Asymptotic waveform evaluation (AWE) provides a generalized approach to linear RLC circuit response approximations. The RLC interconnect model may contain floating capacitors, grounded resistors, inductors, and even linear controlled sources. The transient portion of the response is approximated by matching the initial boundary conditions and the first 2q-1 moments of the exact response to a lower-order q-pole model. For the case of an RC tree model, a first-order AWE approximation reduces to the RC tree methods. >

Asymptotic waveform evaluation for timing analysis

Concern about the performance of wires wires in scaled technologies has led to research exploring other communication methods. This paper examines wire and gate delays as technologies migrate from 0.18-/spl mu/m to 0.035-/spl mu/m feature sizes to better understand the magnitude of the the wiring problem. Wires that shorten in length as technologies scale have delays that either track gate delays or grow slowly relative to gate delays. This result is good news since these "local" wires dominate chip wiring. Despite this scaling of local wire performance, computer-aided design (CAD) tools must still become move sophisticated in dealing with these wires. Under scaling, the total number of wires grows exponentially, so CAD tools will need to handle an ever-growing percentage of all the wires in order to keep designer workloads constant. Global wires present a more serious problem to designers. These are wires that do not scale in length since they communicate signals across the chip. The delay of these wives will remain constant if repeaters are used meaning that relative to gate delays, their delays scale upwards. These increased delays for global communication will drive architectures toward modular designs with explicit global latency mechanisms.

The future of wires

This paper describes an algorithm for generating provably passive reduced-order N-port models for RLC interconnect circuits. It is demonstrated that, in addition to macromodel stability, macromodel passivity is needed to guarantee the overall circuit stability once the active and passive driver/load models are connected. The approach proposed here, PRIMA, is a general method for obtaining passive reduced-order macromodels for linear RLC systems. In this paper, PRIMA is demonstrated in terms of a simple implementation which extends the block Arnoldi technique to include guaranteed passivity while providing superior accuracy. While the same passivity extension is not possible for MPVL, comparable accuracy in the frequency domain for all examples is observed.

/pdf/prima-passive-reduced-order-interconnect-macromodeling-4a2e1xctkb.pdf

PRIMA: passive reduced-order interconnect macromodeling algorithm

In this paper, we introduce PVL, an algorithm for computing the Pade approximation of Laplace-domain transfer functions of large linear networks via a Lanczos process. The PVL algorithm has significantly superior numerical stability, while retaining the same efficiency as algorithms that compute the Pade approximation directly through moment matching, such as AWE and its derivatives. As a consequence, it produces more accurate and higher-order approximations, and it renders unnecessary many of the heuristics that AWE and its derivatives had to employ. The algorithm also computes an error bound that permits to identify the true poles and zeros of the original network. We present results of numerical experiments with the PVL algorithm for several large examples. >

Efficient linear circuit analysis by Pade approximation via the Lanczos process

The objective of this paper is to outline a methodology for the computation of the response of a multiconductor transmission line terminated by linear networks. The lines are embedded in a multilayered lossy dielectric media and have arbitrary cross sections, but uniform along the length. To check the accuracy of the theoretical results, extensive experimental verification has been carried out.

Analysis of Multiconductor Transmission Lines

The universality of the state-variable approach to network analysis is demonstrated in general discussions and specific examples. The method of formulation of the state equations for an arbitrary lumped, linear, finite, reciprocal, passive, time-invariant network is presented fully, while the relaxation of these restrictions is indicated in detail; i.e., the state-variable characterization of active, nonreciprocal, time-variable, and nonlinear networks is discussed. Finally, there is a brief guide of the current research where the state-variable analysis is brought to bear upon certain qualitative aspects of classical and nonclassical network behavior.

The state-variable approach to network analysis

Powdered acidophil fermented milk products that can be readily reconstituted are prepared by spray drying milk which has been fermented with acidophil bacteria to produce a powdered product, agglomerating the powdered product, lyophilizing a culture of acidophil bacteria under specific conditions to insure maximum survival of the bacteria to produce a foamy dried mass containing live acidophil bacteria, grinding the foamy dried mass and mixing the resultant ground powdered product with the agglomerated powdered product to produce a powdered acidophil milk product that can be readily reconstituted to produce an acidophil milk containing about 200 million acidophil bacteria per cc.

Theory of Linear Active Networks

The sensitivity of a control system is usually taken to be the normalized variation of some desired characteristic with the variation of plant or controller parameters. Rather than the usual absolute sensitivity described above, a new definition of relative sensitivity is introduced for the optimal control problem, wherein the system performance is always compared with its optimum under the given circumstances. The implications of the relative sensitivity and its relevance to optimal system design are discussed in detail. Moreover, a theoretical approach to the problem of system optimization when plant parameters are subject to change or are incompletely specified is presented.

/pdf/sensitivity-considerations-in-optimal-system-design-1i0v91k0uj.pdf

Sensitivity considerations in optimal system design

A method for obtaining the dynamic equations for a broad class of driven nonlinear networks is presented. The parametric approach to element value characterization leads to a mathematical description for any unicursal network element. The parametric representation allows the mathematical description of any RLC network which contains such elements and independent sources by means of a set of coupled algebraic-differential equations. The conditions under which these governing equations can be reformulated in the mathematically convenient normal form are given with the explicit means for doing so. Finally, simple methods are presented for revising the original network model so that the normal form exists over the entire dynamic space under mild restrictions.

R.A. Rohrer

Papers

Asymptotic waveform evaluation for timing analysis

The state-variable approach to network analysis

Theory of Linear Active Networks

Sensitivity considerations in optimal system design

On the Dynamic Equations of a Class of Nonlinear RLC Networks