The 14'h IEEE 2003 International Symposium on Persona1,lndoor and Mobile Radio Communication Proceedings
Design and simulation of novel microstrip bluetooth antenna
Y u Weiige College of Optoelectronic Engineering Chongqing University Chongqing, China Wengey789@ 1 63 .coin Zhoiig Xiaiixin, Wu Zhengzliong, Li Xiaoyi College of Optoelectronic Engineering Chongqing University Chongqing, China
4bstractwith the rapid development of bluetooth wireless communication, it's highlighted now to applying MicroElectroMechanical Systems(MEMS) technique in the Radio Frequency(RF) field to manufacture broadband bluetooth antennas. The lOdB bandwidth and efficiency of the micromachined Bluetooth antenna designed in this paper are more than 1 1 % and 68% respectively, the length is less than 1/10 wavelength. The alternating direction implicit finitedifference timedomain (ADIFDTD) method for a full threedimensional (3D) wave presented is used for modeling and analyzing the micromachine antenna for the first time. Numerical simulation results are compared to those using the conventional 3D finitedifference timedomain (FDTD) method. I t is more efficient than the conventional 3D FDTD method in terms of the central processing unit time if the size of the local minimum cell in the computational domain is much smaller than the other cells and the wavelength.
fm/e.v Tmnbluetooth; ADIFDTD method; FDTD method; microstrip antenna; MEMS
cell size in a computation domain. In this paper, we first adopted the method of the alternating direction implicit finitedifference timedomain (ADIFDTD) method [6] for a fLtll threedimensional (3D) wave to Yee's staggered cell 14' to analyze and simulate the bluetooth antenna. The numerical method is unconditionally stable and is not dissipative. Therefore, the timestep size can be arbitrarily set when this method is used. The limitation of the maximum the timestep size of the method does not depend on the CFL condition, but rather on numerical errors. Associated with practical model, a kind of approximate absorbing boundary condition was developed. Comparing with the full Si antenna and that of paper [7], The antenna in this paper has more wider bandwidth and higher efficiency. Numerical results manifested that the 3D ADIFDTD method was more efficient than the conventional FDTD method within numerical errors.. 11.
SHORTED MICROSTRIP BI_UFI'OOTtl ANTENNA
The 2.44GHz shorted microstrip bluetooth antenna is shown in Fig. 1. Because siliconbased micromaching process is compatible with standard I C technology, and prone to
I.
[NTKODUCTION
As microwave equipnients require low profile and lightweight to assure reliability, an antenna with these characteristics is essentially required and a microstrip antenna satisfies such requirement. Microstrip antennas have coldformal structure, low cost, and ease of integration with solidstate devices as well as low profile and lightweight. But the microstrip antennas have a narrow bandwidth which is about 0.63%. In the last decade, many researchers have studied the bandwidth widening technique of microstrip antennas [ 131, For a serial of salient features, the microstrip antennas are used widely in the con~nunicationand other applications. The finitedifference timedomain (FDTD) method [4] is widely used .for solving problems related to electromagnetism. As the tradition FDTD method' is based on an explicit finitedifference algorithm, the CourantFriedrichLevy (CFL) condition [ 5 ] must be satisfied when this method is used. Therefore, a maximum timestep size is limited by ninimum
I'rc7,ject Suppoi.ted by The Major State Basic Research Developnieiit I'ro@raiii"Iiiteyraled Mic~oOptical'ElectronicMechanical System" (Prqlecc No.G 1999033 105).
SMA coiinector
(a) Top view
>lli)l.l III?' 2 I I $ .
grouiid plate
(b) Crosssection
Fig. 1. iii~croiiiacliined bluetootti antenna
0780378229/03/$17.00 02003 IEEE.
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The 14thIEEE 2003 InternationalSymposium on Persona1,lndoorand Mobile Radio Communication Proceedings
integration with other components, silicon wafer ( E,. =11.7) was selected as a layer of microstrip substrate. Between the ground plate and the wafer there is a layer of air ( E , .=1),. which could suppress surface wave induced in the wafer substrate, as a result, the efficiency and the bandwidth of the antelma were increased, and the radiation pattern improved. while by setting a short wall at one end of the patch, the antenna was greatly miniaturized.
 & [ E t ( ; + I,;,
P
k + 1 1 2 )  E: (i,,j,k
+I /2)J/ArAz
At
(I*)
where
At & ' 7 l = y ' ?'2 =+?'IAt P(&)
forE,,+~/2
+'73>'73
=T. ,4&)
the Same way, we can obtain the modified equation I ' and component.
111.
A.
3D ADIFDTD ALGORITHM
P + l ( i +1/ 2,j, k) =P(i 2J, k)++1/
X
X
A t
E
Nuiiiei.icnI.forniiilrrtions ojrhe 3  0 ADIFDTD method
For E , component, the numerical formulation of the ADIFDTD method for a full 3D wave is presented as follows. The electromagnetic field components are arranged on the cells in the same way as that using the conventional FDTD method. These formulations are available for homogeneous lossles medium and for using nonunifomi cells. The calculation for one discrete time step is performed using two procedures.
.{[q" 2,j +1/ 2, k) y '+1/ 2, j 1/ 2, k)]/ Ay (i +1/ "(i
(3)
~n 1(i +1/ 2, j +1/ 2,k>= Z
+
+
f k 2(i+1/ 2 j +1/ 2 k)+, ,
P
.{ [q' 2 j +1, k) E,"'(i +1/ 2 j ,k)]/ Ay (i +1/
(4)
'
En 1'2(i +1 / 2J, k) = EI(i+ 1/2,j,k) +s E
+
A f
[qy(i +\ j +1/2k) E y 2 (i,j +1/ 2,k)]/ Ax}
In the second procedure, the E,. component on the lefthand side and the H , component on the righthand side are defined as synchronous variables in (3), thus, a modified (2*)for the E, component is derived from (3) and (4) by eliminating the components. In the suffix j, (2") indicates j maximum number of simultaneous linear equations and also means ydirectional scan of the E,. components as follows:
 q q ~ $ + ' ( i I+/ 2, j  I , / c ) +q 7 2 ~ : + ' ( i + I / 2 , j , k )
H" + 1 / 2(.1 +1 / 2j ,k + 1/2) =P(i+1/2j , k + 1/2) +A?
Y
.
P
{[E +l, j , k +I/ 2) g (i,j,k +1/2)]/Ax (i
[E,"Il2(i
(2)
q3~.:.l+' I / 2 , j + ~ , k = 5 E:+''' (i+ ) At
( i +I / 2 , ,j,/O
+1/ 2j ,k +1) E,"'12(i +1/ Z j ,k)]/&}
+ [H:+"'(i + l/2,; + 1 / 2 ,k )  H ; + ' / ' ( i + 1 / 2 , j  112, k ) ] / A j
 [ H ~ ~ + ' ~ 2 ( i + 1 / 2 , j , k + 1 / 2 )  H ~ + "1 / (2i ,+ , k  1 / 2 ) ] / A z 2 J
In this procedure, the E,,component on the lefthand side and the H ,. component on the righthand side are defined as
synchronous variables in (l), thus, a modified (1*) for the E,. coniponent is derived from (1) and (2) by eliminating the N + I 1 2 components. In the suffix k, (1*) indicates k ,.
+
t[ElJ+1/2( i + 1 ,, ;,
P At
P
I / 2 , k )  E:!+"' ( i ,j  I / 2 , k ) ] / ArAk

(i+ I, j
+ 1 / 2, k )  E','+'/2(i, j + 1 / 2, k ) ] / AuAv
(2*)
*
where
maximum number of simultaneous linear equations and also means zdirectional scan of the E,r components as follows:
 ,71 ~ ; + l i ?( i + 1 / 2 , j , k  I ) + '7*E:'+l/2(i
+I / 2,j,k)
 / 7 3 ~ : ! + l ~ ' ( i +/ 2 , , j , / c+ I ) = 5 E: ( i + I / 2 , j , k ) I At
+ [ H : ( i +I / 2 , j + 1 / 2 , k )  H : ( i + l / 2 , ;  1 / 2 , k ) ] / A y
 [ H : ! ( i + 1/ 2 , j , k
The modified equation for E{:+' and E:+' component can be obtained accordingly. By solving these simultaneous linear equations, we can get' the values of the electricfield components at the time of n+l. Thereafter, we can get the values of the magneticfield components at the time of n+1.
B. Accurac,v and Stabitity
+ 112) H :!(I+ 1/ 2 , j , k  I / 2 ) ] / A z
+[E:,'(i+ I,;,
P
A/
k  I / 2)  E ; ( i , j , k  1 / 2)]/ AxAz
To ensure the accuracy of computed results, the spatial increment must be small compared to the wavelength at the frequency of computation, usually,
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The 14mIEEE 2003 International Symposium on PersonalJndoorand Mobile Radio Communication Proceedings
max(Ax, Ay, A z ) < 2 I 1 0 (5) Since the simultaneous linear equations such as (1*) and (2*) can be written in a tridiagonal matrix form, and their coefficients on the lefthand side satisfy strict superiority on the cross. The 3D ADIFDTD algorithm is unconditionally stable.
The response value of the frequency domain can be calculated by Fouriertransforming the time domain value. As the microstrip feedline is an open stub, the nlicrostrip antenna is a 1port circuit. So the reflection coefficient SI I of the microstrip antenna is
C. Setting qf absorbing Boundary conditions The field computation domain must be limited in size because the computer can not store an unlimited amount of datum. Several absorbing boundary conditions (ABCs)[8] are developed nowadays. Mur ABCs and superabsorption boundary conditions are used in this paper respectively. For different reflection characterization manifested along whose direction the electromagnetic wave propagated, Now we will discuss which ABCs should be selected for top, side, front and rear surface individually. In the rear surface (k=G), the first order Mur ABCs are set. Electromagnetic waves are propagated along +z direction, the electronic field component ( E , = E 2 = 0 ) satisfies the oneway wave equation:
()E & I>
where V,(t) is a reflected voltage, Vi(t) is an incident voltage, and F is a Fourier transform . From the calculated reflection coefficient, voltage standing wave ratio (VSWR) can be calculated as
a la a/ .' = o
its finite difference form is
L
Y+'(,,
/./L)
= E:'(/,J,G I )
+ vAI  AZ [ E ~ + ~ ( / , J , G  I )  E :j(, IG ) , vAt + AZ
(7)
where v is the phase velocity of electromagnetic wave at the boundary surface. The setting of the other surface are similar to that of the rear surface. Iv.
NUMERICAL RESULTS
For reaching the match of impedance, there are some offsets for microstrip feedline. In fig.2, Let Ax = Ay = 0.25mm, Az = 0.125" , the domain of total computation is 60 x I 00 x 40 . In microwave circuit analysis, Gauss impulse is generally selected as an excitation for smoothness in time domain and easy spectrum width setting. The width of gauss pulse is T = I 5 p s , Assume that the time delay to = 3T = 45p.s ,
The percent bandwidth of the antennas was determined from the impedance datum. For ease of notion, the bandwidth refers to percent bandwidth that is normally defined as percent BW = [ ( f r 2  , f , . l ) / f,.]xIOO% ( I O ) where ,f,.is the resonance frequency, while f . , and ,f,.* are the frequencies between which reflection coefficient of the antenna is less than or equal to 1/3, which corresponds to VSWRG2. The circle wave loss of antenna measured and computed are shown in Fig.3. from Fig.3, we can find the measured results are in good agreement with computed results by using FDTD method and ADIFDTD method. The measurements carried out on an Agilent 8720C vector network analyzer show that its resonant frequency is 2.44GHz, The drift between the design and measured frequencies is less than3%. the length of the novel antenna is less than 1/10 wavelength, the relative bandwidth of the antenna is approximately 11%, while that of a conventional microstrip antenna is only 0.63%.The efficiency of the novel antenna arrive at 68%. The characteristic parameters such as effective dielectric constant, the characteristic impedance in spectrum domain could be worked out by Fourier transition. Through dealing with the computed datum using MATLAB, The antenna radiation patterns are shown in Fig.4 .
I ........... ............................................... .;,;; . .
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:
...? .
........................;* .j . . .
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. . . . .............:............ .. ............. .......................... ....................... : : . . . . . . . ..
i
i
. i
. .
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Vig.2. bluetooth antenna and its calculation domain
X
. . .
. . .
. .
.. .
..
0.5
1.0
I .5
2.0
2.5
3.0
frequency GHz Fig 3 Retuin loss ofsilicon iniciomachined patch antenna
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The 14'h IEEE 2003 International Symposium on Persona1,lndoor and Mobile Radio Communication Proceedings
REFERENCES
[ I ] ZhangFa Liu, PangShyan Kooi, et.al. A Method for
Designing BroadBand MicrostripAntenna in Multilayered Planar Structures. IEEE Trans. Antennasand Propagat., 1999, 47(9): 14161420. [2] Wu Zhengzhong, Zhong Xianxin, Li Xiaoyi, Yu Wenge. Broadband micromachined antenna for Bluetooth device. ISIST'2002. Jinan, China. Aug. 1822, 2002, l(2): 728732. [3] Wu Zhengzhong, Zhong Xianxin, Li Xiaoyi, Yu Wenge. Broadband nlicroniachined Bluetooth antenna. Pa cific Rim Workshop on Micromano Technologies. Xiainen. China. July. 2224, 2002, 5095 12. [4] K. S. Yee. Numerical solution of Initial Boundary Value Problems Involving Maxwell's Equations in Isotropic Media [J], IEEE AP, 1996,14(5):302307. [5] A. Tafloqe, M. E. Brodwin, Numerical Solution of Steady State Electromagnetic Scattering Problem Using the Time Dependent Maxwell's Equations [J], IEEE Trans. MTT, 1975,23(8):623630. [6] T.Namiki. A new FDTD algorithm based on altemating direction implicit method. IEEE Trans. Microwave Theory Tech., 1999,47(9):20032007. [ 71 Wu Zhengzhong, Zhong Xianxin, Li Xiaoyi,Cheng Wentao. Multiplayershorted micromachined Bluetooth antenna. Optics and Precision Engineering.200 I , 9(6):572576. 0 [ 81 G.Mur. Absorbing boundary conditions for the. finitedifference approximation of the timedomain electromagnetic field equations[J]. IEEE Trans. EMC. 1981,23(4): 377382.
1
(b)
niialybi\ tacliatioii patleiti of Bluetooth mtenna
Wplme
(13)
I 16I 1 till
U'IVC
(d)
Eplme
These simulations were performed by XFDTD, the CPU time of these siniulations are shown in Table], with the timestep size and total time steps In case of the ADIFDTD, the timestep size can be set 15 times as large as the conventional FDTD, and total time steps can be reduced by a factor of 15 The CPU time is also reduced to 28 2%
V.
,
CONCLUSION
A novel shorted microstrip bluetooth antenna has been presented in this paper, it performs excellently especially in ininiatuiization and bandwidth broadening. it has been proved to suit bluetooth conmunication. ADIFDTD method was used to model the structure of the antenna. The algorithm of the method is unconditionally stable Thus, the limitation of the maximum thestep size does not depend on the CFL condition, but rather on numerical errors. The fact that there is a good agreement between the ADIFDTD computed values and the measured results or FDTD computed values manifests that the 3D ADIFDTD method is iiiore efficient than the conventional FDTD method.
. .
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