Classical Transmission Line Theory Research Articles

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.

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.

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

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.

High frequency performance of GE high density interconnect modules

The layout and routing of high-frequency multichip modules (MCMs) require a detailed electromagnetic characterization of the interconnect structure in order to manage required design trade-offs intelligently. To provide this characterization for the GE high-density-interconnect (HDI) process, a number of test coupons containing a variety of transmission line structures were prepared. S-parameter data were measured using a vector network analyzer (VNA), and these measured data were compared to the theoretical predictions based upon classical transmission line theory. Reasonable agreement is obtained provided that skin and proximity effects in the lines and ground planes are taken into account and that the nonrectangular natures of the conductor cross sections are accurately modeled. Results suggest that insertion loss rather than crosstalk is likely to be limiting for frequencies up to 9 GHz. For 20% (2-dB) attenuation, line lengths are 3-12 cm for the frequency range of 1-9 GHz.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Skin-effect considerations on transient response of a transmission line excited by an electromagnetic pulse

The electromagnetic pulse can cause degradation of modern digital and analog devices. Many analytical models have been used extensively to study the susceptibility of equipment related to EMI/EMC (electromagnetic interference/electromagnetic compatibility) engineering, but the emphasis has been mainly on lossless transmission lines. This work takes into account the transient skin-effect of a transmission line exposed to a time-varying electromagnetic field. Beginning with the classical transmission line theory, the transient skin-effect of a transmission line and the equivalent sources due to the external fields are incorporated. As a result, an integral-differential equation is derived. By using the finite-difference-time-domain (FD-TD) approach, the induced voltages onto the line are predicted. There is also a discussion of the numerical approach and the propagation of the predicted induced voltage.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Tutorial note on the general transmission line theory for a thin wire above the ground

Transmission along an overhead wire or cable conductor is considered. It is shown that the rigorous solution of the problem can be put in the context of classical transmission line theory that has been used by power engineers for many years. However, the effective line parameters are spatially dispersive in the sense that they depend on the actual propagation constant of the mode in question.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An insulated dipole applicator for intracavitary hyperthermia.

Specific absorption rate (SAR) patterns for an insulated sleeve dipole applicator, operating at 433 MHz, were measured by infrared thermography. The applicator was modeled using classical transmission-line theory, and experimental and theoretical results were compared. In general, agreement between measured and calculated SAR values was good. However, at the antenna feedpoint, the measured values were appreciably higher than the calculated values. This indicates that inclusion of junction effects would improve the model.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Multiport network analysis by matrix renormalisation: extension to four ports

Two- and three-port network analysis by scattering renormalisation, the principle of which was described in earlier papers, is extended to the 4-port case by derivation of the 4-port renormalisation transforms. The transforms are completely general and take into account complex normalising impedances that are different for all ports as well as passive and active nonreciprocal networks. As in previous associated papers, scattering parameter definitions are based on the voltage-wave concept with complex normalisation derived directly from classical transmission line theory in which the characteristic impedance and propagation constant are both complex. A few examples of 4-port circuit analysis are given including a rigorous solution of the 4-port directional coupler. The method employed in deriving the transforms is briefly described.

Transfer functions of hearing-aid earmolds: empirically and computer-generated data

Acoustic transfer functions for two different configuration hearing-aid earmolds (solid, side-branch vented) were measured empirically and the transfer functions for the earmolds were generated by computer programming techniques using classical acoustic transmission line theory. In the empirical phase of the study a special signal source designed to provide a constant sound pressure to the earmold over a wide frequency range was used. The earmolds were loaded by a Zwislocki coupler mounted in the head of KEMAR. The physical dimensions of the two earmolds were used as the bases for generating the analogous computer transfer functions. The empirical data and the computer curves were in good agreement. The data indicate that, by the use of a constant pressure source, acoustic characteristics of earmolds are amenable to investigation and modeling, providing information as to the role of the earmold as part of the overall amplification system.

A linear voltage-tunable distributed null device

A linear voltage-tunable null device was predicted, fabricated, and tested. This filter is conceptually a distributed parameter RC representation of the channel of a MOSFET in a network configuration with a second MOSFET that is treated as a variable resistor. Classical transmission-line theory is used to predict a linear tuning curve with applied bias for the device. This concept was used to design a null device having a null that is linearly tunable in the range of 100 kHz. Such devices were fabricated and tested. Typical MOS processing steps were used and the resulting structures are compatible with the planar technology. The compatibility leads towards extension of this work to different frequency ranges for other specific applications.

Apparent impedances of very long multiconductor transmission lines

Classical transmission-line theory predicts that the locus of the input impedance of a short-circuited line is a symmetrical spiral in the complex impedance plane, with antiresonance frequencies at odd multiples of a quarter wavelength. In the present work, modern multiconductor transmission-line theory is used to study the problem of faulted transmission lines in greater detail than has hitherto been possible. By this means, it is shown that the short-circuit loci for unbalanced faults are unsymmetrical, and furthermore that resonances are liable to occur for line lengths considerably lower than those previously predicted. It is indicated that this is most probably due to the interaction between inductance of the faulty phase and the capacitance of the sound phases. The topic is developed by considering the practical problem of the protection of long lines when taking into account the complex nature of the short-circuit-impedance locus. In conclusion, it is indicated that digital-computer studies are, in all probability, necessary to establish the parameters necessary to apply distance relays to the protection of very long lines.

A contribution to the electromagnetic theory of the unmyelinated axon

The unmyelinated axon of negligibly thin axolemma is idealized as a right circular cylinder of infinite length imbedded in an unbounded aqueous electrolyte. The scalar wave equation is solved in this geometry subject to the boundary conditions (i) that the electric scalar potential vanish at infinity and be a known function along the cylinder axis, and (ii) that the radial current be continuous across the axolemma. Exact solutions for the infinite reluctivity limit are obtained for the interior potential, the total axial current, and the radial current at the axolemma; an approximate solution is obtained for the exterior potential. These solutions are compared with predictions of the classical transmission line theory commonly employed in describing the electrical properties of axons.

Surge Protection of Unit-Connected Generators

In a unit-connected generator scheme where the transformer is protected by lightning arresters installed adjacent to its high voltage terminals, the maximum surge voltage that can appear at the highvoltage terminals is limited to the discharge voltage of the arresters given in Fig. 2. The surges can be transferred electrostatically and electromagnetically through the transformer winding to the generator terminals. The electrostatic transfer is governed by the capacitive network of the transformer windings; see Fig. 20. Formulas for an equivalent circuit are derived for simple computations of the effect of the terminal conditions. This component is of subtransient nature. For the two cases studied, the crest magnitude of the electrostatic component does not exceed 21 kv. This voltage decays rapidly and vanishes within 0.4 μsec. Its effect is negligible. The electromagnetic transfer is analyzed for the unit-connected scheme and formulas are derived for the transferred surge voltage at the generator terminals. Twelve cases most commonly met in practice were analyzed with and without terminal capacitance. The result is an envelope voltage of 10 kv per μsec linear front and 40-kv crest magnitude which is not exceeded in any of the investigated cases. The voltage distribution along the generator winding is analyzed by classical transmission line theory. An actual distribution computed for a 100-mva generator with the above envelope voltage at the terminals showed that no points within the winding attain a voltage higher than the terminal voltage of 40-kv crest.

The application of transmission-line theory to closed aerials

The paper contains an analysis of the behaviour of frame aerials consisting of a single turn of conductor. It is assumed that the behaviour of such systems, including the mutual interactions of the various elements, can, to a useful degree of approximation, be represented by the differential equations of classical transmission-line theory. Formulae are obtained for the effective induced e. m. f. and the effective impedance (at the tuning point) of frame aerials the dimensions of which are not small compared with the wavelength, both for symmetrical and asymmetrical systems of tuning. It is found that in the case of symmetrically tuned systems the output voltages across the two equal halves of the tuning impedance will not in general be quite equal.It is shown that the “resonance factor” of a frame aerial (i.e. the ratio of output voltage to induced e. m. f.) can be determined by the usual method of reactance-variation at a constant frequency, in spite of the non-uniformity of the current distribution along the length of the conductor, but that the same process carried out by variation of frequency will not, in general, be valid.It is shown that for a given total length of conductor the optimum shape of a rectangular frame aerial, with respect to induced e. m. f., is square. In particular, a square frame with side equal to half a wavelength appears, to have useful practical characteristics in respect of sensitivity and symmetry, both for field-strength measurement and direction-finding.The method of applying the formulae to circular loops by a process of integration is given and illustrated by particular cases. It is found that in the case of small closed aerials the magnitude of the induced e. m. f. is not very sensitive to shape.

The application of transmission-line theory to closed aerials

The paper contains an analysis of the behaviour of frame aerials consisting of a single turn of conductor. It is assumed that the behaviour of such systems, including the mutual interactions of the various elements, can, to a useful degree of approximation, be represented by the differential equations of classical transmission-line theory. Formulae are obtained for the effective induced e.m.f. and the effective impedance (at the tuning point) of frame aerials the dimensions of which are not small compared with the wavelength, both for symmetrical and asymmetrical systems of tuning. It is found that in the case of symmetrically tuned systems the output voltages across the two equal halves of the tuning impedance will not in general be quite equal.It is shown that the “resonance factor” of a frame aerial (i.e. the ratio of output voltage to induced e.m.f.) can be determined by the usual method of reactance-variation at a constant frequency, in spite of the non-uniformity of the current distribution along the length of the conductor, but that the same process carried out by variation of frequency, will not, in general, be valid.It is shown that for a given total length of conductor the optimum shape of a rectangular frame aerial, with respect to induced e.m.f., is square. In particular, a square frame with side equal to half a wavelength appears to have useful practical characteristics in respect of sensitivity and symmetry, both for field-strength measurement and direction-finding.The method of applying the formulae to circular loops by a process of integration is given and illustrated by particular cases. It is found that in the case of small closed aerials the magnitude of the induced e.m.f. is not very sensitive to shape.