Propagation Modes, Equivalent Circuits, and Characteristic Terminations for Multiconductor Transmission Lines with Inhomogeneous Dielectrics

The theory of wave propagation on Iossless multiconductor transmission lines with inhomogeneous dielectrics is developed using matrix analysis. The treatment is concise and complete and has the advantage of identifying propagation modes in a way that permits straightforward physical interpretation. The equivalent circuit for the general line is derived and its application to the solution of wave problems with reflections is demonstrated. Special consideration is given to the problem of characteristically terminating a multiconductor line, i.e., terminating without reflections. The realizability of such a characteristic termination network is discussed, and proofs of realizability are given for the important cases of all lines with homogeneous dielectrics and all three-conductor lines, regardless of dielectric inhomogeneities. Symmetric three-conductor lines are discussed to exemplify the general theory, and an application to the problem of mode conversion on symmetric and asymmetric shielded strip lines is given.     

Clarke components for a system of busbars with pronounced proximity effect

The equations governing multiple straight transmission lines are applied to a configuration of three lines in the same plane. By a transformation with a matrix T, corresponding to the Clarke components, the propagation coefficients and modes can easily be found. A numerical example is given of three busbars showing pronounced proximity effect. The example is calculated by analogue simulation on a capacitor-resistor network.     

Time-domain analysis of lossy coupled transmission lines

A novel method based on numerical inversion of the Laplace transform is presented for the analysis of lossy coupled transmission lines with arbitrary linear terminal and interconnecting networks. The formulation of the network equations is based on a Laplace-domain admittance stamp for the transmission line. The transmission line stamp can be used to formulate equations representing arbitrarily complex networks of transmission lines and interconnects. These equations can be solved to get the frequency-domain response of the network. Numerical inversion of the Laplace transform allows the time-domain response to be calculated directly from Laplace-domain equations. This method is an alternative to calculating the frequency-domain response and using the fast Fourier transform to obtain the time-domain response. The inversion technique is equivalent to high-order, numerically stable integration methods. Numerical examples showing the general application of the method are presented. It is shown that the inverse Laplace technique is able to calculate the step response of a network. The time-domain independence of the solution is exploited by an efficient calculation of the propagation delay of the network     

Identification of propagation regimes on integrated microstriptransmission lines

There has been a resurgence of interest in the propagation characteristics of open integrated microstrip transmission lines. This is due in part to the discovery of diverse propagation regimes for higher-order modes on open lines. In contrast to the dominant EH₀ mode, three distinct propagation regimes exist for higher-order modes on microstrip transmission lines. In this paper, a rigorous spectral-domain integral equation formulation is used to analyze propagation in all three regimes. This formulation provides a clear physical picture of the different propagation regimes based on the mathematical location of poles and branch points in the complex spectral-variable plane. As an illustration, the formulation is applied to the case of an isolated uniform microstrip transmission line. The integral equation is discretized via the method of moments, and entire-domain basis functions incorporating suitable edge behavior are utilized to provide convergence with relatively few terms. The results obtained are compared to the results of other workers, and good agreement is observed     

Numerical solution of lossy waveguides: t.l.m. computer program

The transmission-line-matrix method is a time-domain numerical method for solving wave problems. The method uses a mesh of transmission lines to represent a propagation space, and the losses in the space are accounted for by making the transmission lines lossy. Lossy boundaries are simulated by imperfect boundary reflections on the transmission lines. A FORTRAN program implementing this technique is presented.     

Application of Modal Analysis to the Transient Response of Multiconductor Transmission Lines with Branches

An effective method for computing the time-domain response of lossless multiconductor transmission lines with branches in cross-sectionally inhomogeneous dielectric media is presented. Lines of this type are characterized by multiple propagation modes having different velocities. The theory of wave propagation on lossless multiconductor transmission lines with inhomogeneous dielectrics is used to obtain the modal amplitudes on the uniform sections of the line. The scattering matrix for the junction is used to compute the transmitted and reflected waves in the different branches at the junction. Each mode arriving at the junction excites multiple modes in all branches. The method described in this paper identifies all propagation modes in all branches of the line, and leads to the direct physical interpretation of the results. The method is general and can be applied to either partially or completely nondegenerate cases. Experimental results for a six-conductor transmission line with a single branch are found to be in good agreement with the results computed using the described method.     

Analysis of coaxial waveguide partially filled with chiral media

In this paper, the canonical problem of coaxial waveguide partially filled with chiral media is analyzed by a new equivalent transmission line network method. Both radial transmission lines in the cross section and multi-mode transmission lines in the longitudinal direction are introduced. The symmetrical properties of the structure are also discussed. Therefore, this method brings a clear physical picture into the wave propagation phenomena. Based on the analysis, the notable features and the role of the chirality parameter of the medium on the reflected and transmitted guided waves are discussed.     

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     

On the realization of resistively matched three-ports and theramp-waveform responses of resistive, signal-split three-porttransmission-line networks

Three-port networks consisting of three transmission lines and three branching resistors at a junction are discussed, assuming TEM wave propagation and lossless lines. The matching conditions for the resistive three-port are modeled by scattering matrices. As transmission lines of unequal length are used, the network transfer functions are derived for three different delay variables. These functions are obtained in a matrix form after their expansions with respect to these variables are derived, so that output waveforms can be calculated from the network transfer functions or their expansions. Three characteristics of output waveforms are discussed. Ideal networks that furnish the same output waveforms as their inputs and practical networks that have parameters as close as possible to the ideal are described. Examples of networks that keep the ringing of output waveforms within given tolerances, from the first arriving wave to the steady state, are presented. Power dissipation is discussed     

Wave Propagation on Nonuniform Transmission Lines (Short Papers)

The problem of wave propagation on nonuniform transmission lines is studied. Equations are presented not only for the reflection coefficient but for the transmission and admittance properties as well. They are valid under the assumption that only one mode of propagation exists on the line and that the properties do not change so rapidly that the fundamental transmission line equations are no longer applicable. Since all equations are derived for arbitrary load conditions, an extremely versatile solution of the problem has been obtained.     

Propagation model for ultrafast signals on superconductingdispersive striplines

The algorithm suitable for the computer-aided design of transmission lines is used to model the propagation of picosecond and subpicosecond electrical signals on superconducting planar transmission lines. Included in the computation of a complex propagation factor are geometry-dependent modal dispersion and the frequency-dependent attenuation and phase velocity which arise as a result of the presence of a superconductor in the structure. The results of calculations are presented along with a comparison to experimental data. The effects of modal dispersion and the complex surface conductivity of the superconductor are demonstrated, with the conclusion that it is necessary to incorporate both phenomena for accurate modeling of transient propagation in strip transmission lines     

Network representation and transverse resonance for layeredchirowaveguides

This paper presents an equivalent network method for dispersion analysis of general chirowaveguides. First, wave propagation in each homogeneous layer is represented by two pairs of transmission lines, the matrix wave impedance is defined. Next, the transformation properties of the input impedance are established. It is then demonstrated that the transverse resonance condition involving the previously obtained matrix impedance leads to the dispersion equation for the waveguides. The numerical results show that this network approach is feasible and practicable     

Propagation Parameters of Coupled Microstrip-Like Transmission Lines for Millimeter-Wave Applications

A variational expression is derived for the propagation parameters of coupled microstrip-like transmission lines for millimeter-wave applications using the "transverse transmission line" method. Numerical results are presented for the coupled inverted microstrip lines, and for the coupled suspended microstrip lines. The effects of the top and sidewalls and also of the finite thickness of strip conductors on the even- and odd-mode impedances are studied. The use of a dielectric overlay in equalizing the even- and odd-mode phase velocities is investigated.     

Static analysis of V transmission lines

A static analysis of V-shaped transmission lines is performed using a moment method formulation. Measurements were performed on a sample, and the validity of the theoretical results is verified by the experimental data. Characteristic impedance and propagation velocity are found to be strongly dependent on the angle parameter. Comparison with microstrip indicates a lower characteristic impedance and higher effective permittivity for V transmission lines. For multiple lines, the shape of the ground reference leads to lower coupling coefficients and lower mutual inductance and capacitance between adjacent lines     

微带传输线特性的数值分析

本文应用混合模有限元方法分析和计算了微带传输线的各种特性,包括特性阻抗、速度比、色散特性以及带厚的影响,并与有关文献结果作了比较。结果表明,有限元法是对微带传输线进行数值分析的有效方法。     

Application of anisotropic EBG for suppressing common-mode resonances in CPW-to-CPS transitions

The phenomenon of common-mode radiation limits the in-band performance of balanced transmission lines such as the coplanar strip (CPS). When such transmission lines are measured single-endedly, by connecting them between practical baluns/transitions, resonances in the frequency response are observed owing to common-mode propagation. It is proposed, and demonstrated for the first time, that an electromagnetic-bandgap ground (EBG) method can help to suppress the unwanted propagation of common-modes along balanced transmission lines.     

Wave propagation in nonlinear transmission lines with simple losses

Heaviside's condition for distortionless wave propagation in linear transmission lines with losses is generalised to cover nonlinear transmission lines. Analytical expressions are given for voltage and current in these lines.     

屏蔽平面传输线的色散特性分析

本文利用横向谐振法结合变分技术分析了屏蔽平面传输线的色散特性。在传输线波的传播方向,横向放置两个假想的理想短路面,构造谐振腔。根据横向谐振条件,建立了传输线的传播常数与谐振状态下的短路面之间距离的关系。应用谐振腔的变分公式,导出了确定短路面之间距离的特征方程。作为示例,数值计算了鳍线的色散特性,结果与相应文献中的数据相吻合。     

Uniform Multimode Transmission Lines (Short Papers)

A consistent normal-mode theory for coupled uniform transmission lines is developed which properly accounts for the fact that some propagation constants may be equal. Explicit responses are calculated. The results are interpreted in terms of transmission-line networks which consist of simple lines and which are coupled via conductor sharing.