5. CONCLUSION A novel fractal DGS has been presented. The DGS lattice is a fractal Sierpinski-carpet type, instead of the rectangular holes used previously so that DGS can be adjusted by the filling factor. Simulation has shown that the proposed fractal DGS can provide more efficient size-reduction of the microstrip structure and better bandgap characteristics than the dumbbell-shaped DGS. A low- pass filter with the fractal DGS is designed and fabricated. Simu- lation and measurement confirms the validity of the proposed fractal DGS and the LPF configuration and design procedure. The LPF is simple. Additionally, the power-handling capability of low-pass filters can be improved by using the microstrip line with DGS. REFERENCES 1. C.S. Kim, J.S. Park, A. Ahn, et al., A novel 1D periodic defected ground structure for planar circuits, IEEE Microwave Guided Wave Lett 10 (2000), 131–133. 2. Y.Q. Fu, N.C. Yuan, and G.H. Zhang, A novel fractal microstrip PBG structure, Microwave Opt Technol Lett 32 (2002), 316 –318. 3. J.S. Park, J.H. Kim, J.H. Lee, et al., A novel equivalent circuit and modeling method for defected ground structure and its application to optimization of a DGS lowpass filter, IEEE MTT-S 1 (2002), 417– 420. 4. J.S. Lim, J.S. Park, Y.T. Lee, et al., Application of defected ground structure in reducing the size of amplifiers, IEEE Microwave Guided Wave Lett 12 (2002), 261–263. 5. S.G. Jeong, D.K. Hwang, Y.C. Jeong, et al., Amplifier design using /4 high impedance bias line with defect ground structure (DGS), IEEE MTT-S 2 (2002), 1161–1164. 6. A. Dal, J.S. Park, C.S. Kim, J. Kim, Y.X. Qian, and T. Itoh, A design of the low-pass filter using the novel microstrip defected ground struc- ture, IEEE Trans MTT 49 (2001), 86 –93. 7. N.C. Karmaker, Improved performance of photonic band-gap microstrip line structures with the use of chebyshev disribytions, Microwave Opt Technol Lett 33 (2002), 1–5. © 2003 Wiley Periodicals, Inc. EFFICIENT ANALYSIS OF A CLASS OF MICROSTRIP ANTENNAS USING THE CHARACTERISTIC BASIS FUNCTION METHOD (CBFM) Junho Yeo, V. V. S. Prakash and Raj Mittra Electromagnetic and Communication Laboratory Pennsylvania State University University Park, PA 16802 Received 12 June 2003 ABSTRACT: This paper presents a novel approach for the efficient solution of a class of microstrip antennas using the newly introduced characteristic basis functions (CBFs) in conjunction with the method of moments (MoM). The CBFs are special types of high-level basis func- tions, defined over domains that encompass a relatively large number of conventional subdomain basis functions, for example, triangular patches or rooftops. The advantages of applying the CBF method (CBFM) are illustrated by several representative examples, and the accuracy as well as the computation time are compared to those of conventional direct computation. It is demonstrated that the use of CBFs can result in sig- nificant savings in computation time, with little or no compromise in the accuracy of the solution. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 39: 456 – 464, 2003; Published online in Wiley Inter- Science (www.interscience.wiley.com). DOI 10.1002/mop.11247 Key words: characteristics basis function method; method of moments; microstrip array antennas; fractal antenna 1. INTRODUCTION Microstrip antennas and arrays are attractive candidates for many communication applications because they are compact, conformal, and well suited for low-cost design. Among the various numerical techniques, the method of moments (MoM) has been widely used for the analysis and design of a class of microstrip antennas and arrays [1, 2]. However, the conventional MoM using subsectional basis functions and a /10 or /20 discretization becomes highly inefficient for the analysis of large or complex antennas and arrays. This is because the size of the associated MoM matrix grows very rapidly as the dimensions become large in terms of the wavelength, or a fine mesh is used to model a complex structure to guarantee good solution accuracy, and this in turn places an inordinately heavy burden on the CPU in terms of both memory and time, which increase with O( N 2 ) and O( N 3 ), respectively, in the direct solution, where N is the number of unknowns. A number of researchers have investigated ways to circumvent these problems and accelerate the MoM calculation. Wavelet ex- pansions based on the theory of multiresolution analysis have been proposed to render moment matrices sparse after performing a thresholding process [3]. The fast-multipole method (FMM) [4], the impedance matrix localization (IML) technique [5], and several other approaches have been proposed for speeding up the MoM. The FMM realizes savings of the memory requirements by storing only the near-field interaction part of the large matrix, and a speeding up the solution of the linear equations by carrying out the matrix vector product needed in the iterative solvers—almost always employed for the solution of large matrices—in a highly efficient manner by using the spherical harmonic expansion tech- nique. But even the FMM is bounded by a discretization size ranging from /10 to /20, which makes the MoM matrix grow at a rapid pace, as the geometry becomes electrically large. The IML utilizes a matrix transformation which effectively changes the basis (testing) functions into ones resembling traveling waves or standing waves, but the accuracy of the IML approximations Figure 6 Transmission characteristics of the LPF with a 1 = 1.8 mm, a 2 = 0.9 mm, w = 2.4 mm, and g = 0.4 mm 456 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 39, No. 6, December 20 2003