Lossy Coupled Transmission Lines Research Articles

A Phenomenological Approach Based on Two Unified Loss Parameters for Transient Analysis of Transmission Lines

This article proposes a causal, accurate, and case-independent model, which can be used for the transient analysis of lossy coupled transmission lines. In addition to propagation delay and characteristic impedance, the method uses a phenomenological study on the frequency dependence of the transmission lines and identifies two unified parameters that, respectively, correspond to conductor (skin-effect) and dielectric loss. An accurate transient response is derived, and a generic circuit library is established for efficient and case-independent SPICE simulation. Using peak distortion analysis, the eye diagram versus loss parameters is plotted into unified design charts for eye height and width, which depicts the signal quality without the need for pseudorandom bit sequence simulation. The proposed model is also generalized to coupled transmission lines. The far-end crosstalk noise is found to be significantly affected by the loss parameters, and the proposed circuit model ensures accurate simulation.

Waveform Relaxation-Based Large-Scale Circuit Simulation for MOSFET and Lossy Coupled Transmission Line Circuits

In this paper, we propose a modified Waveform Relaxation algorithm to perform large-scale circuit simulation for MOSFET circuits containing lossy coupled transmission lines that have been encountered in modern circuit design community, in which a full time-domain transmission line calculation algorithm based on the Method of Characteristic is adopted. New software techniques are proposed to enhance the robustness as well as efficiency of the simulation process. All proposed methods have been implemented and executed to justify the claimed advantages.

Full-wave analysis of coupled lossy transmission lines using multiwavelet-based method of moments

Full-wave analysis for coupled lossy transmission lines with finite thickness is conducted using a multiwavelet-based method of moments (MBMM). We use the multiscalets with multiplicity r=2 as the basis and testing functions, and take the discrete Sobolev-type inner products to discretize the integral equation and its derivative at the testing points. Since the numerical integration is not needed in the testing procedure, the new approach is faster, yet preserves high accuracy due to the derivative sampling. In the new approach, we compute the incoming fields in the spatial domain directly without resorting to the inverse Fourier transform. Hence, the local coordinate system used to perform the Sommerfeld integral is avoided and the computational cost is reduced remarkably. In addition, a coarser mesh can be used owing to the smoothness of the multiscalets. Numerical examples show that the MBMM speeds up the traditional method of moments 3 /spl sim/ 10 times.

Transient analysis of transmission line circuits based on the semidiscretization of telegraph equations

A new transient analysis method for the transmission line circuits is presented in this paper. Based on the semidiscretization of the telegraph equations, a discretized time domain companion models for the transmission lines which can be conveniently implemented in a general circuit simulator such as SPICE is derived. The computation required for the model is linear with time, equivalent to the recursive convolution-based method. The formulations for both single and coupled lossy transmission lines are given. Numerical experiments are carried out to demonstrate the validity of the method.

Analysis of high-speed interconnects using efficient multipoint Padé approximation

An efficient method is presented for analysis of large interconnect circuits including lossy coupled transmission lines. Based on multipoint Padé approximations and a new expansion point search algorithm, the method can obtain single close-form frequency-domain and transient solutions of the interconnect problem with a minimum of frequency expansion points.

Nonlinear circuit-reduction of high-speed interconnect networks using congruent transformation techniques

A new algorithm based on Krylov subspace methods is proposed for efficient simulation of large interconnect networks with nonlinear terminations. Reduction is obtained by projecting the original system described by nonlinear differential equations into a subspace of a lower dimension. The reduced circuit can be simulated using conventional numerical integration techniques. Significant reduction in computational expense is achieved as the size of the reduced equations is much less than that of the original system. The new algorithm is potentially useful for analysis of lossy coupled transmission lines with nonlinear terminations.

Frequency- and time-domain analyses of nonuniform lossy coupled transmission lines with linear and nonlinear terminations

A new technique for the frequency- and time-domain characterization of nonuniform coupled transmission lines is presented in this paper. In the frequency domain, a method-of-moments-based approach is used to compute the 2N/spl times/2N scattering parameter matrix of the N-coupled lines using special frequency-dependent basis functions that give good accuracy over very large bandwidths. In the time domain, the structure's S-parameters are used as its Green's function and are combined with source and terminating load conditions to obtain its transient response. The proposed method can account for loss and is particularly suitable for wideband microwave component designs and ultrahigh-speed/large-bandwidth digital interconnects, including nonlinear terminating loads. A detailed formulation of both the frequency- and time-domain approaches is presented. Several examples of two- and three-line structures are analyzed and the results are compared to published results and other computer-aided-design simulations.

Efficient sensitivity analysis of transmission-line networks using model-reduction techniques

An efficient algorithm, based on congruent transformation and model reduction, is proposed for evaluation of frequency- and time-domain sensitivity of large linear networks containing lossy coupled transmission lines. The sensitivity of the voltage and current waveforms can be calculated with respect to lumped components and parameters of transmission lines. The algorithm is based on projecting the adjoint network equations on a reduced-order subspace that preserves the circuit moments. The proposed algorithm provides a significant decrease in the computational expense for sensitivity analysis.

Making a better interconnection through modeling

Introduces a simple technique for implementing nonuniform coupled transmission lines with frequency-dependent parameters into SPICE. The proposed method relies on the analog behavioral modeling option, which bypasses the problems of circuit synthesis and the need to develop sophisticated techniques for analysis of these kind of structures. We describe basic principles that serve to construct the model, derive a generalized model of characteristics typical of an n-conductor nonuniform lossy coupled transmission line system, establish the relationship between the S-parameters and the voltage-dependent voltage sources of the model, and deal with the implementation of the developed model to each port. Examples that illustrate the advantages of the model and concordance with previously published results are also presented.

Fast analytical approximations of the transient response of coupled lossy interconnects in VLSI circuits with frequency-dependent parameters for higher hierarchical simulation levels

This paper presents a quasi-analytical approach to analyse cross-talk, propagation delay, distortion on interconnects in high-speed integrated circuits, packages and boards. The approach is based upon a novel multipoint Padé approximation technique and approximates the transfer functions of single as well as coupled lossy transmission lines in the complex s-domain as rational functions. Transmission lines with both frequency- dependent (due to substrate losses) as well as frequency- independent parameters can be taken into account. This makes the method useful for the simulation of interconnects at higher hierarchical simulation levels where mostly only an RC-modelling of the transmission lines are carried out. Simulation results of four examples are presented to illustrate the application of the analysis. A comparison with results obtained from more stringent numerical simulations show very good agreement.

Comments on "Sensitivity analysis of lossy coupled transmission lines" [with reply

For the original article see ibid., vol. 39, no. 12, p. 2089-2099 (1991). In the aforementioned paper, a good agreement between the numerical inversion of Laplace transform (NILT) and HSPICE is presented for the transient response of a transmission line system with lumped terminal and interconnecting networks. Here Sakagami provides some comments on the derived transient response. In reply the authors clarify several points and give a summary of some results obtained in a numerical verification.

TLM diakoptics for coupled-mode analysis of GaAs MESFET distributed amplifier

A new model of the application of diakoptics in the transmission-line-matrix (TLM) method for the coupled-mode analysis of GaAs MESFET distributed amplifiers is proposed. The model takes into account the major coupling effect caused by C/sub dg/ and g/sub m/ of the active devices. Techniques are developed by representing the whole system as two coupled lossy transmission lines. The numerical effort required can be reduced by representing the response of the resultant coupled system as that of superposition of two independent modes. The scattering matrix of the system obtained in the time domain leads to a process of discrete time domain convolutions based on the TLM numerical procedure. The results are compared with other analytical and computed results and show good agreement.

Transient simulation of lossy coupled transmission lines using iterative linear least square fitting and piecewise recursive convolution

We present a computationally efficient method to stimulate lossy transmission lines using iterative linear least square fitting (ILLSF) model synthesis and piecewise recursive convolution (PRC). Based on the generalized method of characteristics, transmission lines are modeled with characteristic impedances and waveform generators. Thus the first major task involves network synthesis. The second is efficient computation of the synthesized waveform generators which requires computationally expensive convolution integral evaluation during transient simulation of transmission lines. The superior performance of ILLSF and the efficiency of PRC are demonstrated for the transient simulation of coupled lossy transmission lines.

Transient analysis of lossy coupled transmission lines in a lossy medium using the waveform relaxation method

The waveform relaxation method has been shown to be both efficient and accurate when applied to coupled transmission lines with conductor losses. In this paper, the method is generalized to include the dielectric loss surrounding the transmission lines. The distributed loss model assumes that the conductance matrix is approximately diagonal and its product with the resistive matrix is a scalar matrix. Computational results using the model is presented and compared with HSPICE solutions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Transient analysis of nonlinear circuits by combining asymptotic waveform evaluation with Volterra series

A new method is proposed for the transient analysis of circuits with large number of linear lumped elements and lossy coupled transmission lines, and with few mildly nonlinear terminations. The method combines the Volterra-series technique with Asymptotic Waveform Evaluation approach and corresponds to recursive analysis of a linear equivalent circuit. >

Analysis of interconnect networks using complex frequency hopping (CFH)

With increasing miniaturization and operating speeds, loss of signal integrity due to physical interconnects represents a major performance limiting factor of chip-, board- or system-level design. Moment-matching techniques using Pade approximations have recently been applied to simulating modelled interconnect networks that include lossy coupled transmission lines and nonlinear terminations, giving a marked increase in efficiency over traditional simulation techniques. Nevertheless, moment-matching can be inaccurate in high-speed circuits due to critical properties of Pade approximations. Further, moment-generation for transmission line networks can be shown to have increasing numerical truncation error with higher order moments. These inaccuracies are reflected in both the frequency and transient response and there is no criterion for determining the limits of the error. In this paper, a multipoint moment-matching, or complex frequency hopping (CFH) technique is introduced which extracts accurate dominant poles of a linear subnetwork up to any predefined maximum frequency. The method generates a single transfer function for a large linear subnetwork and provides for a CPU/accuracy tradeoff. A new algorithm is also introduced for generating higher-order moments for transmission lines without incurring increasing truncation error. Several interconnect examples are considered which demonstrate the accuracy and efficiency in both the time and frequency domains of the new method. >

Efficient approximation of the time domain response of lossy coupled transmission line trees

A new technique for rapidly estimating the transient response of lossy transmission line interconnect structures is introduced. The new approach, Reciprocal Expansion (REX), is similar to Asymptotic Waveform Evaluation (AWE) in that it approximates the interconnect by a low-order system. However, unlike AWE, REX expands the reciprocal of the transfer function as a Taylor series. REX has been extended to handle distributed elements directly, compute crosstalk between coupled trees, and account for frequency-dependent effects. Experimental results demonstrate that for critical underdamped interconnects, REX provides better accuracy than AWE.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Waveform relaxation analysis of lossy coupled transmission line sets in cascade

Waveform relaxation has been shown to provide an efficient way to evaluate the transient response of transmission line systems through the generalisation of the method of characteristics. This method has been extended to the simulation of coupled transmission line sets connected in cascade. The algorithms proposed have been applied to systems with linear and nonlinear terminations and the results are consistent with those found by the time-stepping method with speed improvement of at least 75 times.

Adaptation of "SPICE3" to simulation of lossy multiple-coupled transmission lines

Design of high-speed, high-performance electronic circuits requires simulation of transients in networks that include multiple, coupled lossy transmission lines. A widely used circuit simulator, SPICE, does not have facilities for simulation of multiconductor transmission lines. Recently a modification to SPICE3 to include multi-conductor lossless lines was reported. In many situations line losses must be included in the model and networks with lossy transmission simulated. In general simulation of lossy transmission lines is complex and computationally very intensive. The situation is simpler when D-C losses are considered. A recent study concluded that D-C losses provide an adequate modeling of signal transmission in many practical situations. This paper describes the implementation of multi-conductor, coupled lines with D-C losses in SPICE3e2. This implementation ties SPICE transient analysis with a special algorithm for the analysis of a transmission line and is more efficient than another approach based an the concept of a transmission line subcircuit. Internal tests of the new program, LSPICE3, were successfully performed and now this program is available to SPICE3 users. >

Sensitivity analysis of lossy coupled transmission lines with nonlinear terminations

An analysis method is described for the evaluation of the time domain sensitivity of nonlinear networks which include lossy coupled transmission lines. The method combines a linear sensitivity analysis method based on the numerical inversion of Laplace transform with the piecewise decomposition technique. The sensitivity can be calculated with respect to network components and parameters of the transmission lines. Sensitivity analysis is useful for waveform shaping and optimization. Examples and comparisons with sensitivity determined by perturbation are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>