Classical Transmission Line Research Articles

ELECTROMAGNETIC RADIATION FROM UNBALANCED TRANSMISSION LINES

Abstract—A theory for the electromagnetic radiation from unbalanced transmission lines is developed. It is shown that radiation results from the convection current that develops in unbalanced transmission lines where the resistances of the lines are unequal. The process that leads to the generation of the nonlinear convection current in unbalanced transmission lines is explained. It is proved that the classical transmission line theory is not valid for unbalanced lines. The convection current and the radiation forces are included in the transmission line equations to develop a generalized model valid for all two-conductor transmission lines. The generalized model is validated via comparisons of its numerical solutions with laboratory measurements.

Transmission Line Characteristics Based on Metamaterials Substrate

The novel transmission line based on metamaterials substrate was studied theoretically. The characteristic impedance and transmission wavelength of such transmission line are analytically calculated in framework of classical transmission-line theory. Moreover, the characteristic of similar micro-strip line were also studied with FEM simulation. Results showed that using metamaterials as a substrate, the characteristic impedance would be greatly increased, providing a new method to reduce the loss in the RF circuit. The transmission wavelength would be effectively extended at the same frequency. That was the electromagnetic radiation would greatly reduce in such RF circuit. Once the transmission wavelength was much larger than the size of the circuit board, the circuit theory could be adopted in RF design. Which would greatly reduce the difficulty of RF design.

Conducting properties of classical transmission lines with Ornstein–Uhlenbeck type disorder

In this work we study the behavior of bands of extended states and localized states which appear in classical disordered electrical transmission lines, when we use a ternary map and the Ornstein–Uhlenbeck process to generate the long-range correlated disorder, instead of using the Fourier filtering method. By performing finite-size scaling we obtain the asymptotic value of the map parameter b in the thermodynamic limit in a selected range of values of the parameters γ and C of the Ornstein–Uhlenbeck process. With these data we obtain the phase diagrams which separate the localized states from the extended states. These are the fundamental results of this article.

Conducting to non-conducting transition in dual transmission lines using a ternary model with long-range correlated disorder

In this work we study the behavior of the allowed and forbidden frequencies in disordered classical dual transmission lines when the values of capacitances { C j } are distributed according to a ternary model with long-range correlated disorder. We introduce the disorder from a random sequence with a power spectrum S ( k ) ∝ k − ( 2 α − 1 ) , where α ⩾ 0.5 is the correlation exponent. From this sequence we generate an asymmetric ternary map using two map parameters b 1 and b 2 , which adjust the occupancy probability of each possible value of the capacitances C j = { C A , C B , C C , } . If the sequence of capacitance values is totally at random α = 0.5 (white noise), the electrical transmission line is in the non-conducting state for every frequency ω. When we introduce long-range correlations in the distribution of capacitances, the electrical transmission lines can change their conducting properties and we can find a transition from the non-conducting to conducting state for a fixed system size. This implies the existence of critical values of the map parameters for each correlation exponent α. By performing finite-size scaling we obtain the asymptotic value of the map parameters in the thermodynamic limit for any α. With these data we obtain a phase diagram for the symmetric ternary model, which separates the non-conducting state from the conducting one. This is the fundamental result of this Letter. In addition, introducing one or more impurities in random places of the long-range correlated distribution of capacitances, we observe a dramatic change in the conducting properties of the electrical transmission lines, in such a way that the system jumps from conducting to non-conducting states. We think that this behavior can be considered as a possible mechanism to secure communication.

AN HYBRID MODEL FOR THE EVALUATION OF THE FULL-WAVE FAR-FIELD RADIATED EMISSION FROM PCB TRACES

The paper deals with the evaluation of the far-fleld radiated emissions from high-speed interconnects when the frequencies are such that the distribution of the currents along the traces is no longer of TEM-type. Instead of a computationally expensive numerical full-wave model, here a generalized transmission line model is used to obtain the current distributions. This full-wave transmission line model is derived from an integral formulation and is here extended to include in e-cient way the layered media Green's Functions. The proposed tool is successfully benchmarked to references given in literature and case-studies of practical interest are carried out, referring to a coupled microstrip, driven either by difierential and common mode currents. This analysis highlights the existence of a transition range where the error made by evaluating the emission using the classical transmission line current distribution is still negligible. Here a rule of thumb is derived which provides a simple criterion to estimate this extension of the range of validity of the classical transmission line.

Problem Solving in Electromagnetics, Microwave Circuit, and Antenna Design for Communications Engineering (Warnick, K. and Russer, P.; 2006) [Reviews and Abstracts

Students and researchers have always seen classical electromagnetic theory as a hard-to-digest concept. In this book, attempts have been made to explain the facts in an approachable manner. The contents of this book have been divided into two sections. The first half is the theoretical part, and the second half contains applications and numerical methods. Topics covered include: the fundamentals of differential calculus, a brief review of basic electromagnetics; potentials and wave concepts; the concepts, methods, and theorems about the distribution of electromagnetic energy through space; static and quasistatic fields; the analysis of various waveguides' classical transmission-line theory; resonant circuits and resonators; microwave circuits; periodic structures and filters; radiation from dipoles; antenna basics; and numerical methods used in solving electromagnetic problems.

A novel neural Smith chart for use in microwave circuitry

In this article, briefly the Smith chart is mapped with an artificial neural network (ANN) covering its whole details to be exploited CAD of the microwave circuitry. Thus, relative to the similar works in the existing literature, this article provides the continuous Smith chart domain to facilitate the “Smith chart” methodology in solving the highly nonlinear transformation equations between the rectangular impedance and polar reflection planes for an infinite number of passive impedance to be used in design tasks of the microwave circuits. Data ensembles for the training and testing processes are obtained from the systematically selected locations on the Smith chart with the adaptive radius sampling algorithm. The ANN architecture is also simple, which consists of the two simple multilayer perceptron (MLP) modules with the common inputs which are the termination ZS = RS + jXS, line {ℓ, Z0} operation bandwidth B between the defined fmin, fmax and the dielectric ε. Briefly, the outputs of these ANN modules are the standing waves and the impedance transformation, which are the characteristic features of the transmission line circuits. Activation of the hidden layers of the modules are performed by the tangential-sigmoid type of function while the output layers are activated linearly. Furthermore, the neural unit element (NUE) is defined by the two independent neural networks as problems in the forward and reverse directions to be incorporated into the analysis and design algorithms of the unit element (UE). This can also be considered as solving the simultaneous nonlinear equation set for (ℓ, Z0) parameters of the required impedance transformations ZOUT(ω) = ROUT (ω) + XOUT (ω) from the given complex termination ZS = RS + jXS. Applications of the Neural Smith chart are given by the numerous examples with the proved accuracy. Thus it has been verified that this neural Smith chart can be exploited for the whole classical transmission line theory including impedance matching. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009.

Performance Comparison Between Metallic Carbon Nanotube and Copper Nano-Interconnects

This paper addresses the problem of scaling interconnects to nanometric dimensions in future very-large-scale integration applications. Traditional copper interconnects are compared to innovative interconnects made by bundles of metallic carbon nanotubes. A new model is presented to describe the propagation of electric signals along carbon nanotube (CNT) bundles, in the framework of the classical transmission line theory. A possible implementation of a future scaled microstrip based on CNT bundle is analyzed and compared to a conventional microstrip.

Application of negative group delay active circuits to the design of broadband and constant phase shifters

AbstractThe new phase‐shifter configuration described in this report uses a negative group delay (NGD) active circuit. In this topology, a classical transmission line is set in cascade with an NGD circuit whose phase slopes are alike, but opposite, to get a constant and broadband phase shift. The proposed approach was validated through the design and measurement of a phase shifter, which exhibited a constant phase of 90° ± 5° over a 75% relative bandwidth around 1.6 GHz. Moreover, as the group delay of the NGD circuit compensated the transmission line one, the overall circuit group delay was kept to a small value in the operating frequency band. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 3078–3080, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23883

Modelling the electrical properties of concrete for shielding effectiveness prediction

Concrete is a porous, heterogeneous material whose abundant use in numerous applications demands a detailed understanding of its electrical properties. Besides experimental measurements, material theoretical models can be useful to investigate its behaviour with respect to frequency, moisture content or other factors. These models can be used in electromagnetic compatibility (EMC) to predict the shielding effectiveness of a concrete structure against external electromagnetic waves. This paper presents the development of a dispersive material model for concrete out of experimental measurement data to take account of the frequency dependence of concrete's electrical properties. The model is implemented into a numerical simulator and compared with the classical transmission-line approach in shielding effectiveness calculations of simple concrete walls of different moisture content. The comparative results show good agreement in all cases; a possible relation between shielding effectiveness and the electrical properties of concrete and the limits of the proposed model are discussed.

Accelerated Chip-Level Thermal Analysis Using Multilayer Green's Function

Continual scaling of transistors and interconnects has exacerbated the power and thermal management problems in the design of ultralarge-scale integrated (ULSI) circuits. This paper presents an efficient thermal-analysis method of O(NlgN) complexity, where N is the number of blocks that discretize the heat-source or temperature-observation regions. The method is named LOTAGre and formulated using the Green's function for heat conduction through multiple-layer materials, which account for the structure of ULSI chips and the accompanying heat sinks and mounting accessories. In addition to analyzing the thermal effects of the distributive heat sources, LOTAGre also considers the ambient temperature effects that are generally excluded in conventional Green's function-based thermal-analysis tools in order to avoid the concomitant analytical complexity. By employing the well-known eigen-expansion technique and classical transmission-line theory, fully analytical and explicit formulas are derived in this paper for the multilayer Green's function with the inclusion of the s-domain version, the homogeneous and inhomogeneous solutions to the heat-conduction equation. Then, the discrete cosine transform and its inversion are employed to accelerate the numerical computation of the homogeneous and inhomogeneous solutions. This paper includes extensive experimental results to demonstrate that LOTAGre can be as accurate as FLUENT, a sophisticated computational fluid dynamics tool, while speeding up the simulation run time by two to three orders of magnitude in comparison to FLUENT as well as conventional Green's function-based thermal-analysis methods. This paper also discusses the limitations of using the traditional single-layer thermal model in thermal analysis for approximating a multilayer chip structure

Determination of lightning currents from far electromagnetic fields: Effect of a strike object

We discuss in this paper the influence of the presence of an elevated strike object on the peak of the lightning return stroke current determined from remote field measurements. We develop analytical expressions relating the lightning return stroke channel-base current and the far electromagnetic field for different specific cases, namely, (1) ground-initiated return strokes (classical transmission line (TL) model), (2) ground-initiated return strokes including possible reflections at ground level, (3) tall strike objects for which the current's zero-to-peak time is smaller than the travel time along the object, and (4) electrically short strike objects. It is shown that for tall structures, the field enhancement relative to a return stroke initiated at ground level is expressed through a factor equal to k tall = [ 1 + c / v ( 1 - 2 ρ t ) ] / ( 1 - ρ t ) , where v and c are the return stroke front speed and the speed of light in vacuum, respectively, and ρ t is the top reflection coefficient. For very short towers and/or very slow return stroke current wavefronts, when the condition t f ⪢ h / c applies, expressions relating the far electromagnetic field and the return stroke current were also derived. For case (2), return strokes initiated at ground level, the field enhancement relative to a return stroke initiated at ground level, case (1), is expressed through a factor equal to k short = ( 1 + ( c / v ) ρ ch – g ) / ( 1 + ρ ch – g ) , where ρ ch–g represents the reflection coefficient between the lightning channel and the grounding impedance.

Far-Field–Current Relationship Based on the TL Model for Lightning Return Strokes to Elevated Strike Objects

New general expressions relating lightning return stroke currents and far radiated electric and magnetic fields are proposed, taking into account the effect of an elevated strike object, whose presence is included as an extension to the transmission line (TL) model. Specific equations are derived for the case of tall and electrically short objects. The derived expressions show that, for tall structures (when the round-trip propagation time from top to bottom within the tower is greater than the current zero-to-peak risetime), the far field is enhanced through a factor with respect to an ideal return stroke initiated at ground level. The enhancement factor can be expressed in terms of the return stroke wavefront speed v, the speed of light in vacuum c, and the current reflection coefficient at the top of the elevated strike object. For typically negative values of this top reflection coefficient, lightning strikes to tall towers result in a significant enhancement of the far electromagnetic field. Expressions relating the far electromagnetic field and the return stroke current are also presented for electrically short towers and for very long return stroke current wavefronts. For the case of return strokes initiated at ground level (h=0), these expressions represent a generalization of the classical TL model, in which the reflections at the ground are now taken into account. We describe also simultaneous measurements of return stroke current and its associated electric and magnetic fields at two distances related with lightning strikes to the 553-m-high Toronto Canadian National (CN) Tower performed during 2000 and 2001. The derived expressions for tall strike objects are tested versus obtained sets of simultaneously measured currents and fields associated with lightning strikes to the CN Tower, and a reasonable agreement is found. Additionally, it is shown that the peak of the electromagnetic field radiated by a lightning strike to a 553-m-high structure is relatively insensitive to the value of the return stroke velocity, in contrast to the lightning strikes to ground.

A full‐Maxwell algorithm for the field‐to‐multiconductor line‐coupling problem

A general method to study the response of a system of multiconductors, lying above a perfectly conducting ground and excited by a HF electromagnetic field wave, is presented in this paper. The governing system of integro‐differential equations is solved by means of a numerical procedure based on a Fourier series transformation. It can be proved that the series in which the unknowns of the problem, namely the currents along the conductors, are developed converge to the exact solution and only few terms are needed. The obtained results have been compared with those of a widely employed scattering code, showing faster performances for a given accuracy. Therefore, the algorithm can be seen as a more accurate alternative to the classical transmission line theory (TL) for all the situations (short transmission line, interconnects, etc.) in which the line geometrical parameters and the frequencies of interest make TL a rough approximation.

Generalized transmission-line theory for the treatment of nonuniform multiconductor transmission lines

This paper presents a generalized transmission-line theory which is useful to describe the wave propagation along almost arbitrary three-dimensional wire structures. In contrast to the classical transmission-line theory this new approach is an approximate full-wave description based on generalized telegrapher's equations. Whereas the mathematical structure of the classical telegrapher's equations is preserved, the coefficients (the per-unit-length parameters) are generalized in order to represent the intrinsic behavior of the wire structure. MoM simulations were performed to validate the predicted data.

A physical method to analyse scattered waves from burnt coal seam and its application to estimate thickness of fire scars in central Borneo using L-Band SAR data

A physical method was conducted to analyse scattered waves from burnt coal seam in order to estimate the thickness of fire scars. The model was composed of three media namely; air, burnt coal seam and peat. For computation purposes, the equivalent circuit of this model was conducted using a classical transmission line circuit method. The relationship between backscattering coefficient and thickness of burnt coal seam was defined in terms of the logarithm of the reflection coefficient (in power). The analysis result was confirmed by simulation using a Finite Difference Time Domain (FDTD) method. The simulation was performed using a two-dimensional (2-D) finite-difference model for scattered waves from a burnt coal seam. The model used the equations of scattered electromagnetic fields that were derived from Maxwell's equations. A Mur method was used to surround the simulation space and absorb the outward travelling waves. Analysis and simulation results were similar. Subsequently, the model was applied to estimate the thickness of burnt coal seam in central Borneo fire events, that occurred in 1997, using a Japanese Earth Resources Satellite (JERS-1) SAR data. Results showed that fire scars in the study area reached 0.52 m in depth (thickness). This agrees with ground measurements.

Discrete-time modeling of woodwind instrument bores using wave variables.

A method for simulation of acoustical bores, useful in the context of sound synthesis by physical modeling of woodwind instruments, is presented. As with previously developed methods, such as digital waveguide modeling (DWM) [Smith, Comput. Music J. 16, 74-91 (1992)] and the multi convolution algorithm (MCA) [Martinez et al., J. Acoust. Soc. Am. 84, 1620-1627 (1988)], the approach is based on a one-dimensional model of wave propagation in the bore. Both the DWM method and the MCA explicitly compute the transmission and reflection of wave variables that represent actual traveling pressure waves. The method presented in this report, the wave digital modeling (WDM) method, avoids the typical limitations associated with these methods by using a more general definition of the wave variables. An efficient and spatially modular discrete-time model is constructed from the digital representations of elemental bore units such as cylindrical sections, conical sections, and toneholes. Frequency-dependent phenomena, such as boundary losses, are approximated with digital filters. The stability of a simulation of a complete acoustic bore is investigated empirically. Results of the simulation of a full clarinet show that a very good concordance with classic transmission-line theory is obtained.

An equivalent transmission-line model containing dispersion for high-speed digital lines-with an FDTD implementation

The increase in processor speeds in the last few years has created a growing need for the accurate characterization of waveform propagation on lossy printed-circuit-board (PCB) transmission lines. Due to the dispersive nature of pulse propagation on lossy transmission lines, approximations of the classic transmission-line model can fail in this application (i.e., lossless or DC losses approximations). This paper shows how an equivalent transmission-line model can be used to analyze dispersive transmission lines for high-speed digital applications. The equivalent-circuit elements of this transmission-line model incorporate the frequency dependence of the per unit length impedance and admittance caused by the finite conductivity of the conductors as well as the dielectric losses. We show that these equivalent circuit elements can be readily implemented into finite-difference time-domain (FDTD) transmission-line codes, and we present such a FDTD implementation. S-parameters and pulsed waveforms for a circular wire, coplanar waveguides (CPW) and microstrip lines are shown. Finally, we present approximate expressions for analytically obtaining the resistance and inductance per length of a microstrip line.

An identification procedure for lightning return strokes

In this paper an inverse procedure for the identification and the reconstruction of the waveform of the lightning return stroke current is presented. It is based on the acquisition of the vertical component of the electric field radiated by the discharge channel at different locations on the ground and it does not require any information about the channel base current. The approach has been validated by means of the numerical simulation of the classical Transmission Line, Modified Transmission Line Linear and Modified Transmission Line Exponential engineering models, showing good accuracy in all cases.

Net and partial inductance of a microstrip ground plane

A knowledge of the net inductance of the ground plane can aid in the analysis and investigation of printed circuit board emissions. In this paper, we present a method, based on the concept of partial inductance, to determine the net inductance of the ground plane associated with a microstrip line. This method is based on a previously derived expression for the current density on the ground plane. We show calculations for the net, self-partial, and mutual-partial inductance of the ground plane for various trace geometries of practical interest. We also illustrate how the classical transmission line inductance of a microstrip line can be obtained from the concept of partial inductance. Comparisons to different experimental results are also given.