Frequency-dependent Transmission Line Parameters Research Articles

A Spice-Compatible Macromodel for Field Coupling to Multiconductor Transmission Lines Based on the Analog Behavioral Modeling

This article presents a time-domain macromodeling algorithm for buried transmission lines subject to coupling of an incident field and terminated with linear and nonlinear loads. Different from overhead lines, the determination of the transient ground admittance is of great importance due to the complexity of the analytical expressions and the necessity of assuring a good approximation over a wide frequency range. The proposed macromodel adopts the analog behavioral modeling (ABM) library of Spice solvers to model frequency-dependent transmission line parameters directly, and calculate convolution in time domain, making it simple and convenient to treat time-domain field-to-line coupling equations without the need of time and spatial discretization and curve fitting used in other time-domain numerical algorithms. Besides, the model complexity is not limited by the line length. Hence, the proposed algorithm can significantly simplify the modeling process and improve simulation efficiency, especially for long multiconductor transmission lines. Furthermore, an effective and simplified expression for self and mutual ground impedance and admittance of underground lines is proposed in this article. With the proposed expression, the time-consuming numerical integration can be avoided, leading to a saving of 98% of the computational time. Finally, several validation examples of field coupling to buried power cables terminated with linear and nonlinear devices are investigated. The comparison of calculated waveshapes and CPU times shows the accuracy and efficiency of the proposed method.

A de-embedding technique for metallic nanowires in microwave characterization

The application of metallic nanowires as transmission lines at microwave frequencies has attracted interest of the nanoelectronics community in recent years. The size reduction of wires down to nano-scale inevitably introduces more challenges not only in the fabrication but in the characterization techniques. The aim of this work is to build a reliable framework to characterize a single metallic nanowire in the millimeter wave range by means of a tailored-designed coplanar waveguide platform. We conduct a comprehensive analysis on the characteristic impedances and the propagation constants of nano-scale aluminum metallic wires in relation to the change of line dimension as a function of frequency from 1 to 100GHz. A method to subtract the effect of pads and contact impedance from the measurement based on an equivalent circuit model and a cascade-based de-embedding theory is employed. We propose a quasi-TEM equivalent circuit model in the analysis to predict the measured frequency-dependent transmission line parameters. A comparison between simulated and measured result will be presented.

Triangle impulse response (TIR) calculation for lossy transmission line simulation

Triangle impulse responses (TIRs) for lossy transmission lines are accurately calculated using both an inverse fast Fourier transform algorithm and an accelerated inverse Laplace transform algorithm. Frequency dependent transmission line parameters, i.e., R, L, G, and C, are employed to model the skin effect and the frequency dependent electrical properties of the substrate material. The calculated TIR can be further used to carry out time domain simulations for a large number of lossy transmission lines. Frequency dependent line parameters, R, L, G, and C should be used in specific cases to assure the causality of signal waveform, the accuracy of the time delay, and the amplitude of the waveform evaluations in the time domain.

Transient analysis of lossy multiconductor transmission lines in nonlinear circuits

Using the frequency-dependent transmission line parameters, two time-domain models are developed for lossy multiconductor transmission lines. It is shown that the end-points of a lossy multiconductor line can be represented at each time step by discretized Thevenin or Norton equivalent circuits. Because these models contain only lumped elements, they can be easily implemented in a general circuit analysis program for simulating the transient responses of nonlinear circuits. The analysis procedure developed makes exclusive use of infinite line impulse responses in the formulation of the time-domain models. Because infinite lines are matched, there are no reflections in the impulse responses. The result is that these impulse responses are relatively short. Results are shown for the most general case of lossy multiconductor transmission lines with discontinuities and nonlinear terminations in which the modal transformation matrices are necessarily frequency dependent.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Signal degradation through module pins in VLSI packaging

This paper investigates chip-to-chip communication through the modules and board in VLSI packaging. Transmission line models and frequency-dependent transmission line parameters are used in finding the frequency response. The time-domain solution is then obtained through the inverse Fast Fourier Transform. The results show that uncoated module pins, even of relatively short length, can cause severe signal degradation because of their magnetic property. The signal behavior is improved dramatically, however, when the module pins are coated with nonmagnetic conductive material.

Transient characteristics of power cables: a new approach based on Poynting's theorem

Frequency-dependent transmission line parameters are analysed using Poynting's theorem. Using the general formulation of impedance and admittance matrices and solution for electromagnetic field vectors, wave propagation characteristics of the transmission line are obtained. The method is particularly useful for power cables, in which electromagnetic effects such as the proximity effect and electromagnetic shielding are strong. Calculations of underground eccentric cable characteristics illustrate the method. New formulae for inductances and conductor internal impedances are derived and new results for the propagation constant are given.

Theoretical Evaluation of Multiphase Propagation

The theoretical transient solution of multiphase transmission line propagation is reviewed by comparison of the Fourier and Laplace transform techniques applicable to this problem. The results show that the Fourier transform technique is more general, because it can include consideration of frequency dependent transmission line parameters and frequency dependent eigenvectors. The Laplace transform technique is applied to a lossy, completely transposed, transmission line using a new shorthand matrix notation for balanced matrices in the analysis. These results show that modal analysis canbe used in the balanced transmission line analysis. A discussion of possible simulation techniques are discussed and it is concluded that further work is required in this area to adequately incorporate attenuation and distortion on long duration switching surges.