以完成雙頻濾波器設計。接著，為了進一步縮小雙頻濾波器的面積，本文使用山型雙模諧振腔的雙模特性來設計縮小化的雙頻濾波器。透過山型諧振腔的奇、偶模分析可以找出其適當的濾波器耦合架構即為雙路徑式耦合架構，並且可以透過分析將耦合矩陣對應至濾波器設計參數上。此對應方法為一全解析式的流程，可以提供設計者有效率的雙模雙頻濾波器設計。同樣的，在三頻與四頻濾波器設計中，三路徑式與四路徑式的架構可以用來設計其所需要的耦合矩陣。接著透過將兩相鄰頻帶當作一個群組，變成雙頻濾波器加單頻濾波器(針對三頻濾波器)或者雙頻濾波器加雙頻濾波器(針對四頻濾波器)的群組。其中雙頻濾波器或單頻濾波器均可由其耦合矩陣對應之耦合係數和山形諧振腔的設計參數進行合成。最後再將所產生的兩個濾波器透過兩個同向雙工器相接，形成所需要的三頻或四頻濾波器。

The research topic in this dissertation is a complete design flow for dual-band and multi-band filter synthesis, and these synthesized filters are implemented using microstrip parallel-coupled lines structures. First of all, a novel fully analytical multi-band coupling matrix synthesis technique is provided. By simple operations, the well-known single-band coupling matrix synthesis technique is then extended for the multi-band filter design. The proposed technique guarantees the original single-band equal-ripple property within each passbands following each single-band generalized Chebyshev characteristic. Furthermore, the requested coupling matrix should be transferred into the realistic coupling schemes for the practical implementation. In this dissertation, single-path and dual-path coupling schemes are provided, and the properties of each coupling scheme will be discussed. Moreover, the design parameters of the parallel-coupled filter are related with the components of the coupling matrix, the practical parallel-coupled filter for each path will be synthesized. For the dual-path topology, the synthesized dual-band filter needs double-diplexing configuration to connect two filters of two paths. In order to further reduce the size of dual-band filters, the E-shaped resonator is proposed for its two-mode property and is useful for the development of miniaturized dual-band filters. By even- and odd-mode analysis of the E-shaped resonator, the dual-path coupling scheme is chosen for the dual-band filter design, and the practical design parameters of the dual-band filter will be extracted based on the corresponding coupling matrix. And such synthesis procedure is fully analytical and it provides an efficient design flow for the designer. Similarly, for the tri-band and quad-band filter design, the tri-path and quad-path coupling schemes are used for the coupling matrix synthesis. After grouping two adjacent passbands, the tri-band response will be separated into one dual-band response and one single-band response; and the quad-band response will be separated into two dual-band responses. In each grouped dual-band and single-band response, the corresponding E-shaped filter can be synthesized based on the corresponding coupling matrices. Finally, the double-diplexing configuration is used to connect two filters and then the tri-band or quad-band filter synthesis will be completed.