RADIOENGINEERING, VOL. 20, NO. 4, DECEMBER 2011 775 Broadband Microwave Filters Based on Open Split Ring Resonators (OSRRs) and Open Complementary Split Ring Resonators (OCSRRs): Improved Models and Design Optimization Miguel DURÁN-SINDREU 1 , Paris VÉLEZ 1 , Jordi BONACHE 1 , Ferran MARTÍN 1 1 GEMMA/CIMITEC Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, 08193 BELLATERRA (Barcelona), Spain Ferran.Martin@uab.es Abstract. The paper is focused on the design of broadband bandpass filters at microwave frequencies. The proposed filters are based on a combination of open split ring reso- nators (OSRRs) and open complementary split ring reso- nators (OCSRRs) loaded in a host transmission line. Since these resonators (OSRRs and OCSRRs) are electrically small, the resulting filters are compact. As compared to previous papers by the authors on this topic, the main aim and originality of the present paper is to demonstrate that by including a new series inductance in the circuit model of the OCSRR, it is possible to improve the predictions of these filter models and better fit the measured filter responses. Moreover, the parameter extraction method of the new circuit model and an automated filter design technique is introduced and demonstrated. The paper is complemented with the design and comparison of several prototypes. Keywords Bandpass filters, metamaterials, open split ring resonator, open complementary split ring resonator. 1. Introduction The wideband bandpass filters of the present paper are based on the open versions of the split ring resonator (SRR) [1] and the complementary split ring resonator (CSRR) [2]. SRRs and CSRRs, among other particles [3], [4], have been used for the synthesis of negative effective permeability and permittivity media, respectively, and also for the synthesis of left handed metamaterials. In planar technology, these particles have been used for the imple- mentation of composite right/left handed (CRLH) trans- mission lines, namely, lines exhibiting backward wave propagation at low frequencies, and forward wave propa- gation at high frequencies [5], [6], and also for the imple- mentation of broadband filters based on them [7]. However, by using the open versions of the SRR and the CSRR combined, i.e., the open split ring resonator (OSRR) [8] and the open complementary split ring reso- nator (OCSRR) [9], it has been recently demonstrated the possibility of implementing CRLH lines in both microstrip and coplanar waveguide technology [10] without the pres- ence of a transmission zero below the first (left handed) transmission band (such transmission zero is present in the CRLH lines implemented by using SRRs or CSRRs [5], [6]). It has been also pointed out that by sacrificing perio- dicity in OSRR- and OCSRR-based CRLH lines, it is pos- sible to implement compact wideband bandpass filters subject to specifications, and several prototype devices covering different orders and bandwidths have been reported [11], [12]. In the present paper we report an improvement of the circuit model of these OSRR and OCSRR-based filters and also a method to automatically synthesize the required filter responses. This new circuit model is necessary to better predict the response of the filter in the upper region of the band-pass and also the upper transition band. The paper is organized as follows: in section 2, the filter to- pology and the improved circuit model is presented. In section 3, the parameter extraction method to infer the circuit values of the new proposed model is shown. The automated synthesis method is reported in section 4. In section 5, the design of several prototype devices is re- ported. Finally, the main conclusions are highlighted in section 6. 2. Filter Topology and Circuit Models The proposed filters are based on alternating sections of host lines loaded with series connected OSRRs and shunt connected OCSRRs. Fig. 1 presents the topology and the formerly proposed lumped element equivalent circuit models of these filter sections, corresponding to CPW technology [10]. CPW is the technology used for the im- plementation of the OSRR and OCSRR based filters since