MEASURING HEAT FLUX FROM A COMPONENT ON A PCB
|
|
- Daniela Merritt
- 6 years ago
- Views:
Transcription
1 MEASURING HEAT FLUX FROM A COMPONENT ON A PCB INTRODUCTION Elctronic circuit boards consist of componnts which gnrats substantial amounts of hat during thir opration. A clar knowldg of th lvl of hat dissipation from lctronic componnts during thir opration is dsirabl for rliabl and optimal dsign of cooling systms and slction of th appropriat hat rmoval mthodologis, as hat dissipation from a componnt in an lctronic packag not only influncs its own prformanc but also affcts th prformanc of nighboring componnts, lading to thir failur. th hlp of which an Error Indicator is dvlopd. In ordr to validat and prov th ffctivnss of this nw mthod, xprimnts ar carrid out and xhibitd a clos match btwn th masurd and xprimntal valus. MEASUREMENT METHOD Considr a 2-nod thrmal rsistanc ntwork as shown in figur 1 blow Progrssivly, th dmand for highr powr dnsity and fficincy in lctronic products is incrasing. This lads to a gratr nd for accurat mans of masuring th dissipativ losss of powr and th knowldg of this hat dissipation from lctronic componnts is a critical input for thrmal dsignrs. Convntional tchniqus for masuring th hat dissipation includ th intgration of th product of masurd voltag and currnt and th us of insulatd calorimtry chambrs to masur th hat flow from th dvics. Calorimtric mthods hav bn usd to mak loss masurmnts of lctric machins or standalon componnts such as powr lctronic dvic, transformr, frrit and capacitor tc. A mthod proposd [1] in this articl, to masur hat dissipation of componnts on a printd circuit board (PCB) undr oprating conditions, utilizs a hat flux snsor and thmistors, and calculats hat dissipation from a thrmal standpoint. Masurmnt is pron to rror du to intrfrnc of th nighboring componnt (hat sourcs) and this is compnsatd by carrying out rror analysis, with Figur 1. 2-Nod Thrmal Rsistanc Ntwork [1] Thr ar 2 nods, A and B that ar hat sourcs. Nods A and B ar connctd to ach othr and to th ambint sink. Nod A dtails: Hat dissipation: Q 0 Tmpratur: T 0 Hat dissipation from nod A to sink: Q a0 Nod B dtails: Hat dissipation: Q 1 Hat dissipation from nod B to sink: Q a1 Also, T a rprsnts ambint tmpratur and Q ab is th hat xchang btwn nods A and B.
2 5 FEATURED ARTICLE For this ntwork, hat dissipation from nod A to sink is givn in quation 1. Th tmpratur diffrnc btwn tmpratur at nod A and ambint tmpratur is basically a combination of hat dissipation at nod A and som hat from nod B and is givn in quation 2 blow. Equation 3 shows that th rsistanc 1/R 1 is proportional to rsistancs only. Q a0 = Q 1 Q 0 Q 0 (1) Q 1 = 1 R 1 (T 0 ) (2) 1 = R 1 R (3) a1 Thrmal rsistanc ntwork shown in figur 2 blow dpicts diffrnt componnts on PCB. Nods labld as A, B, C, D and E ar dissipating hat whil othr nods shown do not dissipats hat. Nod A is th Dvic Undr Tst (DUT) whos hat dissipation is masurd by this mthod. Plas not that this tchniqu is ignoring all radiation hat transfr gain and loss. Th abov quation has two unknowns and two masurabl paramtrs. K is an unknown constant and is th rciprocal of thrmal rsistanc from T 0 to T a. QE is anothr unknown constant. Q is th total hat dissipation from DUT and E is th ffct of othr hat sourcs on th PCB. Q m in th quation is basically a masurd quantity. It is part of total hat dissipation Q which is drawn away through componnts cas top and not through th ntwork. This is don and masurd using thrmolctric modul, which draw diffrnt amounts of hat from th componnt cas top and monitors th chang in Q m. As Q m changs, T 0 also changs and is also monitord. Figur 3 shows th rsult of calculation basd on quations 1-3 whr QE is th prdictd hat dissipation for th DUT. Of this, Q is th actual hat dissipation and E is artificial part. Equation 4 has two unknowns K and QE. Q m can b varid using a TEC which rsults in diffrnt T 0. By taking two sts of data QE can b calculatd. Figur 3. Calculation Graph [1] Figur 2. Thrmal Rsistanc Ntwork for th Gnral Cas [1] As xplaind in th prvious sction, (T 0 ) is basically proportional to th hat dissipation at nod A and combination of hat dissipation from othr nods in th ntwork, lik from nod B, C, D, E and is givn by: Q E = Q m K (T 0 ) (4) TEST METHOD Hat flux snsor, Thrmolctric cooling modul (TEC), thrmistor ar usd in tsting th ntir PCB assmbly which is placd in a wind tunnl with high cooling air flow rat. Th arrangmnt is as shown in figur 4 whrin, hat flux snsor is placd btwn th DUT and th TEC with activ hat sink. A total of fiv thrmistors ar usd and attachd on othr sid of PCB (sid othr than whr DUT is mountd). On thrmistor is attachd xactly blow th DUT Qpdia ISSUE 95
3 6 During tsting, only cooling rat can b controlld, whras othr two factors ar out of masurmnt control. In ordr to compnsat th ffct of rror ovrall and achiv highly accurat masurmnt, an Error Indicator is rquird which can b usd during tsting and rval th masurmnt mthod rror. Figur 4. Tsting Apparatus [1] at th cntr and four othr thrmistors ar attachd at th mid points of th four dgs of DUT. TEC usd is modulatd to draw diffrnt amounts of hat from th DUT. Th intnt is, th hat flow should b maximum from th cntr and should sprad from cntr to th sids. To achiv this, th avrag tmpratur from th four surrounding points of DUT is lowr than or qual to that in th middl of DUT. This tsting st up and mthod is OK if th DUT is th only hat sourc on th PCB, but dos not hold tru if thr ar hat sourcs othr than DUT. In that cas, as shown in quation 4, intrfrnc from narby hat sourcs (E) coms in to pictur and should b considrd to avoid th obvious rror in hat dissipation stimation. A concpt of Isothrm Hirarchy is usd to dfin an rror indicator. Figur 5 shows a topology of hat transfr from DUT and othr n hat sourcs flowing through a hirarchy of isothrms to ambint sink. Figur 6 shows th isothrms hirarchy on PCB plan and thrmal rsistanc ntwork. Lt T b locats at th cntr of DUT. Lt T n b th 1st isothrm surrounding th DUT only, T n1 b th 2nd isothrm surrounding th DUT and first closst nighbor hat sourc, T n2 b th 3rd isothrm surrounding th DUT and th first two closst nighbor hat sourcs, so on and so forth, till T nn circls all th n nighbor hat sourcs. It is not ncssary for T ni to b highr than T ni1. Hat flow Q bi (i=1,..., n) will altr dirction to comply with th law of hat flowing from a high tmpratur nod to a lowr tmpratur nod. Figur 7 is th quivalnt ntwork for all th hat sourcs and is basically a transformation of figur 6. NEED FOR ERROR INDICATOR AND ITS DERIVATION From quation 2 and quation 4 abov, th intrfrnc trm E is givn as E = Q 1 (5) Figur 5. A Topology of Hat Flow to Ambint [1] Looking at th intrdpndncy of th paramtrs in quation 5, thr ar thr factors that affct th thortical masurmnt rror and raiss th nd to driv an Error Indicator: 1. Whn hat flow from narby sourc (Q 1 ) is smallr, th rror bcoms smallr 2. Whn th narby hat sourc is far away from DUT or th board in plan conductivity is lss, thn is largr and th rror bcoms smallr 3. Whn thr is highr cooling rat nar Q 1, is smallr and th rror bcoms smallr Figur 6. n-nod Thrmal Rsistanc Ntwork [1] Qpdia ISSUE 95
4 7 FEATURED ARTICLE ( R ( R ) R b a0 ) R Q = (T b )(whnq m =0) - (T n )(whnq m = 0) (9) Figur 7. Equivalnt Thrmal Rsistanc Ntwork [1] All th narby hat sourcs ar rplacd with an quivalnt hat sourc Q xt. Rarranging quation 4 and including T b, w gt quation 6 as follows, Q = Q m R 1 R b ( ) R Q xt ( ) R 1 R b ( ) R (T b ) (6) Th rror prcntag calculatd using th abov quations and applying thm to xprimntal st up, is th masurmnt mthod rror du to th narby hat sourcs intrfrnc. Comparison btwn Simulations and Masurmnt using Error Indicator Tn cass of diffrnt powr lvls and diffrnt distanc of sourcs from th DUT, varying PCB conductivitis and ambint cooling rats ar simulatd with ANSYS Icpak. Figurs 8, 9, 10, 11 show four simulatd cass rsults with diffrnt narby hat sourcs on PCB. Th rror prcntag du to nighbor hat sourcs Q xt is givn in quation 7, Error% = Q R xt R Q 1 R b ( ) Figur 8. Cas 0 No Nighbor Hat Sourc [1] R Q xt = ( R ( R ) R b a0 ) R (7) Whn TEC draws all th hat from th componnt cas top, Q - Q m is clos to zro. Thrfor, R Q xt = T n (whn Q m = Q) (8) Whn TEC draws almost non of th hat through cas top, Q is clos to (Q - Q m ). Equation 9 thrfor is: Figur 9. Cas 1 Rmot Nighbor Hat Sourcs [1] Qpdia ISSUE 95
5 8 Figur 13. Error % Indicator Effctivnss [1] Figur 10. Cas 2 Intrmdiat Nighbor Hat Sourcs [1] As indicatd by Equation (7), th modl rror bfor compnsation is affctd by narby hat sourcs and thir distancs to DUT, PCB conductivity, and ambint cooling rat. Th rrors bfor compnsation ar plottd in Figur 12 from cas simulation rsults. SUMMARY This nw mthod of masuring th hat flux from a componnt on PCB undr oprating condition is innovativ and practical way to stimat componnt hat loss with rasonabl rror. Comparing this mthod with traditional calorimtric mthod, it taks lss ffort to stup tsts by allowing hat sprading through PCB and modulating hat from th cas top. Figur 11. Cas 3 Immdiat Nighbor Hat Sourcs [1] REFERENCES 1. Zhongwi, Qi., A Mthod to Masur Hat Dissipation from Componnt on PCB, Gnral Elctric Tchnology Infrastructur Halthcar 2. Sajith, V., Balakrishna, C., Sobhan, P., Charactrization of Hat Dissipation from a Microprocssor Chip Using Digital Intrfromtry 3. Zhang, Y., Janhs, T., Powr Elctronics Loss Masurmnt Using Nw Hat Flux Snsor Basd on Thrmolctric Dvic With Activ Control Figur 12. Error (bfor compnsation) Snsitivity [1] Qpdia ISSUE 95
Voltage, Current, Power, Series Resistance, Parallel Resistance, and Diodes
Lctur 1. oltag, Currnt, Powr, Sris sistanc, Paralll sistanc, and Diods Whn you start to dal with lctronics thr ar thr main concpts to start with: Nam Symbol Unit oltag volt Currnt ampr Powr W watt oltag
More informationDesign Guidelines for Quartz Crystal Oscillators. R 1 Motional Resistance L 1 Motional Inductance C 1 Motional Capacitance C 0 Shunt Capacitance
TECHNICAL NTE 30 Dsign Guidlins for Quartz Crystal scillators Introduction A CMS Pirc oscillator circuit is wll known and is widly usd for its xcllnt frquncy stability and th wid rang of frquncis ovr which
More informationDefinition1: The ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions.
Dirctivity or Dirctiv Gain. 1 Dfinition1: Dirctivity Th ratio of th radiation intnsity in a givn dirction from th antnna to th radiation intnsity avragd ovr all dirctions. Dfinition2: Th avg U is obtaind
More informationStatus of LAr TPC R&D (2) 2014/Dec./23 Neutrino frontier workshop 2014 Ryosuke Sasaki (Iwate U.)
Status of LAr TPC R&D (2) 214/Dc./23 Nutrino frontir workshop 214 Ryosuk Sasaki (Iwat U.) Tabl of Contnts Dvlopmnt of gnrating lctric fild in LAr TPC Introduction - Gnrating strong lctric fild is on of
More informationForces. Quantum ElectroDynamics. α = = We have now:
W hav now: Forcs Considrd th gnral proprtis of forcs mdiatd by xchang (Yukawa potntial); Examind consrvation laws which ar obyd by (som) forcs. W will nxt look at thr forcs in mor dtail: Elctromagntic
More informationEXST Regression Techniques Page 1
EXST704 - Rgrssion Tchniqus Pag 1 Masurmnt rrors in X W hav assumd that all variation is in Y. Masurmnt rror in this variabl will not ffct th rsults, as long as thy ar uncorrlatd and unbiasd, sinc thy
More informationSection 11.6: Directional Derivatives and the Gradient Vector
Sction.6: Dirctional Drivativs and th Gradint Vctor Practic HW rom Stwart Ttbook not to hand in p. 778 # -4 p. 799 # 4-5 7 9 9 35 37 odd Th Dirctional Drivativ Rcall that a b Slop o th tangnt lin to th
More informationSliding Mode Flow Rate Observer Design
Sliding Mod Flow Rat Obsrvr Dsign Song Liu and Bin Yao School of Mchanical Enginring, Purdu Univrsity, Wst Lafaytt, IN797, USA liu(byao)@purdudu Abstract Dynamic flow rat information is ndd in a lot of
More informationExtraction of Doping Density Distributions from C-V Curves
Extraction of Doping Dnsity Distributions from C-V Curvs Hartmut F.-W. Sadrozinski SCIPP, Univ. California Santa Cruz, Santa Cruz, CA 9564 USA 1. Connction btwn C, N, V Start with Poisson quation d V =
More informationEstimation of apparent fraction defective: A mathematical approach
Availabl onlin at www.plagiarsarchlibrary.com Plagia Rsarch Library Advancs in Applid Scinc Rsarch, 011, (): 84-89 ISSN: 0976-8610 CODEN (USA): AASRFC Estimation of apparnt fraction dfctiv: A mathmatical
More informationA Control Strategy for Photovoltaic-Solid Polymer Electrolysis System Based on Surface Temperature of PV Panel
Amrican Journal of Applid Scincs 5 (7): 5-, ISSN 1546-939 Scinc Publications Corrsponding Author: A Control Stratgy for Photovoltaic-Solid Polymr Elctrolysis Systm Basd on Surfac Tmpratur of PV Panl 1
More information4. Money cannot be neutral in the short-run the neutrality of money is exclusively a medium run phenomenon.
PART I TRUE/FALSE/UNCERTAIN (5 points ach) 1. Lik xpansionary montary policy, xpansionary fiscal policy rturns output in th mdium run to its natural lvl, and incrass prics. Thrfor, fiscal policy is also
More informationText: WMM, Chapter 5. Sections , ,
Lcturs 6 - Continuous Probabilit Distributions Tt: WMM, Chaptr 5. Sctions 6.-6.4, 6.6-6.8, 7.-7. In th prvious sction, w introduc som of th common probabilit distribution functions (PDFs) for discrt sampl
More informationP. Bruschi - Notes on Mixed Signal Design
Chaptr 1. Concpts and dfinitions about Data Acquisition Systms Elctronic systms An lctronic systms is a complx lctronic ntwor, which intracts with th physical world through snsors (input dvics) and actuators
More informationMor Tutorial at www.dumblittldoctor.com Work th problms without a calculator, but us a calculator to chck rsults. And try diffrntiating your answrs in part III as a usful chck. I. Applications of Intgration
More informationThe pn junction: 2 Current vs Voltage (IV) characteristics
Th pn junction: Currnt vs Voltag (V) charactristics Considr a pn junction in quilibrium with no applid xtrnal voltag: o th V E F E F V p-typ Dpltion rgion n-typ Elctron movmnt across th junction: 1. n
More informationDealing with quantitative data and problem solving life is a story problem! Attacking Quantitative Problems
Daling with quantitati data and problm soling lif is a story problm! A larg portion of scinc inols quantitati data that has both alu and units. Units can sa your butt! Nd handl on mtric prfixs Dimnsional
More informationSearch sequence databases 3 10/25/2016
Sarch squnc databass 3 10/25/2016 Etrm valu distribution Ø Suppos X is a random variabl with probability dnsity function p(, w sampl a larg numbr S of indpndnt valus of X from this distribution for an
More informationBasic Polyhedral theory
Basic Polyhdral thory Th st P = { A b} is calld a polyhdron. Lmma 1. Eithr th systm A = b, b 0, 0 has a solution or thr is a vctorπ such that π A 0, πb < 0 Thr cass, if solution in top row dos not ist
More informationCollisions between electrons and ions
DRAFT 1 Collisions btwn lctrons and ions Flix I. Parra Rudolf Pirls Cntr for Thortical Physics, Unirsity of Oxford, Oxford OX1 NP, UK This rsion is of 8 May 217 1. Introduction Th Fokkr-Planck collision
More informationHigher order derivatives
Robrto s Nots on Diffrntial Calculus Chaptr 4: Basic diffrntiation ruls Sction 7 Highr ordr drivativs What you nd to know alrady: Basic diffrntiation ruls. What you can larn hr: How to rpat th procss of
More information4.2 Design of Sections for Flexure
4. Dsign of Sctions for Flxur This sction covrs th following topics Prliminary Dsign Final Dsign for Typ 1 Mmbrs Spcial Cas Calculation of Momnt Dmand For simply supportd prstrssd bams, th maximum momnt
More informationIYPT 2000 Problem No. 3 PLASMA
IYPT 000 Problm No. 3 PLASMA Tam Austria Invstigat th lctrical conducivity of th flam of a candl. Examin th influnc of rlvant paramtrs, in particular, th shap and polarity of th lctrods. Th xprimnts should
More informationMCE503: Modeling and Simulation of Mechatronic Systems Discussion on Bond Graph Sign Conventions for Electrical Systems
MCE503: Modling and Simulation o Mchatronic Systms Discussion on Bond Graph Sign Convntions or Elctrical Systms Hanz ichtr, PhD Clvland Stat Univrsity, Dpt o Mchanical Enginring 1 Basic Assumption In a
More informationGeneral Notes About 2007 AP Physics Scoring Guidelines
AP PHYSICS C: ELECTRICITY AND MAGNETISM 2007 SCORING GUIDELINES Gnral Nots About 2007 AP Physics Scoring Guidlins 1. Th solutions contain th most common mthod of solving th fr-rspons qustions and th allocation
More informationSeebeck and Peltier Effects
Sbck and Pltir Effcts Introduction Thrmal nrgy is usually a byproduct of othr forms of nrgy such as chmical nrgy, mchanical nrgy, and lctrical nrgy. Th procss in which lctrical nrgy is transformd into
More informationEFFECT OF BALL PROPERTIES ON THE BALL-BAT COEFFICIENT OF RESTITUTION
EFFECT OF BALL PROPERTIES ON THE BALL-BAT COEFFICIENT OF RESTITUTION A. M. NATHAN 1 AND L. V. SMITH 2 1 Univrsity of Illinois, 1110 W. Grn Strt, Urbana, IL 61801, USA, E-mail: a-nathan@illinois.du 2 Washington
More informationIn this lecture... Subsonic and supersonic nozzles Working of these nozzles Performance parameters for nozzles
Lct-30 Lct-30 In this lctur... Subsonic and suprsonic nozzls Working of ths nozzls rformanc paramtrs for nozzls rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay Lct-30 Variation of fluid
More informationThat is, we start with a general matrix: And end with a simpler matrix:
DIAGON ALIZATION OF THE STR ESS TEN SOR INTRO DUCTIO N By th us of Cauchy s thorm w ar abl to rduc th numbr of strss componnts in th strss tnsor to only nin valus. An additional simplification of th strss
More informationExam 1. It is important that you clearly show your work and mark the final answer clearly, closed book, closed notes, no calculator.
Exam N a m : _ S O L U T I O N P U I D : I n s t r u c t i o n s : It is important that you clarly show your work and mark th final answr clarly, closd book, closd nots, no calculator. T i m : h o u r
More informationChapter 14 Aggregate Supply and the Short-run Tradeoff Between Inflation and Unemployment
Chaptr 14 Aggrgat Supply and th Short-run Tradoff Btwn Inflation and Unmploymnt Modifid by Yun Wang Eco 3203 Intrmdiat Macroconomics Florida Intrnational Univrsity Summr 2017 2016 Worth Publishrs, all
More information2/12/2013. Overview. 12-Power Transmission Text: Conservation of Complex Power. Introduction. Power Transmission-Short Line
//03 Ovrviw -owr Transmission Txt: 4.6-4.0 ECEGR 45 owr ystms Consrvation of Complx owr hort in owr Transmission owr Transmission isualization Radial in Mdium and ong in owr Transmission oltag Collaps
More informationCOHORT MBA. Exponential function. MATH review (part2) by Lucian Mitroiu. The LOG and EXP functions. Properties: e e. lim.
MTH rviw part b Lucian Mitroiu Th LOG and EXP functions Th ponntial function p : R, dfind as Proprtis: lim > lim p Eponntial function Y 8 6 - -8-6 - - X Th natural logarithm function ln in US- log: function
More informationCh. 24 Molecular Reaction Dynamics 1. Collision Theory
Ch. 4 Molcular Raction Dynamics 1. Collision Thory Lctur 16. Diffusion-Controlld Raction 3. Th Matrial Balanc Equation 4. Transition Stat Thory: Th Eyring Equation 5. Transition Stat Thory: Thrmodynamic
More informationMath-3. Lesson 5-6 Euler s Number e Logarithmic and Exponential Modeling (Newton s Law of Cooling)
Math-3 Lsson 5-6 Eulr s Numbr Logarithmic and Eponntial Modling (Nwton s Law of Cooling) f ( ) What is th numbr? is th horizontal asymptot of th function: 1 1 ~ 2.718... On my 3rd submarin (USS Springfild,
More informationAddition of angular momentum
Addition of angular momntum April, 0 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat th
More informationPrinciples of Humidity Dalton s law
Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid
More informationFinite element discretization of Laplace and Poisson equations
Finit lmnt discrtization of Laplac and Poisson quations Yashwanth Tummala Tutor: Prof S.Mittal 1 Outlin Finit Elmnt Mthod for 1D Introduction to Poisson s and Laplac s Equations Finit Elmnt Mthod for 2D-Discrtization
More information22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches.
Subjct Chmistry Papr No and Titl Modul No and Titl Modul Tag 8/ Physical Spctroscopy / Brakdown of th Born-Oppnhimr approximation. Slction ruls for rotational-vibrational transitions. P, R branchs. CHE_P8_M
More informationContemporary, atomic, nuclear, and particle physics
Contmporary, atomic, nuclar, and particl physics 1 Blackbody radiation as a thrmal quilibrium condition (in vacuum this is th only hat loss) Exampl-1 black plan surfac at a constant high tmpratur T h is
More informationChapter 13 Aggregate Supply
Chaptr 13 Aggrgat Supply 0 1 Larning Objctivs thr modls of aggrgat supply in which output dpnds positivly on th pric lvl in th short run th short-run tradoff btwn inflation and unmploymnt known as th Phillips
More informationCoupled Pendulums. Two normal modes.
Tim Dpndnt Two Stat Problm Coupld Pndulums Wak spring Two normal mods. No friction. No air rsistanc. Prfct Spring Start Swinging Som tim latr - swings with full amplitud. stationary M +n L M +m Elctron
More informationMath 34A. Final Review
Math A Final Rviw 1) Us th graph of y10 to find approimat valus: a) 50 0. b) y (0.65) solution for part a) first writ an quation: 50 0. now tak th logarithm of both sids: log() log(50 0. ) pand th right
More informationAnswer Homework 5 PHA5127 Fall 1999 Jeff Stark
Answr omwork 5 PA527 Fall 999 Jff Stark A patint is bing tratd with Drug X in a clinical stting. Upon admiion, an IV bolus dos of 000mg was givn which yildd an initial concntration of 5.56 µg/ml. A fw
More informationNTHU ESS5850 Micro System Design F. G. Tseng Fall/2016, 7-2, p1. Lecture 7-2 MOSIS/SCNA Design Example- Piezoresistive type Accelerometer II
F. G. Tsng Fall/016, 7-, p1 ctur 7- MOSIS/SCNA Dsign Exampl-!! Pizorsistivity Pizorsistiv typ Acclromtr II a Considr a conductiv lock of dimnsion a as shown in th figur. If a currnt is passd through th
More informationPipe flow friction, small vs. big pipes
Friction actor (t/0 t o pip) Friction small vs larg pips J. Chaurtt May 016 It is an intrsting act that riction is highr in small pips than largr pips or th sam vlocity o low and th sam lngth. Friction
More informationELECTRON-MUON SCATTERING
ELECTRON-MUON SCATTERING ABSTRACT Th lctron charg is considrd to b distributd or xtndd in spac. Th diffrntial of th lctron charg is st qual to a function of lctron charg coordinats multiplid by a four-dimnsional
More informationSearching Linked Lists. Perfect Skip List. Building a Skip List. Skip List Analysis (1) Assume the list is sorted, but is stored in a linked list.
3 3 4 8 6 3 3 4 8 6 3 3 4 8 6 () (d) 3 Sarching Linkd Lists Sarching Linkd Lists Sarching Linkd Lists ssum th list is sortd, but is stord in a linkd list. an w us binary sarch? omparisons? Work? What if
More informationBackground: We have discussed the PIB, HO, and the energy of the RR model. In this chapter, the H-atom, and atomic orbitals.
Chaptr 7 Th Hydrogn Atom Background: W hav discussd th PIB HO and th nrgy of th RR modl. In this chaptr th H-atom and atomic orbitals. * A singl particl moving undr a cntral forc adoptd from Scott Kirby
More informationCO-ORDINATION OF FAST NUMERICAL RELAYS AND CURRENT TRANSFORMERS OVERDIMENSIONING FACTORS AND INFLUENCING PARAMETERS
CO-ORDINATION OF FAST NUMERICAL RELAYS AND CURRENT TRANSFORMERS OVERDIMENSIONING FACTORS AND INFLUENCING PARAMETERS Stig Holst ABB Automation Products Swdn Bapuji S Palki ABB Utilitis India This papr rports
More informationAddition of angular momentum
Addition of angular momntum April, 07 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat
More informationThe University of Alabama in Huntsville Electrical and Computer Engineering Homework #4 Solution CPE Spring 2008
Th Univrsity of Alabama in Huntsvill Elctrical and Comutr Enginring Homwork # Solution CE 6 Sring 8 Chatr : roblms ( oints, ( oints, ( oints, 8( oints, ( oints. You hav a RAID systm whr failurs occur at
More informationInflation and Unemployment
C H A P T E R 13 Aggrgat Supply and th Short-run Tradoff Btwn Inflation and Unmploymnt MACROECONOMICS SIXTH EDITION N. GREGORY MANKIW PowrPoint Slids by Ron Cronovich 2008 Worth Publishrs, all rights rsrvd
More informationOn the Hamiltonian of a Multi-Electron Atom
On th Hamiltonian of a Multi-Elctron Atom Austn Gronr Drxl Univrsity Philadlphia, PA Octobr 29, 2010 1 Introduction In this papr, w will xhibit th procss of achiving th Hamiltonian for an lctron gas. Making
More informationSara Godoy del Olmo Calculation of contaminated soil volumes : Geostatistics applied to a hydrocarbons spill Lac Megantic Case
wwwnvisol-canadaca Sara Godoy dl Olmo Calculation of contaminatd soil volums : Gostatistics applid to a hydrocarbons spill Lac Mgantic Cas Gostatistics: study of a PH contamination CONTEXT OF THE STUDY
More informationSCALING OF SYNCHROTRON RADIATION WITH MULTIPOLE ORDER. J. C. Sprott
SCALING OF SYNCHROTRON RADIATION WITH MULTIPOLE ORDER J. C. Sprott PLP 821 Novmbr 1979 Plasma Studis Univrsity of Wisconsin Ths PLP Rports ar informal and prliminary and as such may contain rrors not yt
More informationINC 693, 481 Dynamics System and Modelling: The Language of Bound Graphs Dr.-Ing. Sudchai Boonto Assistant Professor
INC 693, 48 Dynamics Systm and Modlling: Th Languag o Bound Graphs Dr.-Ing. Sudchai Boonto Assistant Prossor Dpartmnt o Control Systm and Instrumntation Enginring King Mongkut s Unnivrsity o Tchnology
More informationGradebook & Midterm & Office Hours
Your commnts So what do w do whn on of th r's is 0 in th quation GmM(1/r-1/r)? Do w nd to driv all of ths potntial nrgy formulas? I don't undrstand springs This was th first lctur I actually larnd somthing
More informationMA 262, Spring 2018, Final exam Version 01 (Green)
MA 262, Spring 218, Final xam Vrsion 1 (Grn) INSTRUCTIONS 1. Switch off your phon upon ntring th xam room. 2. Do not opn th xam booklt until you ar instructd to do so. 3. Bfor you opn th booklt, fill in
More informationTwo Products Manufacturer s Production Decisions with Carbon Constraint
Managmnt Scinc and Enginring Vol 7 No 3 pp 3-34 DOI:3968/jms9335X374 ISSN 93-34 [Print] ISSN 93-35X [Onlin] wwwcscanadant wwwcscanadaorg Two Products Manufacturr s Production Dcisions with Carbon Constraint
More informationDifferentiation of Exponential Functions
Calculus Modul C Diffrntiation of Eponntial Functions Copyright This publication Th Northrn Albrta Institut of Tchnology 007. All Rights Rsrvd. LAST REVISED March, 009 Introduction to Diffrntiation of
More informationA Propagating Wave Packet Group Velocity Dispersion
Lctur 8 Phys 375 A Propagating Wav Packt Group Vlocity Disprsion Ovrviw and Motivation: In th last lctur w lookd at a localizd solution t) to th 1D fr-particl Schrödingr quation (SE) that corrsponds to
More informationIntroduction to Condensed Matter Physics
Introduction to Condnsd Mattr Physics pcific hat M.P. Vaughan Ovrviw Ovrviw of spcific hat Hat capacity Dulong-Ptit Law Einstin modl Dby modl h Hat Capacity Hat capacity h hat capacity of a systm hld at
More informationLaboratory work # 8 (14) EXPERIMENTAL ESTIMATION OF CRITICAL STRESSES IN STRINGER UNDER COMPRESSION
Laboratory wor # 8 (14) XPRIMNTAL STIMATION OF CRITICAL STRSSS IN STRINGR UNDR COMPRSSION At action of comprssing ffort on a bar (column, rod, and stringr) two inds of loss of stability ar possibl: 1)
More informationAbstract Interpretation: concrete and abstract semantics
Abstract Intrprtation: concrt and abstract smantics Concrt smantics W considr a vry tiny languag that manags arithmtic oprations on intgrs valus. Th (concrt) smantics of th languags cab b dfind by th funzcion
More informationu x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula
7. Intgration by Parts Each drivativ formula givs ris to a corrsponding intgral formula, as w v sn many tims. Th drivativ product rul yilds a vry usful intgration tchniqu calld intgration by parts. Starting
More informationDetermination of Vibrational and Electronic Parameters From an Electronic Spectrum of I 2 and a Birge-Sponer Plot
5 J. Phys. Chm G Dtrmination of Vibrational and Elctronic Paramtrs From an Elctronic Spctrum of I 2 and a Birg-Sponr Plot 1 15 2 25 3 35 4 45 Dpartmnt of Chmistry, Gustavus Adolphus Collg. 8 Wst Collg
More informationData Assimilation 1. Alan O Neill National Centre for Earth Observation UK
Data Assimilation 1 Alan O Nill National Cntr for Earth Obsrvation UK Plan Motivation & basic idas Univariat (scalar) data assimilation Multivariat (vctor) data assimilation 3d-Variational Mthod (& optimal
More informationSAFE HANDS & IIT-ian's PACE EDT-15 (JEE) SOLUTIONS
It is not possibl to find flu through biggr loop dirctly So w will find cofficint of mutual inductanc btwn two loops and thn find th flu through biggr loop Also rmmbr M = M ( ) ( ) EDT- (JEE) SOLUTIONS
More informationSeptember 23, Honors Chem Atomic structure.notebook. Atomic Structure
Atomic Structur Topics covrd Atomic structur Subatomic particls Atomic numbr Mass numbr Charg Cations Anions Isotops Avrag atomic mass Practic qustions atomic structur Sp 27 8:16 PM 1 Powr Standards/ Larning
More informationME 321 Kinematics and Dynamics of Machines S. Lambert Winter 2002
3.4 Forc Analysis of Linkas An undrstandin of forc analysis of linkas is rquird to: Dtrmin th raction forcs on pins, tc. as a consqunc of a spcifid motion (don t undrstimat th sinificanc of dynamic or
More informationUnit 7 Charge-to-mass ratio of the electron
Unit 7 Charg-to-ass ratio of th lctron Kywords: J. J. Thoson, Lorntz Forc, Magntic Filds Objctiv: Obsrv th rsults of lctron ba influncd by th agntic fild and calculat th charg-to-ass ratio of th lctron.
More informationObserver Bias and Reliability By Xunchi Pu
Obsrvr Bias and Rliability By Xunchi Pu Introduction Clarly all masurmnts or obsrvations nd to b mad as accuratly as possibl and invstigators nd to pay carful attntion to chcking th rliability of thir
More informationSolution: APPM 1360 Final (150 pts) Spring (60 pts total) The following parts are not related, justify your answers:
APPM 6 Final 5 pts) Spring 4. 6 pts total) Th following parts ar not rlatd, justify your answrs: a) Considr th curv rprsntd by th paramtric quations, t and y t + for t. i) 6 pts) Writ down th corrsponding
More informationMicrocalorimeter and bolometer model
JOURNAL OF APPLIED PHYSICS VOLUME 93, NUMBER 8 5 APRIL 2003 Microcalorimtr and bolomtr modl M. Galazzi a) Physics Dpartmnt, Univrsity of Wisconsin, Madison, Wisconsin 53706 and NASA/Goddard Spac Flight
More informationTRANSISTOR AND DIODE STUDIES. Prof. H. J. Zimmermann Prof. S. J. Mason C. R. Hurtig Prof. R. B. Adler Dr. W. D. Jackson R. E.
XI. TANSISTO AND DIODE STUDIES Prof. H. J. Zimmrmann Prof. S. J. Mason C.. Hurti Prof.. B. Adlr Dr. W. D. Jackson. E. Nlson A. DESIGN OF TANSFOMEESS TANSISTO AUDIO AMPIFIES Considrabl ffort by many oranizations
More informationStatistical Thermodynamics: Sublimation of Solid Iodine
c:374-7-ivap-statmch.docx mar7 Statistical Thrmodynamics: Sublimation of Solid Iodin Chm 374 For March 3, 7 Prof. Patrik Callis Purpos:. To rviw basic fundamntals idas of Statistical Mchanics as applid
More informationLecture 28 Title: Diatomic Molecule : Vibrational and Rotational spectra
Lctur 8 Titl: Diatomic Molcul : Vibrational and otational spctra Pag- In this lctur w will undrstand th molcular vibrational and rotational spctra of diatomic molcul W will start with th Hamiltonian for
More informationSER/BER in a Fading Channel
SER/BER in a Fading Channl Major points for a fading channl: * SNR is a R.V. or R.P. * SER(BER) dpnds on th SNR conditional SER(BER). * Two prformanc masurs: outag probability and avrag SER(BER). * Ovrall,
More informationWhere k is either given or determined from the data and c is an arbitrary constant.
Exponntial growth and dcay applications W wish to solv an quation that has a drivativ. dy ky k > dx This quation says that th rat of chang of th function is proportional to th function. Th solution is
More informationEngineering 323 Beautiful HW #13 Page 1 of 6 Brown Problem 5-12
Enginring Bautiful HW #1 Pag 1 of 6 5.1 Two componnts of a minicomputr hav th following joint pdf for thir usful liftims X and Y: = x(1+ x and y othrwis a. What is th probability that th liftim X of th
More informationECE 344 Microwave Fundamentals
ECE 44 Microwav Fundamntals Lctur 08: Powr Dividrs and Couplrs Part Prpard By Dr. hrif Hkal 4/0/08 Microwav Dvics 4/0/08 Microwav Dvics 4/0/08 Powr Dividrs and Couplrs Powr dividrs, combinrs and dirctional
More informationu r du = ur+1 r + 1 du = ln u + C u sin u du = cos u + C cos u du = sin u + C sec u tan u du = sec u + C e u du = e u + C
Tchniqus of Intgration c Donald Kridr and Dwight Lahr In this sction w ar going to introduc th first approachs to valuating an indfinit intgral whos intgrand dos not hav an immdiat antidrivativ. W bgin
More informationIVE(TY) Department of Engineering E&T2520 Electrical Machines 1 Miscellaneous Exercises
TRANSFORMER Q1 IE(TY) Dpartmnt of Enginring E&T50 Elctrical Machins 1 Miscllanous Exrciss Q Q3 A singl phas, 5 ka, 0/440, 60 Hz transformr gav th following tst rsults. Opn circuit tst (440 sid opn): 0
More informationCIRCULAR GRATING ECCENTRIC TESTING AND ERROR COMPENSATION FOR ROBOT JOINT USING DOUBLE READING HEAD
10 th April 013. Vol. 50 No.1 005-013 JATIT & LLS. All rights rsrvd. ISSN: 199-8645 www.jatit.org E-ISSN: 1817-3195 CIRCULAR GRATING ECCENTRIC TESTING AND ERROR COMPENSATION FOR ROBOT JOINT USING DOUBLE
More informationph People Grade Level: basic Duration: minutes Setting: classroom or field site
ph Popl Adaptd from: Whr Ar th Frogs? in Projct WET: Curriculum & Activity Guid. Bozman: Th Watrcours and th Council for Environmntal Education, 1995. ph Grad Lvl: basic Duration: 10 15 minuts Stting:
More informationLearning Spherical Convolution for Fast Features from 360 Imagery
Larning Sphrical Convolution for Fast Faturs from 36 Imagry Anonymous Author(s) 3 4 5 6 7 8 9 3 4 5 6 7 8 9 3 4 5 6 7 8 9 3 3 3 33 34 35 In this fil w provid additional dtails to supplmnt th main papr
More informationsurface of a dielectric-metal interface. It is commonly used today for discovering the ways in
Surfac plasmon rsonanc is snsitiv mchanism for obsrving slight changs nar th surfac of a dilctric-mtal intrfac. It is commonl usd toda for discovring th was in which protins intract with thir nvironmnt,
More informationChapter 6 Folding. Folding
Chaptr 6 Folding Wintr 1 Mokhtar Abolaz Folding Th folding transformation is usd to systmatically dtrmin th control circuits in DSP architctur whr multipl algorithm oprations ar tim-multiplxd to a singl
More informationModule 8 Non equilibrium Thermodynamics
Modul 8 Non quilibrium hrmodynamics ctur 8.1 Basic Postulats NON-EQUIIRIBIUM HERMODYNAMICS Stady Stat procsss. (Stationary) Concpt of ocal thrmodynamic qlbm Extnsiv proprty Hat conducting bar dfin proprtis
More informationThe influence of electron trap on photoelectron decay behavior in silver halide
Th influnc of lctron trap on photolctron dcay bhavior in silvr halid Rongjuan Liu, Xiaowi Li 1, Xiaodong Tian, Shaopng Yang and Guangshng Fu Collg of Physics Scinc and Tchnology, Hbi Univrsity, Baoding,
More informationcycle that does not cross any edges (including its own), then it has at least
W prov th following thorm: Thorm If a K n is drawn in th plan in such a way that it has a hamiltonian cycl that dos not cross any dgs (including its own, thn it has at last n ( 4 48 π + O(n crossings Th
More informationElements of Statistical Thermodynamics
24 Elmnts of Statistical Thrmodynamics Statistical thrmodynamics is a branch of knowldg that has its own postulats and tchniqus. W do not attmpt to giv hr vn an introduction to th fild. In this chaptr,
More informationSECTION where P (cos θ, sin θ) and Q(cos θ, sin θ) are polynomials in cos θ and sin θ, provided Q is never equal to zero.
SETION 6. 57 6. Evaluation of Dfinit Intgrals Exampl 6.6 W hav usd dfinit intgrals to valuat contour intgrals. It may com as a surpris to larn that contour intgrals and rsidus can b usd to valuat crtain
More informationHigh Energy Physics. Lecture 5 The Passage of Particles through Matter
High Enrgy Physics Lctur 5 Th Passag of Particls through Mattr 1 Introduction In prvious lcturs w hav sn xampls of tracks lft by chargd particls in passing through mattr. Such tracks provid som of th most
More informationKoch Fractal Boundary Single feed Circularly Polarized Microstrip Antenna
1 Journal of Microwavs, Optolctronics and Elctromagntic Applications, Vol. 6, No. 2, Dcmbr 2007 406 Koch Fractal Boundary Singl fd Circularly Polarizd Microstrip Antnna P. Nagswara Rao and N. V. S.N Sarma
More informationTitle: Vibrational structure of electronic transition
Titl: Vibrational structur of lctronic transition Pag- Th band spctrum sn in th Ultra-Violt (UV) and visibl (VIS) rgions of th lctromagntic spctrum can not intrprtd as vibrational and rotational spctrum
More informationA novel method for determining and improving the quality of a quadrupolar fiber gyro coil under temperature variations
A novl mthod for dtrmining and improving th quality of a quadrupolar fibr gyro coil undr tmpratur variations Zhihong Li, 1,2 Zhuo Mng, 1,2 Tign Liu, 1 and X. Stv Yao 1,* 1 Polarization Rsarch Cntr, Collg
More informationCalculus II (MAC )
Calculus II (MAC232-2) Tst 2 (25/6/25) Nam (PRINT): Plas show your work. An answr with no work rcivs no crdit. You may us th back of a pag if you nd mor spac for a problm. You may not us any calculators.
More informationChapter 13 GMM for Linear Factor Models in Discount Factor form. GMM on the pricing errors gives a crosssectional
Chaptr 13 GMM for Linar Factor Modls in Discount Factor form GMM on th pricing rrors givs a crosssctional rgrssion h cas of xcss rturns Hors rac sting for charactristic sting for pricd factors: lambdas
More information