Research Article Design of Miniaturized Multiband Filters Using Zero Order Resonators for WLAN Applications Maryam Shafiee, 1 Mohammad Amin Chaychi Zadeh, 2 and Homayoon Oraizi 2 1 Department of Electrical Engineering, Arizona State University, Tempe, AZ 85287, USA 2 Department of Electrical Engineering, Iran University of Science and Technology, Narmak, Tehran 16846 13114, Iran Correspondence should be addressed to Maryam Shafee; mshafei@asu.edu Received 23 November 2014; Revised 15 February 2015; Accepted 18 February 2015 Academic Editor: Giancarlo Bartolucci Copyright © 2015 Maryam Shafee et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Te objective of this paper is to design miniaturized narrow- and dual-band flters for WLAN application using zero order resonators by the method of least squares. Te miniaturization of the narrow-band flter is up to 70% and that of the dual-band flter is up to 64% compared to the available models in the literature. Two prototype models of the narrow-band and dual-band flters are fabricated and measured, which verify the proposed structure for the flter and its design by the presented method, using an equivalent circuit model. 1. Introduction Mobility of components and equipment is a requirement in mobile communication systems. Terefore, considerable efort has gone into the miniaturization of devices. Further- more, various techniques of multibanding have been devised for various functions. Particularly, diferent techniques have been proposed to make components dual-band, which are considered conventional methods, such as series connection of two separate band pass flters, step impedance resonators, and defected ground structures. All of these methods have some limitations on the reduction of device dimensions, because they are based on half-wave resonators [1, 2]. Recently, metamaterials have found wide applications, such as miniaturization of microwave devices, due to their unique properties and nonlinear dispersion curves. Zero order resonance (ZOR) metamaterials have the distinct property of infnite wavelength, which makes the resonance frequency independent of their dimensions. Consequently, the ZOR component may be fabricated as small as specifed to realize the desired circuit elements for the required resonance frequency [3]. Tis unique characteristic of ZORs has been used in microwave components, such as flters [4–6]. In this paper, we use the method of least mean square error (LMS) as a contribution to design and fabricate a narrow-band metamaterial flter and also a dual-band flter for application in WLAN systems. Te main advantage and feature of the proposed flters are their compactness and miniaturization, which is up to 70% smaller than conven- tional components in the literature [7]. 2. Design Procedure Te proposed zero order resonance (ZOR) cell is depicted in Figure 1. Te two interdigital capacitors provide the lef-handed capacitance and right-handed inductance. Te meander inductance and T-junction are inserted in the circuit to control and adjust the right-handed section of the device. Its equivalent circuit is shown in Figure 2. Te values of capacitors and inductors are extracted from the formulas in the literature [8–11]. Te error function is explicitly expressed as the function of geometrical dimensions of various sections of the flter. In other words, the lumped elements ( and ) of the equivalent circuit of the flter in Figure 2 are expressed in terms of the geometrical dimensions of the flter structure, which are given in literature. Te overall transmission matrix of the equivalent circuit is frst derived, which is then converted to the scattering parameters. Tus, the scattering parameters of equivalent circuit might be obtained by the available relations of the T-matrix in terms of its physical dimensions [12]. Hindawi Publishing Corporation International Journal of Microwave Science and Technology Volume 2015, Article ID 345326, 7 pages http://dx.doi.org/10.1155/2015/345326