IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES,VOL. 53, NO. 8, AUGUST 2005 2539 Design of Low-Pass Filters Using Defected Ground Structure Jong-Sik Lim, Member, IEEE, Chul-Soo Kim, Member, IEEE, Dal Ahn, Senior Member, IEEE, Yong-Chae Jeong, Member, IEEE, and Sangwook Nam, Member, IEEE Abstract—A method to design low-pass filters (LPF) having a de- fected ground structure (DGS) and broadened transmission-line elements is proposed. The previously presented technique for ob- taining a three-stage LPF using DGS by Lim et al. is generalized to propose a method that can be applied in design -pole LPFs for . As an example, a five-pole LPF having a DGS is de- signed and measured. Accurate curve-fitting results and the suc- cessive design process to determine the required size of the DGS corresponding to the LPF prototype elements are described. The proposed LPF having a DGS, called a DGS-LPF, includes transmis- sion-line elements with very low impedance instead of open stubs in realizing the required shunt capacitance. Therefore, open stubs, tee- or cross-junction elements, and high-impedance line sections are not required for the proposed LPF, while they all have been es- sential in conventional LPFs. Due to the widely broadened trans- mission-line elements, the size of the DGS-LPF is compact. Index Terms—Defected ground structure (DGS), low-pass filters (LPFs), periodic structures. I. INTRODUCTION I T IS well known that typical properties of low-pass filters (LPFs) can be obtained by adding periodic structures to transmission lines. The representative periodic structures for planar transmission lines and/or microwave circuits are pho- tonic bandgap (PBG) and defected ground structure (DGS) [2]–[5]. The PBG has been known as a popular periodic structure for planar transmission lines. However, drawbacks of PBGs have been also discussed as follows. 1) A large area is needed because a number of periodic pat- terns should be adopted. 2) It is obscure to define the unit element, and difficult to extract the equivalent-circuit elements for the PBG unit element. 3) Therefore, it is very restricted to extend its practical ap- plication to microwave circuits. To the contrary, one can easily define the unit element of the DGS and model the equivalent circuit. Manuscript received July 15, 2004; revised February 14, 2005. This work was supported by the RRC Program through the Soonchunhyang University Wire- less Components Research Center. J.-S. Lim and D. Ahn are with the Division of Information Technology Engineering, Soonchunhyang University, Asan, Chungnam 336-745, Korea (e-mail: jslim@sch.ac.kr). C.-S. Kim is with the Samsung Advanced Institute of Technology, Yongin 449-712, Korea. Y.- C. Jeong is with the Division of Electronics and Information Engineering, Chonbuk National University, Jeonju 561-756, Korea. S. Nam is with the School of Electrical Engineering and Computer Science, Seoul National University, Seoul 151-742, Korea. Digital Object Identifier 10.1109/TMTT.2005.852765 In addition, since only a few DGS elements show the typical properties of periodic structures, the resultant circuit size be- comes relatively small. Furthermore, the structure of the DGS is simple and it is easy to design the DGS pattern. For these rea- sons, since [4] has introduced the structure and called it a DGS for the first time, the DGS has been extensively applied to de- sign microwave circuits such as filters, power dividers, couplers, amplifiers, oscillators, and so on [1], [6]–[12]. There is much previous research about the characteristics of LPFs having periodic structures on microstrip or coplanar wave- guide (CPW) transmission lines [13]–[16]. However most of them are not analytical because they mainly depend on elec- tromagnetic (EM) simulations to design LPFs and predict cir- cuit performances. To the contrary, in the design of LPFs using DGSs including this study, all design steps are based on theories and reasonable explanations as follows. • The equivalent-circuit elements of the DGS is extracted and used for replacing the series inductances in the LPF prototype circuit. • The LPF is composed of the extracted equivalent lumped elements, thus, it is an ideal LPF, is designed, and is com- pared to the realized LPF using the DGS practically. Two methods to design a three-pole LPF using the DGS has been proposed in [1] and [6]. In these papers, the sizes of two DGS patternsintheLPFwereexactlythesamebecausetwoinductances in the three-pole “ (series)- (shunt)- (series)” prototype LPF are identical. In [6], discontinuity elements such as tee- or cross-junctions were adopted to connect open stubs to realize the shunt capacitance. However, in the three-pole LPF proposed in [1], there are no junction elements, thin transmission lines for high impedance, or open stubs. In addition, the width of the transmis- sion-line elements in the LPF has been remarkably broadened. Thus, advantages such as compact design and error-robust real- ization in fabricating the layout have been obtained. However, in order to design -stage LPFs using the DGS, e.g., a five-stage like “ (series)- (shunt)- (series)- (shunt)- (series),” two different dimensions of the DGS have to be adopted because is not equal to , although . In order to select the proper dimension of the DGS for , careful consideration based on filter theories, extracted equiva- lent-circuit elements of various DGS dimensions, and some re- lated topics of transmission lines should be taken. The size of the DGS for is determined by accurate curve-fitting results for equivalent-circuit elements to correspond exactly to the re- quired inductance. In addition, the length of transmission-line elements between DGS patterns is determined through the con- sideration for the equivalent capacitance and additional para- 0018-9480/$20.00 © 2005 IEEE