Multiline Overview. Karl Bois, PhD Lead SI Engineer Servers & Blades. December 5th, 2016

Size: px
Start display at page:

Download "Multiline Overview. Karl Bois, PhD Lead SI Engineer Servers & Blades. December 5th, 2016"

Transcription

1 Multlne Overvew Karl Bos, PhD Lead SI Engneer Servers & Blades December 5th, 216

2 Why are we here? Orgnal Equpment Manufacturers (OEMs) and Orgnal Desgn Manufacturers (ODMs) have desgns that requre that the nterconnect such as the Prnted Crcut Board (PCB) has a requred electrcal performance Typcally, PCB constructons are desgned to a gven metrc of attenuaton per length (e.g. db/n) IPC D24B went to great lengths to provde four methods that correlated n behavor wth each other, but dd not yeld a consstent answer; that s correlaton but not agreement PCB assembly houses can chose whchever method they would lke and stll consder themselves to be IPC complant There s the opportunty to get t rght ths tme

3 Lmtatons of current technques SET2DIL: great hgh volume manufacturng mplementaton but lacks de-embeddng, va effect usually contamnate the results. 1X Thru: verfyng the fxture qualty of 1X thru s really hard, and the methodology s very user/mplementer dependent. Targeted for 1 Ohm test envronment. 2X thru: n ts raw form where only (SDD 21B -SDD 21A )/(L B -L A ) s used, t requres that the length L A be long enough to reduce the near/far end reflectons so that the subtracton can be relatvely close to that of a VNA. The coupon sze cannot be guaranteed to be >4 for L A, and there wll always be rpple n the measurements. SPP: NIST verfed for propagaton constant measurement. However user short-cuts (e.g. low bandwdth scopes) tend to produce results varablty. 3

4 What are tryng to acheve? Use a technque to determne frequency varyng propagaton and loss parameters of PCBs The technque must be smple but no corners must be cut n regards to accuracy The technque cannot have prebult assumptons for t to correlate to tradtonal measurements No specal launches No non-lnear operatons No requrement on mpedance Ths technque exsts snce 1991: Marks, R.B. A multlne method of network analyzer calbraton, IEEE Transactons on Mcrowave Theory and Technques, vol. 39, Jul. 1991, pp

5 Multlne n a nutshell Measure S-parameters of two (or more) TL lnes Lne 1 (length a) Lne 2 (length b) Compute propagaton and attenuaton constants Extract R s, e r and tan d Optonal 5

6 Theory X l T Y 1 S12 S21 S 11S22 S 11 M S 21 S22 1 M XT Y Wave Cascade Matrces T s a homogeneous transmsson lne The egenvalues of T are. 1,2 e l Complex propagaton s. T e 1 1 ln l l e l 6

7 Theory (2) X l T Y X l T Y M XT Y M XT Y 1 S12 S21 S 11S22 S 11 M S 21 S22 1 M 1 S12S 21 S11S 22 S 11 S 21 S22 1 T e l e l T e l e l M X XT 1 M M M 1 T T T

8 Theory (3) 1M 2M M s calculated from measurable parameters M and T have the same egenvalues, T s related to the propagaton constant,, T e ( l l ) e ( l l ) l 1 M,2 M e l So can be calculated as, ln l l where M 2 2M 8

9 Choosng the egenvalues l l 2M 1M e Choose the root that expresses a wave propagatng n postve drecton along TL. 9

10 Choosng the egenvalues (2) For each frequency pont, choose such that > 1

11 Optonal gong from complex propagaton constant to materal propertes c d e r c c R dc 2Z o f R s f d e r tand c If c can be found, All other quanttes are known 11

12 Sample measurement Alpha_measured Alpha_conductor Alpha_delectrc Alpha_reconstructed Frequency (GHz) 12

13 Comments and applcaton notes The lnes should not be multple wavelengths of each other Can brng some nose n the data Same methodology n choosng Thru-Reflect-Lne standards Only two lnes are requres and the length s not crtcal If there are more than two lnes, then a covarance matrx mplementaton proposed by Dr. DeGroot can be used to flter out measurement nose n a analytc and theoretcal manner. Hewlett Packard Enterprse s currently usng ths technque wth domestc and nternatonal ODMs wth great success. 13

Chapter 11: Simple Linear Regression and Correlation

Chapter 11: Simple Linear Regression and Correlation Chapter 11: Smple Lnear Regresson and Correlaton 11-1 Emprcal Models 11-2 Smple Lnear Regresson 11-3 Propertes of the Least Squares Estmators 11-4 Hypothess Test n Smple Lnear Regresson 11-4.1 Use of t-tests

More information

Traceability and uncertainty for phase measurements

Traceability and uncertainty for phase measurements Traceablty and ncertanty for phase measrements Karel Dražl Czech Metrology Insttte Abstract In recent tme the problems connected wth evalatng and expressng ncertanty n complex S-parameter measrements have

More information

TOPICS MULTIPLIERLESS FILTER DESIGN ELEMENTARY SCHOOL ALGORITHM MULTIPLICATION

TOPICS MULTIPLIERLESS FILTER DESIGN ELEMENTARY SCHOOL ALGORITHM MULTIPLICATION 1 2 MULTIPLIERLESS FILTER DESIGN Realzaton of flters wthout full-fledged multplers Some sldes based on support materal by W. Wolf for hs book Modern VLSI Desgn, 3 rd edton. Partly based on followng papers:

More information

Statistical Energy Analysis for High Frequency Acoustic Analysis with LS-DYNA

Statistical Energy Analysis for High Frequency Acoustic Analysis with LS-DYNA 14 th Internatonal Users Conference Sesson: ALE-FSI Statstcal Energy Analyss for Hgh Frequency Acoustc Analyss wth Zhe Cu 1, Yun Huang 1, Mhamed Soul 2, Tayeb Zeguar 3 1 Lvermore Software Technology Corporaton

More information

Inner Product. Euclidean Space. Orthonormal Basis. Orthogonal

Inner Product. Euclidean Space. Orthonormal Basis. Orthogonal Inner Product Defnton 1 () A Eucldean space s a fnte-dmensonal vector space over the reals R, wth an nner product,. Defnton 2 (Inner Product) An nner product, on a real vector space X s a symmetrc, blnear,

More information

Prof. Paolo Colantonio a.a

Prof. Paolo Colantonio a.a Pro. Paolo olantono a.a. 3 4 Let s consder a two ports network o Two ports Network o L For passve network (.e. wthout nternal sources or actve devces), a general representaton can be made by a sutable

More information

Errors for Linear Systems

Errors for Linear Systems Errors for Lnear Systems When we solve a lnear system Ax b we often do not know A and b exactly, but have only approxmatons  and ˆb avalable. Then the best thng we can do s to solve ˆx ˆb exactly whch

More information

Lecture 12: Classification

Lecture 12: Classification Lecture : Classfcaton g Dscrmnant functons g The optmal Bayes classfer g Quadratc classfers g Eucldean and Mahalanobs metrcs g K Nearest Neghbor Classfers Intellgent Sensor Systems Rcardo Guterrez-Osuna

More information

Time-Varying Systems and Computations Lecture 6

Time-Varying Systems and Computations Lecture 6 Tme-Varyng Systems and Computatons Lecture 6 Klaus Depold 14. Januar 2014 The Kalman Flter The Kalman estmaton flter attempts to estmate the actual state of an unknown dscrete dynamcal system, gven nosy

More information

Frequency-Domain Analysis of Transmission Line Circuits (Part 1)

Frequency-Domain Analysis of Transmission Line Circuits (Part 1) Frequency-Doman Analyss of Transmsson Lne Crcuts (Part ) Outlne -port networs mpedance matrx representaton Admttance matrx representaton catterng matrx representaton eanng of the -parameters Generalzed

More information

Lectures - Week 4 Matrix norms, Conditioning, Vector Spaces, Linear Independence, Spanning sets and Basis, Null space and Range of a Matrix

Lectures - Week 4 Matrix norms, Conditioning, Vector Spaces, Linear Independence, Spanning sets and Basis, Null space and Range of a Matrix Lectures - Week 4 Matrx norms, Condtonng, Vector Spaces, Lnear Independence, Spannng sets and Bass, Null space and Range of a Matrx Matrx Norms Now we turn to assocatng a number to each matrx. We could

More information

Formulas for the Determinant

Formulas for the Determinant page 224 224 CHAPTER 3 Determnants e t te t e 2t 38 A = e t 2te t e 2t e t te t 2e 2t 39 If 123 A = 345, 456 compute the matrx product A adj(a) What can you conclude about det(a)? For Problems 40 43, use

More information

Lecture 16 Statistical Analysis in Biomaterials Research (Part II)

Lecture 16 Statistical Analysis in Biomaterials Research (Part II) 3.051J/0.340J 1 Lecture 16 Statstcal Analyss n Bomaterals Research (Part II) C. F Dstrbuton Allows comparson of varablty of behavor between populatons usng test of hypothess: σ x = σ x amed for Brtsh statstcan

More information

55:141 Advanced Circuit Techniques Two-Port Theory

55:141 Advanced Circuit Techniques Two-Port Theory 55:4 Adanced Crcut Technques Two-Port Theory Materal: Lecture Notes A. Kruger 55:4: Adanced Crcut Technques The Unersty of Iowa, 205 Two-Port Theory, Slde Two-Port Networks Note, the BJT s all are hghly

More information

Mathematical Preparations

Mathematical Preparations 1 Introducton Mathematcal Preparatons The theory of relatvty was developed to explan experments whch studed the propagaton of electromagnetc radaton n movng coordnate systems. Wthn expermental error the

More information

PHYS 450 Spring semester Lecture 02: Dealing with Experimental Uncertainties. Ron Reifenberger Birck Nanotechnology Center Purdue University

PHYS 450 Spring semester Lecture 02: Dealing with Experimental Uncertainties. Ron Reifenberger Birck Nanotechnology Center Purdue University PHYS 45 Sprng semester 7 Lecture : Dealng wth Expermental Uncertantes Ron Refenberger Brck anotechnology Center Purdue Unversty Lecture Introductory Comments Expermental errors (really expermental uncertantes)

More information

Structure and Drive Paul A. Jensen Copyright July 20, 2003

Structure and Drive Paul A. Jensen Copyright July 20, 2003 Structure and Drve Paul A. Jensen Copyrght July 20, 2003 A system s made up of several operatons wth flow passng between them. The structure of the system descrbes the flow paths from nputs to outputs.

More information

2.3 Nilpotent endomorphisms

2.3 Nilpotent endomorphisms s a block dagonal matrx, wth A Mat dm U (C) In fact, we can assume that B = B 1 B k, wth B an ordered bass of U, and that A = [f U ] B, where f U : U U s the restrcton of f to U 40 23 Nlpotent endomorphsms

More information

Tornado and Luby Transform Codes. Ashish Khisti Presentation October 22, 2003

Tornado and Luby Transform Codes. Ashish Khisti Presentation October 22, 2003 Tornado and Luby Transform Codes Ashsh Khst 6.454 Presentaton October 22, 2003 Background: Erasure Channel Elas[956] studed the Erasure Channel β x x β β x 2 m x 2 k? Capacty of Noseless Erasure Channel

More information

Parametric fractional imputation for missing data analysis. Jae Kwang Kim Survey Working Group Seminar March 29, 2010

Parametric fractional imputation for missing data analysis. Jae Kwang Kim Survey Working Group Seminar March 29, 2010 Parametrc fractonal mputaton for mssng data analyss Jae Kwang Km Survey Workng Group Semnar March 29, 2010 1 Outlne Introducton Proposed method Fractonal mputaton Approxmaton Varance estmaton Multple mputaton

More information

The Analysis Procedure An Overview

The Analysis Procedure An Overview The Procedure An Overvew From ~ 1990 to present From to frequency ratos The Overvew on the Overvew... Procedure Talk by Georges Tools Fttng Statstcal Stuff Systematcal Stuff Uncertanty Sketch of Procedure

More information

LINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity

LINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity LINEAR REGRESSION ANALYSIS MODULE IX Lecture - 31 Multcollnearty Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur 6. Rdge regresson The OLSE s the best lnear unbased

More information

Prof. Dr. I. Nasser Phys 630, T Aug-15 One_dimensional_Ising_Model

Prof. Dr. I. Nasser Phys 630, T Aug-15 One_dimensional_Ising_Model EXACT OE-DIMESIOAL ISIG MODEL The one-dmensonal Isng model conssts of a chan of spns, each spn nteractng only wth ts two nearest neghbors. The smple Isng problem n one dmenson can be solved drectly n several

More information

3.1 Expectation of Functions of Several Random Variables. )' be a k-dimensional discrete or continuous random vector, with joint PMF p (, E X E X1 E X

3.1 Expectation of Functions of Several Random Variables. )' be a k-dimensional discrete or continuous random vector, with joint PMF p (, E X E X1 E X Statstcs 1: Probablty Theory II 37 3 EPECTATION OF SEVERAL RANDOM VARIABLES As n Probablty Theory I, the nterest n most stuatons les not on the actual dstrbuton of a random vector, but rather on a number

More information

EE 508 Lecture 7. Degrees of Freedom The Approximation Problem

EE 508 Lecture 7. Degrees of Freedom The Approximation Problem EE 508 Lecture 7 Degrees of Freedom The Approxmaton Problem vew from Last Tme Desgn Strategy Theorem: A crcut wth transfer functon T(s) can be obtaned from a crcut wth normalzed transfer functon T n (s

More information

Analytical Chemistry Calibration Curve Handout

Analytical Chemistry Calibration Curve Handout I. Quck-and Drty Excel Tutoral Analytcal Chemstry Calbraton Curve Handout For those of you wth lttle experence wth Excel, I ve provded some key technques that should help you use the program both for problem

More information

Section 8.3 Polar Form of Complex Numbers

Section 8.3 Polar Form of Complex Numbers 80 Chapter 8 Secton 8 Polar Form of Complex Numbers From prevous classes, you may have encountered magnary numbers the square roots of negatve numbers and, more generally, complex numbers whch are the

More information

f(x,y) = (4(x 2 4)x,2y) = 0 H(x,y) =

f(x,y) = (4(x 2 4)x,2y) = 0 H(x,y) = Problem Set 3: Unconstraned mzaton n R N. () Fnd all crtcal ponts of f(x,y) (x 4) +y and show whch are ma and whch are mnma. () Fnd all crtcal ponts of f(x,y) (y x ) x and show whch are ma and whch are

More information

Lecture 6/7 (February 10/12, 2014) DIRAC EQUATION. The non-relativistic Schrödinger equation was obtained by noting that the Hamiltonian 2

Lecture 6/7 (February 10/12, 2014) DIRAC EQUATION. The non-relativistic Schrödinger equation was obtained by noting that the Hamiltonian 2 P470 Lecture 6/7 (February 10/1, 014) DIRAC EQUATION The non-relatvstc Schrödnger equaton was obtaned by notng that the Hamltonan H = P (1) m can be transformed nto an operator form wth the substtutons

More information

Spectral Graph Theory and its Applications September 16, Lecture 5

Spectral Graph Theory and its Applications September 16, Lecture 5 Spectral Graph Theory and ts Applcatons September 16, 2004 Lecturer: Danel A. Spelman Lecture 5 5.1 Introducton In ths lecture, we wll prove the followng theorem: Theorem 5.1.1. Let G be a planar graph

More information

Unfolding with Singular Value Decomposition

Unfolding with Singular Value Decomposition Unfoldng wth Sngular Value Decomposton V. Kartvelshvl Lancaster Unversty, Unted Kngdom 1 Introducton Abstract An overvew s gven of the SVD approach to unfoldng, ncludng basc prncples, error propagaton

More information

Chapter 3 Describing Data Using Numerical Measures

Chapter 3 Describing Data Using Numerical Measures Chapter 3 Student Lecture Notes 3-1 Chapter 3 Descrbng Data Usng Numercal Measures Fall 2006 Fundamentals of Busness Statstcs 1 Chapter Goals To establsh the usefulness of summary measures of data. The

More information

E40M Device Models, Resistors, Voltage and Current Sources, Diodes, Solar Cells. M. Horowitz, J. Plummer, R. Howe 1

E40M Device Models, Resistors, Voltage and Current Sources, Diodes, Solar Cells. M. Horowitz, J. Plummer, R. Howe 1 E40M Devce Models, Resstors, Voltage and Current Sources, Dodes, Solar Cells M. Horowtz, J. Plummer, R. Howe 1 Understandng the Solar Charger Lab Project #1 We need to understand how: 1. Current, voltage

More information

ECE559VV Project Report

ECE559VV Project Report ECE559VV Project Report (Supplementary Notes Loc Xuan Bu I. MAX SUM-RATE SCHEDULING: THE UPLINK CASE We have seen (n the presentaton that, for downlnk (broadcast channels, the strategy maxmzng the sum-rate

More information

Lab 2e Thermal System Response and Effective Heat Transfer Coefficient

Lab 2e Thermal System Response and Effective Heat Transfer Coefficient 58:080 Expermental Engneerng 1 OBJECTIVE Lab 2e Thermal System Response and Effectve Heat Transfer Coeffcent Warnng: though the experment has educatonal objectves (to learn about bolng heat transfer, etc.),

More information

Chat eld, C. and A.J.Collins, Introduction to multivariate analysis. Chapman & Hall, 1980

Chat eld, C. and A.J.Collins, Introduction to multivariate analysis. Chapman & Hall, 1980 MT07: Multvarate Statstcal Methods Mke Tso: emal mke.tso@manchester.ac.uk Webpage for notes: http://www.maths.manchester.ac.uk/~mkt/new_teachng.htm. Introducton to multvarate data. Books Chat eld, C. and

More information

MAE140 - Linear Circuits - Winter 16 Final, March 16, 2016

MAE140 - Linear Circuits - Winter 16 Final, March 16, 2016 ME140 - Lnear rcuts - Wnter 16 Fnal, March 16, 2016 Instructons () The exam s open book. You may use your class notes and textbook. You may use a hand calculator wth no communcaton capabltes. () You have

More information

ELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM

ELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM ELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM An elastc wave s a deformaton of the body that travels throughout the body n all drectons. We can examne the deformaton over a perod of tme by fxng our look

More information

ENGR-4300 Electronic Instrumentation Quiz 4 Fall 2010 Name Section. Question Value Grade I 20 II 20 III 20 IV 20 V 20. Total (100 points)

ENGR-4300 Electronic Instrumentation Quiz 4 Fall 2010 Name Section. Question Value Grade I 20 II 20 III 20 IV 20 V 20. Total (100 points) ENGR-43 Electronc Instrumentaton Quz 4 Fall 21 Name Secton Queston Value Grade I 2 II 2 III 2 IV 2 V 2 Total (1 ponts) On all questons: SHOW LL WORK. EGIN WITH FORMULS, THEN SUSTITUTE VLUES ND UNITS. No

More information

CS4495/6495 Introduction to Computer Vision. 3C-L3 Calibrating cameras

CS4495/6495 Introduction to Computer Vision. 3C-L3 Calibrating cameras CS4495/6495 Introducton to Computer Vson 3C-L3 Calbratng cameras Fnally (last tme): Camera parameters Projecton equaton the cumulatve effect of all parameters: M (3x4) f s x ' 1 0 0 0 c R 0 I T 3 3 3 x1

More information

P R. Lecture 4. Theory and Applications of Pattern Recognition. Dept. of Electrical and Computer Engineering /

P R. Lecture 4. Theory and Applications of Pattern Recognition. Dept. of Electrical and Computer Engineering / Theory and Applcatons of Pattern Recognton 003, Rob Polkar, Rowan Unversty, Glassboro, NJ Lecture 4 Bayes Classfcaton Rule Dept. of Electrcal and Computer Engneerng 0909.40.0 / 0909.504.04 Theory & Applcatons

More information

Example: (13320, 22140) =? Solution #1: The divisors of are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 41,

Example: (13320, 22140) =? Solution #1: The divisors of are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 41, The greatest common dvsor of two ntegers a and b (not both zero) s the largest nteger whch s a common factor of both a and b. We denote ths number by gcd(a, b), or smply (a, b) when there s no confuson

More information

Electrical Engineering Department Network Lab.

Electrical Engineering Department Network Lab. Electrcal Engneerng Department Network Lab. Objecte: - Experment on -port Network: Negate Impedance Conerter To fnd the frequency response of a smple Negate Impedance Conerter Theory: Negate Impedance

More information

Singular Value Decomposition: Theory and Applications

Singular Value Decomposition: Theory and Applications Sngular Value Decomposton: Theory and Applcatons Danel Khashab Sprng 2015 Last Update: March 2, 2015 1 Introducton A = UDV where columns of U and V are orthonormal and matrx D s dagonal wth postve real

More information

Frequency dependence of the permittivity

Frequency dependence of the permittivity Frequency dependence of the permttvty February 7, 016 In materals, the delectrc constant and permeablty are actually frequency dependent. Ths does not affect our results for sngle frequency modes, but

More information

ECEN 667 Power System Stability Lecture 21: Modal Analysis

ECEN 667 Power System Stability Lecture 21: Modal Analysis ECEN 667 Power System Stablty Lecture 21: Modal Analyss Prof. Tom Overbye Dept. of Electrcal and Computer Engneerng Texas A&M Unversty, overbye@tamu.edu 1 Announcements Read Chapter 8 Homework 7 s posted;

More information

16 Reflection and transmission, TE mode

16 Reflection and transmission, TE mode 16 Reflecton transmsson TE mode Last lecture we learned how to represent plane-tem waves propagatng n a drecton ˆ n terms of feld phasors such that η = Ẽ = E o e j r H = ˆ Ẽ η µ ɛ = ˆ = ω µɛ E o =0. Such

More information

Grover s Algorithm + Quantum Zeno Effect + Vaidman

Grover s Algorithm + Quantum Zeno Effect + Vaidman Grover s Algorthm + Quantum Zeno Effect + Vadman CS 294-2 Bomb 10/12/04 Fall 2004 Lecture 11 Grover s algorthm Recall that Grover s algorthm for searchng over a space of sze wors as follows: consder the

More information

Econ107 Applied Econometrics Topic 3: Classical Model (Studenmund, Chapter 4)

Econ107 Applied Econometrics Topic 3: Classical Model (Studenmund, Chapter 4) I. Classcal Assumptons Econ7 Appled Econometrcs Topc 3: Classcal Model (Studenmund, Chapter 4) We have defned OLS and studed some algebrac propertes of OLS. In ths topc we wll study statstcal propertes

More information

ISQS 6348 Final Open notes, no books. Points out of 100 in parentheses. Y 1 ε 2

ISQS 6348 Final Open notes, no books. Points out of 100 in parentheses. Y 1 ε 2 ISQS 6348 Fnal Open notes, no books. Ponts out of 100 n parentheses. 1. The followng path dagram s gven: ε 1 Y 1 ε F Y 1.A. (10) Wrte down the usual model and assumptons that are mpled by ths dagram. Soluton:

More information

Lecture 8 Modal Analysis

Lecture 8 Modal Analysis Lecture 8 Modal Analyss 16.0 Release Introducton to ANSYS Mechancal 1 2015 ANSYS, Inc. February 27, 2015 Chapter Overvew In ths chapter free vbraton as well as pre-stressed vbraton analyses n Mechancal

More information

Fall 2012 Analysis of Experimental Measurements B. Eisenstein/rev. S. Errede

Fall 2012 Analysis of Experimental Measurements B. Eisenstein/rev. S. Errede Fall 0 Analyss of Expermental easurements B. Esensten/rev. S. Errede We now reformulate the lnear Least Squares ethod n more general terms, sutable for (eventually extendng to the non-lnear case, and also

More information

Computational Biology Lecture 8: Substitution matrices Saad Mneimneh

Computational Biology Lecture 8: Substitution matrices Saad Mneimneh Computatonal Bology Lecture 8: Substtuton matrces Saad Mnemneh As we have ntroduced last tme, smple scorng schemes lke + or a match, - or a msmatch and -2 or a gap are not justable bologcally, especally

More information

Application of Nonbinary LDPC Codes for Communication over Fading Channels Using Higher Order Modulations

Application of Nonbinary LDPC Codes for Communication over Fading Channels Using Higher Order Modulations Applcaton of Nonbnary LDPC Codes for Communcaton over Fadng Channels Usng Hgher Order Modulatons Rong-Hu Peng and Rong-Rong Chen Department of Electrcal and Computer Engneerng Unversty of Utah Ths work

More information

Linear Feature Engineering 11

Linear Feature Engineering 11 Lnear Feature Engneerng 11 2 Least-Squares 2.1 Smple least-squares Consder the followng dataset. We have a bunch of nputs x and correspondng outputs y. The partcular values n ths dataset are x y 0.23 0.19

More information

Temperature. Chapter Heat Engine

Temperature. Chapter Heat Engine Chapter 3 Temperature In prevous chapters of these notes we ntroduced the Prncple of Maxmum ntropy as a technque for estmatng probablty dstrbutons consstent wth constrants. In Chapter 9 we dscussed the

More information

Introduction to circuit analysis. Classification of Materials

Introduction to circuit analysis. Classification of Materials Introducton to crcut analyss OUTLINE Electrcal quanttes Charge Current Voltage Power The deal basc crcut element Sgn conventons Current versus voltage (I-V) graph Readng: 1.2, 1.3,1.6 Lecture 2, Slde 1

More information

FE REVIEW OPERATIONAL AMPLIFIERS (OP-AMPS)( ) 8/25/2010

FE REVIEW OPERATIONAL AMPLIFIERS (OP-AMPS)( ) 8/25/2010 FE REVEW OPERATONAL AMPLFERS (OP-AMPS)( ) 1 The Op-amp 2 An op-amp has two nputs and one output. Note the op-amp below. The termnal labeled l wth the (-) sgn s the nvertng nput and the nput labeled wth

More information

Problem Do any of the following determine homomorphisms from GL n (C) to GL n (C)?

Problem Do any of the following determine homomorphisms from GL n (C) to GL n (C)? Homework 8 solutons. Problem 16.1. Whch of the followng defne homomomorphsms from C\{0} to C\{0}? Answer. a) f 1 : z z Yes, f 1 s a homomorphsm. We have that z s the complex conjugate of z. If z 1,z 2

More information

Calculation of time complexity (3%)

Calculation of time complexity (3%) Problem 1. (30%) Calculaton of tme complexty (3%) Gven n ctes, usng exhaust search to see every result takes O(n!). Calculaton of tme needed to solve the problem (2%) 40 ctes:40! dfferent tours 40 add

More information

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur Analyss of Varance and Desgn of Experment-I MODULE VII LECTURE - 3 ANALYSIS OF COVARIANCE Dr Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur Any scentfc experment s performed

More information

Norms, Condition Numbers, Eigenvalues and Eigenvectors

Norms, Condition Numbers, Eigenvalues and Eigenvectors Norms, Condton Numbers, Egenvalues and Egenvectors 1 Norms A norm s a measure of the sze of a matrx or a vector For vectors the common norms are: N a 2 = ( x 2 1/2 the Eucldean Norm (1a b 1 = =1 N x (1b

More information

Some Comments on Accelerating Convergence of Iterative Sequences Using Direct Inversion of the Iterative Subspace (DIIS)

Some Comments on Accelerating Convergence of Iterative Sequences Using Direct Inversion of the Iterative Subspace (DIIS) Some Comments on Acceleratng Convergence of Iteratve Sequences Usng Drect Inverson of the Iteratve Subspace (DIIS) C. Davd Sherrll School of Chemstry and Bochemstry Georga Insttute of Technology May 1998

More information

Scatter Plot x

Scatter Plot x Construct a scatter plot usng excel for the gven data. Determne whether there s a postve lnear correlaton, negatve lnear correlaton, or no lnear correlaton. Complete the table and fnd the correlaton coeffcent

More information

LOW BIAS INTEGRATED PATH ESTIMATORS. James M. Calvin

LOW BIAS INTEGRATED PATH ESTIMATORS. James M. Calvin Proceedngs of the 007 Wnter Smulaton Conference S G Henderson, B Bller, M-H Hseh, J Shortle, J D Tew, and R R Barton, eds LOW BIAS INTEGRATED PATH ESTIMATORS James M Calvn Department of Computer Scence

More information

1. Inference on Regression Parameters a. Finding Mean, s.d and covariance amongst estimates. 2. Confidence Intervals and Working Hotelling Bands

1. Inference on Regression Parameters a. Finding Mean, s.d and covariance amongst estimates. 2. Confidence Intervals and Working Hotelling Bands Content. Inference on Regresson Parameters a. Fndng Mean, s.d and covarance amongst estmates.. Confdence Intervals and Workng Hotellng Bands 3. Cochran s Theorem 4. General Lnear Testng 5. Measures of

More information

Answers Problem Set 2 Chem 314A Williamsen Spring 2000

Answers Problem Set 2 Chem 314A Williamsen Spring 2000 Answers Problem Set Chem 314A Wllamsen Sprng 000 1) Gve me the followng crtcal values from the statstcal tables. a) z-statstc,-sded test, 99.7% confdence lmt ±3 b) t-statstc (Case I), 1-sded test, 95%

More information

MAGNETISM MAGNETIC DIPOLES

MAGNETISM MAGNETIC DIPOLES MAGNETISM We now turn to magnetsm. Ths has actually been used for longer than electrcty. People were usng compasses to sal around the Medterranean Sea several hundred years BC. However t was not understood

More information

TLCOM 612 Advanced Telecommunications Engineering II

TLCOM 612 Advanced Telecommunications Engineering II TLCOM 62 Advanced Telecommuncatons Engneerng II Wnter 2 Outlne Presentatons The moble rado sgnal envronment Combned fadng effects and nose Delay spread and Coherence bandwdth Doppler Shft Fast vs. Slow

More information

Polynomial Regression Models

Polynomial Regression Models LINEAR REGRESSION ANALYSIS MODULE XII Lecture - 6 Polynomal Regresson Models Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur Test of sgnfcance To test the sgnfcance

More information

1 Matrix representations of canonical matrices

1 Matrix representations of canonical matrices 1 Matrx representatons of canoncal matrces 2-d rotaton around the orgn: ( ) cos θ sn θ R 0 = sn θ cos θ 3-d rotaton around the x-axs: R x = 1 0 0 0 cos θ sn θ 0 sn θ cos θ 3-d rotaton around the y-axs:

More information

Appendix B: Resampling Algorithms

Appendix B: Resampling Algorithms 407 Appendx B: Resamplng Algorthms A common problem of all partcle flters s the degeneracy of weghts, whch conssts of the unbounded ncrease of the varance of the mportance weghts ω [ ] of the partcles

More information

Chapter 5 Multilevel Models

Chapter 5 Multilevel Models Chapter 5 Multlevel Models 5.1 Cross-sectonal multlevel models 5.1.1 Two-level models 5.1.2 Multple level models 5.1.3 Multple level modelng n other felds 5.2 Longtudnal multlevel models 5.2.1 Two-level

More information

Copyright 2017 by Taylor Enterprises, Inc., All Rights Reserved. Adjusted Control Limits for U Charts. Dr. Wayne A. Taylor

Copyright 2017 by Taylor Enterprises, Inc., All Rights Reserved. Adjusted Control Limits for U Charts. Dr. Wayne A. Taylor Taylor Enterprses, Inc. Adjusted Control Lmts for U Charts Copyrght 207 by Taylor Enterprses, Inc., All Rghts Reserved. Adjusted Control Lmts for U Charts Dr. Wayne A. Taylor Abstract: U charts are used

More information

U.C. Berkeley CS294: Beyond Worst-Case Analysis Luca Trevisan September 5, 2017

U.C. Berkeley CS294: Beyond Worst-Case Analysis Luca Trevisan September 5, 2017 U.C. Berkeley CS94: Beyond Worst-Case Analyss Handout 4s Luca Trevsan September 5, 07 Summary of Lecture 4 In whch we ntroduce semdefnte programmng and apply t to Max Cut. Semdefnte Programmng Recall that

More information

Linear Correlation. Many research issues are pursued with nonexperimental studies that seek to establish relationships among 2 or more variables

Linear Correlation. Many research issues are pursued with nonexperimental studies that seek to establish relationships among 2 or more variables Lnear Correlaton Many research ssues are pursued wth nonexpermental studes that seek to establsh relatonshps among or more varables E.g., correlates of ntellgence; relaton between SAT and GPA; relaton

More information

is the calculated value of the dependent variable at point i. The best parameters have values that minimize the squares of the errors

is the calculated value of the dependent variable at point i. The best parameters have values that minimize the squares of the errors Multple Lnear and Polynomal Regresson wth Statstcal Analyss Gven a set of data of measured (or observed) values of a dependent varable: y versus n ndependent varables x 1, x, x n, multple lnear regresson

More information

Endogenous timing in a mixed oligopoly consisting of a single public firm and foreign competitors. Abstract

Endogenous timing in a mixed oligopoly consisting of a single public firm and foreign competitors. Abstract Endogenous tmng n a mxed olgopoly consstng o a sngle publc rm and oregn compettors Yuanzhu Lu Chna Economcs and Management Academy, Central Unversty o Fnance and Economcs Abstract We nvestgate endogenous

More information

THE SUMMATION NOTATION Ʃ

THE SUMMATION NOTATION Ʃ Sngle Subscrpt otaton THE SUMMATIO OTATIO Ʃ Most of the calculatons we perform n statstcs are repettve operatons on lsts of numbers. For example, we compute the sum of a set of numbers, or the sum of the

More information

Module 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur

Module 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Verson ECE IIT, Kharagpur Lesson 6 Theory of Quantzaton Verson ECE IIT, Kharagpur Instructonal Objectves At the end of ths lesson, the students should be able to:

More information

CS 468 Lecture 16: Isometry Invariance and Spectral Techniques

CS 468 Lecture 16: Isometry Invariance and Spectral Techniques CS 468 Lecture 16: Isometry Invarance and Spectral Technques Justn Solomon Scrbe: Evan Gawlk Introducton. In geometry processng, t s often desrable to characterze the shape of an object n a manner that

More information

Inductance Calculation for Conductors of Arbitrary Shape

Inductance Calculation for Conductors of Arbitrary Shape CRYO/02/028 Aprl 5, 2002 Inductance Calculaton for Conductors of Arbtrary Shape L. Bottura Dstrbuton: Internal Summary In ths note we descrbe a method for the numercal calculaton of nductances among conductors

More information

Experience with Automatic Generation Control (AGC) Dynamic Simulation in PSS E

Experience with Automatic Generation Control (AGC) Dynamic Simulation in PSS E Semens Industry, Inc. Power Technology Issue 113 Experence wth Automatc Generaton Control (AGC) Dynamc Smulaton n PSS E Lu Wang, Ph.D. Staff Software Engneer lu_wang@semens.com Dngguo Chen, Ph.D. Staff

More information

Generalized Linear Methods

Generalized Linear Methods Generalzed Lnear Methods 1 Introducton In the Ensemble Methods the general dea s that usng a combnaton of several weak learner one could make a better learner. More formally, assume that we have a set

More information

2016 Wiley. Study Session 2: Ethical and Professional Standards Application

2016 Wiley. Study Session 2: Ethical and Professional Standards Application 6 Wley Study Sesson : Ethcal and Professonal Standards Applcaton LESSON : CORRECTION ANALYSIS Readng 9: Correlaton and Regresson LOS 9a: Calculate and nterpret a sample covarance and a sample correlaton

More information

Radar Trackers. Study Guide. All chapters, problems, examples and page numbers refer to Applied Optimal Estimation, A. Gelb, Ed.

Radar Trackers. Study Guide. All chapters, problems, examples and page numbers refer to Applied Optimal Estimation, A. Gelb, Ed. Radar rackers Study Gude All chapters, problems, examples and page numbers refer to Appled Optmal Estmaton, A. Gelb, Ed. Chapter Example.0- Problem Statement wo sensors Each has a sngle nose measurement

More information

The Decibel and its Usage

The Decibel and its Usage The Decbel and ts Usage Consder a two-stage amlfer system, as shown n Fg.. Each amlfer rodes an ncrease of the sgnal ower. Ths effect s referred to as the ower gan,, of the amlfer. Ths means that the sgnal

More information

Week 11: Differential Amplifiers

Week 11: Differential Amplifiers ELE 0A Electronc rcuts Week : Dfferental Amplfers Lecture - Large sgnal analyss Topcs to coer A analyss Half-crcut analyss eadng Assgnment: hap 5.-5.8 of Jaeger and Blalock or hap 7. - 7.3, of Sedra and

More information

Problem Set 9 Solutions

Problem Set 9 Solutions Desgn and Analyss of Algorthms May 4, 2015 Massachusetts Insttute of Technology 6.046J/18.410J Profs. Erk Demane, Srn Devadas, and Nancy Lynch Problem Set 9 Solutons Problem Set 9 Solutons Ths problem

More information

Department of Statistics University of Toronto STA305H1S / 1004 HS Design and Analysis of Experiments Term Test - Winter Solution

Department of Statistics University of Toronto STA305H1S / 1004 HS Design and Analysis of Experiments Term Test - Winter Solution Department of Statstcs Unversty of Toronto STA35HS / HS Desgn and Analyss of Experments Term Test - Wnter - Soluton February, Last Name: Frst Name: Student Number: Instructons: Tme: hours. Ads: a non-programmable

More information

Composite Hypotheses testing

Composite Hypotheses testing Composte ypotheses testng In many hypothess testng problems there are many possble dstrbutons that can occur under each of the hypotheses. The output of the source s a set of parameters (ponts n a parameter

More information

β0 + β1xi. You are interested in estimating the unknown parameters β

β0 + β1xi. You are interested in estimating the unknown parameters β Ordnary Least Squares (OLS): Smple Lnear Regresson (SLR) Analytcs The SLR Setup Sample Statstcs Ordnary Least Squares (OLS): FOCs and SOCs Back to OLS and Sample Statstcs Predctons (and Resduals) wth OLS

More information

DEMO #8 - GAUSSIAN ELIMINATION USING MATHEMATICA. 1. Matrices in Mathematica

DEMO #8 - GAUSSIAN ELIMINATION USING MATHEMATICA. 1. Matrices in Mathematica demo8.nb 1 DEMO #8 - GAUSSIAN ELIMINATION USING MATHEMATICA Obectves: - defne matrces n Mathematca - format the output of matrces - appl lnear algebra to solve a real problem - Use Mathematca to perform

More information

Regularized Discriminant Analysis for Face Recognition

Regularized Discriminant Analysis for Face Recognition 1 Regularzed Dscrmnant Analyss for Face Recognton Itz Pma, Mayer Aladem Department of Electrcal and Computer Engneerng, Ben-Guron Unversty of the Negev P.O.Box 653, Beer-Sheva, 845, Israel. Abstract Ths

More information

Lecture 14: Forces and Stresses

Lecture 14: Forces and Stresses The Nuts and Bolts of Frst-Prncples Smulaton Lecture 14: Forces and Stresses Durham, 6th-13th December 2001 CASTEP Developers Group wth support from the ESF ψ k Network Overvew of Lecture Why bother? Theoretcal

More information

Quadratic speedup for unstructured search - Grover s Al-

Quadratic speedup for unstructured search - Grover s Al- Quadratc speedup for unstructured search - Grover s Al- CS 94- gorthm /8/07 Sprng 007 Lecture 11 001 Unstructured Search Here s the problem: You are gven a boolean functon f : {1,,} {0,1}, and are promsed

More information

A property of the elementary symmetric functions

A property of the elementary symmetric functions Calcolo manuscrpt No. (wll be nserted by the edtor) A property of the elementary symmetrc functons A. Esnberg, G. Fedele Dp. Elettronca Informatca e Sstemstca, Unverstà degl Stud della Calabra, 87036,

More information

Resource Allocation with a Budget Constraint for Computing Independent Tasks in the Cloud

Resource Allocation with a Budget Constraint for Computing Independent Tasks in the Cloud Resource Allocaton wth a Budget Constrant for Computng Independent Tasks n the Cloud Wemng Sh and Bo Hong School of Electrcal and Computer Engneerng Georga Insttute of Technology, USA 2nd IEEE Internatonal

More information

Properties of Least Squares

Properties of Least Squares Week 3 3.1 Smple Lnear Regresson Model 3. Propertes of Least Squares Estmators Y Y β 1 + β X + u weekly famly expendtures X weekly famly ncome For a gven level of x, the expected level of food expendtures

More information

Lectures on Multivariable Feedback Control

Lectures on Multivariable Feedback Control Lectures on Multvarable Feedback Control Al Karmpour Department of Electrcal Engneerng, Faculty of Engneerng, Ferdows Unversty of Mashhad June 200) Chapter 9: Quanttatve feedback theory Lecture Notes of

More information