EE5900 Spring Lecture 4 IC interconnect modeling methods Zhuo Feng
|
|
- Moris Garrett
- 5 years ago
- Views:
Transcription
1 EE59 Spring Parallel LSI AD Algoriths Lecture I interconnect odeling ethods Zhuo Feng. Z. Feng MTU EE59
2 So far we ve considered only tie doain analyses We ll soon see that it is soeties preferable to odel in the coplex frequency doain, s Priarily when circuits are linear or even weakly nonlinear LTI ckt We ll first consider analysis in the real frequency doain. Z. Feng MTU EE59
3 Analog circuits are generally analyzed in the frequency doain ( j) Transient response is of short duration copared to periodic response of interest: ( t ) t transient. Z. Feng MTU EE59
4 9 cos t f 9 8 5x F H j j R Steady state response will be of sae frequency but different ag & phase. Z. Feng MTU EE59
5 Focusing on the steady state solution we can analyze the ag and phase responses.667. H = radians/sec - H = atan radians/sec.5 Z. Feng MTU EE59
6 Under sall-signal assuption, nonlinear eleents are linearized i about dc operating pt. First step is to solve for nonlinear dc solution Ex: siple coon eitter ckt R R c c RL R R e.6 Z. Feng MTU EE59
7 D gain establishes bias pt for the aplifier Linearized odel at final N-R iteration represents sall-signal signal ac odel and soe dc bias currents i c v ce.7 Z. Feng MTU EE59
8 ac analysis for analog ckts. Solve for dc operating pt. via N-R. hange RHS vector ters to generate sall-signal ac odels fro final N-R linearization. Asseble coplex ipedance equations Y j. Solve for agnitude and phase at discrete frequency points for variables of interest.8 Z. Feng MTU EE59
9 Sall-signal assuption: input voltages are so sall that t nonlinearities iti are negligible ibl Not really true for all analog circuits and all responses of interest Nonlinearities cause distortion of analog signals which are often design constraints Later we will consider nonlinearities in the frequency doain via other analyses.9 Z. Feng MTU EE59
10 Exaple:. Solve for dc bias point R R c R R e. Z. Feng MTU EE59
11 To siplify we ll use an Ebers-Moll odel for the forward active region B F I F I F E. Z. Feng MTU EE59
12 Nonlinear dc solution for this ckt is a -D proble R R R R e I F I F. Z. Feng MTU EE59
13 i d Load line Last N-R iteration Diode odel EQ I EQ v d I EQ. Z. Feng MTU EE59
14 . Build ckt equations for ac sall signal analysis id EQ EQ v d. Z. Feng MTU EE59
15 . dv s dt j dc operating pt. is used to specify capacitance values for nonlinear s too.5 Z. Feng MTU EE59
16 ac Analysis Model: R R I I F j bc jj c IN j R EQ j be jj js R L Re je.6 Z. Feng MTU EE59
17 Forulate nodal equations: Y ( j) ( j) I ( j) n iven a particular value, solve for ( j) Translate coplex voltage into agnitude and phase Probles with s as Bigger proble for L as Z L j L Y L jl n.7 Z. Feng MTU EE59
18 Nodal analysis does not like infinite conductance Z L j L Y L jl eneral solution is to treat L like a voltage source and use auxiliary equations for inductor currents.8 Z. Feng MTU EE59
19 Soeties analog designers prefer poles / zeros instead of a freq. doain ag. and phase plots We start by forulating the equations using s instead of s j x( s) x( s) B u( s).9 Z. Feng MTU EE59
20 onsider a linear interconnect ckt exaple sl s 6 5 s 5 s 8 5 in s s s s We can stap these eqns. into the for s x ( s ) x ( s ) Bu ( s ). Z. Feng MTU EE59
21 s S L i i L Z. Z. Feng Feng MTU EE59 MTU EE59..
22 5 5 IN i L S i Z. Z. Feng Feng MTU EE59 MTU EE59..
23 Isolating one response variable of interest: s x ( s ) Bu ( s ) x ( s ) s Bu ( s ) and i ( s) L T s Bu( s). Z. Feng MTU EE59
24 For exaple, if we are interested in the response at node 7: s Bu ( ) T 7 ( s ) L s T where L For a transfer fct at node 7, u( s) H ( s L s 7 ) B T. Z. Feng MTU EE59
25 i s Bu ( s ) T ( s ) L s We know fro raer s Rule that any node voltage solution will be of the for: i ( s) dett T det s s z s z s z s p s p s p n det s The roots of are the ckt poles.5 Z. Feng MTU EE59
26 det s s singular s p i Muller s root finding algorith: Search for points for which det(s+)= Select points in s-plane Interpolate with polynoial Solve for polynoial root Use root to prune search Fit new polynoial And so on.6 Z. Feng MTU EE59
27 How do we test to see if Y s LU Factor Y det Y det L det U dt det L Difficult to find all of the poles in a freq. range reliably We ll actually show a better way of doing this using odel order reduction ethods.7 Z. Feng MTU EE59
28 An alternative way of perforing frequency doain analysis is via oents We ll first show how oents can be used to represent linear syste responses Including generation of transfer functions Becae very popular for interconnect analysis probles Then we ll show how we can extend these techniques to tie-varying nonlinear systes.8 Z. Feng MTU EE59
29 Start with a linear interconnect ckt s6 5 s 5 s sl 8 5 in s s s s We know that we can stap these eqns. into the for: sx( s) x( s) Bu( s).9 Z. Feng MTU EE59
30 s S L i i L Z. Z. Feng Feng MTU EE59 MTU EE59..
31 5 5 IN i L S i Z. Z. Feng Feng MTU EE59 MTU EE59..
32 s x ( s ) Bu ( s ) Y (s) x ( s) s Bu( s) If we are interested in the response at node 7: where s Bu ( s ) T 7 ( s ) L s T L For a transfer fct at node 7, u( s) H7 ( s) L s T B. Z. Feng MTU EE59
33 enerally, we express transfer functions in a siilar for: H s a b as a b s b n s s n n It s ipractical, however, to calculate transfer functions sybolically ll for large ckts in either for Therefore, we instead start with series expansions in s. Z. Feng MTU EE59
34 By definition of the Laplace transfor: H st s h t e dt Expanding about s H s h t st s t s t dt 6 k k k! s k t k h t dt Like oents fro probability theory H s s s We call the -ters oents here. Z. Feng MTU EE59
35 We can use value for s= b a a s an s b s b s a b since can be used to represent n s s n zeros & poles But how any oents do I need to copletely specify y -pole syste?.5 Z. Feng MTU EE59
36 n a a s a s b s b s s n hapter 6 shows a th order syste exaple: a as as as bs bs bs bs s s ollect the coefficients for equations in ters of unknown coefficients Assuing we have calculated as any oents L T as necessary fro L S B.6 Z. Feng MTU EE59
37 a as as as bs bs bs bs s s a a a a b b b b b b b b b b b b b b 5 b b b b b b b b Z. Feng MTU EE59
38 The next equation would be: b b b b 5 6 But it can be shown that this is not linearly independent of original equations 7 8 In general, oents uniquely specify an order syste th linear equations in ters of unknowns when oents are known last equations can be used to calculate the b-coefficients.8 Z. Feng MTU EE59
39 b b b b 5 b b b b b b b b 6 5 b b b b b b b b b 5 b b b b b Z. Z. Feng Feng MTU EE59 MTU EE Hankel atrix ill-conditioned
40 This Hankel atrix can be LU factored to solve for denoinator coefficients: b, b, b, b The roots of the ckt poles b s bs bs bs are Once we have the b-ters, the a-ters are easily obtained fro the first four equations iven the nuerator coefficients, the roots of: a a s a s a s are the ckt zeros -- at a specific node of interest!. Z. Feng MTU EE59
41 Poles are the inverse of our tie constants Responses are sus of decaying exponentials with decay rates specified by poles pit kie i k i ' s Zeros specify the residues, -- the aount of energy at a particular frequency. Z. Feng MTU EE59
42 All of this assues that we can calculate oents easily For an ipulse response: x( s) s B x xs xs since U s L T We pre-ultiply by to get a response at one node: T s L s B s s Z. Feng MTU EE59
43 7 T s L s B L T s B set A L T sa B L T sa B L T sa B set R B sa R L T expand about s. Z. Feng MTU EE59
44 T 7 s L sa R d d s s s s s 7 ds 7 s ds 7 s d ds d ds d ds s s 7 7 s s n n s s 7 s L T sa A R L T AR sa A R L T L T A R n!! L T A n R. Z. Feng MTU EE59
45 ` learly we can solve for A and and fro the recursively calculate oents R B Then solving the Hankel atrix forulation we can obtain the coefficients for poles characteristic eqn Not a well conditioned atrix proble however - - ore on this later.55 Z. Feng MTU EE59
46 A L R B k k If and, how do we solve for the oents, K fro to A R T ust be nonsingular LU factor -- dc equivalent ckt solution Recursive application of.66 Z. Feng MTU EE59
47 dc recursive for oents v s sl v s 7 6 s 6 5 s 5 s 8 5 in i L s s s s in s s s i L L L s.77 Z. Feng MTU EE59
48 Moents are unknown, but we can express capacitor currents in ters of capacitor voltages, and inductor voltages in ters of inductor currents I s o s sl L L L o s.88 Z. Feng MTU EE59
49 dc equivalent ckt 6 I 6 5 s I 5 L sl I L i L I I I L s I s s Solve for the oents recursively.99 Z. Feng MTU EE59
50 6 k k 5 k 6 6 k c k k L Lk k k k in k L k k k k k.5 Z. Feng MTU EE59
51 oupling capacitors can be split into two current sources to aintain a tree structure for interconnect s 5 5 k c k s k I 6 6 s o s o s.5 Z. Feng MTU EE59
52 Tree-like interconnect structures can be solved efficiently via path tracing In general we won t attept to solve for oents to get an exact solution Instead we ll calculate p oents in an attept to capture the p-ost doinant poles Asyptotic Wavefor Evaluation (AWE).5 Z. Feng MTU EE59
53 Model Order Reduction Take an -th order syste alculate q oents (q<<) enerate a q-th order odel as if it were a q-th order syste Moent atching or Pade approxiation Used in any areas of science & engineering Sees straightforward, but there are any probles and issues to be dealt with.5 Z. Feng MTU EE59
54 Exaple: first order odel of -th order syste alculate first two oents at a response node of interest kˆ pˆ t s or v t ke ˆ s pˆ Single-pole ipulse response odels Moents are ˆ ˆ pt ke dt tke ˆ pt ˆ dt kˆ pˆ kˆ ˆp.5 Z. Feng MTU EE59
55 Moents are calculated fro ckt so we can use the to deterine the values for kˆ and pˆ kˆ pˆ kˆ p ˆ Two equations in ters of two unknowns.55 Z. Feng MTU EE59
56 pˆ is an approxiation of the doinant (sallest) pole (largest tie constant) v t k e p t k e p t k e p t vv t t.56 Z. Feng MTU EE59
57 Ipulse Response: n n s b b s s a s a s H If dc gain = In ters of poles & zeros: z s z s z s n p s p s p s z z z s H Z. Z. Feng Feng MTU EE59 MTU EE
58 To see the relationship to oents, we can expand H s Which is equivalent to: as ans b s b s n b s b s a s a s.58 Z. Feng MTU EE59
59 a b Fro b n a Z j P j P j If there are no low frequency zeros, is sall If p Then b is uch saller than all other poles b p p p j for j Z j,, p a.59 Z. Feng MTU EE59
60 First oent of ipulse response is a reasonable doinant pole approxiation under certain conditions Basis for use of Elore Delay as a doinant tie constant approxiation O X j s-plane X O X O XX O X But note that while varies fro node to node, the actual poles do not.6 Z. Feng MTU EE59
61 What about odels for q>? Moents are fro expansion about s= so we expect q-th order odel to capture the lower frequency poles nd order odel atching oents: ˆ ˆ pˆ t pˆ t h t ke ke After integration by parts to obtain oent forulas: kˆ kˆ kˆ pˆ ˆ p pˆ ˆ p kˆ p ˆ ˆ p ˆ pˆ p kˆ kˆ ˆ kˆ kˆ.6 Z. Feng MTU EE59
62 ould solve nonlinear equations in ters of unknown, but a better way is via Hankel atrix equations Treat this as a nd order syste: b b Solve for b-coefficients, then solve For the poles b ˆ ˆ p b p pˆ and pˆ p.6 Z. Feng MTU EE59
63 iven the poles, we can solve for the zeros and/or residues directly via a linear set of equations: kˆ kˆ pˆ ˆ p kˆ kˆ p ˆ ˆ p In atrix for we write this as k anderonde atrix Diagonal atrix of /p s First q oents *pg. 7-7 of the textbook.6 Z. Feng MTU EE59
64 Siple Exaple:. 5 5 in Z. Feng MTU EE59
65 onvergence of pole approxiations: Exact poles st order nd order rd order th order Z. Feng MTU EE59
66 R clock tree with 765 nodes v(t) input voltage rap nd, rd order AWE, and SPIE siulation st order AWE tie.66 Z. Feng MTU EE59
67 RL clock tree with 97 nodes v(t) input nd order AWE st order AWE rd order AWE SPIE siulation tie.67 Z. Feng MTU EE59
68 In theory we can apply oent atching for any order of approxiation But in practice it s not so siple: Approxiations of stable systes can be unstable Finite precision probles Inherent instability of Pade approxiations.68 Z. Feng MTU EE59
Chapter 2. Small-Signal Model Parameter Extraction Method
Chapter Sall-Signal Model Paraeter Extraction Method In this chapter, we introduce a new paraeter extraction technique for sall-signal HBT odeling. Figure - shows the sall-signal equivalent circuit of
More informationlecture 37: Linear Multistep Methods: Absolute Stability, Part I lecture 38: Linear Multistep Methods: Absolute Stability, Part II
lecture 37: Linear Multistep Methods: Absolute Stability, Part I lecture 3: Linear Multistep Methods: Absolute Stability, Part II 5.7 Linear ultistep ethods: absolute stability At this point, it ay well
More informationChapter 10: Sinusoidal Steady-State Analysis
Chapter 0: Sinusoidal Steady-State Analysis Sinusoidal Sources If a circuit is driven by a sinusoidal source, after 5 tie constants, the circuit reaches a steady-state (reeber the RC lab with t = τ). Consequently,
More informationChapter 10 Objectives
Chapter 10 Engr8 Circuit Analysis Dr Curtis Nelson Chapter 10 Objectives Understand the following AC power concepts: Instantaneous power; Average power; Root Mean Squared (RMS) value; Reactive power; Coplex
More information13.2 Fully Polynomial Randomized Approximation Scheme for Permanent of Random 0-1 Matrices
CS71 Randoness & Coputation Spring 018 Instructor: Alistair Sinclair Lecture 13: February 7 Disclaier: These notes have not been subjected to the usual scrutiny accorded to foral publications. They ay
More informationUfuk Demirci* and Feza Kerestecioglu**
1 INDIRECT ADAPTIVE CONTROL OF MISSILES Ufuk Deirci* and Feza Kerestecioglu** *Turkish Navy Guided Missile Test Station, Beykoz, Istanbul, TURKEY **Departent of Electrical and Electronics Engineering,
More informationThe Wilson Model of Cortical Neurons Richard B. Wells
The Wilson Model of Cortical Neurons Richard B. Wells I. Refineents on the odgkin-uxley Model The years since odgkin s and uxley s pioneering work have produced a nuber of derivative odgkin-uxley-like
More informationA Simplified Analytical Approach for Efficiency Evaluation of the Weaving Machines with Automatic Filling Repair
Proceedings of the 6th SEAS International Conference on Siulation, Modelling and Optiization, Lisbon, Portugal, Septeber -4, 006 0 A Siplified Analytical Approach for Efficiency Evaluation of the eaving
More informationList Scheduling and LPT Oliver Braun (09/05/2017)
List Scheduling and LPT Oliver Braun (09/05/207) We investigate the classical scheduling proble P ax where a set of n independent jobs has to be processed on 2 parallel and identical processors (achines)
More informationModel Fitting. CURM Background Material, Fall 2014 Dr. Doreen De Leon
Model Fitting CURM Background Material, Fall 014 Dr. Doreen De Leon 1 Introduction Given a set of data points, we often want to fit a selected odel or type to the data (e.g., we suspect an exponential
More informationPERIODIC STEADY STATE ANALYSIS, EFFECTIVE VALUE,
PERIODIC SEADY SAE ANALYSIS, EFFECIVE VALUE, DISORSION FACOR, POWER OF PERIODIC CURRENS t + Effective value of current (general definition) IRMS i () t dt Root Mean Square, in Czech boo denoted I he value
More informationlecture 36: Linear Multistep Mehods: Zero Stability
95 lecture 36: Linear Multistep Mehods: Zero Stability 5.6 Linear ultistep ethods: zero stability Does consistency iply convergence for linear ultistep ethods? This is always the case for one-step ethods,
More informationKernel Methods and Support Vector Machines
Intelligent Systes: Reasoning and Recognition Jaes L. Crowley ENSIAG 2 / osig 1 Second Seester 2012/2013 Lesson 20 2 ay 2013 Kernel ethods and Support Vector achines Contents Kernel Functions...2 Quadratic
More information26 Impulse and Momentum
6 Ipulse and Moentu First, a Few More Words on Work and Energy, for Coparison Purposes Iagine a gigantic air hockey table with a whole bunch of pucks of various asses, none of which experiences any friction
More informationMeasuring Temperature with a Silicon Diode
Measuring Teperature with a Silicon Diode Due to the high sensitivity, nearly linear response, and easy availability, we will use a 1N4148 diode for the teperature transducer in our easureents 10 Analysis
More informationECEG 351 Electronics II Spring 2017
ECEG 351 Electronics Sprin 017 Review Topics for Exa #3 Please review the Exa Policies section of the Exas pae at the course web site. You should especially note the followin: 1. You will be allowed to
More informationa a a a a a a m a b a b
Algebra / Trig Final Exa Study Guide (Fall Seester) Moncada/Dunphy Inforation About the Final Exa The final exa is cuulative, covering Appendix A (A.1-A.5) and Chapter 1. All probles will be ultiple choice
More informationChapter 28: Alternating Current
hapter 8: Alternating urrent Phasors and Alternating urrents Alternating current (A current) urrent which varies sinusoidally in tie is called alternating current (A) as opposed to direct current (D).
More informationEE5900 Spring Lecture 5 IC interconnect model order reduction Zhuo Feng
EE59 Spring Parallel VLSI CAD Algorithms Lecture 5 IC interconnect model order reduction Zhuo Feng 5. Z. Feng MU EE59 In theory we can apply moment matching for any order of approximation But in practice
More informationChapter 10: Sinusoidal Steady-State Analysis
Chapter 0: Sinusoidal Steady-State Analysis Sinusoidal Sources If a circuit is driven by a sinusoidal source, after 5 tie constants, the circuit reaches a steady-state (reeber the RC lab with t τ). Consequently,
More informationECEG 351 Electronics II Spring 2017
G 351 lectronics Sprin 2017 Review Topics for xa #1 Please review the xa Policies section of the xas pae at the course web site. Please especially note the followin: 1. You will be allowed to use a non-wireless
More informationAnalyzing Simulation Results
Analyzing Siulation Results Dr. John Mellor-Cruey Departent of Coputer Science Rice University johnc@cs.rice.edu COMP 528 Lecture 20 31 March 2005 Topics for Today Model verification Model validation Transient
More informationKeywords: Estimator, Bias, Mean-squared error, normality, generalized Pareto distribution
Testing approxiate norality of an estiator using the estiated MSE and bias with an application to the shape paraeter of the generalized Pareto distribution J. Martin van Zyl Abstract In this work the norality
More informationA method to determine relative stroke detection efficiencies from multiplicity distributions
A ethod to deterine relative stroke detection eiciencies ro ultiplicity distributions Schulz W. and Cuins K. 2. Austrian Lightning Detection and Inoration Syste (ALDIS), Kahlenberger Str.2A, 90 Vienna,
More informationChapter 10 ACSS Power
Objectives: Power concepts: instantaneous power, average power, reactive power, coplex power, power factor Relationships aong power concepts the power triangle Balancing power in AC circuits Condition
More informationFeature Extraction Techniques
Feature Extraction Techniques Unsupervised Learning II Feature Extraction Unsupervised ethods can also be used to find features which can be useful for categorization. There are unsupervised ethods that
More informationBEF BEF Chapter 2. Outline BASIC PRINCIPLES 09/10/2013. Introduction. Phasor Representation. Complex Power Triangle.
BEF 5503 BEF 5503 Chapter BASC PRNCPLES Outline 1 3 4 5 6 7 8 9 ntroduction Phasor Representation Coplex Power Triangle Power Factor Coplex Power in AC Single Phase Circuits Coplex Power in Balanced Three-Phase
More informationEE 330 Lecture 31. Basic amplifier architectures. Common Emitter/Source Common Collector/Drain Common Base/Gate
33 Lecture 3 asic aplifier architectures oon itter/source oon ollector/drain oon ase/gate eview fro arlier Lecture Two-port representation of aplifiers plifiers can be odeled as a two-port y 2 2 y y 22
More informationUsing a De-Convolution Window for Operating Modal Analysis
Using a De-Convolution Window for Operating Modal Analysis Brian Schwarz Vibrant Technology, Inc. Scotts Valley, CA Mark Richardson Vibrant Technology, Inc. Scotts Valley, CA Abstract Operating Modal Analysis
More informationCSE525: Randomized Algorithms and Probabilistic Analysis May 16, Lecture 13
CSE55: Randoied Algoriths and obabilistic Analysis May 6, Lecture Lecturer: Anna Karlin Scribe: Noah Siegel, Jonathan Shi Rando walks and Markov chains This lecture discusses Markov chains, which capture
More informationSome Perspective. Forces and Newton s Laws
Soe Perspective The language of Kineatics provides us with an efficient ethod for describing the otion of aterial objects, and we ll continue to ake refineents to it as we introduce additional types of
More informationDonald Fussell. October 28, Computer Science Department The University of Texas at Austin. Point Masses and Force Fields.
s Vector Moving s and Coputer Science Departent The University of Texas at Austin October 28, 2014 s Vector Moving s Siple classical dynaics - point asses oved by forces Point asses can odel particles
More informationDESIGN OF MECHANICAL SYSTEMS HAVING MAXIMALLY FLAT RESPONSE AT LOW FREQUENCIES
DESIGN OF MECHANICAL SYSTEMS HAVING MAXIMALLY FLAT RESPONSE AT LOW FREQUENCIES V.Raachran, Ravi P.Raachran C.S.Gargour Departent of Electrical Coputer Engineering, Concordia University, Montreal, QC, CANADA,
More informationStudy Committee B5 Colloquium 2005 September Calgary, CANADA
36 Study oittee B olloquiu Septeber 4-6 algary, ND ero Sequence urrent opensation for Distance Protection applied to Series opensated Parallel Lines TKHRO KSE* PHL G BEUMONT Toshiba nternational (Europe
More informationReducing Vibration and Providing Robustness with Multi-Input Shapers
29 Aerican Control Conference Hyatt Regency Riverfront, St. Louis, MO, USA June -2, 29 WeA6.4 Reducing Vibration and Providing Robustness with Multi-Input Shapers Joshua Vaughan and Willia Singhose Abstract
More informationStatistical Logic Cell Delay Analysis Using a Current-based Model
Statistical Logic Cell Delay Analysis Using a Current-based Model Hanif Fatei Shahin Nazarian Massoud Pedra Dept. of EE-Systes, University of Southern California, Los Angeles, CA 90089 {fatei, shahin,
More informationGeneral Properties of Radiation Detectors Supplements
Phys. 649: Nuclear Techniques Physics Departent Yarouk University Chapter 4: General Properties of Radiation Detectors Suppleents Dr. Nidal M. Ershaidat Overview Phys. 649: Nuclear Techniques Physics Departent
More informationCh 12: Variations on Backpropagation
Ch 2: Variations on Backpropagation The basic backpropagation algorith is too slow for ost practical applications. It ay take days or weeks of coputer tie. We deonstrate why the backpropagation algorith
More informationCourse support: Control Engineering (TBKRT05E)
Course Support This course support package is offered to you by TBV Lugus, the study association for Industrial Engineering and Manageent. Although this package is coposed with great care, the association
More informationEE 330 Lecture 33. Basic amplifier architectures Common Emitter/Source Common Collector/Drain Common Base/Gate. Basic Amplifiers
33 Lecture 33 asic aplifier architectures oon itter/source oon ollector/drain oon ase/gate asic plifiers nalysis, Operation, and Desin xa 3 Friday pril 3 eview Previous Lecture Two-Port quivalents of Interconnected
More informationOptical Properties of Plasmas of High-Z Elements
Forschungszentru Karlsruhe Techni und Uwelt Wissenschaftlishe Berichte FZK Optical Properties of Plasas of High-Z Eleents V.Tolach 1, G.Miloshevsy 1, H.Würz Project Kernfusion 1 Heat and Mass Transfer
More informationSymbolic Analysis as Universal Tool for Deriving Properties of Non-linear Algorithms Case study of EM Algorithm
Acta Polytechnica Hungarica Vol., No., 04 Sybolic Analysis as Universal Tool for Deriving Properties of Non-linear Algoriths Case study of EM Algorith Vladiir Mladenović, Miroslav Lutovac, Dana Porrat
More informationScattering and bound states
Chapter Scattering and bound states In this chapter we give a review of quantu-echanical scattering theory. We focus on the relation between the scattering aplitude of a potential and its bound states
More informationA Note on Scheduling Tall/Small Multiprocessor Tasks with Unit Processing Time to Minimize Maximum Tardiness
A Note on Scheduling Tall/Sall Multiprocessor Tasks with Unit Processing Tie to Miniize Maxiu Tardiness Philippe Baptiste and Baruch Schieber IBM T.J. Watson Research Center P.O. Box 218, Yorktown Heights,
More informationPH 222-2C Fall Electromagnetic Oscillations and Alternating Current. Lectures 18-19
H - Fall 0 Electroagnetic Oscillations and Alternating urrent ectures 8-9 hapter 3 (Halliday/esnick/Walker, Fundaentals of hysics 8 th edition) hapter 3 Electroagnetic Oscillations and Alternating urrent
More informationEE 330 Lecture 30. Basic amplifier architectures
33 Lecture 3 asic aplifier architectures asic plifier Structures MOS and ipolar Transistors oth have 3 priary terinals MOS transistor has a fourth terinal that is generally considered a parasitic D terinal
More informationThe accelerated expansion of the universe is explained by quantum field theory.
The accelerated expansion of the universe is explained by quantu field theory. Abstract. Forulas describing interactions, in fact, use the liiting speed of inforation transfer, and not the speed of light.
More informationEE 434 Lecture 16. Small signal model Small signal applications in amplifier analysis and design
EE 434 Lecture 16 Sall sinal odel Sall sinal applications in aplifier analysis and desin Quiz 13 The of an n-channel OS transistor that has a quiescent current of 5A was easured to be 10A/. If the lenth
More informationNon-Parametric Non-Line-of-Sight Identification 1
Non-Paraetric Non-Line-of-Sight Identification Sinan Gezici, Hisashi Kobayashi and H. Vincent Poor Departent of Electrical Engineering School of Engineering and Applied Science Princeton University, Princeton,
More informationAnalysis of Impulsive Natural Phenomena through Finite Difference Methods A MATLAB Computational Project-Based Learning
Analysis of Ipulsive Natural Phenoena through Finite Difference Methods A MATLAB Coputational Project-Based Learning Nicholas Kuia, Christopher Chariah, Mechatronics Engineering, Vaughn College of Aeronautics
More informationOn Constant Power Water-filling
On Constant Power Water-filling Wei Yu and John M. Cioffi Electrical Engineering Departent Stanford University, Stanford, CA94305, U.S.A. eails: {weiyu,cioffi}@stanford.edu Abstract This paper derives
More informationON THE TWO-LEVEL PRECONDITIONING IN LEAST SQUARES METHOD
PROCEEDINGS OF THE YEREVAN STATE UNIVERSITY Physical and Matheatical Sciences 04,, p. 7 5 ON THE TWO-LEVEL PRECONDITIONING IN LEAST SQUARES METHOD M a t h e a t i c s Yu. A. HAKOPIAN, R. Z. HOVHANNISYAN
More informationNUMERICAL MODELLING OF THE TYRE/ROAD CONTACT
NUMERICAL MODELLING OF THE TYRE/ROAD CONTACT PACS REFERENCE: 43.5.LJ Krister Larsson Departent of Applied Acoustics Chalers University of Technology SE-412 96 Sweden Tel: +46 ()31 772 22 Fax: +46 ()31
More informationIntelligent Systems: Reasoning and Recognition. Perceptrons and Support Vector Machines
Intelligent Systes: Reasoning and Recognition Jaes L. Crowley osig 1 Winter Seester 2018 Lesson 6 27 February 2018 Outline Perceptrons and Support Vector achines Notation...2 Linear odels...3 Lines, Planes
More informationESTIMATING AND FORMING CONFIDENCE INTERVALS FOR EXTREMA OF RANDOM POLYNOMIALS. A Thesis. Presented to. The Faculty of the Department of Mathematics
ESTIMATING AND FORMING CONFIDENCE INTERVALS FOR EXTREMA OF RANDOM POLYNOMIALS A Thesis Presented to The Faculty of the Departent of Matheatics San Jose State University In Partial Fulfillent of the Requireents
More informationBlock designs and statistics
Bloc designs and statistics Notes for Math 447 May 3, 2011 The ain paraeters of a bloc design are nuber of varieties v, bloc size, nuber of blocs b. A design is built on a set of v eleents. Each eleent
More informationScalable Symbolic Model Order Reduction
Scalable Sybolic Model Order Reduction Yiyu Shi Lei He -J Richard Shi Electrical Engineering Dept, ULA Electrical Engineering Dept, UW Los Angeles, alifornia, 924 Seattle, WA, 985 {yshi, lhe}eeuclaedu
More informationThis model assumes that the probability of a gap has size i is proportional to 1/i. i.e., i log m e. j=1. E[gap size] = i P r(i) = N f t.
CS 493: Algoriths for Massive Data Sets Feb 2, 2002 Local Models, Bloo Filter Scribe: Qin Lv Local Models In global odels, every inverted file entry is copressed with the sae odel. This work wells when
More informationma x = -bv x + F rod.
Notes on Dynaical Systes Dynaics is the study of change. The priary ingredients of a dynaical syste are its state and its rule of change (also soeties called the dynaic). Dynaical systes can be continuous
More informationCHAPTER 19: Single-Loop IMC Control
When I coplete this chapter, I want to be able to do the following. Recognize that other feedback algoriths are possible Understand the IMC structure and how it provides the essential control features
More informationPrinciples of Optimal Control Spring 2008
MIT OpenCourseWare http://ocw.it.edu 16.323 Principles of Optial Control Spring 2008 For inforation about citing these aterials or our Ters of Use, visit: http://ocw.it.edu/ters. 16.323 Lecture 10 Singular
More informationA new type of lower bound for the largest eigenvalue of a symmetric matrix
Linear Algebra and its Applications 47 7 9 9 www.elsevier.co/locate/laa A new type of lower bound for the largest eigenvalue of a syetric atrix Piet Van Mieghe Delft University of Technology, P.O. Box
More informationDefinition of Work, The basics
Physics 07 Lecture 16 Lecture 16 Chapter 11 (Work) v Eploy conservative and non-conservative forces v Relate force to potential energy v Use the concept of power (i.e., energy per tie) Chapter 1 v Define
More informationLecture 10 OUTLINE. Reading: Chapter EE105 Spring 2008 Lecture 10, Slide 1 Prof. Wu, UC Berkeley
Lecture 0 OUTLIN BJT Aplifiers (3) itter follower (Coon-collector aplifier) Analysis of eitter follower core Ipact of source resistance Ipact of arly effect itter follower with biasin eadin: Chapter 5.3.3-5.4
More informationASSUME a source over an alphabet size m, from which a sequence of n independent samples are drawn. The classical
IEEE TRANSACTIONS ON INFORMATION THEORY Large Alphabet Source Coding using Independent Coponent Analysis Aichai Painsky, Meber, IEEE, Saharon Rosset and Meir Feder, Fellow, IEEE arxiv:67.7v [cs.it] Jul
More informationMutual capacitor and its applications
Mutual capacitor and its applications Chun Li, Jason Li, Jieing Li CALSON Technologies, Toronto, Canada E-ail: calandli@yahoo.ca Published in The Journal of Engineering; Received on 27th October 2013;
More informationA model reduction approach to numerical inversion for a parabolic partial differential equation
Inverse Probles Inverse Probles 30 (204) 250 (33pp) doi:0.088/0266-56/30/2/250 A odel reduction approach to nuerical inversion for a parabolic partial differential equation Liliana Borcea, Vladiir Drusin
More information2.003 Engineering Dynamics Problem Set 2 Solutions
.003 Engineering Dynaics Proble Set Solutions This proble set is priarily eant to give the student practice in describing otion. This is the subject of kineatics. It is strongly recoended that you study
More informationCHAPTER 15: Vibratory Motion
CHAPTER 15: Vibratory Motion courtesy of Richard White courtesy of Richard White 2.) 1.) Two glaring observations can be ade fro the graphic on the previous slide: 1.) The PROJECTION of a point on a circle
More informationChapter 11: Vibration Isolation of the Source [Part I]
Chapter : Vibration Isolation of the Source [Part I] Eaple 3.4 Consider the achine arrangeent illustrated in figure 3.. An electric otor is elastically ounted, by way of identical isolators, to a - thick
More informationPhysics 139B Solutions to Homework Set 3 Fall 2009
Physics 139B Solutions to Hoework Set 3 Fall 009 1. Consider a particle of ass attached to a rigid assless rod of fixed length R whose other end is fixed at the origin. The rod is free to rotate about
More informationA Note on the Applied Use of MDL Approximations
A Note on the Applied Use of MDL Approxiations Daniel J. Navarro Departent of Psychology Ohio State University Abstract An applied proble is discussed in which two nested psychological odels of retention
More informationCONTROL SYSTEMS, ROBOTICS, AND AUTOMATION Vol. IX Uncertainty Models For Robustness Analysis - A. Garulli, A. Tesi and A. Vicino
UNCERTAINTY MODELS FOR ROBUSTNESS ANALYSIS A. Garulli Dipartiento di Ingegneria dell Inforazione, Università di Siena, Italy A. Tesi Dipartiento di Sistei e Inforatica, Università di Firenze, Italy A.
More informationMulti-Scale/Multi-Resolution: Wavelet Transform
Multi-Scale/Multi-Resolution: Wavelet Transfor Proble with Fourier Fourier analysis -- breaks down a signal into constituent sinusoids of different frequencies. A serious drawback in transforing to the
More informationIDAN Shock Mount Isolation Vibration Study November 1, The operation of shock and vibration isolation base plate
dr. Istvan Koller RTD USA BME Laboratory. Background In 998, Real Tie Devices USA, Inc. introduced a novel packaging concept for ebedded PC/04 odules to build Intelligent Data Acquisition Nodes. This syste,
More informationOcean 420 Physical Processes in the Ocean Project 1: Hydrostatic Balance, Advection and Diffusion Answers
Ocean 40 Physical Processes in the Ocean Project 1: Hydrostatic Balance, Advection and Diffusion Answers 1. Hydrostatic Balance a) Set all of the levels on one of the coluns to the lowest possible density.
More information2 Q 10. Likewise, in case of multiple particles, the corresponding density in 2 must be averaged over all
Lecture 6 Introduction to kinetic theory of plasa waves Introduction to kinetic theory So far we have been odeling plasa dynaics using fluid equations. The assuption has been that the pressure can be either
More information+ -d-t-' )=1. = vpi. Aportaciones Matematicas Comunicaciones 17 (1996) 5-10.
Aportaciones Mateaticas Counicaciones 17 (1996) 5-10. 1. A suary of the proble Much of the processing that is used in the petroleu industry requires the consideration of a large nuber of cheical reactions.
More informationLecture #8-3 Oscillations, Simple Harmonic Motion
Lecture #8-3 Oscillations Siple Haronic Motion So far we have considered two basic types of otion: translation and rotation. But these are not the only two types of otion we can observe in every day life.
More information1 Proof of learning bounds
COS 511: Theoretical Machine Learning Lecturer: Rob Schapire Lecture #4 Scribe: Akshay Mittal February 13, 2013 1 Proof of learning bounds For intuition of the following theore, suppose there exists a
More informationPattern Recognition and Machine Learning. Artificial Neural networks
Pattern Recognition and Machine Learning Jaes L. Crowley ENSIMAG 3 - MMIS Fall Seester 2016 Lessons 7 14 Dec 2016 Outline Artificial Neural networks Notation...2 1. Introduction...3... 3 The Artificial
More informationA Generalized Permanent Estimator and its Application in Computing Multi- Homogeneous Bézout Number
Research Journal of Applied Sciences, Engineering and Technology 4(23): 5206-52, 202 ISSN: 2040-7467 Maxwell Scientific Organization, 202 Subitted: April 25, 202 Accepted: May 3, 202 Published: Deceber
More informationIN modern society that various systems have become more
Developent of Reliability Function in -Coponent Standby Redundant Syste with Priority Based on Maxiu Entropy Principle Ryosuke Hirata, Ikuo Arizono, Ryosuke Toohiro, Satoshi Oigawa, and Yasuhiko Takeoto
More informationAccuracy of the Scaling Law for Experimental Natural Frequencies of Rectangular Thin Plates
The 9th Conference of Mechanical Engineering Network of Thailand 9- October 005, Phuket, Thailand Accuracy of the caling Law for Experiental Natural Frequencies of Rectangular Thin Plates Anawat Na songkhla
More informationPh 20.3 Numerical Solution of Ordinary Differential Equations
Ph 20.3 Nuerical Solution of Ordinary Differential Equations Due: Week 5 -v20170314- This Assignent So far, your assignents have tried to failiarize you with the hardware and software in the Physics Coputing
More informationThe Indefinite Admittance Matrix
Subject: ndefinite Adittance Matrices Date: June 6, 998 The ndefinite Adittance Matrix The indefinite adittance atrix, designated F for short, is a circuit analsis technique i,ii,iii which lends itself
More informationAbout the definition of parameters and regimes of active two-port networks with variable loads on the basis of projective geometry
About the definition of paraeters and regies of active two-port networks with variable loads on the basis of projective geoetry PENN ALEXANDR nstitute of Electronic Engineering and Nanotechnologies "D
More informationFigure 1: Equivalent electric (RC) circuit of a neurons membrane
Exercise: Leaky integrate and fire odel of neural spike generation This exercise investigates a siplified odel of how neurons spike in response to current inputs, one of the ost fundaental properties of
More informationHomework 3 Solutions CSE 101 Summer 2017
Hoework 3 Solutions CSE 0 Suer 207. Scheduling algoriths The following n = 2 jobs with given processing ties have to be scheduled on = 3 parallel and identical processors with the objective of iniizing
More informationJordan Journal of Physics
Volue 5, Nuber 3, 212. pp. 113-118 ARTILE Jordan Journal of Physics Networks of Identical apacitors with a Substitutional apacitor Departent of Physics, Al-Hussein Bin Talal University, Ma an, 2, 71111,
More informationElectric Power System Transient Stability Analysis Methods
1 Electric Power Syste Transient Stability Analysis Methods João Pedro de Carvalho Mateus, IST Abstract In this paper are presented the state of the art of Electric Power Syste transient stability analysis
More information13 Harmonic oscillator revisited: Dirac s approach and introduction to Second Quantization
3 Haronic oscillator revisited: Dirac s approach and introduction to Second Quantization. Dirac cae up with a ore elegant way to solve the haronic oscillator proble. We will now study this approach. The
More informationIntelligent Systems: Reasoning and Recognition. Artificial Neural Networks
Intelligent Systes: Reasoning and Recognition Jaes L. Crowley MOSIG M1 Winter Seester 2018 Lesson 7 1 March 2018 Outline Artificial Neural Networks Notation...2 Introduction...3 Key Equations... 3 Artificial
More informationANALYSIS OF REFLECTOR AND HORN ANTENNAS USING MULTILEVEL FAST MULTIPOLE ALGORITHM
European Congress on Coputational Methods in Applied Sciences and Engineering ECCOMAS 2 Barcelona, 11-14 Septeber 2 ECCOMAS ANALYSIS OF REFLECTOR AND HORN ANTENNAS USING MULTILEVEL FAST MULTIPOLE ALGORITHM
More informationChapter 6 1-D Continuous Groups
Chapter 6 1-D Continuous Groups Continuous groups consist of group eleents labelled by one or ore continuous variables, say a 1, a 2,, a r, where each variable has a well- defined range. This chapter explores:
More informationEQUIVALENT CIRCUIT MODEL OF SEMICONDUCTOR LASERS TAKING ACCOUNT OF GAIN SUPPRESSION
EQUIVALENT CIRCUIT MODEL OF SEMICONDUCTOR LASERS TAKING ACCOUNT OF GAIN SUPPRESSION Kaiz Aedi and Mohsen Khanzadeh Departent of Electrical Engineering, Faculty of Electrical and Coputer Engineering, Shahid
More information. The univariate situation. It is well-known for a long tie that denoinators of Pade approxiants can be considered as orthogonal polynoials with respe
PROPERTIES OF MULTIVARIATE HOMOGENEOUS ORTHOGONAL POLYNOMIALS Brahi Benouahane y Annie Cuyt? Keywords Abstract It is well-known that the denoinators of Pade approxiants can be considered as orthogonal
More informationModeling Chemical Reactions with Single Reactant Specie
Modeling Cheical Reactions with Single Reactant Specie Abhyudai Singh and João edro Hespanha Abstract A procedure for constructing approxiate stochastic odels for cheical reactions involving a single reactant
More informationBoosting with log-loss
Boosting with log-loss Marco Cusuano-Towner Septeber 2, 202 The proble Suppose we have data exaples {x i, y i ) i =... } for a two-class proble with y i {, }. Let F x) be the predictor function with the
More informationNow multiply the left-hand-side by ω and the right-hand side by dδ/dt (recall ω= dδ/dt) to get:
Equal Area Criterion.0 Developent of equal area criterion As in previous notes, all powers are in per-unit. I want to show you the equal area criterion a little differently than the book does it. Let s
More information