寬頻濾波器在過去幾年裡引起了國內外學術界與工業界的許多興趣，也提出了許多實用的濾波器結構，其中多模諧振器濾波器結構可以達到很好的寬頻特性，不過其中對於雙諧振及三諧振模態步階阻抗諧振器來實現的微波寬頻濾波器，之後的演進與新發展往往著重在尋找修改與發明適用架構來達到截止帶傳輸零點或倍頻抑制的改善，對於此類寬頻濾波器與傳統平行耦合線帶通濾波器之間的等效特性比較少討論，所以設計流程往往僅止於分析多諧振模態步階阻抗諧振器本身，而沒有辦法將微波寬頻濾波器以完整公式或步驟合成出來，常見的例子在設計合成階段就把實做階段的電磁模擬與微調提早使用。
本論文整理歸納九大項探討的主題，以傳統微波網路合成與分析的手法來研究，將有助於釐清某些濾波器設計方法不盡完整之處，本論文藉由完整合成多諧振模態步階阻抗諧振器架構的寬頻濾波器來討論冗餘式以及非冗餘式的設計，近似解合成方法和精準的合成方法的特點也以實例完整地比較。
本論文又進一步探討另一類小型濾波器的合成理論，藉由引進Z轉換來合成特殊的轉移函數，透過微波網路合成與分析的方法，某些傳統上稱為慢波架構的濾波器其小型化的機制也就可以完整地解釋，本論文的實例為六個組成元件三階特性的負載殘帶多諧振模態諧振器小型濾波器。
除了以Richards’ theorem為運算基礎的數值解法，某些簡化的網路合成問題已經有解析公式，本論文也以雙頻阻抗轉換器為實例進行了詳細的比較與討論。

Wide-band filter synthesis has been of great interest both in academy and industry. Many novel filter structures have been suggested. Multiple-mode stepped-impedance resonator filter structure is one class which can achieve wide-band characteristics. In literature, filters based on dual-mode and triple-mode resonators keep evolving on structure modifications, mainly for the performance improvements such as the introduction of extra stopband transmission zero and the extension of harmonic suppression. The similarity of these wideband designs with conventional parallel coupled-line filters is not studied. They are designed by analyzing the multi-mode resonator structure, then stepping into filter implementation by computer optimization. That is, complete synthesis procedures and design equations are not developed.
In this thesis the observed designing and analyzing ambiguities or myths are classified into nine topics. By the classic network synthesis and analysis approach, those incomplete filter design procedures are clarified. Completed design equations and synthesis procedures are developed for the wide-band multi-mode stepped-impedance resonator filters. Redundant and non-redundant designs are discussed. Features of both the approximate method and exact synthesis method are comprehensive compared with design examples.
The network synthesis procedure is extended to one class of compact stub-loaded multi-mode resonator filters. With the help of Z-plane techniques, approximation function is rigorously synthesized. The “slow-wave mechanism” or “slow-wave filter structure” is well explained by the proposed network synthesis approach. Design example of a six-element third-order stub-loaded multi-mode resonator filter is given to justify the method.
In additional to the numerical solution based on Richards’ theorem, for certain simplified network synthesis problems, there exist analytic solutions. In this thesis detailed comparisons and discussions are given by examples of dual-band impedance transformers.

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