ABCD Matrix: A Unique Tool for Linear Two-Wire Transmission Line Modelling

2003 ◽  
Vol 40 (3) ◽  
pp. 220-229 ◽  
Author(s):  
Pedro L. D. Peres ◽  
Carlos R. de Souza ◽  
Ivanil S. Bonatti
Keyword(s):  
Differential Equations ◽  
Transmission Line ◽  
Frequency Domain ◽  
Transmission Lines ◽  
Time Domain ◽  
Mathematical Concepts ◽  
Frequency Dependent ◽  
Abcd Matrix ◽  
The Time Domain

The aim of this note is to show that all the behaviour of a two-wire transmission line can be directly derived from the application of ABCD matrix mathematical concepts, avoiding the explicit use of differential equations. An important advantage of this approach is that the transmission line modelling arises naturally in the frequency domain. Therefore the consideration of frequency-dependent parameters can be carried out in a simple way compared with the time-domain. Some standard examples of transmission lines are analysed through the use of ABCD matrices and a case study of a balun network is presented.

Time-Domain Nonlinear SSI Analysis of Foundation Sliding Using Frequency-Dependent Foundation Impedance Derived From SASSI

2008 ◽  
Author(s):  
Mansour Tabatabaie ◽  
Thomas Ballard
Keyword(s):  
Frequency Domain ◽  
Linear Systems ◽  
Time Domain ◽  
Soil Structure ◽  
Wave Radiation ◽  
Far Field ◽  
Frequency Dependent ◽  
Nonlinear Springs ◽  
Mat Foundation ◽  
The Time Domain

Dynamic soil-structure interaction (SSI) analysis of nuclear power plants is often performed in frequency domain using programs such as SASSI [1]. This enables the analyst to properly a) address the effects of wave radiation in an unbounded soil media, b) incorporate strain-compatible soil shear modulus and damping properties and c) specify input motion in the free field using the de-convolution method and/or spatially variable ground motions. For structures that exhibit nonlinearities such as potential base sliding and/or uplift, the frequency-domain procedure is not applicable as it is limited to linear systems. For such problems, it is necessary to solve the problem in the time domain using the direct integration method in programs such as ADINA [2]. The authors recently introduced a sub-structuring technique called distributed parameter foundation impedance (DPFI) model that allows the structure to be partitioned from the total SSI system and analyzed in the time domain while the foundation soil is modeled using the frequency-domain procedure [3]. This procedure has been validated for linear systems. In this paper we have expanded the DPFI model to incorporate nonlinearities at the soil/structure interface by introducing nonlinear shear and normal springs arranged in series between the DPFI and structure model. This combination of the linear far-field impedance (DPFI) plus nonlinear near-field soil springs allows the foundation sliding and/or uplift behavior be analyzed in time domain while maintaining the frequency-dependent stiffness and radiation damping nature of the far-field foundation impedance. To check the accuracy of this procedure, a typical NPP foundation mat supported at the surface of a layered soil system and subjected to harmonic forced vibration was first analyzed in the frequency domain using SASSI to calculate the target linear response and derive a linear, far-field DPFI model. The target linear solution was then used to validate two linear time-domain ADINA models: Model 1 consisting of the mat foundation+DPFI derived from the linear SASSI model and Model 2 consisting of the total SSI system (mat foundation plus a soil block). After linear alignment, the nonlinear springs were added to both ADINA models and re-analyzed in time domain. Model 2 provided the target nonlinear solution while Model 1 provided the results using the DPFI+nonlinear springs. By increasing the amplitude of the vibration load, different levels of foundation sliding were simulated. Good agreement between the results of two models in terms of the displacement response of the mat and cyclic force-displacement behavior of the springs validates the accuracy of the procedure presented herein.

A Numerical Method for Representing Retardation Functions With Complex Exponentials

2017 ◽  
Author(s):  
Fushun Liu ◽  
Lei Jin ◽  
Jiefeng Chen ◽  
Wei Li
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Degrees Of Freedom ◽  
Added Mass ◽  
Memory Effects ◽  
Floating Structure ◽  
Frequency Dependent ◽  
Laplace Domain ◽  
The Time Domain ◽  
Frequency Domain Techniques

Numerical time- or frequency-domain techniques can be used to analyze motion responses of a floating structure in waves. Time-domain simulations of a linear transient or nonlinear system usually involve a convolution terms and are computationally demanding, and frequency-domain models are usually limited to steady-state responses. Recent research efforts have focused on improving model efficiency by approximating and replacing the convolution term in the time domain simulation. Contrary to existed techniques, this paper will utilize and extend a more novel method to the frequency response estimation of floating structures. This approach represents the convolution terms, which are associated with fluid memory effects, with a series of poles and corresponding residues in Laplace domain, based on the estimated frequency-dependent added mass and damping of the structure. The advantage of this approach is that the frequency-dependent motion equations in the time domain can then be transformed into Laplace domain without requiring Laplace-domain expressions of the added mass and damping. Two examples are employed to investigate the approach: The first is an analytical added mass and damping, which satisfies all the properties of convolution terms in time and frequency domains simultaneously. This demonstrates the accuracy of the new form of the retardation functions; secondly, a numerical six degrees of freedom model is employed to study its application to estimate the response of a floating structure. The key conclusions are: (1) the proposed pole-residue form can be used to consider the fluid memory effects; and (2) responses are in good agreement with traditional frequency-domain techniques.

3D inversion of airborne electromagnetic data

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. WB59-WB69 ◽  
Author(s):  
Leif H. Cox ◽  
Glenn A. Wilson ◽  
Michael S. Zhdanov
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Test Site ◽  
Electromagnetic Data ◽  
Model Study ◽  
Airborne Electromagnetic ◽  
The Time Domain ◽  
Airborne Electromagnetic Data ◽  
Viable Method

Time-domain airborne surveys gather hundreds of thousands of multichannel, multicomponent samples. The volume of data and other complications have made 1D inversions and transforms the only viable method to interpret these data, in spite of their limitations. We have developed a practical methodology to perform full 3D inversions of entire time- or frequency-domain airborne electromagnetic (AEM) surveys. Our methodology is based on the concept of a moving footprint that reduces the computation requirements by several orders of magnitude. The 3D AEM responses and sensitivities are computed using a frequency-domain total field integral equation technique. For time-domain AEM responses and sensitivities, the frequency-domain responses and sensitivities are transformed to the time domain via a cosine transform and convolution with the system waveform. We demonstrate the efficiency of our methodology with a model study relevant to the Abitibi greenstone belt and a case study from the Reid-Mahaffy test site in Ontario, Canada, which provided an excellent practical opportunity to compare 3D inversions for different AEM systems. In particular, we compared 3D inversions of VTEM-35 (time-domain helicopter), MEGATEM II (time-domain fixed-wing), and DIGHEM (frequency-domain helicopter) data. Our comparison showed that each system is able to image the conductive overburden and to varying degrees, detect and delineate the bedrock conductors, and, as expected, that the DIGHEM system best resolved the conductive overburden, whereas the time-domain systems most clearly delineated the bedrock conductors. Our comparisons of the helicopter and fixed-wing time-domain systems revealed that the often-cited disadvantages of a fixed-wing system (i.e., response asymmetry) are not inherent in the system, but rather reflect a limitation of the 1D interpretation methods used to date.

Circuit Models of Lossy Multic onductor Transmission Lines: Incident Plane Wave Effect

2016 ◽  
Vol 6 (5) ◽  
pp. 2369
Author(s):  
Saih Mohamed ◽  
Rouijaa Hicham ◽  
Ghammaz Abdelilah
Keyword(s):  
Plane Wave ◽  
Frequency Domain ◽  
Transmission Lines ◽  
Time Domain ◽  
Method Of Characteristics ◽  
Incident Plane Wave ◽  
Wave Effect ◽  
Incident Plane ◽  
Simulation Results ◽  
The Time Domain

<p>In this paper, we concentrate on the variety impacts of incident plane wave on multiconductor transmission lines, utilizing Branin’s method, which is alluded to as the method of characteristics. The model can be directly used for the time-domain and frequency-domain analyses, Moreover,  it had the advantage of being used without the need of setting the  preconditions of  the  charges  applied  to  its  ends; this permits it to be effortlessly embedded in circuit simulators, for example Spice, Saber, and Esacap. This model validity is affirmed by contrasting our simulation results under ESACAP and different results, and we will talk about variety impacts of incident plane wave.</p>

The Analysis of a Transmission Line Crosstalk in the Time Domain Based on First-Order Upwind

2014 ◽  
Vol 543-547 ◽  
pp. 813-816
Author(s):  
Yin Han Gao ◽  
Tian Hao Wang ◽  
Jun Dong Zhang ◽  
Kai Yu Yang ◽  
Yu Zhu
Keyword(s):  
Transmission Line ◽  
Transmission Lines ◽  
Time Domain ◽  
Splitting Method ◽  
Discontinuous Solution ◽  
Characteristic Line ◽  
First Order ◽  
The Difference ◽  
Leapfrog Scheme ◽  
The Time Domain

This article will combine the difference scheme of first-order upwind with the multi-conductor transmission lines equation to analysis the multi-conductor transmission lines crosstalk in the time domain. First-order upwind is a finite difference algorithm in the time domain; it has a first order accuracy, in the discontinuous solution there is no non-physics-oscillation, when simulate the signal. The flux splitting method which is applied to the first-order upwind solved the problem that the characteristic line direction of the wind type make plus or minus transformation along with the coefficient, make the programming simple. In this paper, simulation results of transmission line crosstalk in this algorithm will be compared with the traditional leapfrog scheme, to verify its effectiveness.

scholarly journals A novel solution algorithm for nonlinearly loaded transmission lines inside resonating enclosures

2014 ◽  
Vol 12 ◽  
pp. 135-142 ◽  
Author(s):  
R. Rambousky ◽  
S. Tkachenko ◽  
J. Nitsch
Keyword(s):  
Transmission Line ◽  
Transmission Lines ◽  
Time Domain ◽  
Green's Functions ◽  
Green’S Functions ◽  
Frequency Data ◽  
Nonlinear Load ◽  
Right Hand ◽  
Left And Right ◽  
The Time Domain

Abstract. Nonlinearly loaded lossless transmission lines inside a rectangular cavity are studied using the left- and right-hand Green's functions of the problem in time domain. These Green's functions are developed for a transmission line with quasi-matched loads. This ensures Green's functions of a short duration. Therefore, the amount of frequency data necessary to obtain time-domain Green's functions is quite limited. The time-domain Green's functions are finally convolved with the left- and right-hand line voltages. With this technique it is possible to treat arbitrarily loaded transmission lines in resonators. An example is presented to demonstrate the applicability of this technique to a transmission line with a simple diode as nonlinear load.

A Simple but Complete Solution for the Step Response of a Semi-Infinite, Circular Fluid Transmission Line

1972 ◽  
Vol 94 (2) ◽  
pp. 455-456 ◽  
Author(s):  
J. T. Karam
Keyword(s):  
Transmission Line ◽  
Frequency Domain ◽  
Time Domain ◽  
Complete Solution ◽  
Step Response ◽  
Integration Techniques ◽  
Finite Line ◽  
Infinite Line ◽  
The Time Domain ◽  
Operating Regimes

Presently, the only accurate solutions for the step response of a semi-infinite, circular fluid transmission line result from involved, time consuming, numerical finite series or integration techniques [1, 2, 3]. None of these solutions is practically suitable for either a rapid manual prediction for an arbitrary fluid line (liquid or gas), or for extension of the semi-infinite line results to the more meaningful problem of a finite line with arbitrary inputs. In the frequency domain (sinusoidal signals), a complete, verified solution exists [1, 4, 5] and theoretically could be transformed into the time domain. This was the scheme used by Brown and Nelson for liquid lines [2], but it required the numerical techniques referred to above and, in their own words, was a “very complex and tricky business.” However, simpler solutions for most operating regimes also exist in the frequency domain [6, 7]. These simple frequency domain solutions were transformed into the time domain and provided the basis for a simple solution for the step response.

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