Conference Paper

Compact reduced order modeling for multiple-port interconnects

Dept. of Electr. Eng., California Univ., Riverside, CA, USA
DOI: 10.1109/ISQED.2006.35 Conference: Quality Electronic Design, 2006. ISQED '06. 7th International Symposium on
Source: DBLP


In this paper, we propose an efficient model order reduction (MOR) algorithm, called MTermMOR, for modeling interconnect circuits with large number of external ports. The proposed method overcomes the difficulty associated with Krylov subspace based projection MOR methods for reducing circuits with many ports. The novelty of the proposed method lies on the fact that we separately compute the poles and residues of each transfer function in the reduced admittance matrices. Specifically we apply traditional subspace projection method for computing poles and use hierarchical symbolic analysis for computing frequency responses of admittances to determine the residues of transfer functions. In this way, we only use necessary poles (smaller number of poles) to archive the same accuracy than subspace projection based methods. Finally convex programming based optimization is used to enforce the passivity of the reduced models. The new method can lead to much smaller reduced models for a given frequency range or much higher accuracy given the same model sizes than subspace projection based methods for multi-port interconnect circuits. Experimental results on several industry interconnect circuits demonstrate the advantage of the proposed method over the subspace projection based methods.

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    • "Motivated by the expanding complexity of nanoscale integrated circuits, the model order reduction (MOR) of RLC interconnect has been the focal point of substantial research efforts [1] [2] [3] [4] [5]. Model order reduction techniques can be divided into two categories, Singular Value Decomposition (SVD) methods and Krylov subspace projection methods. "
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    ABSTRACT: Model order reduction plays a key role in determining VLSI system performance and the optimization of intercon- nects. In this paper, we develop an accurate and provably passive method for model order reduction using adaptive wavelet-based frequency selective projection. The wavelet- based approach provides an automated means to generate low order models that are accurate in a particular range of frequencies. Theresults indicatethatourapproachprovides more accurate reduced order models than the spectral zero method with uniform interpolation points and the zero-shift and multi-shift Block Arnoldi-based techniques. In this paper, we develop an adaptive, passivity preserv- ing methodology for the selection of interpolation points in spectral zero-based model order reduction. We dynamically select expansion points by applying Haar wavelets to de- tect complex changes in the frequency points spanned by the spectral zeros of the system and select the dominant interpolation points. The adaptive scheme provides a low order realization with optimized matching of the system re- sponse for a given range of frequencies. The preservation of passivity is guaranteed by selecting interpolation points as a subset of the system's spectral zeros. The approximate low-order model can then be directly constructed from the projection matrices derived from these interpolants. In or- der to demonstrate the efficiency of the approach, we ap- ply our technique to an RLC network representing an in- terconnect wire. The results indicate that the wavelet-based method provides higher accuracy approximate models than techniques based on moment matching and uniform inter- polation point selection.
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    ABSTRACT: An efficient clustering scheme for macromodeling of massively coupled interconnect structures is presented. The proposed method addresses the issue of dense reduced models through a novel reduction algorithm that leads to sparse block-diagonal system matrices. It also overcomes the accuracy degradation, normally associated with the existing port-reduction techniques.
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    ABSTRACT: In this paper, a novel algorithm for creating efficient reduced-order macromodels from massively coupled interconnect structures is described. The new algorithm addresses the difficulty associated with the reduction of networks with a large number of input/output terminals, that often results in large and dense reduced-order models. Application of the proposed reduction algorithm leads to reduced-order models that are sparse and block-diagonal in nature. An additional advantage of the proposed algorithm is that it does not assume any correlation between the responses at ports and thereby overcomes the accuracy degradation that is normally associated with the existing singular value decomposition based terminal reduction techniques. Also, the presented algorithm is highly suited for multithreading implementation and thus facilitates parallel transient simulation. Validity and efficiency of the proposed algorithm are demonstrated through computational results.
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