Efficient simulation of lossy and dispersive transmission lines

Abstract

-This paper presents an efficient method, based on the transfer function simulation method, for the transient analysis of lossy and dispersive transmission lines terminated by nonlinear circuits. This method combines the efficiency provided by rational function approximation with the accuracy of using modal decomposition. For the task of computing the convolution integral, the transfer function simulation method was found to be more straightforward for implementation and more efficient than the recursive convolution method, thus providing further improvement in simulation efficiency. A robust and efficient method for the analysis of frequency dependent (dispersive) transmission lines is also reported. This method has been implemented in AS/X, IBM production circuit simulator, and has been used routinely for the analysis of practical lossy and dispersive coupled transmission lines.

An optimum fitting algorithm for generation of reduced-order models

“…Assuming the discrepancy between the initial and new approximation () to be sufficiently small it can be presented after linearization (5) in the form: (6) Let the originals of Laplace functions in (6) be the following:…”

ftd

“…A twoport example is written as: (1) The first equation in (1) can be expressed as: (2) where the general form of any y ij (s) term is: (3) Using recursive convolution [1], state space method [2], or the approach proposed in this paper, the discrete time domain model of (2) at time point t k can be written as: (4) once a time step is chosen. It follows from (1) that: (5) The equivalent circuit realization of (5) is shown in Fig.1, where each port includes an equivalent conductance, current source, and VCCS.…”

“…The second approach is the state-space method [2], whereby a numerical integration scheme such as trapezoidal is applied to the state space realization of the frequency domain model to compute a discrete time domain model. Among the two, recursive convolution achieves the best possible accuracy [3], but can be inefficient due to the inherent complexity of the algorithm. In contrast, the statespace method requires fewer floating-point operations at each time point than recursive convolution, but has inferior accuracy due to the required numerical integration scheme.…”

An optimum fitting algorithm for generation of reduced-order models

“…AWE is a generalized approach of approximating the dominant pole/zeros for linear circuit. Some techniques directed to solve large dimension problems arising in VLSI/ ULSI design have been implemented (see for instance [2][3][4][5][6][7][8][9]). At the present time state-of-art in this research direction can be conditionally characterized by successful exploitation of Pade via Lanczos method [5].…”