about 20 dB. Unfortunately, the maximum scattered field in the H-plane is almost the same as that without coating, as shown in Figure 5(b). When four screw heads are considered, as seen in Figure 1, if the metal screw heads are coated with dielectric material in the same way as with the single screw head just described, there is also an average suppression of the scattered fields as shown in Figure 5(c) and 5(d). These figures show the scattered fields in the E- and H-planes when the four screw heads are with coating and without coating. It has to be pointed out that we could not test this out by measurement in our test antenna, because the scattering from 0.1-radius screw heads is too low to be visible when it is added to the sidelobes of the undisturbed reflector. When the radius of the metal screw head is larger than 0.3, we found that it is not possible to reduce the scattering by a dielectric coating in the form of a spherical shell. It should still be possible to reduce the scattering from such big screws by using dielectrics, but then the screw head should be flat with a plane dielectric layer on it, which our computer program cannot handle at present. 5. THE EFFECTS OF LOCATIONS AND SIZES OF THE SCREWS Figure 6 shows maximum co- and cross-polar scattered fields due to four metal screws with 0.2 radius and 90° separation in the  direction, when the screws are located at different positions in a reflector with 31 diameter and 6.5 focal length. The positions are characterized by their polar angle  and azimuth angle . The antenna is excited for linear y polarization with the E-plane in  = 90°. It is observed that if the screws are located in the 45° planes, the co-polar scattered field has its minimum and the cross-polar scattered field may have its maximum. However, if the screws are located in the 45° plane with  = 22.3° (sin   0.4), good results can be obtained for both the co- and cross-polar scattered fields, which in this case could be 10-dB lower than the other locations. This means that one can use the scattering analysis program to find the optimum locations of the screws in the reflector, which will minimize the contribution to the sidelobes. The effects on the sidelobes due to different screw head diam- eters have been also investigated. Figure 7(a) shows the scattered field from a metal screw with 0.2 radius located at (, ) = (22.3°, 45°) in the same reflector with 31 diameter and 6.5 focal length. If this screw is replaced by three smaller screws with 0.1 radius located at (, ) = (22.8°, 45°), (21.8°, 44.5°), and (21.8°, 45.5°), respectively, the total scattered field from these three screws is about 5-dB lower than that from the big screw, as shown in Figure 7(b). In addition, when the screws have so small diameter as 0.1, it is possible to suppress the scattered field even more by applying a dielectric coating [see Fig. 7(c)], which provides a total of about 10-dB suppression in the E-plane. 6. CONCLUSION By introducing the perturbation theory, the effect on the sidelobe of multilayer screw heads in a reflector can be analyzed very efficiently. The scattered fields due to the metal screw heads can be reduced by coating them with dielectric material at least for small screw-head diameters. By using the program based on GIDMULT, one can find the optimum locations of the screws in the reflector. REFERENCES 1. C.A. Balanis, Advanced engineering electromagnetics, Wiley, New York, 1989, pp. 650 – 658. 2. H.C. Van de Hulst, Light scattering by small particles, Wiley, New York, 1957, pp. 304 –307. 3. A.-K. Hamid, Electromagnetic scattering by a conducting sphere par- tially buried in a ground plane, Proc 1995 IEEE AP-S Int Symp, Newport Beach, CA, 1995, pp. 406 – 409. 4. W.K. Gwarek, V2D-solver version 1.9: A software package for elec- tromagnetic modeling of microwave circuits of vector 2-D class, War- saw University of Technology (gwarek@ire.pw.edu.pl). 5. Z. Sipus, P.-S. Kildal, R. Leijon, and M. Johansson, An algorithm for calculating Green’s functions of planar, circular cylindrical and spher- ical multilayer substrates. Appl Comput Electromagn Soc J 13 (1998), 243–254. © 2003 Wiley Periodicals, Inc. COMPACT INTERNAL QUAD-BAND ANTENNA FOR MOBILE PHONES Irene Ang, Yong-Xin Guo, and M. Y. W. Chia Institute for Infocomm Research 20 Science Park Road #02-34/37, TelelTech Park Science Park II, Singapore 117674 Received 23 January 2003 ABSTRACT: A novel compact internal quad-band handset antenna for covering GSM900, DCS1800, PCS1900, and ISM2450 bands is pre- sented. Details of the antenna are discussed along with measured and simulated results. The simulation is based on the FDTD method. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 38: 217–223, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11019 Key words: antennas; small antennas; PIFA antennas; handset anten- nas 1. INTRODUCTION The market demand for and new technologies of mobile phones have driven the handset antenna to be compact in size and have multi-band functions. Conventional monopole-like antennas have remained relatively large compared to the handset itself. Thus, internal antennas are becoming very promising candi- dates for applications in mobile handsets. Most internal anten- nas currently used in mobile phones are based on planar invert- ed-F antennas (PIFAs) [1]. Currently, many mobile telephones use one or more of the following frequency bands: the GSM band centered at 900 MHz, the DCS band centered at 1800 MHz, and the PCS band centered at 1900 MHz. Many interest- ing designs based on the PIFA concepts for achieving multiple- band operations have been available in the open literature [2– 8]. More recently, it is envisaged that mobile phones require the capability to include the ISM2450 band for Wireless LAN or Bluetooth applications. Several triple-band antenna designs are available in [9 –11] for operations at GSM900, DCS1800 (or PCS1900), and ISM2450 bands. This paper presents a novel compact internal quad-band hand- set antenna for covering GSM900, DCS1800, PCS1900, and ISM2450 bands. The proposed antenna consists of two-layer folded patches sharing a common shorting strip and was developed within the limit of a 36  16  8 mm 3 volume. The simulations are performed using Remcom software XFDTD5.3, which is based on the FDTD method. 2. ANTENNA DESIGN AND STRUCTURE Figure 1 shows the proposed antenna mounted on a ground plane of dimensions 80 mm by 36 mm. The antenna comprises a main MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 38, No. 3, August 5 2003 217