Synthesis of open complementary split ring resonators (OCSRRs) through aggressive space mapping (ASM) and application to bandpass filters

This paper deals with the automated synthesis of open complementary split ring resonators (OCSRRs) using aggressive space mapping (ASM) for the first time. These open resonators are electrically small planar elements useful for the implementation of shunt LC resonators in microstrip or coplanar waveguide technology. However, their synthesis is in general complex and requires the experience of the microwave engineers. To solve this limitation, and to ease any design process involving OCSRRs, we have developed an efficient iterative synthesis tool based on ASM, able to provide the physical dimensions of the resonator from the required reactive elements (given by specifications) and substrate parameters. As an example of application, the tool is used for the synthesis and design of a planar wideband bandpass filter based on OCSRRs coupled through admittance inverters. Due to the inherent transmission zeros associated to the OCSRRs, these filters exhibit good stop band performance, with high selectivity at the upper transition band.

I. Introduction

Open complementary split ring resonators (OCSRRs), first reported in [1], are electrically small open resonant particles, derived from the topology of the complementary split ring resonators (CSRR) [2] by opening the slots. The typical topology of the OCSRR is depicted in Fig. 1, where the terminals are indicated. To a first-order approximation (i.e., in the vicinity of the fundamental resonance), the structure can be described by an open parallel resonant tank, as depicted in Fig. 1(b), where the capacitance is given by the edge capacitance of the slots (of width c), and the inductance is determined by the length and width (d) of the circular metallic strip present between the slots. As it was discussed in [1], since the inductance of the OCSRR is four times larger than the inductance of the CSRR (provided both resonators have identical dimensions and are etched on the same substrate), the OCSRR is electrically smaller than the CSRR by a factor of two (the capacitances are roughly the same in both particles). Thus, it is expected that the lumped element equivalent circuit model of the OCSRR provides an accurate description of the structure up to relatively high frequencies (in reference to the fundamental resonance frequency). OCSRRs have been used in shunt connection in coplanar waveguide technology for the implementation of bandpass filters and metamaterial-inspired components [3]. In microstrip technology, series connected OCSRRs have been applied to the design of lowpass filters with wide stop bands [4] and multiband printed monopole antennas [5]; in shunt connection, OCSRRs have been used for the design of single-ended [6] and common-mode suppressed differential microstrip bandpass filters [7]. Fig. 1.

Typical topology of an OCSRR (a), and approximate circuit model (b). Metallic regions are indicated in grey (white color corresponds to slots).