An efficient approach to transmission line simulation using measured or tabulated S-parameter data

Simulation of lossy multiconductor transmission lines using backward Euler integration

“…With impulse function excitations, the Laplace-domain system equations given in (1) becomes (19) Consider the Taylor-series expansion of the system vector about the frequency point : (20) where is the th-order shifted moment vector and is given as (21) Expanding about (22) and substituting (20) and (22) into (19) (23) where . Using (23), a recursive relationship for the shifted moment vectors can be obtained: (24) with (25) On the other hand, in the case of an impulse function excitation, the backward Euler integration given in (16) becomes (26) with (27) where the impulse function is descretized as (28) Comparison of (24)- (27) shows that shifted moments and backward Euler results are equivalent if the frequencydependent variables of the circuit are normalized such that .…”

“…The lossy coupled lines are characterized in the frequency domain and many techniques have been proposed for transformation into the time domain. They can basically be categorized into three groups: 1) inverse Fourier-transform-based techniques [7]- [10]; 2) inverse Laplace-transform-based techniques [11]- [13]; 3) rational or Padé-approximation-based techniques [14]- [20], [2]. Each method has its own advantages and disadvantages in terms of accuracy, efficiency, and generality, and we will not attempt a complete comparison in this paper.…”

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].…”

Efficient transient simulation of embedded subnetworks characterized by S-parameters in the presence of nonlinear elements

“…However, such an approach suffers in a general circuit environment containing a large number of nonlinear devices due to computational inefficiency and convergence problems. Approaches in the second category are based on obtaining a reduced-order model [6]- [8] for the measured data and performing the transient analysis using recursive convolution [7], [9]. However, there are three main difficulties associated with these approaches: 1) lack of a systematic approach [6] to capture the entire frequency spectrum of interest from the given -parameters; 2) CPU expense and stability problems associated with the convolution-based techniques; and 3) accuracy problems associated with the computation of moments.…”