Digital MOS Integrated Circuits. Chapter 2 Gate Delay and RC Circuits. Practice: Inside the CMOS Inverter. Virtually Parallel Capacitors.
|
|
- Bruce Carter
- 7 years ago
- Views:
Transcription
1 apr 2 Ga Dlay and ircuis Digial MOS Ingrad ircuis MIPS From ompuaion, you av sn a digial Ingrad ircuis ar buil wi MOS ransisors a work as swics Today w will sar our sudy of ir swicing spd 3 firs ordr 1 3 firs ordr 2 Pracic: Insid MOS Invrr Virually Paralll apaciors 2.3 Tis is sudid in ompuaion 3 firs ordr 3 i 2 v 1 Ts wo circuis ibi sam ransin bavior Sow a currn i is idnical in bo circuis d(v V i Lf ck: 1 2 d d dv Eampl 1.4 d d d ( 1 2 d i v 1 2 i ( 1 2 d onsan bias volag across capacior dos no influnc ransin bavior 3 firs ordr 4 Invrr Swicing Modls n pulldown V pullup 5 V n p p n p abov ambin old off Your ar sudying so ard a you forg o drink your coff Skc mpraur as a funcion of im A B anonical circuis subjc of is lcur (Modl will b plaind in ompuaion W ar inrsd in Wavform a capaciors afr swic closs im urv could bs rprsn an acual cooling scdul, sinc ra of cooling (slop of curv is lfasr wn mpraur diffrnc (coff vs ambin is igr 3 firs ordr 5 3 firs ordr 6 1
2 Hydraulic Analogy ommunicaing Vssls Hydraulic Analogy Prssur Diffrnc Ponial Diffrnc War Flow urrn Flow Vry larg war ank Small war ank, mpy wn < Prssur diffrnc proporional o ig diffrnc Iniial condiion TUE/EE 5 nwrk analys 2/3 NvdM 1 fundamnal 8 Valv opns a Skc war ig in small ank as funcion of im War ig im 3 firs ordr 7 3 firs ordr 8 ircui Bavior: Iniial ondiion v i v W ar inrsd in bavior of circui afr swic closs No inrsd for < Eampl: wa is i jus afr swic closs? v mmbr i and no v v V v Tus i S ( ( (: iniial condiion (bginwaard For circuis wi mmory, if w wan o compu bavior afr som im (no only a, w nd o spcify iniial condiion(s a 3 firs ordr 9 ircui Bavior: Final Valu v i v iniial valu Wa is of? Final valu mans c sady sa condiion d i c v mmbr: i d Tus c i v d sady sa Final (sady sa valu is Noaion: ( ( 3 firs ordr 1 ircui Bavior: Final Valu v i v iniial valu Final valu is ( Dos of dpnd on iniial condiion (? No! For linar circuis, dos no dpnd on iniial condiions bu acual ransin rspons dos dpnd on iniial condiions. ircui Bavior: Slop of v i v iniial valu is a funcion of im: ( Wa is slop (llingsok of? i d v V v d i S W can find slop of rspons for ac valu of oupu Sow a i( ( (/ follows dircly as a spcial cas 3 firs ordr 11 3 firs ordr 12 2
3 Summary v i v iniial valu W can compu i( and of, ( and slop of as a funcion of, bu can w find ou mor? mmbr: w wan o say soming abou compur swicing spd using abov circui as a modl Implis a w wan o sudy bavior as a funcion of im spons im: ow fas is ransin from ( o V S Mor gnrally, w wan o find (: ransin rspons (ovrgangs vrscijnsl ircui Bavior: spons Tim v i v iniial valu Wic ings drmin ow fas rspons (ransiion from iniial valu o will b? T valu of (larg will carg mor slowly T valu of (larg will ak longr o rac W will sorly find a in suc (linar circuis wi on, rspons im is proporional o produc No valu of (diffrnc bwn final and iniial valu dos no influnc rspons im, only currns involvd 3 firs ordr 13 3 firs ordr 14 ircui Equaion v i v >: i d V v i S v d Tis diffrnial quaion, ogr wi iniial condiion, fully spcifis bavior of circui afr swic closs Our n callng: larn ow o solv suc quaions Diffrnial Equaions v d circui dy Ky c prooypical d Formulas Aad Equaion no only involving variabl, bu also is drivaiv(s rucial in many filds nginring, biology, conomics, adioaciv dcay, or laws of naur wnvr cang is influncd by prsn sa linar D.E. (diffrnial quaion wn cang proporional o sa Tis quaion, and many ors, producs ponnial soluions 3 firs ordr 15 3 firs ordr 16 f ( a a n sin( 1 Typ of Soluion o Epc v c V s d d d ~ v df ( d a a n n1 cos( ln(1 1 a of cang of v is proporional o v W nd compaibl LHS and HS Equaions of cang proporional o sa produc ponnial soluions Drivaiv proporional o funcion Drivaiv Proporional o Funcion If y b Proof: n dy cb d dy y( y( b b lim lim d Bu: b (b (b Tus: dy b b b lim d No: c dpnds on b b 1 b lim c Tis limi valuas o a consan cb ln( firs ordr 17 3 firs ordr 18 3
4 If W Would Know Abou ln,, c. Sow a a 1 lim is a consan ! ln a. ( ln a. a 1 ln a.... 2! a 1 1 ln a. 1 lim ln a QED T numbr db cb d c dpnds on bas b of ponn b 1 c lim Tr is a b suc a c 1 Tis valu of b is Tis numbr is calld markably spcial numbr is prfrd bas for prssing ponnial soluions o our diffrnial quaions 3 firs ordr 19 3 firs ordr 2 If y b n Wy as bas? dy cb If y n d Tis is wy w us as our bas: simplr formulas, wiou arbirary consans v v Tis circui dy d c d Tis diffrnial quaion v V ( c s 1 Has is soluion 3 firs ordr 21 v v v.5 Soluion c d v V ( c s firs ordr 22 Proof Using Diffrnaion Sow a is diffrnial quaion as is soluion c v d c V c V s s idnical d c v c c V d s d qd 3 firs ordr Evalua ingrals, us 1 d ln K 1 ad a K 2 Soluion by Ingraion. Sar wi Diffrnial Eq. 1. Spara variabls 2. Ingra LHS and HS 4. Absorb K s ino K 3 K 2 K 1 c d c d c d planaion ln( K 1 K 2 ln( K firs ordr 24 4
5 4. from prvious sp 5. ponnia LHS and HS 6. rsul Soluion coninud ln( K 3 K3 v c v v Soluion c d v V ( c s 1 7. wri (dfin K K 3 K v 8. Drmin K from iniial valu: ( V s K K.5 K 9. Final Soluion: V ( s 1 3 firs ordr firs ordr 26 Iniial Valu v v Volag across capacior (v dpnds on isory Any prvious circui aciviy could influnc carg prsn a a Iniial valu (bginwaard mus b known, ir plicily or implicily (from circui con Mamaically rlad o fac a ani drivaivs ar only spcifid up o a consan v V ( c s Tim onsan im consan (ijdconsan, us symbol τ Basic im scal of swicing vn V V s uni: ΩF s A V V s 3 firs ordr 27 3 firs ordr 28 Tim onsan spons can b normalizd wi rspc o τ and V S v ( v V ( c s 1 2 Eampl: (1. 86 ( τ Eac τsp givs 63% V.86 of rmaining swing s τ usually good (1% nginring approimaion for compl ransiion 2τ 4τ 6τ 5%.69τ 8τ Sow a 5%.69τ 3 firs ordr 29 Soluion Procss (viw Mamaics will lar provid mor formal drivaion Sparaion of variabls dy Bu dy (by M M( far ( N no ( y d d c V v c d all diffrnial s c quaions ar d sparabl! Ingra LHS and HS sparaly add consan K o b drmind from iniial condiion (s prvious slids...d... K or us dfini ingraions (s book...d 3 firs ordr 3 5
6 Gnral Iniial ondiion Assum swic closs a (insad of Assum v ( v (insad of v ( Eq 2.14 K /τ / τ K V K s / τ / τ ( / τ / τ ( ( / τ ( Simpl imsif of soluion, and scald ampliud of ransin 3 firs ordr 31 D sady sa rspons oal rspons omponns of Soluion ( o / τ (o ransin rspons 2τ 4τ 6τ 8τ Minus Transin rspons (scaklvrscijnsl sign From ig ampliud o zro: lim > Iniially opposs sady sa rspons: 1 Transin rspons significan jus afr swicing, lar D sady sa rspons dominas 3 firs ordr Gnral Firs Ordr ircuis c d Tis (linar firs ordr ordinary diffrnial quaion is valid for any firs ordr circui wi D sourcs Quick Proof: 1. Firs ordr circui mans a r is only on nod in circui wi mmory (sa (osand 2. If i as only on capacior, proof follows from compuing Tévnin quivaln for rs of circui, bcaus rsul is simpl sris ck. 3. If r ar mulipl capaciors, y mus b virually paralll and can us b rducd ino on quivaln capacior spcial cas τ c ( d gnral rsul 3 firs ordr 33 Unknown variabl as a funcion of im 2.1 of variabl iniial valu of variabl Gnral Soluion c Valid for any firs ordr τ ( d circui wi D sourcs ( / τ ( ( ( sady sa (saionair of variabl ransin [ (im of swicing ] im consan 3 firs ordr 34 Soluion (almos by Inspcion ( / τ ( ( ( 1. Idnify sa variabl: capacior volag 2. Drmin iniial valu of sa variabl 3. alcula 4. alcula im consan Sp 3: alcula Final Valu Sady sa or of capacior volag: I lim c lim c c i d d 1 2 v I 1 2 i mans: plac capacior by opn circui v ( D sady sa quivaln modl of capacior is an opn circui Q: (? I 2 3 firs ordr 35 3 firs ordr 36 6
Transient Thermoelastic Behavior of Semi-infinite Cylinder by Using Marchi-Zgrablich and Fourier Transform Technique
Inrnaional Journal of Mahmaical Enginring and Scinc ISSN : 77-698 Volum 1 Issu 5 (May 01) hp://www.ijms.com/ hps://sis.googl.com/si/ijmsjournal/ Transin Thrmolasic Bhavior of Smi-infini Cylindr by Using
More informationChapter 7. Response of First-Order RL and RC Circuits
Chaper 7. esponse of Firs-Order L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural
More informationModule 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur
Module 4 Single-phase A circuis ersion EE T, Kharagpur esson 5 Soluion of urren in A Series and Parallel ircuis ersion EE T, Kharagpur n he las lesson, wo poins were described:. How o solve for he impedance,
More informationDifferential Equations and Linear Superposition
Differenial Equaions and Linear Superposiion Basic Idea: Provide soluion in closed form Like Inegraion, no general soluions in closed form Order of equaion: highes derivaive in equaion e.g. dy d dy 2 y
More information9. Capacitor and Resistor Circuits
ElecronicsLab9.nb 1 9. Capacior and Resisor Circuis Inroducion hus far we have consider resisors in various combinaions wih a power supply or baery which provide a consan volage source or direc curren
More informationCHARGE AND DISCHARGE OF A CAPACITOR
REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:
More informationRC (Resistor-Capacitor) Circuits. AP Physics C
(Resisor-Capacior Circuis AP Physics C Circui Iniial Condiions An circui is one where you have a capacior and resisor in he same circui. Suppose we have he following circui: Iniially, he capacior is UNCHARGED
More informationCapacitors and inductors
Capaciors and inducors We coninue wih our analysis of linear circuis by inroducing wo new passive and linear elemens: he capacior and he inducor. All he mehods developed so far for he analysis of linear
More informationMany quantities are transduced in a displacement and then in an electric signal (pressure, temperature, acceleration). Prof. B.
Displacmn snsors Many quaniis ar ransducd in a displacmn and hn in an lcric signal (prssur, mpraur, acclraion). Poniomrs Poniomrs i p p i o i p A poniomr is basd on a sliding conac moving on a rsisor.
More informationcooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)
Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer
More informationPulse-Width Modulation Inverters
SECTION 3.6 INVERTERS 189 Pulse-Widh Modulaion Inverers Pulse-widh modulaion is he process of modifying he widh of he pulses in a pulse rain in direc proporion o a small conrol signal; he greaer he conrol
More informationInductance and Transient Circuits
Chaper H Inducance and Transien Circuis Blinn College - Physics 2426 - Terry Honan As a consequence of Faraday's law a changing curren hrough one coil induces an EMF in anoher coil; his is known as muual
More informationVoltage level shifting
rek Applicaion Noe Number 1 r. Maciej A. Noras Absrac A brief descripion of volage shifing circuis. 1 Inroducion In applicaions requiring a unipolar A volage signal, he signal may be delivered from a bi-polar
More informationEconomics Honors Exam 2008 Solutions Question 5
Economics Honors Exam 2008 Soluions Quesion 5 (a) (2 poins) Oupu can be decomposed as Y = C + I + G. And we can solve for i by subsiuing in equaions given in he quesion, Y = C + I + G = c 0 + c Y D + I
More informationAP Calculus AB 2013 Scoring Guidelines
AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a mission-driven no-for-profi organizaion ha connecs sudens o college success and opporuniy. Founded in 19, he College Board was
More informationDifferential Equations. Solving for Impulse Response. Linear systems are often described using differential equations.
Differenial Equaions Linear sysems are ofen described using differenial equaions. For example: d 2 y d 2 + 5dy + 6y f() d where f() is he inpu o he sysem and y() is he oupu. We know how o solve for y given
More informationTransient Analysis of First Order RC and RL circuits
Transien Analysis of Firs Order and iruis The irui shown on Figure 1 wih he swih open is haraerized by a pariular operaing ondiion. Sine he swih is open, no urren flows in he irui (i=0) and v=0. The volage
More informationFull-wave rectification, bulk capacitor calculations Chris Basso January 2009
ull-wave recificaion, bulk capacior calculaions Chris Basso January 9 This shor paper shows how o calculae he bulk capacior value based on ripple specificaions and evaluae he rms curren ha crosses i. oal
More informationMULTINATIONAL FINANCE
MULTINATIONAL FINANCE Drminas and Forcasing o Excang Ras (Capr 2 & 4 Oulin o Lcur 1 Drminaion o xcang ras Floaing xcang ra sysm T Ass Mark Modl Pariy Condiions Purcasing Powr Pariy (PPP Inrnaional Fisr
More informationAnalogue and Digital Signal Processing. First Term Third Year CS Engineering By Dr Mukhtiar Ali Unar
Analogue and Digial Signal Processing Firs Term Third Year CS Engineering By Dr Mukhiar Ali Unar Recommended Books Haykin S. and Van Veen B.; Signals and Sysems, John Wiley& Sons Inc. ISBN: 0-7-380-7 Ifeachor
More informationProjections - 3D Viewing. Overview Lecture 4. Projection - 3D viewing. Projections. Projections Parallel Perspective
Ovrviw Lctur 4 Projctions - 3D Viwing Projctions Paralll Prspctiv 3D Viw Volum 3D Viwing Transformation Camra Modl - Assignmnt 2 OFF fils 3D mor compl than 2D On mor dimnsion Displa dvic still 2D Analog
More informationAP Calculus BC 2010 Scoring Guidelines
AP Calculus BC Scoring Guidelines The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in, he College Board
More informationRapid Estimation of Water Flooding Performance and Optimization in EOR by Using Capacitance Resistive Model
Iranian Journal of Chmical Enginring Vol. 9, No. 4 (Auumn), 22, IAChE Rapid Esimaion of War Flooding Prformanc and Opimizaion in EOR by Using Capacianc Rsisiv Modl A.R. Basami, M. Dlshad 2, P. Pourafshary
More informationCloud and Big Data Summer School, Stockholm, Aug., 2015 Jeffrey D. Ullman
Cloud and Big Data Summr Scool, Stockolm, Aug., 2015 Jffry D. Ullman Givn a st of points, wit a notion of distanc btwn points, group t points into som numbr of clustrs, so tat mmbrs of a clustr ar clos
More informationEstimating Powers with Base Close to Unity and Large Exponents
Divulgacions Mamáicas Vol. 3 No. 2005), pp. 2 34 Esimaing Powrs wih Bas Clos o Uniy and Larg Exponns Esimacón d Poncias con Bas Crcana a la Unidad y Grands Exponns Vio Lampr Vio.Lampr@fgg.uni-lj.si) FGG,
More informationwww.akcp.com Virtual Sensors
www.akcp.cm Irduci: Virual Ssrs Virual ssrs ca b a vry pwrful l i yur mirig sysm. O h scuriyprb yu ca hav up 80 f hs virual ssrs ad hy allw fr a muliud f applicais. Igrai wih MODBUS wrks wih h scuriyprb
More informationRandom Walk in 1-D. 3 possible paths x vs n. -5 For our random walk, we assume the probabilities p,q do not depend on time (n) - stationary
Random Walk in -D Random walks appear in many cones: diffusion is a random walk process undersanding buffering, waiing imes, queuing more generally he heory of sochasic processes gambling choosing he bes
More informationNew Basis Functions. Section 8. Complex Fourier Series
Nw Basis Functions Sction 8 Complx Fourir Sris Th complx Fourir sris is prsntd first with priod 2, thn with gnral priod. Th connction with th ral-valud Fourir sris is xplaind and formula ar givn for convrting
More informationSignal Rectification
9/3/25 Signal Recificaion.doc / Signal Recificaion n imporan applicaion of juncion diodes is signal recificaion. here are wo ypes of signal recifiers, half-wae and fullwae. Le s firs consider he ideal
More informationAppendix A: Area. 1 Find the radius of a circle that has circumference 12 inches.
Appendi A: Area worked-ou s o Odd-Numbered Eercises Do no read hese worked-ou s before aemping o do he eercises ourself. Oherwise ou ma mimic he echniques shown here wihou undersanding he ideas. Bes wa
More informationMTBF: Understanding Its Role in Reliability
Modul MTBF: Undrsanding Is Rol in Rliabiliy By David C. Wilson Foundr / CEO March 4, Wilson Consuling Srvics, LLC dav@wilsonconsulingsrvics.n www.wilsonconsulingsrvics.n Wilson Consuling Srvics, LLC Pag
More informationNumerical Algorithm for the Stochastic Present Value of Aggregate Claims in the Renewal Risk Model
Gn. Mah. Nos, Vol. 9, No. 2, Dcmbr, 23, pp. 4- ISSN 229-784; Copyrigh ICSRS Publicaion, 23 www.i-csrs.org Availabl fr onlin a hp://www.gman.in Numrical Algorihm for h Sochasic Prsn Valu of Aggrga Claims
More informationEndogenous Growth Practice Questions Course 14.451 Macro I TA: Todd Gormley, tgormley@mit.edu
Endogenous Grow Praie Quesions Course 4.45 Maro I TA: Todd Gormley, gormley@mi.edu Here are wo example quesions based on e endogenous grow models disussed by Marios in lass on Wednesday, Mar 9, 2005. Tey
More informationThe Transport Equation
The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be
More informationMATHEMATICS FOR ENGINEERING DIFFERENTIATION TUTORIAL 1 - BASIC DIFFERENTIATION
MATHEMATICS FOR ENGINEERING DIFFERENTIATION TUTORIAL 1 - BASIC DIFFERENTIATION Tis tutorial is essential pre-requisite material for anyone stuing mecanical engineering. Tis tutorial uses te principle of
More informationTraffic Flow Analysis (2)
Traffic Flow Analysis () Statistical Proprtis. Flow rat distributions. Hadway distributions. Spd distributions by Dr. Gang-Ln Chang, Profssor Dirctor of Traffic safty and Oprations Lab. Univrsity of Maryland,
More informationThe Derivative as a Function
Section 2.2 Te Derivative as a Function 200 Kiryl Tsiscanka Te Derivative as a Function DEFINITION: Te derivative of a function f at a number a, denoted by f (a), is if tis limit exists. f (a) f(a+) f(a)
More informationf(a + h) f(a) f (a) = lim
Lecture 7 : Derivative AS a Function In te previous section we defined te derivative of a function f at a number a (wen te function f is defined in an open interval containing a) to be f (a) 0 f(a + )
More informationDept. of Heating, Ventilation and Air-Conditioning. Zentralschweizerisches Technikum Luzern Ingenieurschule HTL
Znralshwizrishs Thnikum Luzrn Ingniurshul HTL Dp. o Haing, Vnilaion Elkrohnik - Mashinnhnik - Hizungs-, Lüungs-, Klimahnik - Arhikur - Bauingniurwsn Dvlopd in h proj Low Tmpraur Low Cos Ha Pump Haing Sysm
More informationAP Calculus AB 2007 Scoring Guidelines
AP Calculus AB 7 Scoring Guidelines The College Board: Connecing Sudens o College Success The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and
More informationCFD-Calculation of Fluid Flow in a Pressurized Water Reactor
Journal of Scincs, Islamic Rpublic of Iran 19(3): 73-81 (008) Univrsiy of Thran, ISSN 1016-1104 hp://jscincs.u.ac.ir CFD-Calculaion of Fluid Flow in a Prssurizd War Racor H. Farajollahi, * A. Ghasmizad,
More informationRemoval of Cu(II) from Water by Adsorption on Chicken Eggshell
Inrnaional Journal of Enginring & Tchnology IJET-IJENS Vol:3 No: 4 Rmoval of u(ii) from War by Adsorpion on hickn Eggshll Nurul Aimi bini Rohaizar*, Norhafizah bini Abd. Hadi*, Wong h Sin* Absrac Th us
More informationName: Algebra II Review for Quiz #13 Exponential and Logarithmic Functions including Modeling
Name: Algebra II Review for Quiz #13 Exponenial and Logarihmic Funcions including Modeling TOPICS: -Solving Exponenial Equaions (The Mehod of Common Bases) -Solving Exponenial Equaions (Using Logarihms)
More informationSteps for D.C Analysis of MOSFET Circuits
10/22/2004 Seps for DC Analysis of MOSFET Circuis.doc 1/7 Seps for D.C Analysis of MOSFET Circuis To analyze MOSFET circui wih D.C. sources, we mus follow hese five seps: 1. ASSUME an operaing mode 2.
More informationIntroduction to Measurement, Error Analysis, Propagation of Error, and Reporting Experimental Results
Inroducion o Masurmn, Error Analysis, Propagaion of Error, and Rporing Exprimnal Rsuls AJ Pinar, TD Drummr, D Caspary Dparmn of Chmical Enginring Michigan Tchnological Univrsiy Houghon, MI 4993 Spmbr,
More informationSecuritization of Motor Insurance Loss Rate Risks
criizaion of Moor Insranc Loss Ra Risks aan Ba and Cangki Kim * Absrac W ry o ransfr loss ra risks in moor insranc o capial mark. W s ranc cniq o dg moor insranc risks. As an xampl, w focs on AXA and ir
More informationCPS 220 Theory of Computation REGULAR LANGUAGES. Regular expressions
CPS 22 Thory of Computation REGULAR LANGUAGES Rgular xprssions Lik mathmatical xprssion (5+3) * 4. Rgular xprssion ar built using rgular oprations. (By th way, rgular xprssions show up in various languags:
More informationAcceleration Lab Teacher s Guide
Acceleraion Lab Teacher s Guide Objecives:. Use graphs of disance vs. ime and velociy vs. ime o find acceleraion of a oy car.. Observe he relaionship beween he angle of an inclined plane and he acceleraion
More information11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements
Inroducion Chaper 14: Dynamic D-S dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuing-edge
More informationECEN4618: Experiment #1 Timing circuits with the 555 timer
ECEN4618: Experimen #1 Timing circuis wih he 555 imer cæ 1998 Dragan Maksimović Deparmen of Elecrical and Compuer Engineering Universiy of Colorado, Boulder The purpose of his lab assignmen is o examine
More information4 Convolution. Recommended Problems. x2[n] 1 2[n]
4 Convoluion Recommended Problems P4.1 This problem is a simple example of he use of superposiion. Suppose ha a discree-ime linear sysem has oupus y[n] for he given inpus x[n] as shown in Figure P4.1-1.
More informationLecture 2: Telegrapher Equations For Transmission Lines. Power Flow.
Whies, EE 481 Lecure 2 Page 1 of 13 Lecure 2: Telegraher Equaions For Transmission Lines. Power Flow. Microsri is one mehod for making elecrical connecions in a microwae circui. I is consruced wih a ground
More informationLecture 20: Emitter Follower and Differential Amplifiers
Whits, EE 3 Lctur 0 Pag of 8 Lctur 0: Emittr Followr and Diffrntial Amplifirs Th nxt two amplifir circuits w will discuss ar ry important to lctrical nginring in gnral, and to th NorCal 40A spcifically.
More informationAP Calculus AB 2010 Scoring Guidelines
AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in 1, he College
More information1. y 5y + 6y = 2e t Solution: Characteristic equation is r 2 5r +6 = 0, therefore r 1 = 2, r 2 = 3, and y 1 (t) = e 2t,
Homework6 Soluions.7 In Problem hrough 4 use he mehod of variaion of parameers o find a paricular soluion of he given differenial equaion. Then check your answer by using he mehod of undeermined coeffiens..
More informationSection 7.4: Exponential Growth and Decay
1 Sction 7.4: Exponntial Growth and Dcay Practic HW from Stwart Txtbook (not to hand in) p. 532 # 1-17 odd In th nxt two ction, w xamin how population growth can b modld uing diffrntial quation. W tart
More informationLectures # 5 and 6: The Prime Number Theorem.
Lecures # 5 and 6: The Prime Number Theorem Noah Snyder July 8, 22 Riemann s Argumen Riemann used his analyically coninued ζ-funcion o skech an argumen which would give an acual formula for π( and sugges
More informationNewton s Laws of Motion
Newon s Laws of Moion MS4414 Theoreical Mechanics Firs Law velociy. In he absence of exernal forces, a body moves in a sraigh line wih consan F = 0 = v = cons. Khan Academy Newon I. Second Law body. The
More informationQUALITY OF DYING AND DEATH QUESTIONNAIRE FOR NURSES VERSION 3.2A
UNIVERSITY OF WASHINGTON SCHOOL OF MEDICINE QUALITY OF DYING AND DEATH QUESTIONNAIRE FOR NURSES VERSION 3.2A Plas rurn your compld qusionnair in h nclosd nvlop o: [Rurn Addrss] RNID PID Copyrigh by h Univrsiy
More informationPI4ULS5V202 2-Bit Bi-directional Level Shifter with Automatic Sensing & Ultra Tiny Package
Feaures can be Less han, Greaer han or Equal o V CCB 1.2V o 5.5V on A Por and 1.2V o 5.5V on B Por High Speed wih 20 Mb/s Daa Rae for push-pull applicaion High Speed wih 2 Mb/s Daa Rae for open-drain applicaion
More informationStochastic Optimal Control Problem for Life Insurance
Sochasic Opimal Conrol Problem for Life Insurance s. Basukh 1, D. Nyamsuren 2 1 Deparmen of Economics and Economerics, Insiue of Finance and Economics, Ulaanbaaar, Mongolia 2 School of Mahemaics, Mongolian
More informationQuestion 3: How do you find the relative extrema of a function?
ustion 3: How do you find th rlativ trma of a function? Th stratgy for tracking th sign of th drivativ is usful for mor than dtrmining whr a function is incrasing or dcrasing. It is also usful for locating
More informationGENETIC ALGORITHMS IN SEASONAL DEMAND FORECASTING
forcasing, dmand, gnic algorihm Grzgorz Chodak*, Wiold Kwaśnicki* GENETIC ALGORITHMS IN SEASONAL DEMAND FORECASTING Th mhod of forcasing sasonal dmand applying gnic algorihm is prsnd. Spcific form of usd
More informationJCUT-3030/6090/1212/1218/1325/1530
JCUT CNC ROUTER/CNC WOODWORKING MACHINE JCUT-3030/6090/1212/1218/1325/1530 RZNC-0501 Users Guide Chapter I Characteristic 1. Totally independent from PC platform; 2. Directly read files from U Disk; 3.
More information1.- L a m e j o r o p c ió n e s c l o na r e l d i s co ( s e e x p li c a r á d es p u é s ).
PROCEDIMIENTO DE RECUPERACION Y COPIAS DE SEGURIDAD DEL CORTAFUEGOS LINUX P ar a p od e r re c u p e ra r nu e s t r o c o rt a f u e go s an t e un d es a s t r e ( r ot u r a d e l di s c o o d e l a
More informationPRICING OF EXOTIC OPTIONS ON LIFE INSURANCE CONTRACTS Rami Yosef *
PRICING OF EOIC OPIONS ON LIFE INSURANCE CONRACS Rami Yosf * ABSRAC W considr a Europan and Amrican pu opion dfind on pur ndowmn insuranc and risk insuranc conracs rspcivl. s xoic opions giv oldr of opion
More informationKrebs (1972). A group of organisms of the same species occupying a particular space at a particular time
FW 662 Lcur 1 - Dnsiy-indpndn populaion modls Tx: Golli, 21, A Primr of Ecology Wha is a populaion? Krbs (1972). A group of organisms of h sam spcis occupying a paricular spac a a paricular im Col (1957).
More informationChapter 2 Kinematics in One Dimension
Chaper Kinemaics in One Dimension Chaper DESCRIBING MOTION:KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings moe how far (disance and displacemen), how fas (speed and elociy), and how
More informationHFCC Math Lab Intermediate Algebra - 13 SOLVING RATE-TIME-DISTANCE PROBLEMS
HFCC Mah Lab Inemeiae Algeba - 3 SOLVING RATE-TIME-DISTANCE PROBLEMS The vaiables involve in a moion poblem ae isance (), ae (), an ime (). These vaiables ae elae by he equaion, which can be solve fo any
More informationSignal Processing and Linear Systems I
Sanford Universiy Summer 214-215 Signal Processing and Linear Sysems I Lecure 5: Time Domain Analysis of Coninuous Time Sysems June 3, 215 EE12A:Signal Processing and Linear Sysems I; Summer 14-15, Gibbons
More informationThe Torsion of Thin, Open Sections
EM 424: Torsion of hin secions 26 The Torsion of Thin, Open Secions The resuls we obained for he orsion of a hin recangle can also be used be used, wih some qualificaions, for oher hin open secions such
More informationPart II Converter Dynamics and Control
Par II onverer Dynamics and onrol 7. A equivalen circui modeling 8. onverer ransfer funcions 9. onroller design 1. Inpu filer design 11. A and D equivalen circui modeling of he disconinuous conducion mode
More information5.4 Exponential Functions: Differentiation and Integration TOOTLIFTST:
.4 Eponntial Functions: Diffrntiation an Intgration TOOTLIFTST: Eponntial functions ar of th form f ( ) Ab. W will, in this sction, look at a spcific typ of ponntial function whr th bas, b, is.78.... This
More informationFrequency Modulation. Dr. Hwee-Pink Tan http://www.cs.tcd.ie/hweepink.tan
Frequency Modulaion Dr. Hwee-Pink Tan hp://www.cs.cd.ie/hweepink.tan Lecure maerial was absraced from "Communicaion Sysems" by Simon Haykin. Ouline Day 1 Day 2 Day 3 Angle Modulaion Frequency Modulaion
More information1 HALF-LIFE EQUATIONS
R.L. Hanna Page HALF-LIFE EQUATIONS The basic equaion ; he saring poin ; : wrien for ime: x / where fracion of original maerial and / number of half-lives, and / log / o calculae he age (# ears): age (half-life)
More informationApplication Note: Cisco A S A - Ce r t if ica t e T o S S L V P N Con n e ct ion P r of il e Overview: T h i s a p p l i ca ti o n n o te e x p l a i n s h o w to co n f i g u r e th e A S A to a cco m
More informationSecond Order Linear Differential Equations
Second Order Linear Differenial Equaions Second order linear equaions wih consan coefficiens; Fundamenal soluions; Wronskian; Exisence and Uniqueness of soluions; he characerisic equaion; soluions of homogeneous
More informationMath 113 HW #5 Solutions
Mat 3 HW #5 Solutions. Exercise.5.6. Suppose f is continuous on [, 5] and te only solutions of te equation f(x) = 6 are x = and x =. If f() = 8, explain wy f(3) > 6. Answer: Suppose we ad tat f(3) 6. Ten
More information1 9 / m S t a n d a r d w y m a g a ń - e g z a m i n m i s t r z o w s k i dla zawodu M E C H A N I K P O J A Z D Ó W S A M O C H O D O W Y C H Kod z klasyfikacji zawodów i sp e cjaln oś ci dla p ot r
More informationCHAPTER 8: DIFFERENTIAL CALCULUS
CHAPTER 8: DIFFERENTIAL CALCULUS 1. Rules of Differentiation As we ave seen, calculating erivatives from first principles can be laborious an ifficult even for some relatively simple functions. It is clearly
More informationCHAPTER FIVE. Solutions for Section 5.1
CHAPTER FIVE 5. SOLUTIONS 87 Soluions for Secion 5.. (a) The velociy is 3 miles/hour for he firs hours, 4 miles/hour for he ne / hour, and miles/hour for he las 4 hours. The enire rip lass + / + 4 = 6.5
More informationA Probability Density Function for Google s stocks
A Probabiliy Densiy Funcion for Google s socks V.Dorobanu Physics Deparmen, Poliehnica Universiy of Timisoara, Romania Absrac. I is an approach o inroduce he Fokker Planck equaion as an ineresing naural
More informationPresent Value Methodology
Presen Value Mehodology Econ 422 Invesmen, Capial & Finance Universiy of Washingon Eric Zivo Las updaed: April 11, 2010 Presen Value Concep Wealh in Fisher Model: W = Y 0 + Y 1 /(1+r) The consumer/producer
More informationIT Update - August 2006
IT Nws Saus: No Aciv Til: Da: 7726 Summay (Opional): Body: Wlcom Back! Offic of Infomaion Tchnology Upda: IT Upda - Augus 26 Rob K. Blchman, Ph.D. Associa Dico, Offic of Infomaion Tchnology Whil You W
More information17 Laplace transform. Solving linear ODE with piecewise continuous right hand sides
7 Laplace ransform. Solving linear ODE wih piecewise coninuous righ hand sides In his lecure I will show how o apply he Laplace ransform o he ODE Ly = f wih piecewise coninuous f. Definiion. A funcion
More information= r t dt + σ S,t db S t (19.1) with interest rates given by a mean reverting Ornstein-Uhlenbeck or Vasicek process,
Chaper 19 The Black-Scholes-Vasicek Model The Black-Scholes-Vasicek model is given by a sandard ime-dependen Black-Scholes model for he sock price process S, wih ime-dependen bu deerminisic volailiy σ
More informationChapter 5. Aggregate Planning
Chaper 5 Aggregae Planning Supply Chain Planning Marix procuremen producion disribuion sales longerm Sraegic Nework Planning miderm shorerm Maerial Requiremens Planning Maser Planning Producion Planning
More information2.5 Life tables, force of mortality and standard life insurance products
Soluions 5 BS4a Acuarial Science Oford MT 212 33 2.5 Life ables, force of moraliy and sandard life insurance producs 1. (i) n m q represens he probabiliy of deah of a life currenly aged beween ages + n
More informationAnalysis of Planck and the Equilibrium ofantis in Tropical Physics
Emergence of Fokker-Planck Dynamics wihin a Closed Finie Spin Sysem H. Niemeyer(*), D. Schmidke(*), J. Gemmer(*), K. Michielsen(**), H. de Raed(**) (*)Universiy of Osnabrück, (**) Supercompuing Cener Juelich
More informationMathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)
Mahemaics in Pharmacokineics Wha and Why (A second aemp o make i clearer) We have used equaions for concenraion () as a funcion of ime (). We will coninue o use hese equaions since he plasma concenraions
More informationAverage and Instantaneous Rates of Change: The Derivative
9.3 verage and Instantaneous Rates of Cange: Te Derivative 609 OBJECTIVES 9.3 To define and find average rates of cange To define te derivative as a rate of cange To use te definition of derivative to
More informationUsefulness of the Forward Curve in Forecasting Oil Prices
Usefulness of he Forward Curve in Forecasing Oil Prices Akira Yanagisawa Leader Energy Demand, Supply and Forecas Analysis Group The Energy Daa and Modelling Cener Summary When people analyse oil prices,
More informationCommunication Networks II Contents
3 / 1 -- Communicaion Neworks II (Görg) -- www.comnes.uni-bremen.de Communicaion Neworks II Conens 1 Fundamenals of probabiliy heory 2 Traffic in communicaion neworks 3 Sochasic & Markovian Processes (SP
More informationFull-wave Bridge Rectifier Analysis
Full-wave Brige Recifier Analysis Jahan A. Feuch, Ocober, 00 his aer evelos aroximae equais for esigning or analyzing a full-wave brige recifier eak-eecor circui. his circui is commly use in A o D cverers,
More informationInstantaneous Rate of Change:
Instantaneous Rate of Cange: Last section we discovered tat te average rate of cange in F(x) can also be interpreted as te slope of a scant line. Te average rate of cange involves te cange in F(x) over
More informationFetch. Decode. Execute. Memory. PC update
nwpc PC Nw PC valm Mmory Mm. control rad writ Data mmory data out rmmovl ra, D(rB) Excut Bch CC ALU A vale ALU Addr ALU B Data vala ALU fun. valb dste dstm srca srcb dste dstm srca srcb Ftch Dcod Excut
More informationBrussels, February 28th, 2013 WHAT IS
Brussls, Fbruary 28h, 2013 WHAT IS 1 OPEN SOURCE 2 CLOUD 3 SERVICES 4 BROKER 5 INTERMEDIATION AGGREGATION ARBITRAGE Cloud Srvics Brokr provids a singl consisn inrfac o mulipl diffring providrs, whhr h
More informationB I N G O B I N G O. Hf Cd Na Nb Lr. I Fl Fr Mo Si. Ho Bi Ce Eu Ac. Md Co P Pa Tc. Uut Rh K N. Sb At Md H. Bh Cm H Bi Es. Mo Uus Lu P F.
Hf Cd Na Nb Lr Ho Bi Ce u Ac I Fl Fr Mo i Md Co P Pa Tc Uut Rh K N Dy Cl N Am b At Md H Y Bh Cm H Bi s Mo Uus Lu P F Cu Ar Ag Mg K Thomas Jefferson National Accelerator Facility - Office of cience ducation
More informationCharacterization of semi-insulating GaAs:Cr by means of DC-CPM technique
Rvu ds Enrgis Rnouvlabls Vol. 12 N 1 (2009) 125 135 Characrizaion of smi-insulaing GaAs:Cr by mans of DC-CPM chniqu. ibrmacin 1* and A. Mrazga 2 1 Laboraoir ds Maériaux Smi-conducurs Méalliqus, Univrsié
More information