本篇論文主要是針對一維光子能隙(Photonic Bandgap簡稱PBG)結構電路，提出新的設計公式。所提出之公式包含了電路截止帶中心頻率的設計公式與截止帶頻寬大小的預測公式，而此兩個設計公式，分別是利用電磁波多重反射之概念與ABCD矩陣的數值分析方式所推導而得。對於本論文所提出之設計公式，由實際電路的模擬與量測結果可知，電路截止帶之中心頻率與設計目標有良好的一致性。對於電路截止帶之頻寬大小，除了高頻時，因為電路出現寄生電容效應而造成頻寬大小有所誤差外，實際電路量測之截止帶頻寬大小與利用本文預測公式所得的預測值也相互符合。
本論文也利用PBG結構來設計兩種共振器，第一種共振器是利用一共振線與共振線兩邊之PBG結構反射面所構成。第二種是於第一種共振器中加入一電容元件，使其共振器能利用改變電容值大小而達到調整共振頻率的目的。利用本論文提出之設計方式來設計此兩種共振器，由實際電路的模擬與量測結果可知，本論文所提出之設計方式能提供設計者準確的設計共振器之共振頻率。

In this thesis, novel design formulas for the one-dimensional photonic bandgap(PBG) structures are presented. Using the formulas, the center frequency and bandwidth of the bandgap can be accurately predicted. Both the formulas are developed using the multiple reflection concept of electromagnetic waves and the analysis of ABCD matrix. To verifiy the formulas, several one-dimensional PBG structure circuits are manufactured and measured. The results of simulation and measurement are generally in good agreement. When the frequency is higher than the center frequency of the bandgap, the prediction becomes less accurate due to the high frequency effect of parasitic capacitance.
Two types of resonators maily formed by PGB structures are also demonstrated in the thesis. One consists of a center resonant-line surrounded by two PBG reflectors, and the other is formed by mounting a capacitance in the middle of a PBG structure. Using the design procedure presented in this thesis, the resonant frequency of the resonator can be easily determined. Good agreement between simulation and measurement is also obtained.

[1] T. Y. Yun and K. Chang, “Uniplanar One-dimension photonic bandgap
structures and resonators,” IEEE Trans. Microwave Theory Tech. vol.49,
pp. 549-553, Mar. 2001.
[2] D. M. Pozar, Microwave Engineering, Addison Wesley, 1990.
[3] M. Born and E. Wolf, with contributions by A. B. Bhatia ... et al.,
Principles of optics: electromagnetic theory of propagation, interference
and diffraction of light, Oxford /Pergamon Press New York,1980.
[4] R.N. Simons, Coplanar Waveguide Circuit, Components, and systems,
John Wiley & Sons Ltd., 2000.
[5] J.S. Foresi, et al., “Photonic-bandgap microcavities in optical
Waveguides,”Nature, vol. 390, pp.143-145, 1997.
[6] T. Y. Yun and K. Chang, “One-dimension photonic bandgap resonators
and varactor turned resonators,” in IEEE MTT-S Int. Microwave Symp.Dig.,
Anaheim, CA, June 1999, pp.1629-1632.
[7] J. S. Lim, C.S. Kim, Y.T. Lee, D. Ahn, amd S. Nam, “A spiral-sharped
defected ground structure for coplanar waveguide, ” IEEE Microwave and
Wireless Compon. Lett., vol.12, Sept. 2002.
[8] V. Radisic, Y. Qian, R. Coccioli, and T. Itoh, “Novel 2-D photonic bandgap
structure for microstrip lines,” IEEE Microwave Guided Wave Lett., vol. 8,
pp. 69–71, Feb. 1998.
[9] T. Kim and C. Seo, “A novel photonic bandgap structure for Low-pass filter
of wide stopband,” IEEE Microwave and Guided Wave Lett.,vol.10, pp.13-15,
Jan. 2000.
[10] I. Rumsey, P. M. Melinda, and P. K. Kelly, “Photonic bandgap structures
used as filters in microstrip circuits,” IEEE Microwave Guided Wave Lett.,
vol.8, pp. 336–338, Oct. 1998.
[11] J. Yoon and C. Seo, “ Improvement of broadband feedforward amplifier
using photonic bandgap,” IEEE Microwave and Wireless Compon. Lett.,
vol.11, No.11, Nov. 2001.
[12] Yu Ji, Steve Yao and Lute Maleki,” High-Q whispering gallery mode
Resonator filter with photonic bandgap spurious mode suppression,”IEEE/EIA
International Frequency Control Symp.and Exhibition 2000.
[13] F. R. Yang, K. P. Ma, Y. Qian, T. Itoh, ”A uniplanar compact photonic-
bandgap(UC-PBG)structure and its applicationa for microwave circuits,”
IEEE Trans. Microwave Theory Tech., vol.47, No.8, Aug.1999.
[14] F. R. Yang, Y. Qian, T. Itoh, “A novel uniplanar compact PBG structure
for filter and mixer applications,” IEEE MTT-S Int. Microwave Symp.Dig
1999, pp.919-922.
[15] F. R. Yang, Y. Qian, T. Itoh, ”Characteristics of microstrip lines on a
uniplanar compact PBG ground plane,”1998 Asia Pacific Microwave Conf.
Dig., pp.589-592,Dec.1998
[16] Q.Xue, K.M. Shum, and C.H.Chan, ”Novel 1-D microstrip PBG cells,”
IEEE Microwave Guided Wave Lett., vol.10,pp.403-405,Oct.2000.
[17] Y. Q. Fu, G. H. Zhang, and N. C. Yuan, ”A novel PBG coplanar waveguide,”
IEEE Microwave and Wireless Compon. Lett., vol.11,No.11, Nov. 2001
[18] R. E. Collin, Foundations for Microwave Engineering, NewYork:
Mc-Graw-Hill, 1966.
[19] V. Radisic, Y. Qian, T. Itoh, ”Novel architectures for high efficiency
amplifier for wireless applications,” IEEE Trans. On Microwave Theory
and Tech. vol.46 No.11, pp.1901-1909, Nov.1998.
[20] C. K. Wu, H. S. Wu, and C. K. C. Tzuang. “Electric-magnatic-electric slow-
wave microstrip line and bandpass filter of compress size,”
IEEE Trans. On Microwave Theory and Tech.vol.50, No.8, Aug. 2002.
[21] IE3D User’s Manual 2000, release7, Zeland.