通信專業(yè)畢業(yè)設(shè)計(jì)外文翻譯--雙頻微型貼片天線的h-mrtd模擬

1、<p>　　H-MRTD simulation of dual-frequency miniature patch antenna</p><p>　　YU Wen-ge1 , 2, ZHONG Xian-xin1, LI Xiao-yi1, CHEN Shuai1</p><p>　　(1. The Key Lab for Optoelectronic Technology &

2、amp;Systems of Ministry of Education ,</p><p>　　Chongqing University , Chongqing 400044 , China ;</p><p>　　2. Basic Logistical Engineering University , Chongqing 400016 , China)</p><p

3、>　　Abstract: A novel MEMS dual-band patch antenna is designed using slot-loaded and short-circuited size-reduction techniques. By controlling the short-plane width , f10 and f 30 , two resonant frequencies, can be sig

4、nificantly reduced and the frequency radio ( f30/ f10) is tunable in the range 1.7～2.3.The Haar-Wavelet-Based multiresolution time domain (H-MRTD) is used for modeling and analyzing the antenna for the first time. In add

5、ition , the mathematical formulae are extended to an inhomogenous </p><p>　　Key words : dual-frequency antenna; H-MRTD method ; FDTD method ; MEMS; UPML absorbing boundary conditions</p><p>　　1

6、　Introduction1</p><p>　　Recently, patch antenna research has focused on reducing the size of the patch, which is important in many commercial and military applications. It has been shown that the resonant fr

7、equency of a microstrip antenna can be significantly reduced by introducing a Short-circuited plane or a partly short-circuited plane where the electric field of the resonant mode is zero[1-3 ], or a short-pin near the f

8、eed probe[4 ]. Using two stacked short-circuited patches, dual-frequency operation has been obtai</p><p>　　The finite-difference time-domain ( FDTD )method[6 ]is widely used for solving problems related to e

9、lectromagnetism. However , there still exist many restrictive factors , such as memory shortage and CPU time , etc. we first adopted the method of the Haar-Wavelet-Based Multiresolution Time Domain ( H-MRTD)[7-9]with com

10、pactly supported scaling function for a full three-dimensional (3-D) wave to Yee’ s staggered cell to analyze and simulate the dual frequency microstrip antenna. The major advantag</p><p>　　2 　Dual-frequency

11、 slot-loaded patch antenna</p><p>　　2. 1 　 Design of slot-loaded patch antenna</p><p>　　The lay out of the slot-loaded patch antenna designed in this paper is shown in Fig. 1. A single slot with

12、 dimensions L ×W is cut in a rectangular patch with dimensions a ×b with a short-circuited plane of width placed at its other side. The parameters of the antenna are a = 38mm , b = 25mm , L = 36mm ,W =1mm , d =

13、 2mm , h = 3mm , r = 1mm , respectively. Owing to being compatible with standard IC technology , and prone to integration with other components ,silicon wafer (εr = 11.7) was selected </p><p>　　Fig.1 Geometr

14、y of dual-band slot-loaded microstrip antenna</p><p>　　2. 2 　Measured results</p><p>　　The parameters of the slot antenna are selected as above mentioned. The measurements carried out on an Agil

15、ent 8720C vector network analyzer. It is then found that, by controlling the shorted-plane width, both the TM10 and TM30 modes are strongly perturbed. Fig. 2 shows typical results of the measured return loss for the case

16、s with s/ a = 1, 0.25, and 0. 1. Regarding the results shown in Fig. 2, it can be seen that the perturbed TM10 and TM30 modes are excited with good impedance matching. Howev</p><p>　　Fig.2 Measured return lo

17、ss for different shorted-plane widths</p><p>　　3 　 3-D H-MRTD algorithm</p><p>　　3. 1 　Numerical formulations of the 3-D H-MRTD method</p><p>　　Maxwell’ s curl equations in an isotr

18、opic medium:</p><p>　　, (1)</p><p>　　where ε is permittivity, μ is permeability, σ is electric conductivity. Each field component is expanded into scaling functions: <

19、/p><p>　　, (2)</p><p>　　And wavelets:</p><p>　　, (3)</p><p>　　Where, and.</p><p>　　Expansion and testing i

20、s performed for each spatial coordinate s={x, y, z} with corresponding discretization indices u={k, l, m},as well as for time with rectangular pulse hn(t). In compact notations, the x-directed electric field component in

21、 the staggered Yee’s grid of size Δx, Δy, Δz is represented as</p><p>　　, (4)</p><p>　　where x = kΔx, y = lΔy, z = mΔz, t = nΔt .</p><p>　　The summation over ξηζ includes

22、eight terms stemming from all the permutations of scaling functions and wavelets: .The representation of the other field components is easily derived through permutation of the indices and follows the same rule as for st

23、andard FDTD scheme. Inserting the above expressions into the difference equation and performing a Galerkin test procedure[12] leads to the following expressions for the electric field within each cell {k,l,m}:</p>

24、<p>　　, (5)</p><p>　　where{0 ,1 ,2 ,3}denotes , respectively , { u , u + 1/ 2 ,u - 1/ 2 , u + 1}for each u = { k , l , m , n}. In formula (5) , there are three different Εx values within one time

25、step , this brings about inconvenience for program design. In order to avoid the shortcoming, we can adopt approximation as follows:</p><p>　　, (6)</p><

26、p>　　Similar expressions are obtained for the other field components.</p><p>　　3. 2 　Absorbing boundary condition</p><p>　　The field computation domain must be limited in size because the comp

27、uter can not store an unlimited amount of data. The computation domain must be large enough to enclose the structure of interest. In this paper, we adopted uniaxial perfectly matched layer (UPML) absorbing boundary condi

28、tions. Consider one dimension wave equation propagated along + z direction:</p><p>　　， (7)</p><p>　　where σ ′=σ/ε, v is the phase velocity in the concerned volume. Bec

29、ause the conductivity σ is projected in computation domain, it will result in numeric dispersion if we use directly discrete approximation for formula (7) , Let ，then, its finite difference form is ,

30、 (9)</p><p>　　The difference form of formula (7) is where are the MRTD coefficients.</p><p>　　The UPML material parameters are chosen to be for the inner computation region. The maxi

31、mum value of σ at the end of the UPML region is chosen to be, where ⊿ is the cell dimension perpendicular to the UMPL interface to the regular region. The UMPL region is backed by a perfect electric conductor wall implem

32、ented using the mirror principle.</p><p>　　4 　Computed results</p><p>　　In microwave circuit analysis, Gauss impulse is generally selected as an excitation for smoothness in time domain and easy

33、 spectrum width setting. The width of Gauss pulse is T = 18ps, assume that the time delay t0 = 3 T = 54ps, The response value of the frequency domain can be calculated by Fourier transforming the time domain value.</p

34、><p>　　The circle wave losses of the antenna computed are shown in Fig. 3 and Fig. 4 for s/ a = 1 and s/ a =0.25, respectively. The computed curves based computation domain 100 ×120 ×60 and Δx=Δy=0.15

35、mm, Δz=0.015mm. From Fig. 3 and Fig. 4 , we can find the computed results by using FDTD method , and H-MRTD method are in good agreement with measured results. The drifts between them ensured value and the computed value

36、 by using FDTD and H-MRTD are about 2%and 2. 5% in fine-grid, respectively. The lengt</p><p>　　Fig.3 Computed return loss for s/a=1</p><p>　　Fig.4 Computed return loss for s/a=0.25</p>

37、<p>　　These simulations were performed by XFDTD, the information about dual-frequency antenna simulations is shown in Tab. 1. We can find when using different space cell sizes, there will be different simulation res

38、ults. For FDTD method, Although time-step selected satisfied the Courant-Friedrich-Levy (CFL) condition[13 ], the accuracy of the simulation results appears diverse when we adopt fine-grid and coarse-grid , respectively,

39、 it makes clear the numeric errors arrive at 12% in coarse-grid case fo</p><p>　　Tab.1 Information on the dual-frequency antenna</p><p>　　5 　Conclusion</p><p>　　A dual-frequency min

40、iature patch antenna is presented in this paper, it performs excellently and especially in miniaturization. H-MRTD method was used to model the structure of the antenna. The algorithm of the method is real-time time

41、 and space adaptive grids through the efficient thresholding of the wavelet coefficients. Thus, space discretization with only a few cells per wavelength gives accurate results, leading to a reduction of both memory requ

42、irement and computation time. The fact t</p><p>　　discussed in our future papers.</p><p><b>　　參考文獻(xiàn):</b></p><p>　　[1] Yu W G, Zhong X X, Wu ZH ZH ,et.al. Novel stack-sho

43、rted microstrip bluetooth antenna[J]. Optics and Precision Engineering, 2003 , 11 (4) :3942399.</p><p>　　[2] LIU ZH F , KOOI P SH , et . al. A method for designing broad-band microstrip antenna in multilaye

44、red planar structures [J] .IEEE Trans Antennas and Propagat,1999 , 47 (9) :141621420.</p><p>　　[3] YU W G, ZHONG X X, WU ZH ZH , et al . Numerical analysis of micromachine patch antenna using FDTD technique

45、[C]. The International Computer Science Conference 2003. Active Media Technology (ICAMT2003). Chongqing, China. 2003, 29231 , 3462351.</p><p>　　[4] WU ZH ZH , ZHONG X X, LI X Y, et al .Multiplayer2shorted m

46、icromachined Bluetooth antenna[J]. Optics and Precision Engineering. 2001 , 9 (6) :5722576.</p><p>　　[5] ZAID L , K OSSIAVAS G, et al . Dual2 frequency and broad2band antennas with stacked quarter wavelengt

47、h elements[J]. IEEE Trans, 1999, AP 247 (4) : 6542660.</p><p>　　[6] YEE K S. Numerical solution of initial boundary value problems involving Maxwell’ s equation in isotropic media[J] . IEEE Trans Antennas P

48、ropagation, 1966, 14 (5) : 3022307.</p><p>　　[7] KRUMPHOLZM, K ATEHI L P B. MRTD: new time2domains schemes based on multiresolution analysis[J]. IEEE Trans Microwave Theory Tech, 1996,44 (4) :5552571.</p

49、><p>　　[8] 　TENTZERIS E , ROBERTSON R , CANGE LLARIS A , et al. Space-and time-adaptive gridding using MRTD[C]. Proc. MTTS, 1997. 3372340.</p><p>　　[9] TENTZERIS E , HARVEYJ ,K ATEHI L P B. Time a

50、daptive time-domain techniques for the design of microwave circuits [J ] .IEEE Microwave and Guided Wave Letter s , 1999 , 9 (3) : 96298.</p><p>　　[10] GEDNEY S D. An anisotropic perfectly matched layer abs

51、orbing media for the truncation of FDTD lattices[J] . IEEE Trans Antennas and Propagation, 1996 , 44 (12) :163021639.</p><p>　　[11] 　MAC S , BIFFI G G, PIAZZES L P , et al . Dual2band slot2loaded patch anten

52、na[C] . IEE Proc Microw Antennas Propag , 1995 ,142 (3) :2252232.</p><p>　　[12] 　CHEONG YW, LEE YM, RA K H ,et al . Wavelet-Galerkin scheme of time-dependent inhomogeneous electromagnetic problems[J] . IEEE

53、Microwave Guided Wave Lett , 1999 , 9 (8) :2972299.</p><p>　　[13] 　TAF LOVE A , BRODWIN M E , Numerical solution of steady state electromagnetic scattering problem using the time dependent Maxwell’ s equatio

54、ns [J] . IEEE Trans MTT , 1975 , 23 (8) :6232630.</p><p>　　作者簡(jiǎn)介:余文革(1967- ),男,四川渠縣人,重慶大學(xué)光電工程學(xué)院博士研究生 ,主要研究方向?yàn)?MEMS天線及電磁場(chǎng)數(shù)值分析;</p><p>　　鐘先信(1935- ),男,重慶人,重慶大學(xué)光電工程學(xué)院教授,博士生導(dǎo)師,主要研究方向?yàn)榫軝C(jī)械及MEMS。</p

55、><p>　　雙頻微型貼片天線的H-MRTD模擬</p><p>　　余文革1，2，鐘先信1，李小毅1，陳帥1</p><p>　　（1.重慶大學(xué) 光電技術(shù)及系統(tǒng)教育部重點(diǎn)實(shí)驗(yàn)室，重慶400044；2.后勤工程學(xué)院基礎(chǔ)部，重慶400016）</p><p>　　摘要：利用槽隙加截及短接技術(shù)設(shè)計(jì)了雙頻小型微帶天線。通過調(diào)節(jié)短接面寬度，兩諧振頻率f1

56、0及f30可明顯降低，天線尺寸顯著減小，而且頻比（f30/f10）的可調(diào)范圍為1.7～2.3。首次將三維H-MRTD（Haar-Wavelet-Based Multiresolution Time Domain）全波分析方法應(yīng)用于該天線的建模和分析，并將H-MRTD數(shù)值計(jì)算公式推廣到了非均勻有耗媒質(zhì)中。數(shù)值模擬結(jié)果同傳統(tǒng)FDTD（Finite Difference Time Domain）方法及實(shí)驗(yàn)結(jié)果進(jìn)行了比較。結(jié)果表明，每個(gè)波長(zhǎng)只需

57、取較少的空間離散網(wǎng)格，三維H-MRTD時(shí)域全波分析方法便能較精確地模擬微機(jī)械微帶天線，并能有效地減少CPU計(jì)算時(shí)間及節(jié)省計(jì)算機(jī)內(nèi)存。</p><p>　　關(guān)鍵詞：雙頻天線；H-MRTD方法；FDTD方法；微機(jī)械；UPML吸收邊界條件</p><p>　　中圖分類號(hào)：TN823 文獻(xiàn)標(biāo)識(shí)碼：A</p><p><b>　　引言1</b>

58、</p><p>　　最近，貼片天線的研究已經(jīng)聚焦于減小貼片的尺寸，這對(duì)于商業(yè)和軍事應(yīng)用非常重要。據(jù)顯示，在共振模電場(chǎng)為0的地方引進(jìn)一個(gè)短路面或一個(gè)部分短路面[1-3]，或者在反饋點(diǎn)附近引進(jìn)一個(gè)短針[4]，這樣就可以顯著減小微帶天線的諧振頻率。使用雙棧短路貼片可以獲得雙頻解[5]。然而，使用堆棧存儲(chǔ)器幾何學(xué)會(huì)導(dǎo)致貼片厚度和復(fù)雜度的增加。在本文中，我們證明，通過短路開槽貼片潛在零電位面，這種開槽貼片是在一種震蕩模式

59、下（TM10）被激勵(lì)，在兩種操作模式下，通過減小短路面的寬度可以使諧振頻率f10和f30降低近一半，甚至降至更小。這表明，與通常的槽載貼片相比，通過預(yù)先設(shè)計(jì)可以顯著減小天線的尺寸。</p><p>　　FDTD（The finite-difference time-domain）被廣泛的應(yīng)用于解決與電磁場(chǎng)有關(guān)的問題中。然而，這種方法依然存在很多局限性，例如計(jì)算機(jī)內(nèi)存缺乏和CPU時(shí)間，比如，我們首先通過了H-MTR

60、TD方法與緊支撐縮放的全三維Yee交錯(cuò)單元波來分析和仿真雙頻微帶天線。MRTD算法的主要優(yōu)點(diǎn)是它們通過有效的小波參數(shù)閥值來建立實(shí)時(shí)和自適應(yīng)網(wǎng)格。使用這種技術(shù)，每個(gè)波長(zhǎng)只需取較少的空間離散網(wǎng)格，就會(huì)產(chǎn)生精確的結(jié)果，并能有效地減少CPU計(jì)算時(shí)間及節(jié)省計(jì)算機(jī)內(nèi)存。與實(shí)際模型相聯(lián)系，一個(gè)可以吸收邊界條件[10]的UMPL（uniaxial perfectly matched layer）[10]就產(chǎn)生了。由麥克斯韋系統(tǒng)定理得到的離散微分方程三維

61、公式首先應(yīng)用于非均勻介質(zhì)中，它被應(yīng)用于雙頻微型貼片天線的分析中。</p><p><b>　　雙頻槽載貼片天線</b></p><p><b>　　槽載貼片天線的設(shè)計(jì)</b></p><p>　　在本篇論文中，槽載貼片天線的設(shè)計(jì)如圖 1所示。一個(gè)尺寸為L(zhǎng)×W的單槽被分割成一個(gè)矩形的貼片，有一個(gè)尺寸為a×

62、b的短接面在它的另一面。這個(gè)天線的參數(shù)各自分別為是a=38mm，b=25mm，L=36mm，W=1mm，d=2mm，h=3mm，r=1mm。為了與標(biāo)準(zhǔn)的集成電路技術(shù)相一致并且易于和其他元件的集成，硅元(εr = 11.7)被作為微帶基底。在接地板和硅元之間有一層泡沫型材料(ε r = 1.07)。這層材料可以抑制由基底產(chǎn)生的表面波，因此，天線的有效性和帶寬就增加了并且改善了輻射形式。</p><p>　　圖1 雙

63、頻槽載微帶天線的幾何圖</p><p><b>　　測(cè)量結(jié)果</b></p><p>　　槽載天線參數(shù)的選擇如上面所示。測(cè)量是在Agilent 8720C向量網(wǎng)絡(luò)分析器上進(jìn)行的?？梢园l(fā)現(xiàn)，通過控制短接面的寬度，TM10和TM30模式都被強(qiáng)烈的干擾。圖2顯示了在s/a分別為1，0.25和0.1情況下測(cè)量到的典型的回波損失結(jié)果。就圖2所顯示的結(jié)果而言，可以看出干擾的TM1

64、0和TM30模式都被激勵(lì)了，并且具有良好的阻抗匹配。然而，當(dāng)s/a＜0.1時(shí),找不到饋點(diǎn)來激勵(lì)兩種頻率,并且具有良好的阻抗匹配。這表明，對(duì)于目前雙頻天線的設(shè)計(jì)有一些限制。可以看出，對(duì)目前設(shè)計(jì)的兩個(gè)頻率的頻率比（f30/f10）的變化范圍為1.7～2.3。另一方面，在s/a=0.1的情況下，如圖2所示，在1.562GHz下頻率f10是通常半波貼片（相同的貼片大?。╊l率（5.038GHz）的0.31倍。換句話說，本文中所設(shè)計(jì)的天線的大小比通

65、常半波貼片天線的尺寸更小。</p><p>　　圖2 不同短接面寬度測(cè)量的回波損失</p><p>　　三維H-MRTD算法</p><p>　　三維H-MRTD方法的數(shù)值依據(jù)</p><p>　　在同性介質(zhì)中的麥克斯韋方程組：</p><p><b>　　（1）</b></p>&

66、lt;p>　　ε為介電常數(shù)，μ為磁導(dǎo)率，σ為電導(dǎo)率。每個(gè)場(chǎng)量被擴(kuò)展到尺度函數(shù)：</p><p><b>　?。?）</b></p><p>　　并且小波為： （3）</p><p>　　其中，。擴(kuò)展和測(cè)試是在每一個(gè)空間坐標(biāo)s={x,y,z}（相應(yīng)的離散指數(shù)為u={k,l,

67、m}）和矩形時(shí)間脈沖hn(t)上進(jìn)行的。在緊湊標(biāo)記中，在大小為Δx ,Δy ,Δz的交叉Yee網(wǎng)格中的x方向電場(chǎng)分量為：</p><p><b>　　（4）</b></p><p>　　其中x = kΔx , y = lΔy , z = mΔz , t = nΔt。</p><p>　　ξηζ的計(jì)算總和包括8個(gè)方面，涵蓋了縮放比例函數(shù)和小波的所

68、有排列組合：。對(duì)于其他場(chǎng)分量的表示可以容易地從參數(shù)的排列組合得到，并遵循與標(biāo)準(zhǔn)FDTD方案相同的規(guī)則。將上式代入到差分方程，完成Galerkin測(cè)試過程[12]，可得下面關(guān)于電場(chǎng)在每一個(gè)元{k,l,m}的表達(dá)式：</p><p><b>　?。?）</b></p><p>　　其中{0 ,1 ,2 ,3}分別代表符號(hào){ u , u + 1/ 2 ,u - 1/ 2 ,

69、 u + 1}，其中，u = { k , l , m , n}。在公式（5）中，在一個(gè)階躍時(shí)間內(nèi)有三個(gè)不同的Ex，這就帶來了編程設(shè)計(jì)的不便。為了避免這些缺點(diǎn)，用下述近似值：</p><p><b>　　（6）</b></p><p>　　其它場(chǎng)分量可以得到類似的表達(dá)式。</p><p><b>　　吸收邊界條件</b>&l

70、t;/p><p>　　場(chǎng)計(jì)算域必須是有限大小，因?yàn)橛?jì)算機(jī)不能存儲(chǔ)無限的數(shù)據(jù)量。計(jì)算域必須足夠大以便包含重要結(jié)構(gòu)。在本文中，我們應(yīng)用了UPML吸收邊界條件。考慮沿+z方向傳播的一維波方程：</p><p><b>　　(7)</b></p><p>　　其中σ ′=σ/ε, v是相關(guān)容量的相位速度。電導(dǎo)率σ是投影在計(jì)算域中的，因此如果我們直接離散化逼

71、近公式（7），它將會(huì)導(dǎo)致數(shù)據(jù)誤差，令，那么，它的有限差形式是：</p><p><b>　　(9)</b></p><p>　　公式（7）的差分形式是，其中是MRTD因子。</p><p>　　對(duì)于內(nèi)部計(jì)算域，UPML材料參數(shù)選擇為。UPML域終端的σ最大值選擇為，其中⊿表示正交于UPML界面固定區(qū)域的區(qū)域大小。UPML區(qū)域被一個(gè)超導(dǎo)體墻支撐著

72、，這個(gè)導(dǎo)體墻使用鏡像原理工作。</p><p><b>　　計(jì)算結(jié)果</b></p><p>　　在微波電路分析中，高斯脈沖通常被選定為激勵(lì)源，因?yàn)樗跁r(shí)間域中是平滑的，并容易設(shè)定頻譜帶寬。高斯脈沖的寬度為T=18ps，假設(shè)時(shí)延為t0=54ps，頻域響應(yīng)值可以通過傅里葉變換由時(shí)間域內(nèi)的值計(jì)算出來。</p><p>　　天線的回波損失計(jì)算結(jié)果如圖

73、3和圖4所示，其中s/a分別為1和0.5。結(jié)果曲線基于計(jì)算域?yàn)?00 ×120 ×60并且Δx =Δy = 0. 15mm , Δz = 0. 015 mm。從圖3和圖4，我們可以發(fā)現(xiàn)，通過FDTD方法的計(jì)算結(jié)果和通過H-MRTD方法的結(jié)果與測(cè)量結(jié)果很一致。在精密網(wǎng)格中，通過應(yīng)用FDTD和H-MRTD方法，確切值和計(jì)算值之間的差別大約在2%和2.5%。新的貼片天線的長(zhǎng)度比1/7波長(zhǎng)更短，并且效率可以達(dá)到70%。頻域中

74、的特有參數(shù)，如有效的介電常數(shù)，特征阻抗可以通過傅里葉變換計(jì)算出來。</p><p>　　圖 3 s/a=1計(jì)算的回波損失</p><p>　　圖4 s/a=1計(jì)算的回波損失</p><p>　　這些仿真是通過XFDTD進(jìn)行的,關(guān)于雙頻天線的仿真信息如表1所示。我們可以發(fā)現(xiàn)當(dāng)使用不同空間域大小時(shí)，將會(huì)有不同的仿真結(jié)果。對(duì)于FDTD方法，盡管階躍時(shí)間選擇滿足CFL（

75、Courant-Friedrich-Levy）條件[13]，但是當(dāng)我們分別使用精密網(wǎng)格和稀疏網(wǎng)格時(shí)，仿真結(jié)果的精確性出現(xiàn)了不同，很顯然，在稀疏網(wǎng)格的情況下使用FDTD方法，數(shù)值誤差達(dá)到12%。這表明使用FDTD方法，不僅階躍時(shí)間而且步進(jìn)距離的大小都會(huì)極大的影響數(shù)值誤差。如果步進(jìn)距離變得越來越大，那么數(shù)值精確性將難以確保。對(duì)于H-MRTD方法，由于MRTD算法通過小波系數(shù)閥值實(shí)現(xiàn)實(shí)時(shí)和空間匹配網(wǎng)格承載能力，因此每個(gè)波長(zhǎng)只需取較少的空間離散

76、網(wǎng)格，步進(jìn)距離的影響比FDTD方法更小，但是在稀疏網(wǎng)格情況下，與FDTD方法相比，有更大的數(shù)值誤差。盡管FDTD方法的階躍時(shí)間幾乎是H-MRTD方法的3倍，但是CPU時(shí)間卻相當(dāng)接近。這被證明是一個(gè)嚴(yán)重的缺點(diǎn)，這個(gè)缺點(diǎn)是小波的增加并沒有有效地改善在FDTD方案下數(shù)值的精確性。怎樣研究來改善H-MRTD方法的數(shù)值精確性，這一問題已經(jīng)成為研究的熱點(diǎn)。</p><p>　　表 1雙頻天線的信息</p>&l

77、t;p><b>　　結(jié)束語</b></p><p>　　本文展示了一種雙頻微型貼片天線，它性能優(yōu)越，特別是在小型化方面更是如此。H-MRTD方法被用于天線結(jié)構(gòu)建模。這種模型算法是通過有效小波參數(shù)閥值實(shí)現(xiàn)實(shí)時(shí)性和空間自適應(yīng)網(wǎng)格的。因此，每個(gè)波長(zhǎng)只需取較少的空間離散網(wǎng)格就可以產(chǎn)生精確結(jié)果，導(dǎo)致對(duì)內(nèi)存和計(jì)算的需求減少。H-MRTD方法的計(jì)算結(jié)果和FDTD方法的測(cè)量結(jié)果相一致，這一事實(shí)表明三維

78、H-MRTD方法比傳統(tǒng)的FDTD方法更有效。但是，該方法依然存在一些問題，例如在兩種工作頻率下數(shù)值仿真的精確性和遠(yuǎn)場(chǎng)輻射模型等，都尚待解決，我們將會(huì)在以后的論文中討論這些問題。</p><p><b>　　參考文獻(xiàn):</b></p><p>　　[1] Yu W G, Zhong X X, Wu ZH ZH ,et.al. Novel stack-shorted m

79、icrostrip bluetooth antenna[J]. Optics and Precision Engineering, 2003 , 11 (4) :3942399.</p><p>　　[2] LIU ZH F , KOOI P SH , et . al. A method for designing broad-band microstrip antenna in multilayered pl

80、anar structures [J] .IEEE Trans Antennas and Propagat,1999 , 47 (9) :141621420.</p><p>　　[3] YU W G, ZHONG X X, WU ZH ZH , et al . Numerical analysis of micromachine patch antenna using FDTD technique[C]. T

81、he International Computer Science Conference 2003. Active Media Technology (ICAMT2003). Chongqing, China. 2003, 29231 , 3462351.</p><p>　　[4] WU ZH ZH , ZHONG X X, LI X Y, et al .Multiplayer2shorted microma

82、chined Bluetooth antenna[J]. Optics and Precision Engineering. 2001 , 9 (6) :5722576.</p><p>　　[5] ZAID L , K OSSIAVAS G, et al . Dual2 frequency and broad2band antennas with stacked quarter wavelength elem

83、ents[J]. IEEE Trans, 1999, AP 247 (4) : 6542660.</p><p>　　[6] YEE K S. Numerical solution of initial boundary value problems involving Maxwell’ s equation in isotropic media[J] . IEEE Trans Antennas Propaga

84、tion, 1966, 14 (5) : 3022307.</p><p>　　[7] KRUMPHOLZM, K ATEHI L P B. MRTD: new time2domains schemes based on multiresolution analysis[J]. IEEE Trans Microwave Theory Tech, 1996,44 (4) :5552571.</p>

85、<p>　　[8] 　TENTZERIS E , ROBERTSON R , CANGE LLARIS A , et al. Space-and time-adaptive gridding using MRTD[C]. Proc. MTTS, 1997. 3372340.</p><p>　　[9] TENTZERIS E , HARVEYJ ,K ATEHI L P B. Time adaptiv

86、e time-domain techniques for the design of microwave circuits [J ] .IEEE Microwave and Guided Wave Letter s , 1999 , 9 (3) : 96298.</p><p>　　[10] GEDNEY S D. An anisotropic perfectly matched layer absorbing

87、 media for the truncation of FDTD lattices[J] . IEEE Trans Antennas and Propagation, 1996 , 44 (12) :163021639.</p><p>　　[11] 　MAC S , BIFFI G G, PIAZZES L P , et al . Dual2band slot2loaded patch antenna[C]

88、. IEE Proc Microw Antennas Propag , 1995 ,142 (3) :2252232.</p><p>　　[12] 　CHEONG YW, LEE YM, RA K H ,et al . Wavelet-Galerkin scheme of time-dependent inhomogeneous electromagnetic problems[J] . IEEE Microw

89、ave Guided Wave Lett , 1999 , 9 (8) :2972299.</p><p>　　[13] 　TAF LOVE A , BRODWIN M E , Numerical solution of steady state electromagnetic scattering problem using the time dependent Maxwell’ s equations [J]

90、 . IEEE Trans MTT , 1975 , 23 (8) :6232630.</p><p>　　作者簡(jiǎn)介:余文革(1967- ),男,四川渠縣人,重慶大學(xué)光電工程學(xué)院博士研究生 ,主要研究方向?yàn)?MEMS天線及電磁場(chǎng)數(shù)值分析;</p><p>　　鐘先信(1935- ),男,重慶人,重慶大學(xué)光電工程學(xué)院教授,博士生導(dǎo)師,主要研究方向?yàn)榫軝C(jī)械及MEMS。</p>