超穎材料於射頻濾波器的應用中，具有改善通帶的隔離度、提供多共振通帶以及微型化等設計上之優勢。左右手複合型傳輸線具有超穎材料之特性，相關特性如傳播係數、群速、相速、介電係數、導磁率與折射率等，可藉由傳輸線方程式及其等效電路做深入探討，其結果有助於進一步改善濾波器之響應。
使用NRW方法進行超穎材料特性之驗證過程中，需根據待測物的反射與透射現象，利用頻率響應中的散射參數，推導反射係數與透射係數，並進一步計算架構的相對導磁率與相對介電係數，在本文中，亦針對NRW方法中透射係數的相位校正問題，提出探討並做適當修正。
最後，為驗證NRW方法之正確性，數種利用超穎材料架構所研製之濾波器，藉由模擬散射參數轉換，及透過MATLAB程式計算，可推導出濾波器於各頻率所對應的相對導磁率、相對介電係數與折射率，三者實部的值可用來判斷濾波器是否具有超穎材料的特性。結果顯示，針對濾波器架構，NRW方法能有效的驗證超穎材料特性。

The metamaterial has advantages of high isolation, multi-resonant bands and miniaturization. It has been applied in the design of high performance radio frequency filters. The Composited Right/Left Hand Transmission Line (CRLH-TL) is a common metamaterial-related structure. The properties of such a CRLH-TL including complex propagation constant, group velocity, phase velocity, permittivity, permeability and refractive index, etc. are required to be further verified. Based on the analysis of transmission line equations and the corresponding equivalent circuit, the properties in frequency domain are simulated and analyzed. Those results are very helpful in improving the performance of passive components.
In this thesis, the properties of the metamaterial are verified using the Nicolson-Ross-Weir (NRW) method. With the considerations of reflection and transmission phenomena of the structure, the reflection and transmission coefficients are extracted from the scattering parameters of the designed components. Then, the corresponding relative permittivity and permeability are further derived. Also, the issue in dealing with phase correction of transmission coefficient is investigated and modified.
To verify the validness of the NRW method, the corresponding scattering parameters from several metamaterial-related radio frequency filters are illustrated and simulated. The functions for the relative permittivity, permeability and refractive index in terms of scattering parameters are derived. With the aid of MATLAB program, the real part of permittivity, permeability and refractive index can be computed and used to verify metamaterial properties. It has proved that the NRW method is an effective method to provide verification for those metamaterial-related components.

目錄
摘要 I
Abstract II
致謝 III
目錄 IV
圖目錄 VI
第一章 序論 1
1.1研究動機 1
1.2文獻回顧 1
1.3各章概要 9
第二章 超穎材料與左右手複合型傳輸線理論 10
2.1超穎材料簡介 10
2.2左右手複合型傳輸線 12
2.2.1傳播係數、衰減係數與色散係數 14
2.2.2特性阻抗、相速與群速 17
2.2.3介電係數、導磁率與折射率 19
2.2.4平衡型與非平衡型左右手複合型濾波器 21
2.2.5頻率響應 26
第三章 Nicolson-Ross-Weir method (NRW方法) 33
3.1 NRW方法介紹 33
3.2相關方程式推導及驗證 33
3.3透射係數之相位校正 39
第四章 NRW方法驗證超穎材料濾波器之特性 45
4.1具指叉電容架構之超穎材料特性驗證 45
4.1.1 具負折射率傳輸線之驗證 45
4.1.2 零階共振器中超穎材料特性之驗證 48
4.1.3 左右手複合式傳輸線之驗證 50
4.2 開口環形共振器之超穎材料特性驗證 52
4.2.1開路式雙面開口環形共振器架構 52
4.2.2雙頻帶止濾波器 54
4.2.3雙各向異性介質傳輸線 56
4.3結論 58
第五章-結論與未來展望 59
參考文獻 60
附錄一 平衡型CRLH-TL截止頻率之推導 62
附錄二 NRW方法程式碼 64

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