Computation of frequency-dependent propagation characteristics ofmicrostriplike propagation structures with discontinuous layers

A general procedure based on the method of lines is presented for the full-wave analysis of propagation structures having layered substrates with step inhomogeneities in each layer. Examples of such structures include microslab lines and microstrip near a substrate edge. It is shown that with this extended method of lines technique the frequency-dependent characteristics, including the modal impedance, current distribution, and other properties of these structures, can be calculated. To illustrate the technique, typical structures such as microstrips on a finite-width dielectric slab and microstrips near a substrate edge are considered, and the effect of the proximity of the edge on the propagation characteristics of the microstrip is computed. For the case of a microstrip near a substrate edge, the numerical results obtained are compared with measured values of propagation constants, showing that the proximity effect is predicted to within 1%     

On a Class of Multiple-Line Directional Couplers

Multiple-line directional couplers that utilize only two linearly independent modes of propagation are possible, provided certain restrictions on the maximum coupling are not exceeded. This paper discusses a class of multiple-line directional couplers which may be considered as a generalization of the familiar double-stub four-port directional coupler. The basic design relations for the symmetrical case are developed, and frequency behavior is investigated. Experimental results for an L-band six-port hybrid junction are presented and compared with theoretical curves. Limitations on maximum coupling and fabrication problems will probably confine the number of lines in practical circuits to a small value. Bandwidths of couplers of this class tend to become narrower for the same total coupling off the main line as the number of lines is increased; however, standard techniques for broadbanding are applicable. Experimental results on the six-port hybrid junction agreed well with theory, and the circuit proved to be relatively compact.     

Complex modes in shielded suspended coupled microstrip lines

The existence of complex modes in electrically shielded suspended coupled microstrip lines has been studied extensively, and the results are presented. A rigorous full-wave spectral-domain approach (SDA) with a newly proposed and tested set of basis functions can efficiently and accurately determine the propagation characteristics of the dominant, higher-order, and complex modes for planar or quasi-planar transmission lines. These basis functions are validated by comparing the convergence study of field solutions with those obtained by various sets of preconditioned bases and by the unconditioned subdomain ones. Excellent agreement is obtained for the propagation constants and the normalized complex longitudinal and transverse current distributions on conducting strips for the strongly coupled microstrip lines. For all the particular case studies discussed, it is shown that the complex modes may exist in all the shielded suspended coupled microstrip lines, even when the substrate dielectric constant is low. Theoretical results for the fundamental, higher-order, evanescent, and complex modes are presented for suspended coupled microstrip lines     

Role of Antennas and Propagation for the Wireless Systems Beyond 2000

By using laws like Shannon's, Friis' and experimental propagation results itis shown that from a theoretical point of view it is possible to overcome theproblems of going to higher bandwidths and higher carrier frequencies.Multi-element antenna arrays at both ends can give the required gains even inhighly scattering environments. The basic joint antenna gain is that of onechannel. In many cases multiple channels with similar properties may beobtained.     

Tolerable Q-Factor Variations in PCM Lines

This paper makes a theoretical assessment of the performance impairments that may be caused on PCM lines by the use of different timing extraction bandwidths in tandem. Two basic situations are examined: 1) random transmitted pattern, and 2) transition between two repetitive patterns. In both cases, the analysis of jitter propagation and acceptance indicates that there is a limited degree of bandwidth inconsistency that may be tolerated. The amount of tolerable inconsistency is derived in both cases, according to different criteria that are established for convenience in each case. The effect of systematic line jitter on the correlation between a repeater performance in the field and in bench tests is also discussed. The study is based on a well-known model of jitter propagation introduced by Byrne et al. [1]. The general conclusion of the paper is thatQ-factor variations in a PCM line should be kept lower than a factor of two in order to avoid errors during pattern transitions and lower than 1.5 in order to avoid noise immunity loss.     

Quasi-TEM Analysis of "Slow-Wave" Mode Propagation on Coplanar Microstructure MIS Transmission Lines

We present a simple quasi-TEM analysis of "slow-wave" mode propagation on micron-size coplanar MIS transmission lines on heavily doped semiconductors and compare theoretical results with measurements on four such structures at frequencies from 1.0 to 12.4 GHz. Excellent agreement is found, which shows that the "slow-wave" mode propagating on these transmission lines is, in fact, a quasi-TEM mode. Relatively low-loss propagation along with significant wavelength reduction is observed. Conduction losses of the metal, which have been tacitly ignored in previously published "full-wave" treatments of "slow-wave" mode propagation, are included in the theory and are shown to dominate the attenuation at frequencies below 25 GHz and to still be significant at frequencies up to at least 100 GHz.     

Sur les méthodes de calcul de l’exposant linéique de propagation et d’impédance caractéristique des câbles aériens et enterrés

The propagation constant of a line or a cable, and its characteristic impedance represent two parameters which are needed in order to calculate the variation as a function of the time of a current induced by an emp.For the aerial lines expressions which take into account the presence of the soil could be developed but the case of the buried conductors is of a more difficult approach. The aim of this study is to present solutions introduced by different authors and to compare them with a calculation method for the propagation constant using iterations, proposed by the authors. If this value is known it is shown that the characteristic impedance calculation of buried cables can be improved by avoiding the necessity to compute with a reasonable precision the impedance of the ground.     

Millimeter-Wave Performance of Shielded Slot-Lines

The high frequency characteristics of shielded slot-lines are investigated using a modified Wiener-Hopf technique. The analysis includes the case of uniaxially anisotropic substrates when the principal axis is directed normal to the substrate. The obtained solution is especially useful at higher frequencies where other methods tend to be less effective. Numerical results are given for lines on high dielectric constant substrates over the full usable frequency range. It is shown that lines can be used as transmission elements up to a certain limiting frequency beyond which they will radiate. Physical aspects of the propagation in slot-lines are discussed and the effect of the shields on the properties of the guided modes is explained.     

Coupling Between Dissimilar Waveguides

Investigators have used coupled-mode theory to analyze the coupling between identical waveguides; in such cases the coupling coefficients are found to be identical. If the waveguides differ, the coupling coefficients are asymmetrical and difficult to evaluate by strictly theoretical methods. An alternate approach to this case is considered in the present work. A pair of coupled-mode equations is first developed from a consideration of the permissible fields within the device. This clarifies the relationship between the coupled-mode theory and the more general classical electromagnetic theory by giving a careful definition of the coupled and the normal modes of a coupled structure. It is shown that the coupled-mode equations are an exact representation of the waveguide fields, although for engineering purposes it is often convenient to use approximate values of the coefficients of these equations. The mutual coupling coefficients are obtained from a two transmission-line model of the structure, with the actual coupling mechanism represented by a mutual impedance common to the two lines. For dissimilar lines, the ratio of the coupling coefficients is found to be equat to the ratio of the characteristic impedances. For the cases considered, this is the same as the ratio of the propagation constants of the uncoupled lines, which permits the coupling coefficients to be determined from relatively simple measurements. The adequacy of the theory has been confirmed by a series of experiments.     

Optical Delay Lines Based on Soliton Propagation in Photonic Crystal Coupled Resonator Optical Waveguides

In this paper, a study of optical delay lines based on soliton propagation in coupled resonator optical waveguides is performed. For a given bit rate and required delay, design equations are given that relate the soliton peak power and collision period to the soliton width. To study the influence of higher order linear and nonlinear dispersion, a continuous wave propagation model incorporating these effects is also derived. Using this model, the soliton stability in the presence of higher order dispersion, optical loss and adjacent soliton pulses is numerically verified. It is also shown that soliton-based delay lines can achieve nanosecond delay at a propagation length of a few millimeters due to the high slow down factors that can be obtained.     

Introduction of radiation losses in the time domain transmission line method

Because the transmission line method only allows to study the propagation of a pure tem mode along a line, all radiation phenomena are neglected. These phenomena become important when lines have discontinuities, then in this case radiating losses must be included in the theoretical formalism. This paper introduces an original approach to consider radiation of lines and to include them in a time domain transmission line method. Some comparisons with full modes method results validate the method.     

Formulation of the Singular Integral Equation Technique for Planar Transmission Lines

The singular integral equation technique is used to determine the normal modes of propagation in general planar transmission lines. Taking finlines as, an example, it is demonstrated how high-order modes can effectively and accurately be calculated. It is also shown that complex and backward-wave modes, which are known to exist in rectangular and circular waveguides with dielectric inserts, can also exist in finlines. Besides a discussion of their characteristic features, this paper describes the conditions under which complex and backward-wave modes are found in finlines.     

An accurate measurement technique for line properties, junctioneffects, and dielectric and magnetic material parameters

Transmission/reflection coefficients of unknown transmission lines are analyzed. The characteristic impedance, the propagation constant, and the parameters of the junctions at the connections with the measurement setup can be calculated if the coefficients of three different lengths of the line being investigated are measured. Therefore it is called the L³ method (line/line/line). Transmission data suffice for the determination of only the propagation constant. They are used in the case of material parameter measurements with loaded lines. Dielectric and magnetic properties of the filling material are calculated using the set of transverse resonance equations     

Radiation from Linear Resonant Antenna in Weakly Ionized Plasma†

A theoretical study of radiation of electromagnetic and electroacoustic waves in lossy compressible weakly ionized plasma has been made and its dependence on the ratio of source to plasma frequencies has been investigated. A linearized theory is used such that the isotropic electron plasma is regarded as a single fluid continuum. A thin linear resonant antenna is used as the source of radiation and the propagation constant on it is assumed to be the same as in free space. The propagation constant is taken to be complex in plasma for both electromagnetic and electroacoustic waves. Also the effect of electron neutral particle collision is taken into account wherever it is effective. It is shown that propagation is almost unaffected by plasma when source frequencies much higher than the plasma frequency are used. But the effect of plasma on radiation is found to be profound at frequencies smaller than the plasma frequency. General expressions of radiation resistance for both the electromagnetic and eloctroacoustic waves have been obtained and under these conditions the half-wave dipole is treated as a special case. The results deduced for these are found to be in agreement with those wherever obtained earlier.     

Complex media microstrip ridge structures: formulation and basiccharacteristics of ferrite structures

Microstrip transmission lines residing on bianisotropic material ridges embedded in a multilayered environment are studied using a coupled set of integral equations (IE's). The full-wave IE formulation accounts for general linear media in the ridge region using equivalent polarization currents residing in a multilayered bianisotropic background. Numerical results showing basic propagation characteristics are presented for a variety of single and coupled ferrite ridge structures. It is shown that the use of finite width ferrite ridges as either substrates or superstrates can produce nonreciprocity while confining the ferrite material to a small area in the vicinity of the transmission line     

Methods of theoretical analysis and computer modeling of theshaping of electrical pulses by nonlinear transmission lines andlumped-element delay lines

The mechanism by which high-power electrical pulses can be sharpened by propagation along nonlinear transmission lines and lumped-element delay lines is described with emphasis on the production of pulses with very fast leading or trailing edges. A survey of some of the mathematical techniques that have been applied to the propagation of electrical signals along nonlinear lines and ladder networks is presented, and the limitations of these techniques are discussed. The processes that both produce and limit pulse sharpening on nonlinear lumped-element delay lines are examined, and it is found that the wave equation, which describes the propagation of electrical signals along such networks, predicts that an electrical pulse will decompose into an array of solitons. An approximate formula for estimating the degree of pulse sharpening that can be produced on a delay line with a given number of sections is derived, and its accuracy is compared with experimental results. Numerical integration techniques for solving the nonlinear differential and difference equations that result from the mathematical analysis of nonlinear lines and networks are discussed, and the propagation of a voltage pulse along a lumped-element delay line containing nonlinear capacitors is simulated using a computer model based on an efficient algorithm     

Linear and Nonlinear Optical Pulse Propagation in Photonic Crystal Waveguides Near the Band Edge

In this paper, the propagation of optical pulses in photonic crystal waveguides (PCWs) near the edge of the guided band is numerically investigated. In the linear regime, it is shown that group velocity dispersion can significantly limit the maximum bit rate of the optical signal. On the other hand, better performance is obtained using soliton waves. Both bright and dark solitons can significantly increase the maximum bit rate that can be achieved in the nanosecond delay regime. The influence of higher order dispersion and optical loss is numerically investigated. The results indicate that near the band edge soliton propagation in PCWs can be stable, provided that the optical losses are kept low. This could open a path towards implementing compact nonlinear elements and delay lines in integrated form.      

Distributed parametric effect in long lines and its applications

The article considers a parametric effect which takes place when the velocity of signal propagation in a long line changes. We found the analytical solution describing the form of the transformed signal for a line with losses, when line parameters change symmetrically. We also considered lines without losses, with asymmetrical change of parameters. Our theoretical results comply with experimental data. In certain conditions, such a line can be used as an amplifier. The parametric effect in optics is described by Maxwell's equations, while in case of a long line, the analysis is based on telegrapher's equations. However, it turns out that in the end, both in optics and electronics, the parametric effect is described by wave equations that are mathematically similar. This is because fundamentally, when the parameters of the propagating medium change, the parametric effect is physically based on energy interchange between the controlling (pump) signal and the transformed one. So, the obtained results can be used for analysis of parametric effects in optics and electronics.     

Effects of inductance on the propagation delay and repeaterinsertion in VLSI circuits

A closed-form expression for the propagation delay of a CMOS gate driving a distributed RLC line is introduced that is within 5% of dynamic circuit simulations for a wide range of RLC loads. It is shown that the error in the propagation delay if inductance is neglected and the interconnect is treated as a distributed RC line can be over 35% for current on-chip interconnect. It is also shown that the traditional quadratic dependence of the propagation delay on the length of the interconnect for RC lines approaches a linear dependence as inductance effects increase. On-chip inductance is therefore expected to have a profound effect on traditional high-performance integrated circuit (IC) design methodologies. The closed-form delay model is applied to the problem of repeater insertion in RLC interconnect. Closed-form solutions are presented for inserting repeaters into RLC lines that are highly accurate with respect to numerical solutions. RC models can create errors of up to 30% in the total propagation delay of a repeater system as compared to the optimal delay if inductance is considered. The error between the RC and RLC models increases as the gate parasitic impedances decrease with technology scaling. Thus, the importance of inductance in high-performance very large scale integration (VLSI) design methodologies will increase as technologies scale     

Propagation of Quasi-Static Modes in Anisotropic Transmission Lines: Application to MIC Lines

In this paper, we analyze the field propagation in a general N-conductor transmission line embedded in an inhomogeneous and anisotropic medium, through the series expansion of the field in powers of frequency. The quasi-static approach is deduced as a zero-order approach upon the field and a first-order approach for the propagation constant. It is shown that it is even possible to decompose the field into a sum of propagating modes with a scalar propagation factor. The special case of transmission lines in nonmagnetic media is explicitly considered. A method to find out the mode characteristics of any open planar MIC line with anisotropic dielectric substrates is developed and applied to some MIC structures of interest, specifically broadside edge-coupled microstrips with inverted and noninverted substrates.