Sensitivity analysis of lossy coupled transmission lines with nonlinear terminations

Abstract-There is a revival of the interest in adjoint sensitivity analysis techniques. This is partly because current computer-aided-design software based on full-wave electromagnetic (EM) solvers remains too slow for the purposes of practical high-frequency structure design despite the increasing capacity of computers. The adjoint-variable methods for design sensitivity analysis offer computational speed and accuracy. They can be used for efficient gradient-based optimization, in tolerance and yield analysis. Adjoint-based sensitivity analysis for circuits has been well studied and extensively covered in the microwave literature. In comparison, sensitivities with full-wave analysis techniques have attracted little attention, and there have been few applications into feasible and versatile algorithms. We review adjoint-variable methods used in high-frequency structure design with both circuit analysis techniques and full-wave EM analysis techniques. A brief discussion on adjoint-based sensitivity analysis for nonlinear dynamic systems is also included.

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“…We define the response function as in (22). The objective is to determine its sensitivity with respect to all as follows:…”

Section: A Direct Differentiation Methods For Linear Systemsmentioning

confidence: 99%

Adjoint Techniques for Sensitivity Analysis in High-Frequency Structure CAD

Nikolova

Bandler

Bakr

2004

IEEE Trans. Microwave Theory Techn.

103

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“…By restricting to be small enough, such that the eigenvalues of will also be small (over a given frequency range), so as not to cause truncation errors or slow convergence. This can be achieved efficiently, by noting that (116) In other words, moments of a line can be generated by squaring half-line moments. Let represent the half-line moments, then (117) which will give (118) The line can be subdivided by power of 2 (i.e., two sections, four sections, eight sections ) and the moments of the smallest section that meets the convergence requirements are calculated.…”

Section: B Computation Of Momentsmentioning

confidence: 99%

Simulation of high-speed interconnects

2001

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With the rapid developments in very large-scale integration (VLSI) technology, design and computer-aided design (CAD) techniques, at both the chip and package level, the operating frequencies are fast reaching the vicinity of gigahertz and switching times are getting to the subnanosecond levels. The ever increasing quest for high-speed applications is placing higher demands on interconnect performance and highlighted the previously negligible effects of interconnects, such as ringing, signal delay, distortion, reflections, and crosstalk. In this review paper, various high-speed interconnect effects are briefly discussed. In addition, recent advances in transmission line macromodeling techniques are presented. Also, simulation of high-speed interconnects using model-reduction-based algorithms is discussed in detail.

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“…Therefore, interconnects, integrated circuits and/or printed circuit boards are processed as systems with distributed parameters where the TL theory is considered. [37][38][39][40] A typical lossy TL can be represented mathematically by a set of PDEs, namely, a pair of telegraphic equations. Introducing the Laplace transform, as it is well known, the TL system equations can be considerably simpli¯ed resulting in ordinary di®erential equations (ODEs).…”

Section: Fractional-order Tl Modelmentioning

confidence: 99%

Application of Numerical Inverse Laplace Transform Methods for Simulation of Distributed Systems with Fractional-Order Elements

R‐Smith

Kartci

Brančík

2018

J CIRCUIT SYST COMP

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The paper presents a computationally e±cient method for modeling and simulating distributed systems with lossy transmission line (TL) including multiconductor ones, by a less conventional method. The method is devised based on 1D and 2D Laplace transforms, which facilitates the possibility of incorporating fractional-order elements and frequency-dependent parameters. This process is made possible due to the development of e®ective numerical inverse Laplace transforms (NILTs) of one and two variables, 1D NILT and 2D NILT. In the paper, it is shown that in high frequency operating systems, the frequency dependencies of the system ought to be included in the model. Additionally, it is shown that incorporating fractional-order elements in the modeling of the distributed parameter systems compensates for losses along the wires, provides higher degrees of°exibility for optimization and produces more accurate and authentic modelling of such systems. The simulations are performed in the Matlab environment and are e®ectively algorithmized.

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Sensitivity analysis of lossy coupled transmission lines with nonlinear terminations

Cited by 46 publications

References 25 publications

Adjoint Techniques for Sensitivity Analysis in High-Frequency Structure CAD

Adjoint Techniques for Sensitivity Analysis in High-Frequency Structure CAD

Simulation of high-speed interconnects

Application of Numerical Inverse Laplace Transform Methods for Simulation of Distributed Systems with Fractional-Order Elements

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