本論文主要分成三大部分：(a) 類環型步階式阻抗共振器之雙頻濾波器設計；(b) 非對稱步階式阻抗共振器之三頻帶通濾波器設計；(c) 具有殘樁負載步階式阻抗共振器之三頻帶通濾波器設計。
首先本研究介紹了基本的傳輸線理論及三種步階式阻抗共振器的基本結構及共振特性。
接著本研究提出了一種類環型步階式阻抗共振器，該共振器之結構由一阻抗之為Z1之部分與一組抗為Z2之類環型結構所組成，其中阻抗Z1小於阻抗Z2，而該類環型結構之部分可視為兩個組抗與電子長度分別為Zin2’ 與 Zin2”、θ2’ 與θ2”的開路樁結構。與傳統之步階式阻抗比較，當該組開路樁並聯時，其於並聯端所看到之輸入組抗與Z2相等(Z2 = Zin2’// Zin2”)，且該組開路樁結構之電子長度總和θ2’ + θ2”則與θ2相等。因此，本研究提出了一個使用具有開路樁鑲埋之類環型步階式阻抗共振器設計之雙頻帶通濾波器，其可應用於無線區域網路(WLAN)之2.4GHz與5.7GHz之頻段。該兩個通帶之中心頻率是藉由傳統步階式阻抗共振器的阻抗比(K)或(R)與電子長度比(u)所決定，此外，在不增加元件尺寸下，透過鑲埋之開路樁結構來改善第二個通帶之特性，實際量測後顯示該雙頻帶通濾波器之量測響應皆與模擬響應一致性。
接著，本研究提出了一個非對稱步階式阻抗共振器，與具有兩個不連續面之傳統步階式阻抗共振器比較，該非對稱步階式阻抗共振器僅具有一個不連續面。該非對稱步階式阻抗共振器之結構由一高阻抗Z1且電子長度為θ1之部分與一低阻抗Z2且電子長度為 θ2之部分所組成。藉由適當地選擇定義為u=θ2/θ1+θ2)之電子長度比(u)，與定義為 R=Z2/Z1之阻抗比(R)，可決定該非對稱步階式阻抗共振器之共振特性。因此，本研究提出了使用非對稱步階式阻抗共振器設計之一超寬頻帶通濾波器及兩個三頻帶通濾波器，第一個超寬頻帶通濾波器為使用終端開路之非對稱步階式阻抗共振器與一組作為輸入/輸出埠之耦合線所組成。第二個為可應用於全球行動通訊系統(GSM)、全球互通微波存取(WiMAX)與無線區域網路系統之三頻帶通濾波器，其中心頻率分別為1.8 GHz、3.5 GHz與5.2 GHz，其結構由一組終端開路之非對稱步階式阻抗共振器與一組作為直接饋入之阻抗轉換器所組成。接著，為了驗證該非對稱步階式組抗共振器可廣泛的滿足不同通訊系統之設計，本研究提出了一個具有雙窄頻與超寬頻通帶響應之三頻帶通濾波器之設計，其結構包含了兩組耦合之非對稱步階式組抗共振器與一組直接耦合之饋入結構。該三頻帶通濾波器之通帶分別設計於全球行動通訊系統(GSM)、全球互通微波存取(WiMAX)與超寬頻系統(UWB)之應用。實際量測後顯示三個三頻帶通濾波器之量測響應與皆與模擬響應一致。
最後，本研究提出了一個具有殘樁負載步階式阻抗共振器，其由具有兩個不連續面之傳統步階式阻抗與一配置於對稱面之開路殘樁所組成。藉由適當地選擇定義為α= 2θ2/2(θ1+θ2),之電子長度比(α)，與定義為r=θS/(θ1+θ2)之阻抗比(r)，可決定該具有殘樁負載步階式阻抗共振器之共振特性。因此，本研究提出了一個可應用於全球定位系統(GPS)、無線區域網路系統(WLAN)與全球互通微波存取(WiMAX)之三頻濾波器設計，其中心頻率分別為1.575 GHz、2.4 GHz與3.5 GHz，以及一中心頻率設計於1.7 GHz, 1.9 GHz,3.5 GHz 及 5.5 GHz 之四頻帶通濾波器。該三頻帶通濾波器使用一組具有殘樁負載步階式阻抗共振器與一零度饋入之饋入結構來達成具有高選擇性的三個通帶，而該四頻帶通濾波器使用一組指插式耦合之具有殘樁負載步階式阻抗共振器及直接饋入耦合結構，其可於四個通帶之間產生七個傳輸零點。實際量測後顯示該三頻帶通濾波器之量測響應與皆與模擬響應一致。

The dissertation is divided into three sections, comprising: (a) design and implementation of dual-band bandpass filter (BPF) by using ring-like stepped-impedance resonator (SIR); (b) design and implementation of ultra-wide-band (UWB) and tri-band bandpass filter (BPF) by using asymmetric SIR and (c) design and implementation of tri-band and quad-band BPFs by using stub-loaded SIR.
Firstly, the basic transmission line theory and the introduction of three kinds of SIRs are proposed. The analyses of the resonant behaviors of these three SIRs are well investigated.
Secondly, the ring-like SIR consists of a section with the impedance of Z1 and a ring section with the impedance of Z2 is proposed, where the Z2 is higher than Z1. The ring section of the proposed ring-like SIR can be interpreted as two open stubs, which have input impedances of Zin2’ and Zin2”, the electrical lengths of θ2’ and θ2”, respectively. As compared with the conventional SIR, the Zin2’ and Zin2” of these two stubs, seen from the parallel terminal, are equal to the section with impedance of Z2 (Z2 = Zin2’// Zin2”), and the summation of electrical lengths of θ2’ and θ2” are equal to the electrical length of the section with impedance of Z2 of (θ2=θ2’+θ2”) while in parallel. Therefore, a dual-band BPF are design by using the ring-like SIR and embedded coupled open stubs for application to a wireless local area network (WLAN), 2.4 GHz and 5.2 GHz. The center frequencies of the dual-passbands are created by optimally selecting the impedance ratio (K) and the length ratio (u) in the resonant behavior of a conventional SIR. Without increasing the circuit size, the performance of the second passband can be enhanced by adding the coupled open stubs in the ring-like SIR. Experimental results show good agreement with the simulated results.
Thirdly, the asymmetric SIR with only one discontinuity as compared with the conventional SIR which has two discontinuity in construction is further proposed, that is, it composed by a high-impedance section (Z1, θ1) and a low-impedance (Z2, θ2), By properly selecting the length ratio (u), defined as u= θ2/(θ1+θ2), and the impedance ratio (R), defined as R=Z2/Z1, of the asymmetric SIRs, the resonant behaviors of the asymmetric SIRs can be determined. The resonant behaviors provide a design guideline for the multi-band BPFs design. Therefore, there are a UWB BPF and two tri-band BPFs proposed in this section. First, we propose a simple method and structure to design a high selectivity and wide stopband UWB filter by only one asymmetric SIR with split-end. The transmission poles for the generation of passband and the transmission zeros for the suppressing of spurious are well investigated. Second, a tri-band BPF located at 1.8 / 3.5 / 5.2 GHz for applications of Global System for Mobile Communications (GSM), Worldwide Interoperability for Microwave Access (WiMAX) and WLAN. The tri-band BPF comprises a pair of split-end asymmetric SIRs and a pair of impedance transformers as the tapped feedline structure. Moreover, in order to verify the asymmetric SIR can be applied to various communication standards, a tri-band BPF with two narrow passbands and UWB responses are proposed. The tri-band comprises two pairs of coupled asymmetric SIRs and a direct coupled feedline structure. The three passbands are designed for GSM and WiMAX and a wide passband at UWB system from 3.3 GHz to 4.8 GHz. The measured results of abovementioned three tri-band filters are all with good agreement with the simulations.
Finally, the stub-loaded SIR, composed of a convention SIR with two discontinuities and a stub-loaded section located on the symmetric plane of the convention SIR, is proposed. The impedance and electrical length of the stub-loaded section are expressed as Zs and θs, respectively. By properly selecting the length ratio (α), defined as α= 2θ2/2(θ1+θ2), and the length ratio (r), defined as r=θS/(θ1+θ2), the resonant behavior of the stub-loaded SIR can be determined. Therefore, a tri-band BPF designed at 1.575 GHz, 2.4 GHz and 3.5 GHz and a quad-band BPF designed at 1.7 GHz, 1.9 GHz 3.5 GHz and 5.5 GHz, are proposed. The tri-band BPF comprises a pair of coupled stub-loaded SIR and a 0o feedline structure which results in high selectivity of the passbands. The quad-band BPF comprises a pair of interdigital coupled stub-loaded SIR and tapped coupling, which provides seven transmission zeros aside the passband. Experimental results show good agreement with the simulated results.

chapter 1
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[5] W. Y. Chen, S. J. Chang, M. H. Weng, Y. H. Su, and H. Kuan, “Simple method to design a tri-band bandpass filter using asymmetric SIRs for GSM, Wimax and WLAN applications, Microwave Opt. Technol. Lett., vol. 53, pp. 1573-1576, 2011.
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[7] F. C. Chen and Q. X Chu, “Design of compact tri-band bandpass filters using assembled resonators,” IEEE Microw. Theory Tech., vol. 57, pp. 165–171, 2009.
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[9] S. Gao , Z. Y. Xiao, H. H. Hu, “A novel compact dual-band bandpass filter using SIRs with open-stub line,” Microwave Conference, 2008 China-Japan Joint, pp. 464-466, 2008.
[10] X. Lai, C. H. Liang, H. Di, and B. Wu, “Design of tri-band filter based on stub loaded resonator and DGS resonator,” IEEE Microw. Wireless Compon. Lett., vol. 20, pp. 265–267, 2010.
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chapter 2
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chapter 3
[1] M. Makimoto and S. Yamashita, “Microwave Resonators and Filters for Wireless Communication: Theory, Design and Application,” Springer-Verlag, 2000.
[2] W. Y. Chen, S. J. Chang, H. Kuan, and M. H. Weng, “A High Selectivity Dual-Band Filter Using Ring-Like SIR with Embedded Coupled Open Stubs Resonators,” Journal of Electromagnetic Waves and Applications, vol. 25, no. 14-15, pp. 2011-2021, 2011
[3] W. Y. Chen, M. H. Weng, S. J. Chang, H. Kuan and Y. H. Su. “A New Tri-Band Bandpass Filter For GSM, WiMAX and Ultra-Wideband Responses by Using Asymmetric Stepped Impedance Resonators,” Progress In Electromagnetics Research, vol. 124, 365-381, 2012.
[4] W. Y. Chen, M. H. Weng and S. J. Chang, “A New Tri-band Bandpass Filter Based on Stub-Loaded Stepped Impedance Resonator,” IEEE Microw. Wireless Compon. Lett . vol. 22, no. 4, pp. 179-181, 2012.

chapter 4
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chapter 5
[1] IE3D Simulator,” Zeland Software, Inc., 2005.
[2] Z. C. Hao, and J. S. Hong, “ High selectivity UWB bandpass filter using dual-mode resonators,” Electronics Letters, vol. 47, pp. 1379-1381, 2011.
[3] R. Li, and L. Zhu, “Compact UWB bandpass filter using stub-loaded multiple-mode resonator,” IEEE Microw. Wireless Compon. Lett., vol. 17, pp. 40–42, 2007.
[4] Y. C. Chang, C. H. Kao, M. H. Weng, and R. Y. Yang, “Design of the compact wideband bandpass filter with low loss, high selectivity and wide stopband,” IEEE Microw. Wireless Compon. Lett., vol. 18, pp. 770-772, 2009.
[5] M. H. Weng, C. Y. Huang, C. Y. Hung, and S. W. Lan, “Design of an ultra-wideband bandpass filter by using coupled three line microstrip structure,” Journal of Electromagnetic Waves and Applications, vol. 26, pp. 716–728, 2012.
[6] H. W. Wu, S. K. Liu, M. H. Weng and C. H. Hung, “Compact microstrip bandpass filter with multi-spurious suppression,” Progress in Electromagnetics Research, vol.107, pp. 21-30, 2010.
[7] K. U-yen, E. Wollack, T. Doiron, J. Papapolymerou, and J. Laskar, “A planar bandpass filter design with wide stopband using double split-end stepped-impedance resonators,” IEEE Trans. Microw. Theory Tech., vol. 54, pp. 1237–1244, 2006.
[8] J. S. Hong and M. J. Lancaster, Microstrip Filters for RF/Microwave Applications, New York: John & Wiley, 2001.
[9] F. C. Chen and Q. X. Chu, “Design of compact tri-band bandpass filters using assembled resonators,” IEEE Trans. Microw. Theory Tech., vol. 57, pp. 165-171, 2009.
[10] C. Y. Kung, Y. C. Chen, C. F. Yang and C. Y. Huang, “ Triple-band parallel coupled microstrip bandpass filter with dual coupled length input/output,” Microwave & Opt. Tech. Lett., vol. 51, pp. 995-997, 2009.
[11] X., Z. Ma Guan and P. Cai, “A novel triple-band microstrip bandpass filter for wireless communication,” Microwave & Opt. Tech. Lett., vol. 51, pp. 1568-1569, 2009.
[12] X. Lai, C.-H. Liang, H. Di and B. Wu, “Design of tri-band filter based on stub loaded resonator and DGS resonator,” IEEE Microw. Wireless Compon. Lett., vol. 20, pp. 265-267, 2010.
[13] Hong, J. S., Microstrip Filters for RF/Microwave Applications, Second Edition, New York: John & Wiley, 2011.
[14] Y. C. Chang, C. H. Kao, M. H. Weng, and R. Y. Yang, “Design of the compact dual-band bandpass filter with high isolation for GPS/WLAN applications,” IEEE Microw. Wireless Compon. Lett., vol. 19, pp. 780-782, 2009.
[15] S. Luo, L. Zhu, and S. Sun, “Compact dual-mode triple-band bandpass filters using three pairs of degenerate modes in a ring resonator,” IEEE Trans. Microw. Theory Tech., vol. 59, pp. 1222-1229, 2011.
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[19] X. Guan, Z. Ma, and P. Cai, “A novel triple-band microstrip bandpass filter for wireless communication,” Microw. Opt. Technol. Lett., vol. 51, pp. 1568-1569 , 2009.

chapter 6
[1] S. Luo, L. Zhu, and S. Sun, “Compact dual-mode triple-band bandpass filters using three pairs of degenerate modes in a ring resonator,” IEEE Trans. Microw. Theory Tech., vol. 59, pp.1222-1229, 2011.
[2] W. Y. Chen, S. J. Chang, M. H. Weng, Y. H. Su, and H. Kuan, “Simple method to design a tri-band bandpass filter using asymmetric SIRs for GSM, Wimax and WLAN applications, Microwave Opt. Technol. Lett., vol. 53, pp. 1573-1576, 2011.
[3] C. F. Chen, T. Y. Huang, and R. B. Wu, “Design of dual- and triple-passband filters using alternately cascaded multiband resonators,” IEEE Trans. Microw. Theory Tech., vol. 54, pp. 3550-3558, 2006.
[4] F. C. Chen and Q. X Chu, “Design of compact tri-band bandpass filters using assembled resonators,” IEEE Microw. Theory Tech., vol. 57, pp. 165–171, 2009.
[5] C. I G. Hsu, C. H. Lee, and Y. H. Hsieh, “Tri-band bandpass filter with sharp passband skirts designed using tri-section SIRs, ’’IEEE Microw. Wireless Compon. Lett., vol. 18, pp. 19-21, 2008.
[6] S. Gao , Z. Y. Xiao, H. H. Hu, “A novel compact dual-band bandpass filter using SIRs with open-stub line,” Microwave Conference, 2008 China-Japan Joint, pp. 464-466, 2008.
[7] X. Lai, C. H. Liang, H. Di, and B. Wu, “Design of tri-band filter based on stub loaded resonator and DGS resonator,” IEEE Microw. Wireless Compon. Lett., vol. 20, pp. 265-267, 2010.
[8] L. Y. Ren, “Tri-band bandpass filters based on dual-plane microstrip/DGS slot structure,” IEEE Microw. Wireless Compon. Lett., vol. 20, pp. 429-431, 2010.
[9] IE3D Simulator Zeland Software, Inc., 2002.
[10] J. S. Hong, Microstrip Filters for RF/Microwave Applications, Second Edition, New York: John & Wiley, Ch. 7, 2011.
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