532 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 13, NO. 12, DECEMBER 2003 Multiple-Coupled Microstrip Hairpin-Resonator Filter Yingjie Di, Peter Gardner, Peter S. Hall, H. Ghafouri-Shiraz, and Jiafeng Zhou Abstract—This letter presents the design of six-resonator multiple-coupled microstrip filter. A low-pass prototype of six-resonator multiple-coupled filter is developed first based on the conventional Chebyshev filter. The characteristics of attenu- ation poles located on both sides of the frequency response are described. According to the low-pass prototype, the design of a six-resonator multiple-coupled microstrip hairpin filter at 6 GHz is completed with the aid of EM simulation. The experimental results are demonstrated and discussed. Index Terms—Cross coupling, multiple-coupled microstrip filter, resonator filter. I. INTRODUCTION T HE cross-coupled microstrip filters are attractive for its high selectivity and compact size. There are two classes of the cross-coupled filter: cascaded quadruplet (CQ) filter [1]–[5] and multiple-coupled filter [6], [7]. Although configuration of these two-class filters is different, the extra couplings are used to eliminate direct coupling and to introduce the transmission poles. There are a pair or more of the attenuation poles on the transmission response of filter. Because each cross coupling af- fects all the transmission poles, the realization of multiple-cou- pled filter is more difficult than CQ filter. The designs of CQ microstrip filter working under 2.0 GHz have been fully investigated using different microstrip res- onators [1], [3]–[5]. These designs are extremely successful except that of microstrip hairpin filter [5] where the stopband rejection is lower. The successful designs of multiple-coupled waveguide filter were presented in [6] and [7]. Due to the open field configuration of microstrip filter, there are undesirable cross couplings between resonators. Compared with the multiple coupled waveguide filter, multiple coupled mi- crostrip filter are more difficult to realize. So few papers of mul- tiple coupled microstrip filter were published. In this letter, we introduce a new design of multiple-coupled microstrip hairpin filter. Based on the conventional Chebyshev filter we developed the low-pass prototype of six- resonator mul- tiple-coupled filter which is described in Section II. The design procedure for six-resonator microstrip hairpin filter and mea- sured results are presented in Section III. The discussion about this filter is given in Section IV. Manuscript received January 27, 2003; revised July 10, 2003. The review of this letter was arranged by Associate Editor Dr. Shigeo Kawasaki. Y. Di is with the Department of Electronic and Communication Engineering, North China Electric Power University, China. P. Gardner, P. S. Hall, H. Ghafouri-Shiraz, and J. Zhou are with the School of Electronic and Computer Engineering, The University of Birmingham, Birm- ingham, B15 2TT, U.K. Digital Object Identifier 10.1109/LMWC.2003.819377 Fig. 1. Low-pass prototype of multiple-coupled filter. II. THEORY A. Frequency Responses Fig. 1 shows the low-pass prototype of six-resonator mul- tiple-coupled filter, where the boxes are the admittance inverters with parameter or 1. Because of weak coupling between , like [2] another appointment we can adopt is , and have respectively the same values with that of low-pass prototype Chebyshev filter. But the value of is different from of Chebyshev filter in order to match the network. So, if , it gives the filter design with Chebyshev re- sponse by choosing . At , the odd-mode and even-mode input admittances should be equal to those of the Chebyshev filter. So, we can obtain the following relation between and where . B. Attenuation Poles The cross couplings between may arise transmis- sion poles (attenuation poles) rather than transmission zeroes in the filter transmission response. So the frequency response at the location of the attenuation poles satisfies where is the derivative of . If cross couplings and are out of phase to , there are a pair of transmission poles. If is out of phase to and has the same phase as , there are a pair or two pairs [see [6]] of transmission poles. The frequency response is given in Fig. 2 when and with the 0.1 dB ripple level in the passband response. Fig. 3 shows variations of the location of attenuation pole and peak magnitude of with cross coupling when and with the same ripple as in Fig. 2. From Figs. 2 and 3, we can reckon that the closer the 1531-1309/03$17.00 © 2003 IEEE