Analog Filter Design. Part. 3: Time Continuous Filter Implementation. P. Bruschi - Analog Filter Design 1
|
|
- Ilene Hilda Evans
- 6 years ago
- Views:
Transcription
1 Aalog Filter Deig Part. 3: Time otiuou Filter Implemetatio P. ruchi - Aalog Filter Deig
2 Deig approache Paive (R) ladder filter acade of iquadratic (iquad) ad iliear cell State Variable Filter Simulatio of filter with active R etwork P. ruchi - Aalog Filter Deig 2
3 Filter Parameter For a give trafer fuctio H(), a particular implemetatio i characterized by everal FOM (Figure Of Merit). The mot frequetly ued are: Dyamic Rage: DR max v Seitivity to compoet variatio ompoet value pread, e.g. V out out max mi v -out = output oie S S x Q x d / d P. ruchi - Aalog Filter Deig 3 x Q dx dq dx / x x dx
4 Paive ole adder Filter Doubly termiated ladder etwork Advatage: miimum eitivity to compoet variatio i the pabad The lowet eitivity i achieved with equally termiated etwork (R =R 2 ). a be ued a tartig poit for the ythei of active R filter Drawback: tuig require chage of al compoet. order () = umber of capacitor + umber of iductor P. ruchi - Aalog Filter Deig 4
5 Prototype Filter ofiguratio (all pole) =2M+ (odd order) =2M (eve order) R2 Pa-bad gai: k R R 2 (.5 for equally termiated etworl) P. ruchi - Aalog Filter Deig 5
6 Alterate olutio (all pole) =2M+ (odd order) =2M (eve order) R2 Pa-bad gai: k R R 2 (.5 for equally termiated etworl) P. ruchi - Aalog Filter Deig 6
7 ladder etwork for TF with imagiary zero (e.g. Ivere hebyhev ad auer Elliptic filter) P. ruchi - Aalog Filter Deig 7
8 Frequecy calig rule P. ruchi - Aalog Filter Deig 8 ladder filter are ythetized i ormalized ( rad/, W) ad lowpa form Frequecy calig allow to chage the ormalizatio frequecy, allowig traformatio of the characteritic frequecie of the filter R R
9 Impedace Scalig Rule Impedace calig i ued to chage compoet value leavig the trafer fuctio ualtered. The target i fidig feaible compoet value for the choe techology If the etwork iclude oly: Two termial impedace (,R, compoet) Voltage otrolled Voltage Source (VVS) i.e Ideal voltage amplifier. urret otrolled urret Source (S) i.e. ideal curret amplifier The: the Vout/VS trafer fuctio i uchaged whe all the impedace are multiplied by the ame fuctio f() P. ruchi - Aalog Filter Deig 9
10 Impedace calig: compoet traformatio A importat cae i whe the fuctio f() i a cotat factor K: K K K K R KR P. ruchi - Aalog Filter Deig
11 Elemet traformatio P. ruchi - Aalog Filter Deig High-Pa ad-pa ad -Stop Goal: to chage the filter repoe from low-pa to the other three poibilitie (high-pa, etc.) ad perform frequecy calig at the ame time. et u recall the followig traformatio: From ow-pa to:
12 Elemet Traformatio P. ruchi - Aalog Filter Deig 2 R R ow-pa to High-pa
13 Elemet Traformatio P. ruchi - Aalog Filter Deig 3 ow-pa to ad-pa 2 P P 2 S S 2 P P 2 S S 2
14 Elemet Traformatio P. ruchi - Aalog Filter Deig 4 ow-pa to ad-top S S 2 2 P P
15 Deig of ladder paive filter A procedure that allow deigig a arbitrary trafer fuctio with a ladder tructure doe ot exit. All-pole fuctio (e.g. utterworth, hebyhev I, eel) ca be deiged with a tadard approach, where the brache of the ladder (Z ad Y elemet) are pure capacitor or iductor. Give a cla of etwork, ot all fuctio are feaible. The rigorou deig of auer (elliptic) filter i le traightforward. Table are available for the mot frequetly ued ladder topologie ad trafer fuctio. Several AD deig tool are alo available. P. ruchi - Aalog Filter Deig 5
16 Example: utterworth Prototype Filter P. ruchi - Aalog Filter Deig 6
17 hebyhev d ripple P. ruchi - Aalog Filter Deig 7
18 Example Deig a ladder hebyhev filter with the followig characteritic: f_pa = khz, Maximum Pa-bad atteuatio d f_top = 2 khz Miimum Stop-ad Atteuatio: 4 d Pytho: chebord: Order=5, = P =62.8 krad/ P. ruchi - Aalog Filter Deig 8
19 Filter deig uig Table = P = rad/ =2.27 F =.28 H 2=3.3 F 2=.28 H 3=2.27 F = P =62.8 krad/ =35. mf =8. mh 2=49.4 mf 2=8. mh 3=35. mf P. ruchi - Aalog Filter Deig 9
EE 508 Lecture 6. Scaling, Normalization and Transformation
EE 508 Lecture 6 Scalig, Normalizatio ad Traformatio Review from Lat Time Dead Network X IN T X OUT T X OUT N T = D D The dead etwork of ay liear circuit i obtaied by ettig ALL idepedet ource to zero.
More informationEE 508 Lecture 6. Dead Networks Scaling, Normalization and Transformations
EE 508 Lecture 6 Dead Network Scalig, Normalizatio ad Traformatio Filter Cocept ad Termiology 2-d order polyomial characterizatio Biquadratic Factorizatio Op Amp Modelig Stability ad Itability Roll-off
More informationState space systems analysis
State pace ytem aalyi Repreetatio of a ytem i tate-pace (tate-pace model of a ytem To itroduce the tate pace formalim let u tart with a eample i which the ytem i dicuio i a imple electrical circuit with
More informationButterworth LC Filter Designer
Butterworth LC Filter Desiger R S = g g 4 g - V S g g 3 g R L = Fig. : LC filter used for odd-order aalysis g R S = g 4 g V S g g 3 g - R L = useful fuctios ad idetities Uits Costats Table of Cotets I.
More informationECEN620: Network Theory Broadband Circuit Design Fall 2014
ECE60: etwork Theory Broadbad Circuit Deig Fall 04 Lecture 3: PLL Aalyi Sam Palermo Aalog & Mixed-Sigal Ceter Texa A&M Uiverity Ageda & Readig PLL Overview & Applicatio PLL Liear Model Phae & Frequecy
More informationChapter 9 - CD companion 1. A Generic Implementation; The Common-Merge Amplifier. 1 τ is. ω ch. τ io
Chapter 9 - CD compaio CHAPTER NINE CD-9.2 CD-9.2. Stages With Voltage ad Curret Gai A Geeric Implemetatio; The Commo-Merge Amplifier The advaced method preseted i the text for approximatig cutoff frequecies
More informationx c the remainder is Pc ().
Algebra, Polyomial ad Ratioal Fuctios Page 1 K.Paulk Notes Chapter 3, Sectio 3.1 to 3.4 Summary Sectio Theorem Notes 3.1 Zeros of a Fuctio Set the fuctio to zero ad solve for x. The fuctio is zero at these
More informationAdaptive control design for a Mimo chemical reactor
Automatio, Cotrol ad Itelliget Sytem 013; 1(3): 64-70 Publihed olie July 10, 013 (http://www.ciecepublihiggroup.com/j/aci) doi: 10.11648/j.aci.0130103.15 Adaptive cotrol deig for a Mimo chemical reactor
More informationSystem Control. Lesson #19a. BME 333 Biomedical Signals and Systems - J.Schesser
Sytem Cotrol Leo #9a 76 Sytem Cotrol Baic roblem Say you have a ytem which you ca ot alter but it repoe i ot optimal Example Motor cotrol for exokeleto Robotic cotrol roblem that ca occur Utable Traiet
More informationSinusoidal Steady-state Analysis
Siusoidal Steady-state Aalysis Complex umber reviews Phasors ad ordiary differetial equatios Complete respose ad siusoidal steady-state respose Cocepts of impedace ad admittace Siusoidal steady-state aalysis
More informationLast time: Ground rules for filtering and control system design
6.3 Stochatic Etimatio ad Cotrol, Fall 004 Lecture 7 Lat time: Groud rule for filterig ad cotrol ytem deig Gral ytem Sytem parameter are cotaied i w( t ad w ( t. Deired output i grated by takig the igal
More informationELEC 372 LECTURE NOTES, WEEK 4 Dr. Amir G. Aghdam Concordia University
ELEC 37 LECTURE NOTES, WEE 4 Dr Amir G Aghdam Cocordia Uiverity Part of thee ote are adapted from the material i the followig referece: Moder Cotrol Sytem by Richard C Dorf ad Robert H Bihop, Pretice Hall
More information1 of 7 7/16/2009 6:06 AM Virtual Laboratories > 6. Radom Samples > 1 2 3 4 5 6 7 6. Order Statistics Defiitios Suppose agai that we have a basic radom experimet, ad that X is a real-valued radom variable
More informationCONTROL SYSTEMS. Chapter 7 : Bode Plot. 40dB/dec 1.0. db/dec so resultant slope will be 20 db/dec and this is due to the factor s
CONTROL SYSTEMS Chapter 7 : Bode Plot GATE Objective & Numerical Type Solutio Quetio 6 [Practice Book] [GATE EE 999 IIT-Bombay : 5 Mark] The aymptotic Bode plot of the miimum phae ope-loop trafer fuctio
More informationBipolar Junction Transistors
ipolar Juctio Trasistors ipolar juctio trasistor (JT) was iveted i 948 at ell Telephoe Laboratories Sice 97, the high desity ad low power advatage of the MOS techology steadily eroded the JT s early domiace.
More informationErick L. Oberstar Fall 2001 Project: Sidelobe Canceller & GSC 1. Advanced Digital Signal Processing Sidelobe Canceller (Beam Former)
Erick L. Obertar Fall 001 Project: Sidelobe Caceller & GSC 1 Advaced Digital Sigal Proceig Sidelobe Caceller (Beam Former) Erick L. Obertar 001 Erick L. Obertar Fall 001 Project: Sidelobe Caceller & GSC
More informationAntenna Engineering Lecture 8: Antenna Arrays
Atea Egieerig Lecture 8: Atea Arrays ELCN45 Sprig 211 Commuicatios ad Computer Egieerig Program Faculty of Egieerig Cairo Uiversity 2 Outlie 1 Array of Isotropic Radiators Array Cofiguratios The Space
More informationLecture 30: Frequency Response of Second-Order Systems
Lecture 3: Frequecy Repoe of Secod-Order Sytem UHTXHQF\ 5HVSRQVH RI 6HFRQGUGHU 6\VWHPV A geeral ecod-order ytem ha a trafer fuctio of the form b + b + b H (. (9.4 a + a + a It ca be table, utable, caual
More informationVoltage controlled oscillator (VCO)
Voltage cotrolled oscillator (VO) Oscillatio frequecy jl Z L(V) jl[ L(V)] [L L (V)] L L (V) T VO gai / Logf Log 4 L (V) f f 4 L(V) Logf / L(V) f 4 L (V) f (V) 3 Lf 3 VO gai / (V) j V / V Bi (V) / V Bi
More information6.003 Homework #3 Solutions
6.00 Homework # Solutios Problems. Complex umbers a. Evaluate the real ad imagiary parts of j j. π/ Real part = Imagiary part = 0 e Euler s formula says that j = e jπ/, so jπ/ j π/ j j = e = e. Thus the
More informationCourse Outline. Designing Control Systems. Proportional Controller. Amme 3500 : System Dynamics and Control. Root Locus. Dr. Stefan B.
Amme 3500 : System Dyamics ad Cotrol Root Locus Course Outlie Week Date Cotet Assigmet Notes Mar Itroductio 8 Mar Frequecy Domai Modellig 3 5 Mar Trasiet Performace ad the s-plae 4 Mar Block Diagrams Assig
More informationCONTROL ENGINEERING LABORATORY
Uiverity of Techology Departmet of Electrical Egieerig Cotrol Egieerig Lab. CONTROL ENGINEERING LABORATORY By Dr. Abdul. Rh. Humed M.Sc. Quay Salim Tawfeeq M.Sc. Nihad Mohammed Amee M.Sc. Waleed H. Habeeb
More information100(1 α)% confidence interval: ( x z ( sample size needed to construct a 100(1 α)% confidence interval with a margin of error of w:
Stat 400, ectio 7. Large Sample Cofidece Iterval ote by Tim Pilachowki a Large-Sample Two-ided Cofidece Iterval for a Populatio Mea ectio 7.1 redux The poit etimate for a populatio mea µ will be a ample
More informationFirst, note that the LS residuals are orthogonal to the regressors. X Xb X y = 0 ( normal equations ; (k 1) ) So,
0 2. OLS Part II The OLS residuals are orthogoal to the regressors. If the model icludes a itercept, the orthogoality of the residuals ad regressors gives rise to three results, which have limited practical
More informationDifferent kinds of Mathematical Induction
Differet ids of Mathematical Iductio () Mathematical Iductio Give A N, [ A (a A a A)] A N () (First) Priciple of Mathematical Iductio Let P() be a propositio (ope setece), if we put A { : N p() is true}
More informationAnalog and Digital Signals. Introduction to Digital Signal Processing. Discrete-time Sinusoids. Analog and Digital Signals
Itroductio to Digital Sigal Processig Chapter : Itroductio Aalog ad Digital Sigals aalog = cotiuous-time cotiuous amplitude digital = discrete-time discrete amplitude cotiuous amplitude discrete amplitude
More informationSpecial Notes: Filter Design Methods
Page Special Note: Filter Deig Method Spectral Poer epoe For j j j exp What i j Magitude (ut be the ae!): N M Q i i p z K j Phae: N M Q i i a p a z a j ta ta ta N M Q i i a p a z a j ta ta ta herefore
More informationDorf, R.C., Wan, Z., Johnson, D.E. Laplace Transform The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
Dorf, R.C., Wa, Z., Joho, D.E. Laplace Traform The Electrical Egieerig Hadbook Ed. Richard C. Dorf Boca Rato: CRC Pre LLC, 6 Laplace Traform Richard C. Dorf Uiverity of Califoria, Davi Zhe Wa Uiverity
More information8.6 Order-Recursive LS s[n]
8.6 Order-Recurive LS [] Motivate ti idea wit Curve Fittig Give data: 0,,,..., - [0], [],..., [-] Wat to fit a polyomial to data.., but wic oe i te rigt model?! Cotat! Quadratic! Liear! Cubic, Etc. ry
More informationmx bx kx F t. dt IR I LI V t, Q LQ RQ V t,
Lecture 5 omplex Variables II (Applicatios i Physics) (See hapter i Boas) To see why complex variables are so useful cosider first the (liear) mechaics of a sigle particle described by Newto s equatio
More informationPH 411/511 ECE B(k) Sin k (x) dk (1)
Fall-27 PH 4/5 ECE 598 A. La Rosa Homework-3 Due -7-27 The Homework is iteded to gai a uderstadig o the Heiseberg priciple, based o a compariso betwee the width of a pulse ad the width of its spectral
More informationTHE APPEARANCE OF FIBONACCI AND LUCAS NUMBERS IN THE SIMULATION OF ELECTRICAL POWER LINES SUPPLIED BY TWO SIDES
THE APPEARANCE OF FIBONACCI AND LUCAS NUMBERS IN THE SIMULATION OF ELECTRICAL POWER LINES SUPPLIED BY TWO SIDES Giuseppe Ferri Dipartimeto di Ihgegeria Elettrica-FacoM di Igegeria, Uiversita di L'Aquila
More informationSTABILITY OF THE ACTIVE VIBRATION CONTROL OF CANTILEVER BEAMS
Iteratioal Coferece o Vibratio Problem September 9-,, Liboa, Portugal STBILITY OF THE CTIVE VIBRTIO COTROL OF CTILEVER BEMS J. Tůma, P. Šuráe, M. Mahdal VSB Techical Uierity of Otraa Czech Republic Outlie.
More informationREVIEW OF SIMPLE LINEAR REGRESSION SIMPLE LINEAR REGRESSION
REVIEW OF SIMPLE LINEAR REGRESSION SIMPLE LINEAR REGRESSION I liear regreio, we coider the frequecy ditributio of oe variable (Y) at each of everal level of a ecod variable (X). Y i kow a the depedet variable.
More informationWe will look for series solutions to (1) around (at most) regular singular points, which without
ENM 511 J. L. Baai April, 1 Frobeiu Solutio to a d order ODE ear a regular igular poit Coider the ODE y 16 + P16 y 16 + Q1616 y (1) We will look for erie olutio to (1) aroud (at mot) regular igular poit,
More informationEE422G Homework #13 (12 points)
EE422G Homework #1 (12 poits) 1. (5 poits) I this problem, you are asked to explore a importat applicatio of FFT: efficiet computatio of covolutio. The impulse respose of a system is give by h(t) (.9),1,2,,1
More informationLecture 11. Course Review. (The Big Picture) G. Hovland Input-Output Limitations (Skogestad Ch. 3) Discrete. Time Domain
MER4 Advaced Cotrol Lecture Coure Review (he ig Picture MER4 ADVANCED CONROL EMEER, 4 G. Hovlad 4 Mai heme of MER4 Frequecy Domai Aalyi (Nie Chapter Phae ad Gai Margi Iput-Output Limitatio (kogetad Ch.
More informationStatistics and Chemical Measurements: Quantifying Uncertainty. Normal or Gaussian Distribution The Bell Curve
Statitic ad Chemical Meauremet: Quatifyig Ucertaity The bottom lie: Do we trut our reult? Should we (or ayoe ele)? Why? What i Quality Aurace? What i Quality Cotrol? Normal or Gauia Ditributio The Bell
More informationLast time: Completed solution to the optimum linear filter in real-time operation
6.3 tochatic Etimatio ad Cotrol, Fall 4 ecture at time: Completed olutio to the oimum liear filter i real-time operatio emi-free cofiguratio: t D( p) F( p) i( p) dte dp e π F( ) F( ) ( ) F( p) ( p) 4444443
More informationHigh-Speed Serial Interface Circuits and Systems. Lect. 4 Phase-Locked Loop (PLL) Type 1 (Chap. 8 in Razavi)
High-Speed Serial Iterface Circuit ad Sytem Lect. 4 Phae-Locked Loop (PLL) Type 1 (Chap. 8 i Razavi) PLL Phae lockig loop A (egative-feedback) cotrol ytem that geerate a output igal whoe phae (ad frequecy)
More information2.004 Dynamics and Control II Spring 2008
MIT OpeCourseWare http://ocw.mit.edu 2.004 Dyamics ad Cotrol II Sprig 2008 For iformatio about citig these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Massachusetts Istitute of Techology
More informationExplicit scheme. Fully implicit scheme Notes. Fully implicit scheme Notes. Fully implicit scheme Notes. Notes
Explicit cheme So far coidered a fully explicit cheme to umerically olve the diffuio equatio: T + = ( )T + (T+ + T ) () with = κ ( x) Oly table for < / Thi cheme i ometime referred to a FTCS (forward time
More informationSUMMARY OF SEQUENCES AND SERIES
SUMMARY OF SEQUENCES AND SERIES Importat Defiitios, Results ad Theorems for Sequeces ad Series Defiitio. A sequece {a } has a limit L ad we write lim a = L if for every ɛ > 0, there is a correspodig iteger
More informationAssignment 1 - Solutions. ECSE 420 Parallel Computing Fall November 2, 2014
Aigmet - Solutio ECSE 420 Parallel Computig Fall 204 ovember 2, 204. (%) Decribe briefly the followig term, expoe their caue, ad work-aroud the idutry ha udertake to overcome their coequece: (i) Memory
More informationFilter banks. Separately, the lowpass and highpass filters are not invertible. removes the highest frequency 1/ 2and
Filter bas Separately, the lowpass ad highpass filters are ot ivertible T removes the highest frequecy / ad removes the lowest frequecy Together these filters separate the sigal ito low-frequecy ad high-frequecy
More informationProperties and Tests of Zeros of Polynomial Functions
Properties ad Tests of Zeros of Polyomial Fuctios The Remaider ad Factor Theorems: Sythetic divisio ca be used to fid the values of polyomials i a sometimes easier way tha substitutio. This is show by
More informationu t u 0 ( 7) Intuitively, the maximum principles can be explained by the following observation. Recall
Oct. Heat Equatio M aximum priciple I thi lecture we will dicu the maximum priciple ad uiquee of olutio for the heat equatio.. Maximum priciple. The heat equatio alo ejoy maximum priciple a the Laplace
More informationChapter V. Microwave Filters
hapter V Microwave Filters otet 5. Filter Desig by the Isertio oss Method ( 8.3) 5. Filter Trasformatios ad Implemetatio ( 8.4-8.5) 5.3 ow-pass ad Bad-Pass Filter Desigs ( 8.6-8.7) 5. Filter Desig by the
More informationEECE 301 Signals & Systems Prof. Mark Fowler
EECE 30 Sigal & Sytem Prof. Mark Fowler Note Set #8 C-T Sytem: Laplace Traform Solvig Differetial Equatio Readig Aigmet: Sectio 6.4 of Kame ad Heck / Coure Flow Diagram The arrow here how coceptual flow
More informationCalculation of Inrush Current During Capacitor Bank Energization
Protectio of lectrical Networks hristophe Preve opyright 0 006, IST td. Appedix B alculatio of Irush urret Durig apacitor Bak ergizatio Fixed bak The equivalet stream etwork sigle-phase diagram durig eergizatio
More informationEE123 Digital Signal Processing
EE123 Digital Sigal Processig Lecture 20 Filter Desig Liear Filter Desig Used to be a art Now, lots of tools to desig optimal filters For DSP there are two commo classes Ifiite impulse respose IIR Fiite
More informationThe Scattering Matrix
2/23/7 The Scatterig Matrix 723 1/13 The Scatterig Matrix At low frequecies, we ca completely characterize a liear device or etwork usig a impedace matrix, which relates the currets ad voltages at each
More informationTHE CONCEPT OF THE ROOT LOCUS. H(s) THE CONCEPT OF THE ROOT LOCUS
So far i the tudie of cotrol yte the role of the characteritic equatio polyoial i deteriig the behavior of the yte ha bee highlighted. The root of that polyoial are the pole of the cotrol yte, ad their
More informationEE 505. Lecture 13. String DACs
EE 505 Lecture 13 Strig DACs -Strig DAC V FF S 1 S 2 Simple structure Iheretly mootoe Very low DNL Challeges: S N-2 S N-1 S N S k d k Maagig INL Large umber of devices for large outig thermometer/bubble
More informationIntroduction to Control Systems
Itroductio to Cotrol Sytem CLASSIFICATION OF MATHEMATICAL MODELS Icreaig Eae of Aalyi Static Icreaig Realim Dyamic Determiitic Stochatic Lumped Parameter Ditributed Parameter Liear Noliear Cotat Coefficiet
More informationPH 411/511 ECE B(k) Sin k (x) dk (1)
Fall-26 PH 4/5 ECE 598 A. La Rosa Homework-2 Due -3-26 The Homework is iteded to gai a uderstadig o the Heiseberg priciple, based o a compariso betwee the width of a pulse ad the width of its spectral
More informationCapacitors and PN Junctions. Lecture 8: Prof. Niknejad. Department of EECS University of California, Berkeley. EECS 105 Fall 2003, Lecture 8
CS 15 Fall 23, Lecture 8 Lecture 8: Capacitor ad PN Juctio Prof. Nikejad Lecture Outlie Review of lectrotatic IC MIM Capacitor No-Liear Capacitor PN Juctio Thermal quilibrium lectrotatic Review 1 lectric
More informationLayered structures: transfer matrix formalism
Layered tructure: trafer matrx formalm Iterface betwee LI meda Trafer matrx formalm Petr Kužel Practcally oly oe formula to be kow order to calculate ay tructure Applcato: Atreflectve coatg Delectrc mrror,
More informationIsolated Word Recogniser
Lecture 5 Iolated Word Recogitio Hidde Markov Model of peech State traitio ad aligmet probabilitie Searchig all poible aligmet Dyamic Programmig Viterbi Aligmet Iolated Word Recogitio 8. Iolated Word Recogier
More informationDiscrete-Time Signals and Systems. Discrete-Time Signals and Systems. Signal Symmetry. Elementary Discrete-Time Signals.
Discrete-ime Sigals ad Systems Discrete-ime Sigals ad Systems Dr. Deepa Kudur Uiversity of oroto Referece: Sectios. -.5 of Joh G. Proakis ad Dimitris G. Maolakis, Digital Sigal Processig: Priciples, Algorithms,
More informationENGI 4421 Confidence Intervals (Two Samples) Page 12-01
ENGI 44 Cofidece Itervals (Two Samples) Page -0 Two Sample Cofidece Iterval for a Differece i Populatio Meas [Navidi sectios 5.4-5.7; Devore chapter 9] From the cetral limit theorem, we kow that, for sufficietly
More informationTHE SYSTEMATIC AND THE RANDOM. ERRORS - DUE TO ELEMENT TOLERANCES OF ELECTRICAL NETWORKS
R775 Philips Res. Repts 26,414-423, 1971' THE SYSTEMATIC AND THE RANDOM. ERRORS - DUE TO ELEMENT TOLERANCES OF ELECTRICAL NETWORKS by H. W. HANNEMAN Abstract Usig the law of propagatio of errors, approximated
More informationExponential Moving Average Pieter P
Expoetial Movig Average Pieter P Differece equatio The Differece equatio of a expoetial movig average lter is very simple: y[] x[] + (1 )y[ 1] I this equatio, y[] is the curret output, y[ 1] is the previous
More information(A sequence also can be thought of as the list of function values attained for a function f :ℵ X, where f (n) = x n for n 1.) x 1 x N +k x N +4 x 3
MATH 337 Sequeces Dr. Neal, WKU Let X be a metric space with distace fuctio d. We shall defie the geeral cocept of sequece ad limit i a metric space, the apply the results i particular to some special
More informationProfessor: Mihnea UDREA DIGITAL SIGNAL PROCESSING. Grading: Web: MOODLE. 1. Introduction. General information
Geeral iformatio DIGITL SIGL PROCESSIG Profeor: ihea UDRE B29 mihea@comm.pub.ro Gradig: Laboratory: 5% Proect: 5% Tet: 2% ial exam : 5% Coure quiz: ±% Web: www.electroica.pub.ro OODLE 2 alog igal proceig
More informationRounding Answers. => Z=12.03±0.15 cm
Roudig Aswers The ucertaity should be rouded off to oe or two sigificat figures. If the leadig figure i the ucertaity is 1, we use two sigificat figures, otherwise we use oe sigificat figure. The aswer
More informationEE / EEE SAMPLE STUDY MATERIAL. GATE, IES & PSUs Signal System. Electrical Engineering. Postal Correspondence Course
Sigal-EE Postal Correspodece Course 1 SAMPLE STUDY MATERIAL Electrical Egieerig EE / EEE Postal Correspodece Course GATE, IES & PSUs Sigal System Sigal-EE Postal Correspodece Course CONTENTS 1. SIGNAL
More informationLinear Programming and the Simplex Method
Liear Programmig ad the Simplex ethod Abstract This article is a itroductio to Liear Programmig ad usig Simplex method for solvig LP problems i primal form. What is Liear Programmig? Liear Programmig is
More informationChapter 7: The z-transform. Chih-Wei Liu
Chapter 7: The -Trasform Chih-Wei Liu Outlie Itroductio The -Trasform Properties of the Regio of Covergece Properties of the -Trasform Iversio of the -Trasform The Trasfer Fuctio Causality ad Stability
More informationFIR Filter Design: Part II
EEL335: Discrete-Time Sigals ad Systems. Itroductio I this set of otes, we cosider how we might go about desigig FIR filters with arbitrary frequecy resposes, through compositio of multiple sigle-peak
More informationEE 435. Lecture 25. Data Converters. Architectures. Characterization
EE 435 Lecture 5 Data Coverters Architectures Characterizatio . eview from last lecture. Data Coverters Types: A/D (Aalog to Digital) Coverts Aalog Iput to a Digital Output D/A (Digital to Aalog) Coverts
More informationComplex Analysis Spring 2001 Homework I Solution
Complex Aalysis Sprig 2001 Homework I Solutio 1. Coway, Chapter 1, sectio 3, problem 3. Describe the set of poits satisfyig the equatio z a z + a = 2c, where c > 0 ad a R. To begi, we see from the triagle
More informationa 1 = 1 a a a a n n s f() s = Σ log a 1 + a a n log n sup log a n+1 + a n+2 + a n+3 log n sup () s = an /n s s = + t i
0 Dirichlet Serie & Logarithmic Power Serie. Defiitio & Theorem Defiitio.. (Ordiary Dirichlet Serie) Whe,a,,3, are complex umber, we call the followig Ordiary Dirichlet Serie. f() a a a a 3 3 a 4 4 Note
More informationCEE 522 Autumn Uncertainty Concepts for Geotechnical Engineering
CEE 5 Autum 005 Ucertaity Cocepts for Geotechical Egieerig Basic Termiology Set A set is a collectio of (mutually exclusive) objects or evets. The sample space is the (collectively exhaustive) collectio
More informationPractical Spectral Anaysis (continue) (from Boaz Porat s book) Frequency Measurement
Practical Spectral Aaysis (cotiue) (from Boaz Porat s book) Frequecy Measuremet Oe of the most importat applicatios of the DFT is the measuremet of frequecies of periodic sigals (eg., siusoidal sigals),
More informationLecture 13. Graphical representation of the frequency response. Luca Ferrarini - Basic Automatic Control 1
Lecture 3 Graphical represetatio of the frequecy respose Luca Ferrarii - Basic Automatic Cotrol Graphical represetatio of the frequecy respose Polar plot G Bode plot ( j), G Im 3 Re of the magitude G (
More informationECE 308 Discrete-Time Signals and Systems
ECE 38-5 ECE 38 Discrete-Time Sigals ad Systems Z. Aliyazicioglu Electrical ad Computer Egieerig Departmet Cal Poly Pomoa ECE 38-5 1 Additio, Multiplicatio, ad Scalig of Sequeces Amplitude Scalig: (A Costat
More informationAnalog Filter Design. Part. 1: Introduction. P. Bruschi - Analog Filter Design 1
Aalog Filter Desig Part. : Itroductio P. Bruschi - Aalog Filter Desig Defiitio of Filter Electroic filters are liear circuits hose operatio is defied i the frequecy domai, i.e. they are itroduced to perform
More informationA First-Order Noise Analysis of the GBT L-Band Receiver Front-End
A First-Order Noise Aalysis of the GB L-Bad eceiver Frot-Ed ichard F. Bradley Jauary 30, 003 Itroductio ecet ivestigatios of GB baselies associated with observatios of cotiuum radio sources have revealed
More informationIntroduction to Signals and Systems, Part V: Lecture Summary
EEL33: Discrete-Time Sigals ad Systems Itroductio to Sigals ad Systems, Part V: Lecture Summary Itroductio to Sigals ad Systems, Part V: Lecture Summary So far we have oly looked at examples of o-recursive
More informationCrash course part 2. Frequency compensation
Crash course part Frequecy compesatio Ageda Frequecy depedace Feedback amplifiers Frequecy depedace of the Trasistor Frequecy Compesatio Phatom Zero Examples Crash course part poles ad zeros I geeral a
More informationMCT242: Electronic Instrumentation Lecture 2: Instrumentation Definitions
Faculty of Egieerig MCT242: Electroic Istrumetatio Lecture 2: Istrumetatio Defiitios Overview Measuremet Error Accuracy Precisio ad Mea Resolutio Mea Variace ad Stadard deviatio Fiesse Sesitivity Rage
More informationELEG 4603/5173L Digital Signal Processing Ch. 1 Discrete-Time Signals and Systems
Departmet of Electrical Egieerig Uiversity of Arasas ELEG 4603/5173L Digital Sigal Processig Ch. 1 Discrete-Time Sigals ad Systems Dr. Jigxia Wu wuj@uar.edu OUTLINE 2 Classificatios of discrete-time sigals
More informationELEC 372 LECTURE NOTES, WEEK 1 Dr. Amir G. Aghdam Concordia University
EEC 37 ECTURE NOTES, WEEK Dr Amir G Aghdam Cocordia Uiverity Part of thee ote are adapted from the material i the followig referece: Moder Cotrol Sytem by Richard C Dorf ad Robert H Bihop, Pretice Hall
More informationZeros of Polynomials
Math 160 www.timetodare.com 4.5 4.6 Zeros of Polyomials I these sectios we will study polyomials algebraically. Most of our work will be cocered with fidig the solutios of polyomial equatios of ay degree
More informationLECTURE 13 SIMULTANEOUS EQUATIONS
NOVEMBER 5, 26 Demad-upply ytem LETURE 3 SIMULTNEOUS EQUTIONS I thi lecture, we dicu edogeeity problem that arie due to imultaeity, i.e. the left-had ide variable ad ome of the right-had ide variable are
More information1.3 Convergence Theorems of Fourier Series. k k k k. N N k 1. With this in mind, we state (without proof) the convergence of Fourier series.
.3 Covergece Theorems of Fourier Series I this sectio, we preset the covergece of Fourier series. A ifiite sum is, by defiitio, a limit of partial sums, that is, a cos( kx) b si( kx) lim a cos( kx) b si(
More informationCS 270 Algorithms. Oliver Kullmann. Growth of Functions. Divide-and- Conquer Min-Max- Problem. Tutorial. Reading from CLRS for week 2
Geeral remarks Week 2 1 Divide ad First we cosider a importat tool for the aalysis of algorithms: Big-Oh. The we itroduce a importat algorithmic paradigm:. We coclude by presetig ad aalysig two examples.
More informationEE 435. Lecture 25. Data Converters
EE 435 Lecture 5 Data Coverters . Review from last lecture. Basic Operatio of CMFB Block V DD V FB V O1 V O CMFB Circuit V FB V OUT C L M 3 M 4 V OUT V IN M 1 M V IN C L V OXX CMFB Circuit V B M 9 V OXX
More informationControl of a Linear Permanent Magnet Synchronous Motor using Multiple Reference Frame Theory
Cotrol of a Liear Permaet Maget Sychroou Motor uig Multiple Referece Frame Theory Jawad Faiz ad B. RezaeiAlam Departmet of Electrical ad Computer Egieerig Faculty of Egieerig Uiverity of Tehra, Tehra,
More informationECE 422/522 Power System Operations & Planning/Power Systems Analysis II : 6 - Small Signal Stability
ECE 4/5 Power System Operatios & Plaig/Power Systems Aalysis II : 6 - Small Sigal Stability Sprig 014 Istructor: Kai Su 1 Refereces Kudur s Chapter 1 Saadat s Chapter 11.4 EPRI Tutorial s Chapter 8 Power
More informationIntro to Learning Theory
Lecture 1, October 18, 2016 Itro to Learig Theory Ruth Urer 1 Machie Learig ad Learig Theory Comig soo 2 Formal Framework 21 Basic otios I our formal model for machie learig, the istaces to be classified
More informationQuestions about the Assignment. Describing Data: Distributions and Relationships. Measures of Spread Standard Deviation. One Quantitative Variable
Quetio about the Aigmet Read the quetio ad awer the quetio that are aked Experimet elimiate cofoudig variable Decribig Data: Ditributio ad Relatiohip GSS people attitude veru their characteritic ad poue
More informationS T A T R a c h e l L. W e b b, P o r t l a n d S t a t e U n i v e r s i t y P a g e 1. = Population Variance
S T A T 4 - R a c h e l L. W e b b, P o r t l a d S t a t e U i v e r i t y P a g e Commo Symbol = Sample Size x = Sample Mea = Sample Stadard Deviatio = Sample Variace pˆ = Sample Proportio r = Sample
More information5.76 Lecture #33 5/08/91 Page 1 of 10 pages. Lecture #33: Vibronic Coupling
5.76 Lecture #33 5/8/9 Page of pages Lecture #33: Vibroic Couplig Last time: H CO A A X A Electroically forbidde if A -state is plaar vibroically allowed to alterate v if A -state is plaar iertial defect
More informationSingle Amplifier, Active-RC, Butterworth, and Chebyshev Filters Using Impedance Tapering
Sigle Amplifier, Active-RC, Butterworth, ad Chebyshev Filters Usig Impedace Taperig Draže Jurišić Faculty of Electrical Egieerig ad Computig, Uska 3, HR-0000, Zagreb, Croatia George S. Moschytz Swiss Federal
More informationBrief Review of Linear System Theory
Brief Review of Liear Sytem heory he followig iformatio i typically covered i a coure o liear ytem theory. At ISU, EE 577 i oe uch coure ad i highly recommeded for power ytem egieerig tudet. We have developed
More informationStability Analysis and Bifurcation Control of Hysteresis Current Controlled Ćuk Converter Using Filippov s Method
Stability Aalysis ad Bifurcatio otrol of Hysteresis urret otrolled Ću overter Usig Filippov s Method I. Daho*, D. Giaouris * (Member IE, B. Zahawi*(Member IE, V. Picer*(Member IE ad S. Baerjee** *School
More informationAnalysis of MOS Capacitor Loaded Annular Ring MICROSTRIP Antenna
Iteratioal OPEN AESS Joural Of Moder Egieerig Research (IJMER Aalysis of MOS apacitor Loaded Aular Rig MIROSTRIP Atea Mohit Kumar, Suredra Kumar, Devedra Kumar 3, Ravi Kumar 4,, 3, 4 (Assistat Professor,
More informationThe Performance of Feedback Control Systems
The Performace of Feedbac Cotrol Sytem Objective:. Secify the meaure of erformace time-domai the firt te i the deig roce Percet overhoot / Settlig time T / Time to rie / Steady-tate error e. ut igal uch
More information