J. Cullum et al., A method for reduced-order modeling and simulation of large interconnect circuits and its application to PEEC models with retardation, IEEE CIR-II, 47(4), 2000, pp. 261-273
Citations number
35
Categorie Soggetti
Eletrical & Eletronics Engineeing
Journal title
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-ANALOG AND DIGITAL SIGNAL PROCESSING
The continuous improvement in the performance and the increases in the size
s of VLSI systems make electrical interconnect and package (EIP) design and
modeling increasingly more important. Special software tools must be used
for the design of high-performance VLSI systems. Furthermore, larger and fa
ster systems require larger and more accurate circuit models. The partial e
lement equivalent circuit (PEEC) technique is used for modeling such system
s with three-dimensional full wave models. In this paper, we present a prac
tical, readily parallelizable procedure for generating reduced-order freque
ncy-domain models from general full wave PEEC systems, We use multiple expa
nsion points, and piecemeal construction of pole-residue approximations to
transfer functions of the PEEC systems, as was used in the complex frequenc
y hopping algorithms. We consider general, multiple-input/multiple-output P
EEC systems, Our block procedure consists of an outer loop of local approxi
mations to the PEEC system, coupled with an inner loop where an iterative m
odel-reduction method is applied to the local approximations. We systematic
ally divide the complex frequency region of interest into small regions and
construct local approximations to the PEEC system in each subregion. The l
ocal approximations are constructed so that the matrix factorizations assoc
iated with each of them are the size of the original system and independent
of the order of the approximation. Results of computations on these local
systems are combined to obtain a reduced-order model for the original PEEC
system. We demonstrate the usefulness of our approach with three interestin
g examples.