High-pass Filters Implemented by Composite Right/Left Handed (CRLH) Transmission Lines Based on Complementary Split Rings Resonators (CSRRs)

Abstract

It was recently shown (1) that it is possible to achieve broadband composite right/left handed (CRLH) transmission lines by using complementary split rings resonators (CSRRs). Making use of balanced CRLH/CSRR-based metamaterial transmission lines, high pass fllters are designed. Good performance and small dimensions are achieved. The results open the door to new design possibilities in microwave circuitry by using this type of CRLH metamaterial transmission lines. DOI: 10.2529/PIERS060802072849 In microwave engineering, two main approaches exist to obtain left-handed transmission lines. One of them is the dual transmission line approach (2{4), which is based on loading transmission lines with series capacitances and shunt inductances. The other one is the resonant-type approach (5,6), which combines resonant sub-wavelength particles, such as split rings resonators (SRRs) or their dual counterparts (CSRRs), with shunt inductances or series capacitances etched on a host transmission line. Traditionally, it was supposed that the use of structures based on the resonant- type model was limited to narrow band applications. However, as occurs in the dual transmission line model, resonant-based left handed structures exhibit also a right-handed transmission band at higher frequencies due line parasitics (7). This allows us to obtain a composite right/left handed (CRLH) behaviour. The line can be tailored in order to collapse the typical frequency gap present between the left handed and right handed transmission bands. Namely, it is possible to make coin- cident the upper and the lower limits of the left and the right-handed bands, respectively (balance case), with the result of a continuous transition between both transmission bands. Although up to now it was not exploited, the balance case is also achievable by means of the resonant approach, what makes possible to obtain broad-band responses by using CRLH resonant-type transmission lines. The basic cell of the structure is represented in Fig. 1(a). It consists on a CSRR etched on the ground plane of a microstrip line, and located underneath a capacitive gap etched on the top layer (conductor strip). The CSRR provides the negative value of the dielectric permittivity in the vicinity of its resonance frequency, whereas the negative value of the magnetic permeability needed to obtain the left-handed behaviour is related to the efiect of the series capacitance due to the gap. This structure is modelled by the equivalent T-circuit model shown in Fig. 1(b) (8). The CSRR is modelled by the resonant tank LC-CC, which is electrically coupled to the line through the capacitance C. The capacitance Cg models the series gap, and L accounts for the line inductance. The right handed transmission band is due to line parasitics (L and C), but also to the CSRR (which behaves capacitively at high frequencies). The analysis of the equivalent circuit model reveals the behaviour of the structure. The phase shift per cell, `, (dispersion relation) and Bloch impedance, ZB, are given by: