A new two-terminal circuit element-called the memristorcharacterized by a relationship between the charge q(t)\equiv \int_{-\infty}^{t} i(\tau) d \tau and the flux-linkage \varphi(t)\equiv \int_{- \infty}^{t} v(\tau) d \tau is introduced as the fourth basic circuit element. An electromagnetic field interpretation of this relationship in terms of a quasi-static expansion of Maxwell's equations is presented. Many circuit-theoretic properties of memistors are derived. It is shown that this element exhibits some peculiar behavior different from that exhibited by resistors, inductors, or capacitors. These properties lead to a number of unique applications which cannot be realized with RLC networks alone. Although a physical memristor device without internal power supply has not yet been discovered, operational laboratory models have been built with the help of active circuits. Experimental results are presented to demonstrate the properties and potential applications of memristors.

Memristor-The missing circuit element

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

Part I. The Haskell 98 Language: 1 Introduction 2 Lexical structure 3 Expressions 4 Declarations and bindings 5 Modules 6 Predefined types and classes 7 Basic input/output 8 Standard prelude 9 Syntax reference 10 Specification of derived instances 11 Compiler pragmas Part II The Haskell 98 Libraries: 12 Rational numbers 13 Complex numbers 14 Numeric functions 15 Indexing operations 16 Arrays 17 List utilities 18 Maybe utilities 19 Character utilities 20 Monad utilities 21 Input/output 22 Directory functions 23 System functions 24 Dates and times 25 Locales 26 CPU time 27 Random numbers Bibliography.

Haskell 98 language and libraries : the revised report

We characterize high-performance streaming applications as a new and distinct domain of programs that is becoming increasingly important. The StreamIt language provides novel high-level representations to improve programmer productivity and program robustness within the streaming domain. At the same time, the StreamIt compiler aims to improve the performance of streaming applications via stream-specific analyses and optimizations. In this paper, we motivate, describe and justify the language features of StreamIt, which include: a structured model of streams, a messaging system for control, a re-initialization mechanism, and a natural textual syntax.

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StreamIt: A Language for Streaming Applications

A geometric program (GP) is a type of mathematical optimization problem characterized by objective and constraint functions that have a special form. Recently developed solution methods can solve even large-scale GPs extremely efficiently and reliably; at the same time a number of practical problems, particularly in circuit design, have been found to be equivalent to (or well approximated by) GPs. Putting these two together, we get effective solutions for the practical problems. The basic approach in GP modeling is to attempt to express a practical problem, such as an engineering analysis or design problem, in GP format. In the best case, this formulation is exact; when this is not possible, we settle for an approximate formulation. This tutorial paper collects together in one place the basic background material needed to do GP modeling. We start with the basic definitions and facts, and some methods used to transform problems into GP format. We show how to recognize functions and problems compatible with GP, and how to approximate functions or data in a form compatible with GP (when this is possible). We give some simple and representative examples, and also describe some common extensions of GP, along with methods for solving (or approximately solving) them.

/pdf/a-tutorial-on-geometric-programming-47sdznbzxw.pdf

A tutorial on geometric programming

In MOS integrated circuits, signals may propagate between stages with fanout. The exact calculation of signal delay through such networks is difficult. However, upper and lower bounds for delay that are computationally simple are presented in this paper. The results can be used 1) to bound the delay, given the signal threshold, or 2) to bound the signal voltage, given a delay time, or 3) certify that a circuit is "fast enough," given both the maximum delay and the voltage threshold.

/pdf/signal-delay-in-rc-tree-networks-523jfr2m16.pdf

Signal Delay in RC Tree Networks

: Contents: Nonrelativistic continuum mechanics and thermodynamics; Electromagnetism and simple polarizable fluid; Nonrelativistic principle of virtual power; Relativistic principle of virtual power; Hamilton's principle; Comparison of several formulations of electrodynamics of moving media; Electrodynamics literature.

Electrodynamics of moving media

In MOS integrated circuits, signals may propagate between stages with fanout. The MOS interconnect may be modeled by an RC tree. Exact calculation of signal delay through such networks is difficult. However, upper and lower bounds for delay that are computationally simple are presented here. The results can be used (1) to bound the delay, given the signal threshold; or (2) to bound the signal voltage, given a delay time; or (3) to certify that a circuit is "fast enough", given both the maximum delay and the voltage threshold.

B. D. H. Tellegen was the first to point out (1952, 1953) the generality and wide-ranging usefulness of the theorem that bears his name. Nevertheless, the theorem is still not as widely known as its utility warrants. The authors of this monograph set out to correct this neglect, noting that "There is hardly a basic network theorem that cannot be proved by invoking Tellegen's theorem. The simplicity and generality of the theorem make it attractive pedagogically, and its ability to generalize known results and lead to new results indicates its research value. This theorem definitely should be in every circuit designer's kit of tools."Tellegen's theorem is unusual in that it depends solely upon Kirchhoff's laws and the topology of the network. The theorem thus applies to all electrical networks that obey Kirchhoff's laws, whether linear or nonlinear, time-invariant or time-variant, reciprocal or nonreciprocal, passive or active, single-valued or multiple-valued, hysteretic or nonhysteretic. The excitation is arbitrary--it may be sinusoidal, exponential, periodic, transient, or random. Also, the initial conditions may be arbitrarily chosen. The modern interest in nonlinear and time-variant networks gives Tellegen's theorem a special new importance, because it is one of the very few general theorems that apply to such networks.To demonstrate its range of applications and the theorem's great power in the derivation of other basic and important theorems about electrical networks (and the extent that these other theorems are special cases of Tellegen's), the authors have collected more than 100 such theorems and have shown that they can be proved from Tellegen's theorem. Most of these were known before; but some are extended in their range of validity, and a few are new. (Apart from Tellegen's theorem, this collection of theorems is valuable in its own right.) Applications are given to automated network synthesis and to nonlinear, time-varying, switching, nonreciprocal, and other networks--all the major areas of network theory are covered. In addition, extensions of the theorem to other physical systems are discussed, including applications to the electromagnetic field, electron beams and plasmas, and quantum mechanics.The theorem is proved in its most general form thus far known. In addition, two weaker forms that have useful properties for certain applications are presented. In these weaker forms, the theorem applies to voltages, currents, and wave (or scattering) variables. The use of wave variables in Tellegen's theorem is believed to be new.Oliver Heaviside used a version of the theorem in 1883 to establish a specific result, and others have used its equivalent in a limited range of applications. Others (Weyl, 1923; Bott, 1949) have derived highly abstract and mathematical versions without regard to applications. But Tellegen was the first to devote a full paper to the subject and the first to grasp the theorem's general importance and applicability. In a similar way, the authors of this monograph are the first to devote a book to the subject and the first to collect (or newly present) all of the most important applications of the theorem in the hope of bringing it into the common currency it deserves.

Tellegen's theorem and electrical networks

De-embedding is the process of deducing the impedance of a device under test from measurernents made at a distance, when the electrical properties of the intervening structure are known. Unterminating is the process of deducing the electrical properties of the intervening structure from a series of measurements with known embedded devices. The mathematical steps necessary for de-embedding and unterminating with theoretically redundant measurements in order to minimize the effect of experimental errors.

Paul Penfield

Papers

Signal Delay in RC Tree Networks

Electrodynamics of moving media

Signal Delay in RC Tree Networks

Tellegen's theorem and electrical networks

De-Embedding and Unterminating