人工材料功率分配器的使用

在前一小節中，藉由Poynting vector 向量圖了解能量傳遞的模式後，我們把 此人工材料與功率分配器結合(Power divider)。

如圖5-29，此功率分配器一樣是用厚度 1.6 mm 的鋁板製程，兩塊平行板間

的距離與人工材料單晶胞圓柱的高度相同，用符號h 表示。人工材料單晶胞金屬

柱在x 方向及 y 方向週期為 5，且兩個方向週期的間距皆為 a，圓形金屬柱的半

徑為r，人工材料到平行板外緣的距離是 e。此功率分配器同樣是使用同軸線饋

入激發源作激發，放置於人工材料的正中央，同軸電纜中心導體進入人工材料的 長度為i。p 為波導埠的大小(waveguide port)，結構圖如圖 5-29 所示。

圖5-33 功率分配器結構圖 (a)上方俯視圖 (b)側面圖 表 5-15

功率分歧器結構係數

Parameter e i r a b h p

Value (mm) 30 8 1.18 15 15 9 30

圖5-30 為此功率分配器之反射係數圖(S11)與穿透係數圖(S21)，實線是反射係 數、虛線是穿透係數。在此改變不同接收埠的大小，以選擇合適的功率分配器尺 寸。

7 7.2 7.4 7.6 7.8 8

Frequency (GHz)

-35 -30 -25 -20 -15 -10 -5 0

S parameters (dB)

S_{11 p=45 mm} S_{21 p=45 mm} S_{11 p=30 mm} S_{21 p=30 mm} S_{11 p=15 mm} S_{21 p=15 mm}

圖5-34 功率分配器的反射係數與穿透係數圖

在這個模擬中，我們發現此人工材料確實有應用於功率分配器的潛力。若應 用於光波的頻段，作短距離的能量分配，應該會有很好的發展。

第六章 結論

利用特徵模態分析法，我們得知損耗(lossy)或無損耗(lossless)的人工材料相 位關係、單晶胞場型分佈、波傳遞的方向及帶隙現象。並且可以針對不同角度入 射的電磁波，逐一分析其特性。第三章結構參數萃取的方法雖然僅適用於垂直入

射的平面波，但是卻能從S 參數的分析及轉換獲得各等效係數值，確認人工材料

是否確實操作於介電係數與導磁係數都趨近於0 的頻率。而最後第四章的

Marcuvitz 結構參數分析與萃取，則可以不必電磁軟體輔助，純粹以數值分析的 方式來完成。最重要的貢獻在於有了等效電路，配合前面兩章的分析，對此人工 材料做完整的報告。

把分析好的人工材料應用於天線結構中，目的為了證明前面三個章節的分析 結果。這套分析方式不僅在本論文結構的模擬與量測中獲得驗證，並且製作出了 一個多方向、高增益、sidelobe 強度極低等良好特性的天線。在通訊系統上，可 以有效降低雜訊的產生，對稱的把能量分配到多個方向，輕易得產生點對點、或 是點對多點的通訊架構，是一個多用途的整合型產品，具有提升未來通訊產品的 功能、簡化電路的前瞻性。

參考文獻

[1] A. M. Nicolson and G. F. Ross, “Measurement of the Intrinsic Properties of Materials by Time-Domain Techniques,” IEEE Trans. Instrum. Meas., Vol. 19, No. 4, 377-382, Nov. 1970.

[2] D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B, Vol. 65, 195104, 2002.

[3] R. W. Ziolkowski, “Design, fabrication, and testing of double negative

metamaterials,” IEEE Trans. Antennas Propag., Vol. 51, No. 7, 1516-1529, Jul. 2003.

[4] X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, Jr., and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev.

E 70, 016608, 2004.

[5] B. -I. Wu, W. Wang, J. Pacheco, X. Chen, T. Grzegorczyk, and J. A. Kong, “A study of using metamaterials as antenna,” Progress In Electromagnetics Research, PIER 51, 295-328, 2005.

[6] M. M. Sigalas, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Metallic photonic band-gap materials,” Phys. Rev. B, Condens. Matter, Vol. 52, 11744-11751, 1995.

[7] H. Y. David Yang, “Finite difference analysis of 2-D photonic crystals,” IEEE Trans. Microw. Theory and Tech., Vol. 44, No. 12, 2688-2695, Dec. 1996.

[8] C. -P. Yu and H. -C. Chang, “Compact finite-difference frequency-domain method for the analysis of two-dimensional photonic crystals,” Optics Express, Vol. 12, No. 7, 1397-1408, Apr. 2004.

[9] N. A. Nicorovici and R. C. Mcphedran, “Photonic Band Gaps Noncommuting Limits and the “Acoustic Band”,” Phys. Rev. Lett., Vol. 75, No. 8, 1507, Aug. 1995.

[10] S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A Metamaterial for Directive Emission,” Phys. Rev. Lett., Vol. 89, No. 21, 213902, Nov. 2002.

[11] D. Sievenpiper, J. Schaffner, R. Loo, G. Tangonan, S. Ontiveros, and R. Harold,

“A tunable impedance surface performing as a reconfigurable beam steering reflector,” IEEE Trans. Antennas and Propag., Vol. 50, No. 3, 384-390, Mar. 2002.

[12] D. Sievenpiper, and J. Schaffner, “Beam steering microwave reflector based on electrically tunable impedance surface,” Elect. Lett., Vol. 38, No. 21, 1237-1238, 10 Oct. 2002.

[13] D. F. Sievenpiper, J. H. Schaffner, H. J. Song, R. Y. Loo, and G. Tangonan,

“Two-dimensional beam steering using an electrically tunable impedance surface,”

IEEE Trans. Antennas and Propag., Vol. 51, No. 10, 2713-2722, Oct. 2003.

[14] L. Liang, B. Li, S. H. Liu, C. H. Liang, “A study of using the double negative structure to enhance the gain of rectangular waveguide antenna arrays,” Progress In Electromagnetics Research, PIER 65, 275-286, 2006.

[15] A. K. Hamid, “Axially slotted antenna on a circular or elliptic cylinder coated with metamaterials,” Progress In Electromagnetics Research, PIER 51 329-341, 2005.

[16] B. Li, B. Wu, C. H. Liang, “Study on high gain circular waveguide array antenna with metamaterial structure,” Progress In Electromagnetics Research, PIER 60, 207-219, 2006.

[17] S.-Y. Lin, V. M. Hietala, L. Wang, and E. D. Jones, “Highly dispersive photonic band-gap prism,” Opt. Lett., Vol. 21, No. 21, 1771-1773, 1996.

[18] H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S.

Kawakami, “Metallic photonic band-gap materials,” Phys. Rev. B, Vol. 58, No. 16, 10096-10099, 1998.

[19] M. Notomi, “Theory of light propagation in strongly modulated photonic crystals Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B, Vol.

62, No. 16, 10696-10705, 2000.

[20] P. Markos and C. M. Soukoulis, “Transmission properties and effective

electromagnetic parameters of double negative metamaterials,” Optics Express, Vol.

11, No. 7, 649-661, Apr. 2003.

[21] J. Baker-Jarvis, E. J. Vanzura, and W. Kissick, “Improved technique for determining complex permittivity with the transmission/reflection method,” IEEE Trans. Microw. Theory and Tech., Vol. 38, No. 8, 1096-1103, Aug. 1990.

[22] N. Marcuvitz, Waveguide handbook, Radiation Laboratory Series, Vol.10, New York: McGraw-Hill, 1951.

[23] R. B. Hwang, “Relations between the reflectance and band structure of 2-D metallodielectric electromagnetic crystals,” IEEE Trans. Antennas and Propag., Vol.

52, No. 6, 1454-1464, Jun. 2004.

[24] P. Russo, R. Rudduck, L. Peters, Jr., “A method for computing E-plane patterns of horn antennas,” IEEE Trans. Antennas and Propag., Vol. 13, No. 2, 219-224, Mar.

1965.

[25] J. Yu, R. Rudduck, L. Peters, Jr., “Comprehensive analysis for E-plane of horn antennas by edge diffraction theory,” IEEE Trans. Antennas and Propag., Vol. 14, No.

2, 138-149, Mar. 1966.

[26] D. R. Rhodes, “An Experimental Investigation of the Radiation Patterns of Electromagnetic Horn Antennas,” Proceedings of the IRE, Vol. 36, No. 9, 1101-1105, Sept. 1984.

[27] E. Jull, “Errors in the predicted gain of pyramidal horns,” IEEE Trans. Antennas and Propag., Vol. 21, No. 1, 25-31, Jan. 1973.

[28] L. S. Warren, A. T. Gary, Antenna Theory and Design, 2nd ed., John Wiley ＆ Sons, Inc., 1998.