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行政院國家科學委員會專題研究計畫 成果報告

應用於多種無線通訊系統之寬頻天線陣列

研究成果報告(精簡版)

計 畫 類 別 : 個別型

計 畫 編 號 : NSC 95-2221-E-002-092-

執 行 期 間 : 95 年 08 月 01 日至 96 年 07 月 31 日

執 行 單 位 : 國立臺灣大學電信工程學研究所

計 畫 主 持 人 : 鄭士康

計畫參與人員: 博士班研究生-兼任助理:蔡志勇、周厚原、賴明佑

報 告 附 件 : 出席國際會議研究心得報告及發表論文

出席國際會議研究心得報告及發表論文

處 理 方 式 : 本計畫可公開查詢

中 華 民 國 96 年 08 月 23 日

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應用於多種無線通訊系統之多頻段天線陣列

A multi-band antenna array for multiple wireless

communication systems

計畫編號

NSC95-2221-E-002-092

執行期限:95 年 8 月 1 日至 96 年 7 月 31 日

主持人:鄭士康 台大電信工程研究所

計畫參與人員:蔡志勇,周厚原,賴明佑

台大電信工程研究所

中文摘要 近年來無線通訊產品大量湧現在生活週 遭的每一個角落,慢慢地成為人們生活中不可 或缺的物品。為達到更優質的通訊,各式各樣 的基地台和橋接器的需求逐漸增加。如果每一 個通訊系統都使用各自的基地台或橋接點,週 遭環境中所需安裝的天線數目將大量增加,眾 多天線的架設亦有礙觀瞻。本研究計畫設計完 成一個適用於各種通訊系統、價廉、精巧的多 功能寬頻相位陣列天線系統。該架構由兩個四 天線元件的陣列所組成。鑒於大部分的無線通 訊使用的頻譜分布在 2.0GHz 到 6.0GHz 之 間,因此我們設計一個工作於此頻帶範圍之陣 列天線作為範例。量測結果顯示:除3GHz 以 下範圍,由於天線耦合較強,場型不如預期 外,其餘頻段測得結果均與設計相符。 關鍵字:陣列天線 Abstract

In this project a new wideband array antenna system for multiple wireless applications is developed. It is composed of two equispaced four-element arrays, phase shifters, diplexers, and power dividers. The two arrays are interleaved and connected to diplexers and power dividers. The proposed antenna system associated with feeding network and antenna elements can be integrated on a single substrate. Consequently, such a design is with low fabrication and assembly cost and compact size. A wideband antenna array with bandwidth from 2.0GHz to 6.0GHz and main beam pointing to 20 degrees is designed and measured as an example. The radiation patterns below 3.0GHz deforms drastically, suffering from mutual couplings between antenna elements. The performance for other frequencies seems to agree with our design.

Keywords: array antenna.

I. Introduction

Recently wireless communication products emerge in large number and gradually become living essentials. The demand of various base stations and access points for different communication standards increases in order to pursue better service quality. As the number of base stations and access points goes up, the number of antennas increases dramatically. Technically, it results in serious couplings between antennas of different communication systems and occupies a large space. For the public, it arouses concerns about their excessive electromagnetic radiation. Thus, a compact multifunctional array antenna to provide a wide variety of wireless services is highly desired.

Consider an equispaced array of 4 elements, a uniform progressive phase factor δ can be introduced to position the main beam to angles θ0 and π-θ0 [1]. If δ is a linear function of

frequency, the direction of main beam still points at θ0 and π-θ0, but the main beam deforms and

the level of side lobe degrades as frequency sweeps. The digital signal processing technique, digital beamforming, can provide a frequency-invariant beam pattern over an arbitrary bandwidth [2]. This approach is very powerful, but for an n-element array each antenna requires an RF transceiver and A/D converter, resulting in high fabrication cost. Consequently, designing an array with lower cost and beam pattern not sensitive to frequency sweeping is in great demand for future wireless applications.

Here we propose a new wideband array antenna system which is composed of two equispaced four-element arrays, phase shifters, diplexers and power dividers. The two arrays are interleaved and connected to diplexers and

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power dividers. The proposed antenna system associated with feeding network and antenna elements can be integrated on a single substrate, offering lower fabrication and assembly cost and more compact size than the conventional solutions. A wideband antenna array with bandwidth from 2.0 GHz to 6.0 GHz and main beam pointing to 20 degrees is designed and measured as an example.

II. Design Concept

The structure of the proposed system is depicted in Fig. 1. The phase shifters are designed to position the main beam to a specific direction. The use of the diplexers is to switch the two arrays as frequency sweeps. Assume that

f1 and f2 are the lowest and the highest

frequencies of the desired band, choose

2 1f f fc= (1)

(

)

2 1 c LO f f f = + (2)

(

)

2 2 c HI f f f = + (3)

Such a choice makes the low- and high-bands of the diplexer have the same fractional bandwidth. The frequency response of the diplexer is plotted in Fig. 2. The delay lines in Fig.1 are designed so that the outputs of the

diplexer are with the same phase at fc. Finally,

the diplexers are fed using wideband power dividers.

The array factor of the proposed system can be expressed in the form

( ) ( )

( ) ( )

( ) = − = − + = 4 1 sin 0 4 1 sin 0 , n HI s k jn HI n LO d k jn LO f e C f A e C f AF θ θδ θδ (4) HI LO HI LO f f , , δ δ = (5) ( )sinθ 0 2 3k ds j e A= − (6) where

k0 wave number in free space;

d and s half-wavelengths in free space at frequencies fLO and fHI, respectively; CLO and CHI frequency responses of the low-band

and the high-band of the diplexer, respectively;

δ system progressive phase factor, a constant;

δLO and δHI progressive phase factors of array

with spacing d and s, respectively.

CLO and CHI are similar to the responses of

bandpass filters with center frequencies at fLO

and fHI, respectively. The array with spacing d

works as frequency being around fLO , and the

array with spacing s works as frequency being around fHI . By introducing the diplexers, the

deformation of the main beam due to frequency sweep can be relieved.

III. Simulation and Measurement Results

A. Simulation Results

A 2.0 GHz to 6.0 GHz wideband antenna array with mainbeam pointing to 20 degrees is designed to validate the proposed concept. According to the equations in Section II, δ=61 degrees, fc=3.46 GHz, fLO=2.73 GHz and fHI=4.73 GHz. The spacings d and s are 54.9 mm

and 31.7 mm, respectively. The minimal spacing between two antenna elements is 11.6 mm, corresponding to 0.13λ0 at fc. Assume that the

mutual couplings between antenna elements can be neglected, the simulated array factors are plotted in Fig. 3, and the side lobe level against frequency and the 3dB beamwidth against frequency are shown in Fig. 4. It is seen that the main beam points to 20 degrees over 2.0 GHz to 6.0 GHz, the 3dB beamwidth is between 22o and

38o, and the side lobe level is larger than 10 dB

from 2.0 GHz to 5.7 GHz.

B. Components Design

The substrate used is an RO4003 with

Fig.1. Proposed System Architecture.

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thickness 0.508 mm and relative dielectric constant 3.38. As discussed previously, the minimal spacing between two antennas is 11.6 mm. As a result, an antenna element with a width smaller than 11.6 mm is needed. However, the design of such a planar antenna with a bandwidth from 2.0 GHz to 6.0 GHz presents many difficulties. One of possible solutions is a loaded monopole antenna, offering a compact size and excellent pattern characteristics over a wide bandwidth. The resultant antenna element is shown in Fig. 5. The antenna gain between 2.0GHz to 6.0 GHz is 1.0dBi in average. Figure 6 presents the couplings between antenna elements, showing that the maximum coupling is -6 dB.

For the diplexer, we connect two broadband bandpass filters based on stub-line filters [3]-[7] together to form the desired diplexer; nevertheless, some unwanted interactions between the filters cause serious performance degradation. As a result, we develop a Matlab program based on fmins subroutine to optimize the designed parameters to meet the desired specifications. Figure 7 presents the layout and

scattering parameters of the designed diplexer. The losses at 2.0 GHz and 6.0 GHz are 0.3 dB and 0.8 dB, respectively. The measured cutoff frequency is at 3.45 GHz, which is almost identical to the simulated one. The measured and simulated phase differences at 3.45 GHz is 32 and 20.7 degrees, respectively. The discrepancy is contributed by the imperfection of the manually soldered SMA connectors at the output ports.

C. Feeding Network

The layout of the feeding network is shown in Fig. 8. Its size is 200 mm by 90mm. The 4-way power divider [8] and the four diplexers are connected together. The delay lines are used to make the outputs of the diplexers have the same phase at the cutoff frequency. The serpentine lines are designed to implement the phase shifters, making the differences between Ports Li and Li+1 at 2.73 GHz and between Ports Hi and Hi+1 at 4.73 GHz be 61 degrees,

respectively. Figure 9 presents the measured reflection coefficients and the insertion losses at output ports of the feed network. Ideally, the

Fig.5. Antenna element. (a) Geometry. (b) Amplitude of

S11..

Fig.6. Couplings between antenna elements.

Fig.7. Frequency responses of the diplexer used in the array system.

Fig.3. Simulated array factors of the proposed array system.

Fig.4. Side lobe level and 3dB beamwidth against frequency.

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insertion losses at the output ports are -6dB. The additional losses at 2.0 GHz and 6.0GHz are 0.5 dB and 1.5dB, respectively, which are contributed by the 4-Way power divider and diplexers.

Table I summaries the measured phases at the output ports and phase differences between output ports at frequencies 2.73 GHz, 3.45 GHz, and 4.73 GHz. The numbers in brackets represent the ideal value. At the column of 3.45 GHz, the ideal phase shift between Ports Li and Hi can be determined by Eq. (7). It can be seen

that the measured phase shifts agree well with the designed ones.

      − ⋅ ⋅ = ∆ HI LO i H i L f f i 1 1 , δ (7) D. Antenna Array

Figure 10 shows the radiation patterns in the

xy-plane at different frequencies. The radiation

patterns below 3.0 GHz deform dramatically,

suffering from mutual couplings between antenna elements.

V. Conclusions

A new wideband planar antenna array has been proposed in this paper. This antenna system associated with feeding network and antenna elements can be integrated in a single substrate. Consequently, such a design is with low fabrication and assembly cost and compact size. So far, the prototype of the array antenna has been completed. Suffering from the strong mutual coupling between antenna elements, the radiation patterns below 3 GHz deform dramatically. The overall system will be improved in the future.

References

[1] R. S. Elliott, Antenna Theory and Design Revised

Edition, Wiley-Interscience, 2003, Ch 4.

[2] D. H. Tuan and Peter Russer, “Signal Processing for Wideband Smart Antenna Array and Applications,”

IEEE Microwave Magazine, pp. 57-67, Mar. 2004.

[3] G. L. Matthaei, L. Young, and E. M. T. Jones,

Microwave Filters, Impedance-Matching Networks, and Coupling Structures, McGraw-Hill, 1964, Chapter

16.

[4] S. Srisathit, S. Patisang, R. Phromoloungsri, S. Bunnjaweht, S. Kosulvit, and M. Chongcheawchamnan, “High isolation and compact size microstrip hairpin diplexer,” IEEE Microwave and Wireless Comp. Lett., vol. 15, pp. 101-103, Feb. 2005.

[5] B. Strassner and K. Chang, “Wide-Band Low-Loss High-Isolation Microstrip Periodic-Stub Diplexer for Multiple-Frequency Applications,” IEEE Trans.

Microwave Theory Tech., vol. 49, pp. 1818-1820, Mar.

2001.

[6] D. M. Pozar, Microwave Engineering, John Wiley & Sons, 1998, Chap. 8.

[7] J. S. Hong and M. J. Lancaster, Microstrip Filters for

RF/Microwave Applications, John Wiley & Sons, 2001.

[8] S. B. Cohn, “A Class of Broadband Three-Port TEM-Mode Hybrids,” IEEE Trans. Microwave and

Tech., vol. 16, pp. 110-116, Feb. 1968.

Fig.8. Layout of the feeding network.

Fig.9. Measured reflection coefficient and the insertion losses at the output ports of the feeding network.

Fig.10. Measured radiation patterns of the designed antenna array.

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參加

2007 IEEE

天線與傳播學會

國際研討會

(2007 IEEE Antennas and

Propagation Society

International Symposium)

報告

鄭士康

台大電機系/電信研究所

中華民國九十六年八月廿三日

(7)

一、引言

此次獲國科會補助,參加 2007 年 IEEE 天線與傳播學會國際研討會( 2007

IEEE AP-S International Symposium and USNC/URSI National Radio Science

Meeting ),由敝人及博士班學生賴明佑各宣讀論文一篇,碩士班學生巫宗佑宣讀

論文兩篇。此一研討會為世界電磁研究人員一年一度,規模最大之盛會之一,重

要論文常於此發表。

本屆會議於六月十一至十四日於美國夏威夷州檀香山市( Honolulu )舉行。敝

人於六月十日星期日下午出發,搭乘華航直飛班機,同機尚有交大林育德教授、

鍾世忠教授、台科大楊成發教授、中山大學郭志文教授、本系瞿大雄教授、林怡

成教授等多人。因時差十八小時,同日早晨抵達,由先到之台科大馬自莊教授載

林怡成與我到會場旅館 Sheraton Waikiki。Check in 後與林教授同住一房,下午報

到,並演練口頭報告。十一日至十二日參加大會,因台灣尚有要務,故於十三日

上午即搭機經東京返國,於十四日星期四下午返抵台北。

此次台灣各大學參加會議人數眾多,除教授外,亦有多位研究生,足見後生

可畏。敝人認為,台灣研究生較缺國際觀,政府應多鼓勵國內研究生參與國際研

討會,培育下一代研發人才,此次多位研究生之參與,正是良好之典範。

二、會議經過

報到

六月十日會場報到後,領到資料袋及論文集光碟片。大會每人發放上有標誌

之夏威夷衫一件作為紀念品,惜尺碼略大。會議分十四個口頭發表場地,同時進

行。進行四天,一共有 126 個口頭發表場次( Session );另外前三天中午於午餐

時間有壁報論文發表(稱為互動論壇,Interactive Forum,以論文主題而非論文評

審成績分配),共 49 場次:口頭與壁報共計發表論文 1700 餘篇,參加人數預估

在兩三千人之譜。與前幾年參加相同會議之經驗相較,場次減少,但論文篇數差

不多,可能是場地分配的問題。

參加會議與發表論文

此次敝人與學生共發表四篇論文,主題分別為場型可調式天線設計、時域混

合計算格網誤差分析、多層印刷電路板 RFID 天線設計、波束方向可切換之智慧

型天線設計等,聽眾反應均甚良好。尤其多層印刷電路板 RFID 天線設計論文發

表後,聽衆討論特別熱烈;主因是之前的 RFID 天線文獻均未深入考慮應用於印

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刷電路板的情形,而我們的研究顯示一般 RFID 天線用於印刷電路板會發生短

路,無法運作;我們在電路板上的狹縫天線設計,則可解決此一問題,效能甚佳。

在所聽的論文發表方面,由於個人對時域數值方法的理論特別有興趣,因此

印象較深刻的論文主題大多屬之。以下簡單介紹幾篇:

1. 韓國Piljun Park

等人的3D次網格FDTD技術,可以使粗細網格大小間的比例

為任意奇數,並完成比例為17的天線分析,相當特別,但缺乏誤差及穩定性

的理論分析。

2. 法國J. Gazave等人也提出3D次網格FDTD技術,粗細網格大小間的比例為任

意整數,並完成比例為12的自由空間傳播計算,同樣也缺少誤差及穩定性的

理論分析。

3. 美國OSU的Ryan A, Chilton與Robert Lee研發出具有穩定性與守恆性的3D

FDTD次網格架構,應用較抽象的數學觀念討論,決定各次網格內插權重。

粗細網格大小間的比例也可以為任意整數,並以導波管的不連續問題驗證其

理論,但未完成誤差之理論分析,僅以實例計算說明其粗細網格交界之反射

甚低。兩位作者並且稱合宜的次網格FDTD技術為許多研究者尋找的「聖

杯」,其困難與重要性可見一斑。

4. 英國Costa等人利用Huygence次網格FDTD技術,加上Debye模型,可處理UWB

超寬頻訊號通過頻率相關媒質的問題。

5. 法國Pascaud等人針對MIMO天線,發展雙網格FDTD技術,以較細網格計算

天線單元之近場,再以之為等效入射場,用正常大小網格計算其輻射場。

6. 巴西de Sousa等人運用TLM技術,將電磁問題區域分成小塊,以電路元件表

示,並與SPICE結合,可分析不少問題。

7. 新竹交大陳富強教授指導學生發展出應用於ADI-FDTD的PML結構,並有理

論分析,為可用於高Courant數之ADI-FDTD方法拓展應用範圍。

三、整體印象及心得

今年再度參與此一 IEEE 天線與傳播學會國際研討會,除了發現生面孔很多

之外,熟識友人又有數人獲選為 IEEE Fellow,足見台諺「戲棚下站久就是你的」

之真確。此外,平行場次之多,使聽眾常有分身乏術之嘆。壁報論文可使論文作

者與有興趣之觀眾互動增加,不失為一種良好的發表方式。另外,因過去英文口

頭報告訓練不夠,國際會議報告常不能令人滿意。去年遂以十餘小時反覆修改背

誦全部講稿,效果甚佳。今年同樣花費甚多時間背誦,自覺表現與去年差不多,

均較以往進步;且因 Session 較晚開始,遭主持人要求提前三分鐘結束,而仍能

臨時彈性調整內容,順利完成演講,皆是熟背講稿之功。此一心得或許可供國內

(9)

研究生參加國際會議時參考。

在探討主題方面,翻開議程手冊,即可發現天線與無線通訊技術場次增加許

多,反應無線通信熱潮。數值電磁計算場次仍多,大多可歸類於時域有限差分法

及有限元素法,頻域快速多極演算法偶而可見,所解之問題也已多為實際三維問

題,進步不可謂不大,然而基本方法上的創新則極為少見,一般均在計算之過程

修改,或充分利用快速之電腦設備,以便提高計算效率。天線方面之論文逐漸以

應用為導向,如 UWB 天線設計、MIMO 天線設計、RFID 天線設計等均是;另

一趨勢則是天線設計中無線通訊理論及通訊規約標準的引用漸多,研究天線的學

者最好也能涉獵相關書籍;也有新材料如 Metamaterial 及非線性元件的導入等,

形成新的研究主流。若干新主題,如奈米電磁學也開始出現,由於奈米科技漸受

重視,而其電磁現象研討為其理論基礎,相關研究未來可能會有很好的發展,值

得注意。

四、結語

感謝國科會於計劃中補助敝人參與此一會議,一方面得以發表一己及指導學

生之研究所得,一方面亦得以了解世界電磁研究之最新情況。明年此一會議將在

美國加州聖地牙哥市( San Diego )舉行,預料盛況當不遜今年,希望能再有機會

參加。

(10)

參加

2007 IEEE

天線與傳播學會

國際研討會

(2007 IEEE Antennas and

Propagation Society

International Symposium)

報告

鄭士康

台大電機系/電信研究所

中華民國九十六年八月廿三日

(11)

一、引言

此次獲國科會補助,參加 2007 年 IEEE 天線與傳播學會國際研討會( 2007

IEEE AP-S International Symposium and USNC/URSI National Radio Science

Meeting ),由敝人及博士班學生賴明佑各宣讀論文一篇,碩士班學生巫宗佑宣讀

論文兩篇。此一研討會為世界電磁研究人員一年一度,規模最大之盛會之一,重

要論文常於此發表。

本屆會議於六月十一至十四日於美國夏威夷州檀香山市( Honolulu )舉行。敝

人於六月十日星期日下午出發,搭乘華航直飛班機,同機尚有交大林育德教授、

鍾世忠教授、台科大楊成發教授、中山大學郭志文教授、本系瞿大雄教授、林怡

成教授等多人。因時差十八小時,同日早晨抵達,由先到之台科大馬自莊教授載

林怡成與我到會場旅館 Sheraton Waikiki。Check in 後與林教授同住一房,下午報

到,並演練口頭報告。十一日至十二日參加大會,因台灣尚有要務,故於十三日

上午即搭機經東京返國,於十四日星期四下午返抵台北。

此次台灣各大學參加會議人數眾多,除教授外,亦有多位研究生,足見後生

可畏。敝人認為,台灣研究生較缺國際觀,政府應多鼓勵國內研究生參與國際研

討會,培育下一代研發人才,此次多位研究生之參與,正是良好之典範。

二、會議經過

報到

六月十日會場報到後,領到資料袋及論文集光碟片。大會每人發放上有標誌

之夏威夷衫一件作為紀念品,惜尺碼略大。會議分十四個口頭發表場地,同時進

行。進行四天,一共有 126 個口頭發表場次( Session );另外前三天中午於午餐

時間有壁報論文發表(稱為互動論壇,Interactive Forum,以論文主題而非論文評

審成績分配),共 49 場次:口頭與壁報共計發表論文 1700 餘篇,參加人數預估

在兩三千人之譜。與前幾年參加相同會議之經驗相較,場次減少,但論文篇數差

不多,可能是場地分配的問題。

參加會議與發表論文

此次敝人與學生共發表四篇論文,主題分別為場型可調式天線設計、時域混

合計算格網誤差分析、多層印刷電路板 RFID 天線設計、波束方向可切換之智慧

型天線設計等,聽眾反應均甚良好。尤其多層印刷電路板 RFID 天線設計論文發

表後,聽衆討論特別熱烈;主因是之前的 RFID 天線文獻均未深入考慮應用於印

(12)

刷電路板的情形,而我們的研究顯示一般 RFID 天線用於印刷電路板會發生短

路,無法運作;我們在電路板上的狹縫天線設計,則可解決此一問題,效能甚佳。

在所聽的論文發表方面,由於個人對時域數值方法的理論特別有興趣,因此

印象較深刻的論文主題大多屬之。以下簡單介紹幾篇:

1. 韓國Piljun Park

等人的3D次網格FDTD技術,可以使粗細網格大小間的比例

為任意奇數,並完成比例為17的天線分析,相當特別,但缺乏誤差及穩定性

的理論分析。

2. 法國J. Gazave等人也提出3D次網格FDTD技術,粗細網格大小間的比例為任

意整數,並完成比例為12的自由空間傳播計算,同樣也缺少誤差及穩定性的

理論分析。

3. 美國OSU的Ryan A, Chilton與Robert Lee研發出具有穩定性與守恆性的3D

FDTD次網格架構,應用較抽象的數學觀念討論,決定各次網格內插權重。

粗細網格大小間的比例也可以為任意整數,並以導波管的不連續問題驗證其

理論,但未完成誤差之理論分析,僅以實例計算說明其粗細網格交界之反射

甚低。兩位作者並且稱合宜的次網格FDTD技術為許多研究者尋找的「聖

杯」,其困難與重要性可見一斑。

4. 英國Costa等人利用Huygence次網格FDTD技術,加上Debye模型,可處理UWB

超寬頻訊號通過頻率相關媒質的問題。

5. 法國Pascaud等人針對MIMO天線,發展雙網格FDTD技術,以較細網格計算

天線單元之近場,再以之為等效入射場,用正常大小網格計算其輻射場。

6. 巴西de Sousa等人運用TLM技術,將電磁問題區域分成小塊,以電路元件表

示,並與SPICE結合,可分析不少問題。

7. 新竹交大陳富強教授指導學生發展出應用於ADI-FDTD的PML結構,並有理

論分析,為可用於高Courant數之ADI-FDTD方法拓展應用範圍。

三、整體印象及心得

今年再度參與此一 IEEE 天線與傳播學會國際研討會,除了發現生面孔很多

之外,熟識友人又有數人獲選為 IEEE Fellow,足見台諺「戲棚下站久就是你的」

之真確。此外,平行場次之多,使聽眾常有分身乏術之嘆。壁報論文可使論文作

者與有興趣之觀眾互動增加,不失為一種良好的發表方式。另外,因過去英文口

頭報告訓練不夠,國際會議報告常不能令人滿意。去年遂以十餘小時反覆修改背

誦全部講稿,效果甚佳。今年同樣花費甚多時間背誦,自覺表現與去年差不多,

均較以往進步;且因 Session 較晚開始,遭主持人要求提前三分鐘結束,而仍能

臨時彈性調整內容,順利完成演講,皆是熟背講稿之功。此一心得或許可供國內

(13)

研究生參加國際會議時參考。

在探討主題方面,翻開議程手冊,即可發現天線與無線通訊技術場次增加許

多,反應無線通信熱潮。數值電磁計算場次仍多,大多可歸類於時域有限差分法

及有限元素法,頻域快速多極演算法偶而可見,所解之問題也已多為實際三維問

題,進步不可謂不大,然而基本方法上的創新則極為少見,一般均在計算之過程

修改,或充分利用快速之電腦設備,以便提高計算效率。天線方面之論文逐漸以

應用為導向,如 UWB 天線設計、MIMO 天線設計、RFID 天線設計等均是;另

一趨勢則是天線設計中無線通訊理論及通訊規約標準的引用漸多,研究天線的學

者最好也能涉獵相關書籍;也有新材料如 Metamaterial 及非線性元件的導入等,

形成新的研究主流。若干新主題,如奈米電磁學也開始出現,由於奈米科技漸受

重視,而其電磁現象研討為其理論基礎,相關研究未來可能會有很好的發展,值

得注意。

四、結語

感謝國科會於計劃中補助敝人參與此一會議,一方面得以發表一己及指導學

生之研究所得,一方面亦得以了解世界電磁研究之最新情況。明年此一會議將在

美國加州聖地牙哥市( San Diego )舉行,預料盛況當不遜今年,希望能再有機會

參加。

數據

Fig. 2. Specification of the diplexer.
Figure 10 shows the radiation patterns in the  xy-plane at different frequencies. The radiation  patterns below 3.0 GHz deform dramatically,

參考文獻

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