1、H-MRTD simulation of dual-frequency miniature patch antenna YU Wen-ge1 , 2, ZHONG Xian-xin1, LI Xiao-yi1, CHEN Shuai1 (1. The Key Lab for Optoelectronic Technology &Systems of Ministry of Education , ChongqingUniversity , Chongqing 400044 , China ； 2. Basic Logistical EngineeringUniversity , Chongqi
2、ng 400016 , China) Abstract: A novel MEMS dual-band patch antenna is designed using slot-loaded and short-circuited size-reductiontechniques. By controlling the short-plane width , f10 and f 30 , two resonant frequencies,can be significantly reduced and the frequency radio ( f30/ f10) is tunable in
3、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 addition , themathematical formulae are extended to an inhomogenous media. Numerical simulation results are compared to thoseachieved using the conventi
4、onal 3-D finite-difference time-domain (FDTD) method and measured. It has beendemonstrated that , with this technique , space discretization with only a few cells per wavelength gives accurate results , leading to a reduction of both memory requirements and computation time. Key words : dual-frequen
5、cy antenna； H-MRTD method ； FDTD method ； MEMS； UPML absorbing boundary conditions 1 Introduction1 Recently, patch antenna research has focused on reducing the size of the patch, which is important inmany commercial and military applications. It has beenshown that the resonant frequency of a microst
6、rip antenna can be significantly reduced by introducing aShort-circuited plane or a partly short-circuited planewhere the electric field of the resonant mode is zero1-3 , or a short-pin near the feed probe4 . Usingtwo stacked short-circuited patches, dual-frequencyoperation has been obtained5 . Howe
7、ver, the use of astacked geometry leads to increases in the thicknessand complexity of the patch. In this paper, we demonstrate that by short-circuiting the zero potential plane ofa slotted patch excited with a dominant mode (TM10),the resonant frequencies , f 10 and f 30 , of the two operating mode
8、s can be approximately halved and can evenbe significantly reduced by decreasing the shorted-plane width. This indicates that a large reduction inantenna size can be obtained by using the proposed design , as compared to that of a regular slot-loadedpatch. The finite-difference time-domain ( FDTD )m
9、ethod6 is widely used for solving problems related toelectromagnetism. However , there still exist many restrictive factors , such as memory shortage and CPUtime , etc. we first adopted the method of the Haar-Wavelet-Based Multiresolution Time Domain ( H-MRTD)7-9with compactly supported scaling func
10、tionfor a full three-dimensional (3-D) wave to Yee s staggered cell to analyze and simulate the dual frequencymicrostrip antenna. The major advantage of the MRTDalgorithms is their capability to develop real-time time and space adaptive grids through the efficient thresholding of the wavelet coeffic
11、ients. Using this technique, space discretization with only a few cells perwavelength gives accurate results , leading to a reduction of both memory requirement and computation time.Associated with practical model , a uniaxial perfectlymatched layer (UPML ) absorbing boundary conditions10 was develo
12、ped , a three-dimensional formulation of the discrete difference equations arising from theMaxwell s system is first extended to an inhomogenousmedium , it is applied to the analysis of dual-frequencyminiature patch antenna. 2 Dual-frequency slot-loaded patch antenna 2. 1 Design of slot-loaded patch
13、 antenna The lay out of the slot-loaded patch antenna designed in this paper is shown in Fig. 1. A single slotwith dimensions L W is cut in a rectangular patchwith dimensions a b with a short-circuited plane ofwidth placed at its other side. The parameters of theantenna are a = 38mm , b = 25mm , L =
14、 36mm ,W =1mm , d = 2mm , h = 3mm , r = 1mm , respectively.Owing to being compatible with standard IC technology , and prone to integration with other components ,silicon wafer (r = 11.7) was selected as a layer of microstrip substrate. Between the ground plate and thewafer there is a layer of foam
15、( r = 1.07) , whichcould suppress surface wave induced in the wafer substrate , as a result , the efficiency and the bandwidth ofthe antenna were increased , and the radiation patternimproved. Fig.1 Geometry of dual-band slot-loaded microstrip antenna 2. 2 Measured results The parameters of the slot
16、 antenna are selected asabove mentioned. The measurements carried out on anAgilent 8720C vector network analyzer. It is then foundthat, by controlling the shorted-plane width, both theTM10 and TM30 modes are strongly perturbed. Fig. 2shows typical results of the measured return loss for thecases wit
17、h s/ a = 1, 0.25, and 0. 1. Regarding theresults shown in Fig. 2, it can be seen that the perturbed TM10 and TM30 modes are excited with goodimpedance matching. However, when s/ a 0. 1,there no feed point can be found for exciting the twofrequencies with good impedance matching. This indicates that
18、there are limitations to the present dual-banddesign. It can be seen that the obtained frequency ratio( f 30/ f 10 ) of the two frequencies for present design varies in the range 1. 7 2. 3. On the other hand, for the case s/ a = 0. 1, shown in Fig. 2, the frequency f10 occurring at 1.562GHz is 0.31
19、times that (5.038GHz) for a regular half-wavelength patch with thesame patch size. In other words, the size of the designed antenna in this paper is much smaller than regular half-wavelength patch antenna. Fig.2 Measured return loss for different shorted-plane widths 3 3-D H-MRTD algorithm 3. 1 Nume
20、rical formulations of the 3-D H-MRTDmethod Maxwell s curl equations in an isotropic medium: HtE Et , (1) whereis permittivity,is permeability,is electricconductivity. Each field component is expanded intoscaling functions: u ( ) ( / )s s s u , (2) And wavelets: ( / )u s s u , (3) Where, ( ) 1, ( 0 ,
21、 1 )( ) 0 ,sss o th e r e ls e and ( ) ( 2 ) ( 2 1 )s s s . Expansion and testing is 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 t
22、he staggered Yees gridof size x,y,z is represented as 1 / 2 , , 1 / 2( , , , ) ( ) ( ) ( ) ( )xx k l m k l m nnk l m nE x y z t E x y z h t , (4) where x = kx, y = ly, z = mz, t = nt . The summation over includes eight termsstemming from all thepermutations of scaling functionsand wavelets: , , , , , , , .The representation of the other field components is easily derived through permutation of the indices and follows the same
