IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 4, APRIL 2006 1519 Study and Suppression of Ripples in Passbands of Series/Parallel Loaded EBG Filters Chu Gao, Zhi Ning Chen, Senior Member, IEEE, Yun Yi Wang, Senior Member, IEEE, Ning Yang, and Xian Ming Qing, Member, IEEE Abstract—This paper presents a method to suppress the ripples in passbands of series/parallel loaded finite period electromag- netic-bandgap (EBG) filters. Based on the study of equivalent circuits, the ripples in passbands of EBG filters with different resonant loads are compared. A four-section resonant slot loaded microstrip EBG filter is exemplified to validate the proposed design method experimentally. Both simulation and measurement show 50-dB attenuation at the center of the first stopband and less than 0.29-dB ripples in the adjacent passbands. Index Terms—Bandstop filters, electromagnetic bandgap (EBG), equivalent circuits, ripples. I. INTRODUCTION E LECTROMAGNETIC bandgap (EBG) is a terminology derived from photonic bandgap (PBG). The structures with bandgap characteristics operating at microwave frequency range are called EBG structures. Most of them are three-dimensional (3-D) periodic structures, which prevent the propagation of elec- tromagnetic waves in a specified band of frequency for all an- gles and polarization states [1]. The solid-state bandgap concept of Bragg Law with traditional periodic structures brought about new structures of 3-D, two-dimensional (2-D), and one-dimen- sional (1-D) configuration in the microwave region [1]–[3]. The applications of EBG structures include resonator filters [4], res- onators [5], artificial magnetic conductor surfaces [6], and par- allel mode reduction slot antennas [7]. EBG filters take the basic properties of the EBG structures and have artificial periodic configurations and typical stopbands response at Bragg frequencies. Planar EBG filters can be real- ized by drilling holes in their substrate or etching patterns on ground planes [8], [9]. Since 1-D and 2-D EBG filters have sim- ilar performance, research studies of planer EBG filters can be simplified to the properties of 1-D etching [10]. Though many 1-D EBG filters have wide stopbands with great attenuation therein, they do have great ripples in adjacent passbands, which are more than 2 dB in many designs [11], [12]. The ripples in passbands deteriorate the characteristics of EBG bandstop fil- ters. Effort has been devoted to reduce the ripples in passbands Manuscript received September 5, 2005; revised December 24, 2005. This work was supported by the National Natural Science Foundation of China under Grant 60471018. C. Gao and Y. Y. Wang are with the State Key Laboratory of Millimeter Waves, Radio Engineering Department, Southeast University, Nanjing 210096, China (e-mail: simag@seu.edu.cn; yywang@seu.edu.cn). Z. N. Chen and X. M. Qing are with the Institute for Infocomm Research, Singapore 117674 (e-mail: chenzn@i2r.a-star.edu.sg; qingxm@i2r.a-star.edu. sg). N. Yang was with the Institute for Infocomm Research, Singapore 117674. He is now with Motorola Electronics, Singapore 569088 (e-mail: ningyang@mo- torola.com). Digital Object Identifier 10.1109/TMTT.2006.871925 Fig. 1. Section of symmetric lossless periodic structures. using nonuniform elements whose dimensions vary in a tapered way, like Bartlett, Hanning, Hamming, Nuttall, Kaiser, etc. [13], [14]. However, this tapering technique needs a theory to predict the magnitude of ripples so as to find the best way to design. In this paper, we aim at studying the magnitude of the ripples in passbands of series/parallel loaded EBG bandstop filters and present a method to design EBG filters with low ripples in pass- bands and great attenuation in the stopband in between. In Sec- tion II, an equivalent-circuit model, which composes half-wave- length transmission lines loaded by lumped lossless elements at the center, is proposed to represent a period of an EBG filter. This model can be applied to analyze EBG filters with lossless loads because of the generality of representation of lumped el- ements. An eigenvalue method is then employed to calculate -parameters of the EBG filters from the matrix of a period. Both locations and magnitudes of the ripples in pass- bands are estimated by the ratio of to . In Section III, the loaded element is simplified to parallel/series combination of lossless elements (inductors and capacitors) for design pur- poses, and periodic structures loaded by three kinds of resonant elements (resonance at zero, finite frequency and infinite fre- quency) are studied in a graphic way. Moreover, periodic struc- tures loaded by resonant elements with the same resonant fre- quency, but different 3-dB bandwidths are studied. Therefore, a design method for EBG filters with low ripples in passbands is developed. In Section IV, an EBG bandstop filter is designed, simulated, and measured so as to validate the proposed method. The analysis on effects of a fabrication error is carried out. Fi- nally, a conclusion, which is based on the above research work, is drawn in Section V. II. RIPPLES IN PASSBANDS OF SYMMETRIC AND LOSSLESS PERIODIC STRUCTURES A section in periodic structures can be represented as a net- work of lumped elements with transmission lines cascaded at both ends, as shown in Fig. 1. The unloaded lines have charac- teristic impedance and propagation constant ; the lengths of both of the transmission-line sections are and phase shifts are . The characteristics of the lumped network and the sec- tions in Fig. 1 are defined by their normalized -parame- 0018-9480/$20.00 © 2006 IEEE