近年來，擁有雙頻功能的通訊產品不斷地被研究與開發。一般在設計雙頻濾波器時，通常會先設計出雙頻諧振器，接著再根據雙頻帶所需的耦合量設計出合適的雙頻倒轉器。本論文則是提出利用頻率轉移函數的方式，將不等頻寬的雙通帶響應轉移至已知且易於分析的頻率座標上，接著根據計算出的頻率轉移函數，以及低通或是帶通原型電路，進而推導出擁有雙頻功能的濾波器架構，而且此雙頻電路可以利用分佈式電路來實現。
在本論文裡介紹了兩種轉移函數，分別為等長性轉移函數以及非等長性轉移函數。利用這些轉移函數並搭配適當的頻率對應方式，雙頻濾波器可以被設計出來。在平面電路實作上，串聯殘段是不容易實現的，因此本論文提出雙頻倒轉器，藉此將串聯殘段轉成並聯殘段。同時也設計出雙頻阻抗轉換器，藉此改變整體電路的阻抗。為了驗證設計的正確性，在論文裡分別設計及實作了兩個雙頻濾波器，並利用網路分析儀進行了量測。最後針對一些現有的雙頻濾波器文獻，本論文分別討論在等頻寬條件下其所呈現的特性，並且找出了其等效的頻率轉移函數。

In recent years, communication systems which can operate at multiple bands are very popular. These require circuits and devices with dual-band characteristics. Usually, one needs dual-band resonators and inverters when designing dual-band filters. However, in this thesis, dual-band filters are designed by using frequency transformation methods, which is similar to Richard’s transformation, so they are ready to be realized using transmission lines.
Since series stubs can not be realized easily on printed circuit boards, dual-band inverters are proposed. A dual-band impedance transformer is also designed to change the circuit’s impedance level. All the elements are distributed, so Kuroda identities can be applied if they are commensurate. Completed designs using non-commensurate transmission-line sections are also proposed. To validate these methods, two dual-band filters have been designed, fabricated, and tested.
Several dual-band filter designs in the literature have been studied. Their corresponding dual-band transformations have been derived. Therefore, they can also be designed by the methods proposed in this thesis.

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