ite quantum-well absorption core, IEICE Trans Electron E88-C (2005),967–972.

7. J. Lim, S. Jeon, J. Kim, and S. Hong, A circuit model of traveling waveelectroabsorption modulator, Proc IEEE MTT-S Int Microwave SympDig 3 (2002), 1707–1710.

8. Y.-S. Kang, Y.-D. Chung, K.-S. Choi, J.-H. Lee, S.-B. Kim, and J.Kim, Traveling-wave electro-absorption modulator (TWEAM) forhigh-frequency radio-over-fiber (ROF) link, Proc IEEE Int Top MtgMicrowave Photon (2004), 285–288.

9. J. Lim, Y.-S. Kang, K.-S. Choi, J.-H. Lee, S.-B. Kim, and J. Kim,Analysis and characterization of traveling-wave electrode in electro-absorption modulator for radio-on-fiber application, J LightwaveTechnol 21 (2003), 3004–3010.

10. K.-S. Choi, Y.-D. Chung, Y.-S. Kang, B.-T. Ahn, J.-T. Moon, and J.Kim, Fabrication and characteristics of traveling-wave electro-absorp-tion modulator (TWEAM) modules for millimeter-wave radio-over-fiber link, Proc Electron Compon Technol (2005), 1792–1797.

11. K.-S. Choi, J. Lim, J.-H. Lee, Y.-S. Kang, Y.-D. Chung, J.-T. Moon,and J. Kim, Optimization of packaging design of TWEAM module fordigital and analog applications, ETRI J 26 (2004), 589–596.

12. W.S. Chang, Multiquantum well electroabsorption modulators for RFphotonic links, RF Photon Technol Optical Fiber Links, W.S. Chang(Ed.), Cambridge University Press, New York, 2002, pp. 165–202.

13. J. Kim, Y.-S. Kang, Y.-D. Chung, and K.-S. Choi, Development andRF characteristics of analog 60-GHz electroabsorption modulatormodule for RF/optic conversion, (submitted).

© 2006 Wiley Periodicals, Inc.

NEAR-FIELD DATA COMPRESSION FORTHE FAR-FIELD COMPUTATION INFDTD

Romain Pascaud,1 Raphael Gillard,1 Renaud Loison,1

Joe Wiart,2 and Man-Faı Wong2

1 Institut d’Electronique et de Telecommunications de Rennes20 avenue des Buttes de Coesmes35043 Rennes Cedex, France2 France Telecom R&D38-40 rue du General Leclerc92794 Issy-Les-Moulineaux Cedex 9, France

Received 1 December 2005

ABSTRACT: This paper presents a technique to compress the near-fielddata required to compute the radiated fields using FDTD. This technique isapplied to the study of a UWB planar diamond antenna. The results show a99.8% gain in memory storage, while maintaining good accuracy: less than1% error on the far-field radiation patterns. © 2006 Wiley Periodicals, Inc.Microwave Opt Technol Lett 48: 1155–1157, 2006; Published online inWiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21553

Key words: FDTD; far-field computation; wavelets; DWT

1. INTRODUCTION

The finite-difference time-domain (FDTD) [1] method has beenextensively used to simulate open problems. However, a near-to-far-field transformation is commonly used to compute radiationpatterns. This transformation is usually carried out as post-pro-cessing according to the equivalence principle. A virtual Huygenssurface is defined to store the tangential components of the near-fields E and H at each time step. Later on, the radiated fields canbe evaluated at any frequency while calculating and integrating theequivalent currents according to the equivalence principle. Inpractice, the near-field data storage can easily lead to a huge data

file because of the large number of time iterations and cells on theHuygens surface. Actually, the large number of cells results fromthe small cell size that is usually required to obtain good accuracyin the FDTD near-field computation. Such a fine grid is not neededfor the far-field computation. Data compression can be used toovercome the spatial oversampling problem.

Recently, a discrete cosine transform (DCT) has been used tocompress the near-field data on the surface of a Huygens box [2].A compression rate of 92.5% has been obtained with good accu-racy in the radiated fields. In [3], a compression technique waspresented based on the multiresolution analysis scheme, in whichthe scaling coefficients are stored. The required near-field datahave been reduced by 98%.

In this paper, the proposed technique consists of a multireso-lution analysis where the scaling and wavelet coefficients superiorto a threshold are kept. Section 2 explains the compression prin-ciple in detail. In section 3, this compression technique is appliedto the near-field data of an UWB antenna, and the radiationpatterns are computed and compared with the initial ones. Finally,some conclusions are discussed in section 4.

2. PRINCIPLE

The proposed compression technique is based on the multiresolu-tion analysis principle. A discrete wavelet transform in two dimen-sions (DWT 2D) is spatially applied as post-processing on thenear-field components on each face of the Huygens surface (Fig.1). For each time step, electric and magnetic fields are decomposedon a Haar basis according to the multiresolution analysis scheme.During the decomposition, the maximum resolution level isreached: one scaling coefficient is used as a coarse approximationof the signal, while details at various resolution levels are broughtby wavelet coefficients [4]. For example, Figure 2(a) presents themagnitude of the near-field component Ez on one face of theHuygens surface at a particular time step, and Figure 2(b) theresulting scaling and wavelet coefficients. The useful informationis concentrated on a small number of coefficients (the clearest ones

Figure 1 DWT 2D applied on each face of the Huygens surface

Figure 2 Ez on one face of the Huygens surface at a particular time step:(a) direct representation; (b) DWT 2D representation

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 48, No. 6, June 2006 1155

in the figure), and only a few of them need to be stored. In practice,we save all the coefficients that are superior to a global threshold,whatever the field component. Before computing the radiatedfields, the near-field data are reconstructed at the fine level thanksto an inverse discrete wavelet transform in two dimensions (IDWT2D).

To evaluate the interest of keeping some wavelet coefficients,we compare the following techniques:

● in the first one, only the scaling coefficients are kept, and thistechnique is equivalent to defining a uniform coarse grid;

● in the second one, the scaling and wavelet coefficients thatare superior to a predefined threshold are kept.

3. NUMERICAL EXAMPLE

The simulations are performed for the ultra-wideband (UWB)planar diamond antenna shown in Figure 3 and described in [5].For UWB antennas, FDTD simulation is recommended. Indeed,only one simulation in the time domain is required to characterizethe antenna over a large range of frequencies. The antenna is fedwith a Gaussian pulse, which is narrow enough in the time domainto cover the overall antenna bandwidth.

Here, the FDTD volume size is 36 � 9 � 27 mm, and isdiscretized into 120 � 30 � 90 uniform cells with a �0/140 cellsize at the central frequency (7 GHz). The antenna geometry(oblique edges) justifies the small cell size. Such a spatial discreti-zation is needed to obtain good accuracy in the FDTD near-fieldcomputation, whereas for the far-field calculation it is over-sampled. The Huygens box is made up of 5 faces (64 � 8 � 64small cells). To compute the far fields, their images are taken sincethe antenna is placed over an infinite ground plane.

Various compression rates are applied to the initial near-fielddata. After the data are reconstructed, radiation patterns are cal-culated for ten frequency points from 5 to 9.5 GHz. This radiationpatterns are compared with the initial ones (without compression)by evaluating the normalized mean squared error, given by

� � �1

M �k�1

M �EuNCk � EuCk�2

�EuNCmax�2, (1)

where u is either � or �, depending on the field component. NCstands for not compressed whereas C is for compressed. M is thetotal number of frequency points. Figure 4 presents this error forthe �E�� component in the � � 0° plane, plotted as a function ofthe compression rate for the two techniques. The number ofnonsaved coefficients over the total number of initial data gives thecompression rate.

These results show that both techniques make a reduction of98% of the required data possible with good accuracy in thefar-field patterns. However, the compression rate for a same erroris better when wavelet coefficients are conserved. Indeed, com-pression rates up to 99.8% can be reached with good accuracy inthe radiated fields. For example, Figure 5 shows the radiationpatterns using original data and reconstructed ones. Concerning thereconstructed radiated fields, both techniques use a 99.8% com-pression rate of the near-field data.

No major differences exist between the original far-field andthe reconstructed one using scaling and wavelet coefficients. Onthe contrary, we observe a 2-dB difference for � � 90° when auniform coarse grid is defined (only scaling coefficients con-

Figure 3 Simulated UWB planar diamond antenna

Figure 4 Error on �E�� as a function of the compression rate for bothtechniques with � � 0°

Figure 5 Comparison between original and reconstructed radiation pat-terns at 9.5 GHz with � � 0° and with a 99.8% compression rate

1156 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 48, No. 6, June 2006 DOI 10.1002/mop

served). In this case, a uniform grid does not make a good approx-imation of the near-field components. Some local near-field vari-ations are not taken into account. On the contrary, our techniqueconserves wavelet coefficients that traduce these variations. Thistechnique can be viewed as a kind of adaptive mesh that is refinedwhere the spatial variations of the near-field are not negligible.

4. CONCLUSION

In this paper, we have presented an efficient technique to compressthe near-field data used to compute radiated fields. This techniqueoptimizes memory storage. Indeed, compression rates up to 99%were obtained for the UWB antenna with good accuracy in far-field radiation patterns. Based on this example, the utility ofkeeping wavelet coefficients has been validated.

ACKNOWLEDGMENTS

This work was supported by France Telecom R&D, contract no.46129586.

REFERENCES

1. K.S. Yee, Numerical solution of initial boundary value problems in-volving Maxwell’s equations in isotropic media, IEEE Trans AntennasPropagat 14 (1966), 302–307.

2. S. Wang, B. Zhou, and W. Yu, Application of data-compressing tech-nique to far field pattern prediction in FDTD simulation, MicrowaveOpt Technol Lett 42 (2004), 437–441.

3. G. Carat, R. Gillard, J. Citerne, and J. Wiart, A discrete wavelettransform (DWT)-based far-field computation using FDTD method,Microwave Opt Technol Lett 25 (2000), 241–243.

4. S.G. Mallat, Multifrequency channel decompositions of images andwavelet models, IEEE Trans Acoustics Speech Signal Process 37(1989).

5. X.H. Wu, Z.N. Chen, and N. Yang, Optimization of planar diamondantenna for single-band and multiband UWB wireless communications,Microwave Opt Technol Lett 42 (2004), 451–455.

© 2006 Wiley Periodicals, Inc.

EMC INTERNAL PATCH ANTENNAINTEGRATED WITH A U-SHAPEDSHIELDING METAL CASE FOR MOBILEDEVICE APPLICATION

Chih-Ming Su,1 Kin-Lu Wong,1 Brian Chen,2 and Sam Yang2

1 Department of Electrical EngineeringNational Sun Yat-Sen University, Kaohsiung 804, Taiwan2 Research & Development Division VCompal Communications Inc., Taipei 105, Taiwan

Received 1 December 2005

ABSTRACT: A novel integration design of a shorted patch antennaand a U-shaped shielding metal case for application in a mobile com-munication device is presented. The shorted patch antenna is mountedwithin the dented portion of the U-shaped shielding metal case, whichcan provide a coupling-free space for accommodating electronic compo-nents such as the RF modules/circuitry and battery in the mobile device.Thus, in this case, the shorted patch antenna can operate as an internalantenna having an electromagnetic compatibility (EMC) property withnearby electronic components. In addition, with the proposed integrationdesign, the shorted patch antenna is isolated from the two side edges ofthe system ground plane of the mobile device. Hence, it can be expectedthat the effects of the user’s hand on the performances of the antennawill be suppressed. The proposed integration design applied to a smartphone for Universal Mobile Telecommunications System (UMTS, 1920–

2170 MHz) operation is studied. © 2006 Wiley Periodicals, Inc.Microwave Opt Technol Lett 48: 1157–1161, 2006; Published online inWiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21552

Key words: antennas; mobile antennas; internal mobile phone anten-nas; GSM/DCS antennas

1. INTRODUCTION

Conventional internal patch antennas that have been applied inmobile communication devices mainly comprise a top patch, abottom ground plane (the system ground plane of the mobiledevice), and a vertical feeding pin and a vertical shorting pinplaced in between the top patch and the bottom ground plane [1].The configuration of the conventional internal patch antenna, how-ever, allows the fringing electromagnetic (EM) fields to easilypenetrate into the surrounding region of the antenna. In this case,some coupling between the antenna and the nearby electroniccomponents will occur, thus resulting in degrading effects on theperformances of the antenna. To reduce this degrading couplingeffect, an isolation distance of about 7 mm or larger between theantenna and the nearby electronic components is usually requiredfor practical applications [2, 3]. This isolation distance leads to aninefficient usage of the valuable board space of the system circuitboard of the mobile device.

To overcome this problem, the internal patch antenna with anEMC property with nearby electronic components has been dem-onstrated [2–4]. In addition to the use of the system ground planeas the bottom ground plane of the antenna, this kind of EMCinternal patch antenna has an additional vertical ground planearranged at the antenna’s side surfaces. This vertical ground planenot only functions as part of the antenna’s ground plane, but alsoas an effective shielding wall to suppress or eliminate the possiblecoupling between the antenna and the nearby electronic compo-nents [2–4].

In this paper, we propose another promising EMC internalpatch antenna suitable to be applied in a mobile communicationdevice such as a smart phone or personal digital assistant (PDA)phone for UMTS (1920–2170 MHz) operation. The proposedEMC internal patch antenna is integrated with a U-shaped shield-ing metal case, which provides a coupling-free space for accom-modating the electronic components such as the RF modules/circuitry and battery in the mobile device [5–8]. This proposedintegration design allows no isolation distance required betweenthe internal patch antenna and nearby electronic components. Inaddition, the proposed U-shaped shielding metal case is differentfrom the simple shielding metal case reported in [5–8]. Theinternal patch antenna fits well within the dented portion of theU-shaped shielding metal case. That is, the internal patch antennais encircled by the U-shaped shielding metal case, and is thusisolated from the two side edges of the system ground plane of themobile device. In this case, it can be expected that the effects of theuser’s hand on the performances of the antenna will be suppressed.Details of the design considerations of the proposed integrationdesign are described, and the experimental results of the con-structed prototype are presented. The technique used in this studyto enhance the impedance bandwidth of the antenna to cover theUMTS band is also discussed. The effects of varying the dimen-sions of the shielding metal case and the system ground plane onthe performances of the antenna are also studied.

2. ANTENNA DESIGN

Figure 1(a) shows the geometry of the proposed EMC internalpatch antenna integrated with the U-shaped shielding metal case

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 48, No. 6, June 2006 1157