Inhomogeneous Transmission Lines Research Articles

An efficient modeling approach of 1D-planar metamaterials in the high-frequency regime

PurposeThe purpose of this paper is to present an alternative modeling approach in terms of the determination of a physically equivalent circuit model for one-dimensional (1D) planar metamaterials in the high-frequency regime, without a postprocessing optimization procedure. Thereby, an efficient implementation of physical relationships is aimed.Design/methodology/approachIn this paper, a method based on quasi-stationary simulations and mathematical conversions to derive the values for a physically equivalent circuit model is proposed. Because the electromagnetic coupling mechanisms are investigated in detail, a simplification for the considered multiconductor transmission line structure is achieved.FindingsThe results show that the proposed modeling approach is an efficient and physically meaningful alternative to classical full-wave simulation techniques for the investigated inhomogeneous transmission line structure in both the time domain as well as in the frequency domain. In the course of this, the effort is reduced while a comparable accuracy is maintained, whereby specific coupling mechanisms are considered in circuit simulations.Originality/valueThe process to obtain information about physically interpretable lumped element values for a given structure or to determine a layout for known ones is simplified with the aid of the proposed approach. An advantageous adaption of the presented procedure to other areas of application is well conceivable.

Calculation of Transmission Characteristics of Shielded Microstrip Lines Filled with Anisotropic Left-Handed and Right-Handed Materials

In this paper, the edge-based finite element formula for calculating the transmission characteristics of shielded microstrip lines filled with anisotropic materials with magnetic field as working variable is derived in detail. The filling materials include anisotropic left-handed materials and anisotropic right-handed materials, and the transmission characteristics include dominant mode cutoff wavelength and electric field structure. We mainly take Rectangular-shaped, V-shaped and Trapezoidal-shaped shielded microstrip lines as examples to calculate the transmission characteristics. The formulas and calculation examples derived in this paper have strong guiding significance for the application of anisotropic left-handed and right-handed materials in inhomogeneous transmission lines, which will further expand the use of shielded microstrip lines in optical devices such as electro-optic waveguide modulators.

A Closed Time-Reversal Cavity for Electromagnetic Waves in Transmission Line Networks

A closed time-reversal (TR) cavity has been considered a purely theoretical concept whose experimental realization was assumed to be impossible. In this article, we demonstrate that it is, in fact, possible to realize a closed TR cavity using a network of transmission lines. The network is excited by either lumped voltage or current sources at arbitrary locations, and it is terminated on matched impedances. This system is an exact closed TR cavity in the sense that, in the backward-propagation stage, by back-injecting time-reversed measured responses (voltage or current) generated by a source at each line terminal, a time-reversed copy of the current and voltage distribution in the forward-propagation stage is obtained. We report for the first time an experimental realization of a TR cavity formed by a network of inhomogeneous transmission lines, in which the spatial and temporal signal distribution along the network is reproduced as in a sequence of the system state (i.e., voltages and or current along the lines) being played in reverse. We also discuss the interfering effect of the so-called diverging wave for observation points in the vicinity of the source. An active realization of a TR sink is proposed to effectively overcome the interfering effect caused by the diverging waves.

Understanding interfacial impedance growth in porous electrodes containing blended active materials

Active material blended electrodes, comprised of physical mixtures of two or more lithium insertion compounds, can have superior balanced performance compared to electrodes with an individual active compound. Due to their high complexity, a good understanding of blended electrodes is still lacking, including their electrolyte/electrode interfacial kinetics, which is a key factor for determining battery service life, safety, and power performance. In this paper, a comprehensive study of the interfacial impedance in Si-alloy/graphite blended electrodes is presented through experiment and theory. Experiments were conducted by the characterization of symmetric cells by electrochemical impedance spectroscopy. An inhomogeneous transmission line model (ITLM) was developed to investigate this binary system on a large scale. Both experimental and theoretical results show that adding a small proportion of low interfacial impedance particles can suppress interfacial impedance growth in blended electrodes.

Signal Propagation Through Piecewise Transmission Lines for Interpretation of Reflectometry in Photovoltaic Systems

We present a framework for analyzing electromagnetic signal propagation through piecewise-defined transmission lines with arbitrary, series-connected impedances. While the formulation is general and scalable, we apply it here to propagation through a photovoltaic module with cables on either side acting, with a home run cable, as a section of an inhomogeneous transmission line. Understanding propagation through this unit of a series-connected string of photovoltaic modules is necessary to enable the use of time-domain reflectometry techniques for monitoring the status of individual components in series-connected strings within large photovoltaic arrays.

A multi-scale approach to describe electrical impulses propagating along actin filaments in both intracellular and in vitro conditions.

An accurate and efficient characterization of the polyelectrolyte properties for cytoskeleton filaments are key to the molecular understanding of electrical signal propagation, bundle and network formation, as well as their potential nanotechnological applications. In this article, we introduce an innovative multi-scale approach able to account for the atomistic details of a protein molecular structure, its biological environment, and their impact on electrical impulses propagating along wild type actin filaments. The formulation includes non-trivial contributions to the ionic electrical conductivity and capacitance coming from the diffuse part of the electrical double layer of G-actins. We utilize this monomer characterization in a non-linear inhomogeneous transmission line prototype model to account for the monomer–monomer interactions, dissipation and damping perturbations along the filament length. A novel, simple, accurate, approximate analytic expression has been obtained for the transmission line model. Our results reveal the propagation of electrical signal impulses in the form of solitons for the range of voltage stimulus and electrolyte solutions typically present for intracellular and in vitro conditions. The approach predicts a lower electrical conductivity with higher linear capacitance and non-linear accumulation of charge for intracellular conditions. Our results show a significant influence of the voltage input on the electrical impulse shape, attenuation and kern propagation velocity. The filament is able to sustain the soliton propagation at almost constant kern velocity for the in vitro condition, whereas the intracellular condition displays a remarkable deceleration. Additionally, the solitons are narrower and travel faster at higher voltage input. As a unique feature, this multi-scale theory is able to account for molecular structure conformation (mutation) and biological environment (protonations/deprotonations) changes often present in pathological conditions. It is also applicable to other highly charged rod-like polyelectrolytes with relevance in biomedicine and biophysics.

An Alternative Method for Locating Faults in Transmission Line Networks Based on Time Reversal

We present an alternative method based on the time-reversal process to locate faults in transmission line networks. The proposed procedure considers different media for the forward and the backward propagation phases. Specifically, the transverse branch representing the fault is removed from the circuit in the backward propagation since its location represents the solution of the process and, therefore, is not known in advance. The advantage of the proposed method is twofold. First, the proposed backward model requires only one simulation for the time-reversed backward propagation phase, thus reducing significantly the computational burden. Second, we demonstrate that this modified backward propagation medium satisfies a property such that the fault location can be identified by computing, in the frequency domain, the argument of the voltage along the line. The theory is first formulated for the case of a lossless homogeneous single-phase transmission line; then, its applicability is extended to lossy inhomogeneous transmission line networks. A single-phase inhomogeneous transmission line and an inhomogeneous Y-shape network are specifically considered to support this claim. We show that the proposed procedure can provide high fault location accuracy (i.e., in the range of $\pm 1$ m), using only one observation point. Furthermore, we propose a criterion to link the bandwidth of the sampling system to the desired fault location accuracy.

Networks of high frequency inhomogeneous transmission lines

Abstract. It is well known from classical transmission line theory, that transmission lines can be folded into impedances and thereby used in an electrical network setting. But it is also possible to create large networks of transmission lines consisting of tubes and junctions. The tubes contain the transmission lines and the junctions consider the mutual influences of the adjacent tubes or the terminals. The calculation of the currents and voltages at the junctions can be performed with the help the BLT-equation. So far this method is not applicable for nonuniform transmission lines described in a full wave method, because the lack of a distinct voltage gives no possibility for junctions. Junctions only make sense, when the considered network offers the possibility to propagate a TEM-Mode. If this requirement is fullfilled, nonuniform transmission lines could be included in an electrical network. This approach is validated in this paper in form of numerical simulations as well as measurements.

Tunable wavelength dependent nanoswitches enabled by simple plasmonic core-shell particles

In this paper we demonstrate the feasibility of using a plasmonic core-shell particle to function as a wavelength dependent switch for integration into nanoantenna structures. First, a quasistatic analysis is performed and the necessary conditions are derived which allow the particle to operate in either a short- or an open-circuit state. These conditions dictate that the core and the shell permittivity values need to have opposite sign. Consequently, at optical wavelengths where noble metals are modeled as Drude dielectrics, these conditions can be easily realized. As a matter of fact, it is demonstrated that a realistic core-shell particle can exhibit both the short- and open-circuit states, albeit at different wavelengths. Our analysis is extended by examining the same problem beyond the quasistatic limit. For this task we utilize an inhomogeneous spherical transmission line representation of the core-shell particle. The conditions are derived for the particle that yield either an input admittance or impedance equal to zero. It is further demonstrated that these conditions are the short wavelength generalization of their quasistatic counterparts.

On the Feasibility of Pressure Profile Measurements With Time-Domain Reflectometry

Many applications in geotechnical engineering require knowledge of total pressure distributions. So far, only measurements at single points at individual locations of interest can be carried out with conventional geotechnical measurement devices. Time-domain reflectometry (TDR) has already been used to assess the amount of shearing at multiple distinct locations along coaxial cables grouted in a rock or soil mass. However, pressure profile determination has not been investigated up to now. A novel approach has been investigated to determine pressure profiles from the time-domain reflection data of transmission lines. Mechanical forces change the distance between rubber-insulated conductors of transmission lines and, therefore, affect the spatial distribution of capacitance and inductance. These variations lead to partial reflections of an incident step pulse from which physical parameter distributions along the inhomogeneous transmission line are reconstructed. A reconstruction algorithm that was originally developed for soil moisture profile determination (Spatial-TDR), was adopted and applied in laboratory experiments. A further experiment illustrates TDR signals that can be expected in actual applications under different load conditions.

Time-Domain Analysis of a Lossy Nonuniform Transmission Line

An analytical solution of the coupled Telegrapher's equations for the voltage and current on a homogeneous lossy transmission line is presented. The resulting expression is obtained in the form of an exact time-domain propagator operating on the line voltage and current. It is shown that an application of Simpson's rule yields a simple accurate numerical representation of the propagator that can be used to analyze both homogeneous and inhomogeneous transmission lines. Numerical dispersion in lossy media is examined proving that this method has no numerical dispersion.

Computation of the Capacitance of the Inhomogeneous Insulated Transmission Line

A boundary element method (BEM) procedure to obtain the capacitance of inhomogeneous insulated transmission lines is presented. The geometry consists of multiple, parallel and insulated conductor cylinders. The BEM matrix equation associated with piecewise homogeneous insulated transmission line is derived. Two representative computational examples, eccentric coaxial cable partially filled with dielectric and transmission line consisting of two parallel dielectric-coated cylinders, are given to validate the accuracy and efficiency of the BEM.

Traceable Correction Method for Complex Reflection Coefficient Using Calculable Air Line Impedance Standards

A correction method for the measurement of complex reflection coefficients using vector network analyzers is presented. The method is based on the invariance property of the cross ratio of the bilinear transformation and is traceable to calculable air line impedance standards. The application of an accurate diameter measurement system (laser micrometer and air gauge system) allows the treatment of air lines as inhomogeneous transmission lines consisting of a cascade connection of a number of equally spaced line sections. Each line section is assumed to be homogeneous and characterized by the characteristic impedance and the propagation constant, which are traceable to the measured diameter values. The presented procedure is an extension and improvement of prior work using the same principle of correction, whereas the air lines were specified by nominal diameter and length values. The aim of this work is to enhance the accuracy of the correction or to reduce the requirements of the manufacturing tolerances of air lines. The derived theory is accompanied by a brief uncertainty consideration and by measurement results obtained by PC-7 air lines at frequencies up to 18 GHz and by numerical simulation results for a hypothetical air line.

Perturbation theory for inhomogeneous transmission lines

We present a novel technique to calculate the transmission and reflection properties of inhomogeneous lossy transmission lines. It is based on a perturbation expansion of the relevant telegrapher's equation around the homogeneous solution. The method reveals that the transmission properties are unaffected to first order in the impedance and admittance, while reflection properties are modified by first-order terms. Extending the analysis to second order, we find correction terms for both transmission and reflection. These allow us to understand the statistical properties of the information bearing capacity and the echo of the inhomogeneous transmission line. The correction to the transmission properties is fully reciprocal, despite the absence of any symmetry properties. We compute scaling laws for echo and capacity.

Investigation of the longitudinal multiconductor transmission line functions for symmetric coupled-microstrip systems

In inhomogeneous multiconductor transmission line (MTL) structures such as coupled microstrip, propagation is characterized by multiple quasi-TEM modes with distinct propagation constants. These "mode delays" cause the MTL functions to exhibit longitudinal behavior that superficially appears problematic in the context of passive lossless reciprocal systems. This paper presents a thorough investigation of the longitudinal MTL functions. Using MTL formulation and computer simulation, we explain the mathematics and physics of mode delays so that their effects are not misinterpreted or attributed to error in the numerical analysis of MTLs.

Impedance matrix representation for exponentially nonuniform transmission lines

This paper deals with the solution of nonhomogeneous transmission line (NUTL) equations in terms of hypergeometric functions. Formal expressions in a closed analytical form for the voltage and the current inside the inhomogeneous transmission line are found and presented. The behavior of the input impedance for an exponentially tapered nonuniform transmission line (ETNUTL) is studied for different values of the tapering factor. Finally, an equivalent two-port circuit representation for the ETNUTL by an impedance matrix, whose elements are dependent on the tapering factor, is derived. © 1998 John Wiley & Sons, Inc. Microwave Opt Technol Lett 18: 300–302, 1998.

Theory of double-chirped mirrors

A theory of double-chirped mirrors (DCMs) for dispersion compensation in ultrashort pulse laser sources is presented. We describe the multilayer interference coating by exact coupled-mode equations. They show that the analysis and synthesis of a coating with a slowly varying chirp in the layer thicknesses can be mapped onto a weakly inhomogeneous transmission line problem. Solutions of the transmission line equations are given using the WKB-method. Analytic expressions for reflectivity and group delay are derived. The solutions show that the main problem in chirped mirror design is the avoidance of spurious reflections, that lead to Gires-Tournois-like interference effects responsible for the oscillations in the group delay. These oscillations are due to an impedance matching problem of the equivalent transmission line. The impedance matching can be achieved by simultaneously chirping the strength of the coupling coefficient and the Bragg wavenumber of the mirror. An adiabatic increase in the coupling coefficient removes the typical oscillations in the group delay and results in broad-band mirrors with a controlled dispersion. Finally, the mirror is matched to air with a broadband antireflection coating. We discuss a complete design of a laser mirror with a reflectivity larger than 99.8% and a controlled dispersion over 300-nm bandwidth. Using such mirrors in a Ti:sapphire laser, we have demonstrated /spl ap/30-fs pulses, tunable over 300 nm, as well as 8-fs pulses from the same setup. A different design resulted in 6.5-fs pulses.

A differential method of reflection coefficient extraction from FDTD simulations

A novel concept for accurate extraction of the reflection coefficient from electromagnetic simulations is proposed and implemented into the finite-difference time-domain (FDTD) method. It uses only the values of an arbitrary tangential E-field component and its derivative with respect to the longitudinal direction at one selected point, and of an arbitrary tangential H-field component and its derivative with respect to the longitudinal direction at another point. No a priori knowledge of reference impedances is needed, and the reflection coefficient is extracted from a single run of FDTD. The proposed method is directly applicable to arbitrarily shaped and inhomogeneous transmission lines.

A novel method to study the electrodynamic behavior of actin filaments. Evidence for cable-like properties of actin

Actin, one of the most abundant intracellular proteins, forms long linear polyelectrolytic polymers in solution. A novel technique to handle single actin filaments in solution was developed that allows the study of ionic currents elicited along the surface of electrically stimulated actin filaments. Electrical currents were observed about the polymer's surface under both high (100 mM KCl) and low (1 mM KCl) ionic strength conditions. The data are consistent with a dynamic behavior of the counterionic cloud surrounding the actin filaments that support ionic movements along their longitudinal axis upon electrical stimulation. Counterionic waves were highly nonlinear in nature and remained long after the electrical stimulation of the actin filaments ceased. In this report therefore, we demonstrate that actin filaments can function as biological "electrical wires" and can thus be conceptualized as nonlinear inhomogeneous transmission lines. This ability of actin filaments to conduct electrical signals may have important implications in the coupling of intracellular signals.

Solid state specific effects in the ac response of RbAg 4I 5/graphite cells

Two regions observed in the impedance of C/RbAg 4I 5/C cells may be represented by constant phase elements. In pressed samples with thick mixed electrodes at low frequencies (<0.1 Hz) the conductance approximately proportional to frequency may be interpreted as an interaction of mobile charge carriers with the crystal lattice. In single crystals at higher frequencies a similar dependence of the conductance evidently results from surface degradation. Its effect is modelled as an inhomogeneous transmission line. Both effects are possible probably in the solid state only and they represent effects not considered or frequently neglected in standard space charge and electrode polarization theories.