Analysis Of Lossy Transmission Lines Research Articles

Analysis of Lossy Transmission Lines Terminated by Schottky Diode Circuit

In the present paper we consider a lossy transmission line terminated by a circuit corresponding to a Schottky diode. On the base of Kirchhoff's law boundary conditions are derived. Then a mixed problem for the lossy transmission line system is formulated. We reduce the mixed problem for the hyperbolic transmission line system to an initial value problem for a system of differential equations with delays on the boundary. We prove existence-uniqueness theorem for oscillatory solution. The paper ends with numerical example with real values of the Schottky diode parameters.

Transient Analysis of CMOS-Gate-Driven $RLGC$ Interconnects Based on FDTD

As the feature size of integrated circuits shrinking in deep submicron technologies, time delay, and crosstalk noise of complementary metal-oxide-semiconductor (CMOS)-gate-driven interconnects become critical issues. Traditionally, CMOS driver is simplified as a linear circuit in which a constant resistance is used to approximate the nonlinear and time-varying MOS resistance, which is inaccurate for signal integrity analysis in high-speed interconnect systems. This paper proposes a finite-difference time-domain (FDTD)-based method for transient analysis of lossy transmission lines in the presence of the nonlinear behavior of CMOS gates. The conventional FDTD with second-order accuracy is used for interconnect analysis and the parameters with frequency-dependent losses are also included. The nonlinear behavior of CMOS gates is represented by alpha-power law model, with the drain current described by piecewise linear function of the drain voltage and discretized in time domain for the FDTD implementation. Explicit forms of the boundary conditions are derived from the implicit interface equations and hence the stability is strictly constrained by Courant condition. Experimental results show that the proposed method has good accuracy and high efficiency with respect to HSPICE. Therefore, it is useful for accurate prediction of time delay and crosstalk noise in high-speed interconnect systems.

Surface Interaction Matrices for Boundary Integral Analysis of Lossy Transmission Lines

A method intended to characterize enclosed computational electromagnetic domains in terms of interaction and response of a defined set of surface excitations is described. The finite-element method is used to compute a matrix relating surface current and tangential field in terms of an appropriate basis set such that a coupled solution with a boundary integral formulation is rendered seamless. The proposed method allows for a decoupled finite-element boundary-integral system through use of a discrete-frequency surface interaction matrix, computed in an alternative way, that is still independent of the properties of the background in which the enclosed region resides. The method is applied to per-unit-length resistance and inductance extraction of a variety of multiconductor lossy transmission lines. The primary advantage the proposed method presents for this particular application is reuse of matrices given recurrence of specific conductor cross sections.

TRANSIENT ANALYSIS OF LOSSY NONUNIFORM TRANSMISSION LINES USING A TIME-STEP INTEGRATION METHOD

This paper presents an effective numerical method for the transient analysis of lossy transmission lines. With the discretization of the spatial variation of voltages and currents along the transmission lines while remaining the temporal derivatives unchanged, a semi- discrete model is derived from the telegrapher's equations. The time- step integration method is utilized to derive the recursive scheme of time advancing. A large time step can be used in the computation, meanwhile, its accuracy is guaranteed. Numerical examples are presented to demonstrate the stability and accuracy of the proposed method.

Transient Analysis of Lossy Transmission Lines: An Efficient Approach Based on the Method of Characteristics

This paper is devoted to transient analysis of lossy transmission lines characterized by frequency-dependent parameters. A public dataset of parameters for three line examples (a module, a board, and a cable) is used, and a new example of on-chip interconnect is introduced. This dataset provides a well established and realistic benchmark for accuracy and timing analysis of interconnect analysis tools. Particular attention is devoted to the intrinsic consistency and causality of these parameters. Several implementations based on generalizations of the well-known method-of-characteristics are presented. The key feature of such techniques is the extraction of the line modal delays. Therefore, the method is highly optimized for long interconnects characterized by significant propagation delay. Nonetheless, the method is also successfully applied here to a short high/loss on-chip line, for which other approaches based on lumped matrix rational approximations can also be used with high efficiency. This paper shows that the efficiency of delay extraction techniques is strongly dependent on the particular circuit implementation and several practical issues including generation of rational approximations and time step control are discussed in detail.

Recursive algorithm for transient analysis of lossy transmission line

A recursive algorithm is presented for the time-domain simulation of lossy transmission lines. It can be used efficiently for the transient analysis of high speed interconnects in high-speed VLSI circuits and multichip modules (MCMs).

Fast simulation and sensitivity analysis of lossy transmission lines by the method of characteristics

In this paper we use the method of characteristics to derive a new simulation model of lossy transmission lines, and we present the sensitivity analysis in the time domain. The simulation model is as fast as the recursive convolution model based on moment matching and Pade' approximation, but does not have the stability problem. The sensitivity analysis model is particularly useful for transmission line circuits containing nonlinear elements, and is believed to be the first time domain model. Both the simulation and sensitivity analysis models are applicable to uniform and nonuniform transmission lines with arbitrary nonzero initial states. Also we show that any nonlinear circuit element has a very simple linear model in sensitivity analysis. Furthermore, we demonstrate that for any circuits, the modified nodal admittance (MNA) matrices in simulation and in sensitivity analysis equations are the same, therefore no LU decomposition is needed in sensitivity analysis. The contributions in this paper have been implemented into a general-purpose program CSSC (Circuit Simulation and Sensitivity Analysis with Characteristics) which shows excellent accuracy and efficiency in both simulation and sensitivity analysis of transmission line circuits.

Finite-difference, time-domain analysis of lossy transmission lines

An active and efficient method of including frequency-dependent conductor losses into the time-domain solution of the multiconductor transmission line equations is presented. It is shown that the usual A+B/spl radic/s representation of these frequency-dependent losses is not valid for some practical geometries. The reason for this the representation of the internal inductance the at lower frequencies. A computationally efficient method for improving this representation in the finite-difference time-domain (FDTD) solution method is given and is verified using the conventional time-domain to frequency-domain (TDFD) solution technique.

Transient analysis of lossy transmission lines with arbitrary initial potential and current distributions

The method of characteristics has been generalized for the transient analysis of lossy transmission lines with arbitrary initial conditions. It is shown that traveling waves generated by the initial potential and current distributions can be simulated by voltage and current generators connecting to the terminals of the lossy transmission-line model consisting of ideal delay-lines and waveshaping networks synthesized by the modified Pade approximation. The discrete-time transient simulation requires neither the FFT nor convolution integral and is as efficient as the iterative waveform relaxation technique. Transient responses of lossy transmission lines with steady-state and transient initial potential and current distributions are simulated for illustration.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Time-domain analysis of lossy transmission lines with arbitrary terminal networks

A numerical method based on traveling wave theory is presented for the transient analysis of lossy transmission lines with arbitrary terminal networks. The method is well suited to computer programming. By introducing the imaginary transmission line, the network is portioned into two parts. An approach by the S-matrix and the z-transform is applied to the arbitrary terminal networks and time convolution is applied to the lossy transmission lines. The time domain S-matrix required for the convolution is obtained by the use of a fast inversion of a Laplace transform. A time-domain wave flow for the network is considered. The voltage waves at the lumped part are obtained by the S-z method, and the time-domain S-matrix is convolved with the voltage waves on the imaginary and lossy transmission lines to obtain a time-stepping solution. Three numerical examples are presented to illustrate the application of the method. >

Analysis of Lossy Transmission Lines with Arbitrary Nonlinear Terminal Networks

A novel method for transient analysis of Iossy transmission lines with arbitrary nonlinear terminal networks is presented. The uniqueness of this approach is that we develop time-domain Green's functions for the multiport transmission-line systems by terminating the ports in quasi-matched loads. This ensures Green's functions of a short duration. Hence, the amount of frequency-domain data necessary to obtain time-domain Green's functions is modest. These Green's functions are then convolved with the line port voltages. With this technique one can analyze responses of multiconductor transmission lines with arbitrary nonlinear loads (even with memory) as we have at any instant of time Thevenin's equivalent of the linear portion of the system. An example is presented to illustrate the application of this technique to multiconductor nonlinearly loaded transmission lines.

Time-domain skin-effect model for transient analysis of lossy transmission lines

A skin-effect equivalent circuit consisting of resistors and inductors is derived from the skin-effect differential equations for simulating the loss of a transmission line. A numerical method is used to analyze the transmission-line differential equations and the skin-effect equivalent circuit, yielding a model which relates the new values of node voltages and line currents to their values at the previous time step. Based on this model, a very simple program was written on a desk-top computer for the transient analysis of lossy trammission lines. Two examples are presented. The first example is an analysis of the step and pulse responses of a 600-m RG-8/U coaxial cable. The computed results show excellent agreement with measured data. The second example studies the current at the end of a 12-in 7-Ω strip line under different loading conditions. Very good agreement has been obtained between the calculated steady-state solution and that obtained by the frequency-domain method.

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