Dual Transmission Line Research Articles

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

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:

Mesoscopic Dual Transmission Line with Electric Charge Discreteness

Considering the potential applications in the artificial composite materials, the mesoscopic dual transmission line model with the discreteness of electric charge is studied. The transmission property affected by the discreteness of electric charge is investigated in the dynamic formulation. In view of the realistic case, the dissipation is inevitable. The effect of resistance is added through employing the canonical transformation. The geometry phase of transverse problem in the transmission line system is also investigated.

Practical limitations of subwavelength resolution using negative-refractive-index transmission-line lenses

Previously, we have demonstrated both analytically and experimentally subwavelength imaging using a negative-refractive-index lens made of a periodically L, C loaded transmission line (TL) network. This loaded transmission line network has been referred to as the dual TL lens. Here, we consider the limitations on subwavelength imaging imposed by impedance mismatches and the component losses of a practical dual TL lens. Simple expressions for estimating the resolving capability of a dual TL lens are given. It is found that the resolution enhancement of the dual lens is proportional to the quality factor of the series loading capacitors divided by the electrical thickness of the lens. The effective material parameters of the dual TL lens are also derived so that these expressions can be directly related to those of previous studies considering uniform and isotropic left-handed lenses. Finally, the resolving capability of an experimental lens that achieves subwavelength imaging is theoretically predicted. These theoretical predictions are then directly compared to previously reported experimental results.

An isotropic three-dimensional negative-refractive-index transmission-line metamaterial

We propose an isotropic three-dimensional (3D) negative-refractive-index medium using transmission lines loaded with reactive elements. The medium is referred to as the 3D dual transmission line (TL). Analytical expressions are derived which provide insight into the backward-wave propagation supported by the proposed medium. The dispersion characteristics of a physically realizable 3D dual TL are computed using a full-wave eigenmode solution of Maxwell’s equations based on the finite-element method. In addition, scattering parameters for a slab made of the 3D dual TL are presented. The described approach can be generalized for synthesizing a wide range of 3D metamaterials with tailored material parameters including both isotropic and anisotropic designs.

Electrochemical impedance spectroscopy of an oxidized poly(3,4-ethylenedioxythiophene) in propylene carbonate solutions

The electrochemical impedance spectroscopy of oxidized poly(3,4-ethylenedioxythiophene) (PEDOT) electrodeposited on a platinum electrode surface was studied in LiClO 4+propylene carbonate solutions. The effects of the electrolyte concentration, the applied potential, and the film thickness were studied. The impedance responses were analyzed within a dual transmission line model. Results showed that the ionic conductivity of the p-doped PEDOT film was controlled by the electrolyte solution in pores, and the interfacial impedance resulted from the double-layer capacitance. A linear variation of the redox pseudo-capacitance and the ionic film resistance as a function of the film thickness was observed. These results showed the porous nature of the PEDOT film deposited on the electrode surface.

Dispersion analysis of a microstrip-based negative refractive index periodic structure

We present the complete band structure of a negative refractive index metamaterial based on the concept of dual transmission lines. The metamaterial is a two-dimensional (2-D) microstrip periodic structure that has cell dimensions much smaller than the wavelength of operation. It can therefore be considered as an effective medium. First, the dispersion characteristics of the metamaterial are explained by way of a 2-D loaded transmission line representation. Subsequently, full-wave analysis is utilized to reveal additional modes that can be excited in the metamaterial.

Growing evanescent waves in negative-refractive-index transmission-line media

We show the enhancement of evanescent waves by a realizable negative-refractive-index (NRI) medium consisting of a periodic 2-D L,C loaded transmission-line (TL) network. This network is referred to as a dual TL structure. Growing evanescent waves within the dual TL structure are predicted analytically and demonstrated through simulation. These findings confirm that the dual TL structure is not simply a phase compensator that corrects the phase of propagating waves, but is in fact a NRI medium, since it also enhances the amplitudes of evanescent waves. This structure is a likely candidate for microwave subwavelength focusing and imaging applications.

Compact linear lead/lag metamaterial phase shifters for broadband applications

A compact one-dimensional phase shifter is proposed using alternating sections of negative refractive index (NRI) metamaterials and printed transmission lines (TL). The NRI metamaterial sections consist of lumped element capacitors and inductors, arranged in a dual TL (high-pass) configuration. By adjusting the NRI-medium lumped element values, the phase shift can be tailored to a given specification. Periodic analysis is applied to the structure and design equations are presented for the determination of the lumped element parameters for any arbitrary phase shift. To validate the design, various phase shifters are simulated and tested in coplanar waveguide (CPW) technology. It is demonstrated that small variations in the NRI-medium lumped element values can produce positive, negative or 0/spl deg/ phase shifts while maintaining the same short overall length. Thus, the new phase shifter offers some significant advantages over conventional delay lines: it is more compact in size, it exhibits a linear phase response around the design frequency, it can incur a phase lead or lag which is independent of the length of the structure and it exhibits shorter group delays.

Electromagnetic modes in conical transmission lines with application to the linearly tapered slot antenna

A transmission line analysis of the bow-tie antenna and the linearly tapered slot antenna (LTSA) is presented. These structures belong to the class of conical transmission lines defined here in terms of conical coordinates. A complete set of solutions of the Helmholtz equation is obtained exhibiting TE and TM modes. Modal fields are expressed by Lame (1837) and Bessel-Schelkunoff functions. TE and TM eigenmode analysis is particularized to the bow-tie structure. Bow-tie antenna and LTSA are shown to be dual conical transmission lines by the image method and Babinet's principle. The modes of LTSA are calculated on the basis of the results obtained for the bow-tie structure. The radiation pattern of the LTSA is computed as the integral of a closed-form expression of the dyadic Green's function weighted by the modal electric field distribution over the slot aperture. The obtained dominant mode radiation patterns are validated by measurements from the literature. The radiation patterns of the first two-order modes are calculated and compared.

General edge element approach to lossy and dispersive structures in anisotropic media

A new functional for general anisotropic 2½D guided-wave structures is derived, based on a rigorous 3D analysis. An impedance boundary condition at the interface between the anisotropic material and the imperfect conducting ground plane is proposed. The computation domain includes the cross-section of the lossy conducting line where the size of the cross-section has the same order as the skin depth, and the standard impedance boundary condition is no longer held. The vector element analysis procedure, and the subspace iteration method, are then used to find the partial or total system modes. Numerical examples of anisotropic dielectric image waveguide, PFEE bilateral fin line, and two coupled asymmetrical dual lossy transmission lines with finite conductivity and finite thickness are presented. Good agreement with previous publications is observed.

Dual transmission line with charge-transfer resistance for conducting polymers

To describe charge conduction in conducting polymers a dual transmission line with one resistance describing electronic motion in the polymer and a second resistance describing ionic motion in the pores has proved applicable to a number of systems. A further feature of ac impedance plots for these polymers is a high-frequency semicircle. This may be attributed to a charge-transfer resistance and double-layer capacitance at either the electrode/polymer or the polymer/electrolyte interface. A general expression for such a charge-transfer resistance is derived and it is shown that the current will be proportional to the difference in Nernst potential across such a resistance. This circuit element together with a double-layer capacity is then combined with the dual transmission line. A general expression for the ac impedance for the combined circuit is obtained. Care has to be taken to use the right potentials, Nernst, Donnan or the actual potential. Depending on the relative resistances in the transmission line different types of behaviour can be found. In particular the variation of the real part of the impedance at high frequency can be used to determine whether the charge-transfer resistance is at the electrode or at the electrolyte interface. The procedure is exemplified with results from polypyrrole.

Coupling of ion and electron transport during impedance measurements on a conducting polymer with similar ionic and electronic conductivities

The ionic and electronic conductivities of poly-[1-methyl-3-(pyrrol-1-ylmethyl)pyridinium perchlorate] have been measured as a function of potential in various solvents by impedance spectroscopy. The ionic conductivity of this polymer shows a strong solvent dependence, ranging from 0.31 mS cm–1 in water to 8.0 µS cm–1 in propylene carbonate. By changing the solvent and the potential, the ionic to electronic conductivity ratio for the polymer has been varied from 1 to 1, allowing a thorough exploration of the validity of a dual resistance transmission line model of the polymer. Overall, the experimental results support the model, and reasonably accurate electronic and ionic conductivities are obtained when data are analysed according to the model. However, an anomalous dependence of ionic conductivity on oxidation state has been observed. There appears to be a direct relationship between the electronic and ionic conductivities of the polymer when they are of similar magnitude, indicating a coupling of ion and electron transport.

An Equivalence Principle for Nonuniform Transmission-Line Directional Couplers

The analysis of transmission-line directional couplers is formulated in terms of a pair of first-order matrix differential equations. It is shown that for every nonuniform directional coupler that is electrically symmetric, there exists an equivalent pair of dual nonuniform transmission lines. It is also shown that a matched, transmission-line directional coupler having an absolutely continuous characteristic impedance matrix must be symmetric. Restrictions on the terminating impedances and the implications of these restrictions on the realizability of transmission-line couplers are investigated. Finally, the tapered-line magic T is treated as an example.