Understanding Basic Analog Ideal Op Amps


 Cleopatra Kelley
 3 years ago
 Views:
Transcription
1 Appliction Report SLAA068A  April 2000 Understnding Bsic Anlog Idel Op Amps Ron Mncini Mixed Signl Products ABSTRACT This ppliction report develops the equtions for the idel opertionl mplifier (op mp). It ssumes tht slient prmeters re perfect. Severl exmples of op mp circuits re described. Contents Introduction The Noninverting Op Amp The Inverting Op Amp The Adder The Differentil Amplifier Complex Feedbck Networks Video Amplifiers Cpcitors Conclusions List of Figures 1 The Noninverting Op Amp The Inverting Op Amp The Adder Circuit The Differentil Amplifier Differentil Amplifier With CommonMode Input Signl T Network in Feedbck Loop Thevenin s Theorem Applied to T Network Video Amplifier LowPss Filter HighPss Filter
2 Introduction The nme Idel Op Amp is pplied to this nd similr nlysis becuse the slient prmeters of the op mp re ssumed to be perfect. There is no such thing s n idel op mp, but present dy op mps come so close to idel tht Idel Op Amp nlysis becomes close to ctul nlysis. Op mps deprt from the idel in two wys. First, dc prmeters, such s input offset voltge, re lrge enough to cuse deprture from the idel. The idel ssumes tht input offset voltge is zero. Second, c prmeters, such s gin, re function of frequency, so they go from lrge vlues t dc to smll vlues t high frequencies. Both error sources re treted in lter Understnding. ppliction notes published in this series. This ssumption simplifies the nlysis, thus it clers the pth for insight. It is so much esier to see the forest when brush nd huge trees do not surround you. Although the idel op mp nlysis mkes use of perfect prmeters, the nlysis is often vlid becuse some op mps pproch perfection. In ddition, when working t low frequencies, severl khz, the idel op mp nlysis produces ccurte nswers. Voltge feedbck op mps re covered in this ppliction note, nd current feedbck op mps re covered in lter ppliction notes. Severl ssumptions hve to be mde before the idel op mp nlysis cn proceed. First, ssume tht the current flow into the input leds of the op mp is zero. This ssumption is lmost true in FET op mps where input currents cn be less thn pa, but this is not lwys true in bipolr highspeed op mps where tens of µa input currents re found. Second, the op mp gin is ssumed to be infinite, hence it drives the output voltge to ny vlue required to stisfy the input conditions. This ssumes tht the op mp output voltge cn chieve ny vlue. Sturtion occurs when the output voltge comes close to power supply ril, but relity does not negte the ssumption, it only bounds it. Also, implicit in the infinite gin ssumption is the need for zero input signl. The gin drives the output voltge until the voltge between the input leds (the error voltge) is zero. This leds to the third ssumption tht the voltge between the input leds is zero. The impliction of zero voltge between the input leds mens tht if one input is tied to hrd voltge source such s ground, then the other input is t the sme potentil. The current flow into the input leds is zero, so the input impednce of the op mp is infinite. Four, the output impednce of the idel op mp is zero. The idel op mp cn drive ny lod without n output impednce dropping voltge cross it. The output impednce of most op mps is frction of n ohm for low current flows, so this ssumption is vlid in most cses. Five, the frequency response of the idel op mp is flt; this mens tht the gin does not vry s frequency increses. By constrining the use of the op mp to the low frequencies, we mke the frequency response ssumption true. PARAMETER NAME PARAMETERS SYMBOL VALUE Input current IIN 0 Input offset voltge VOS 0 Input impednce ZIN Output impednce ZOUT 0 Gin 2 Understnding Bsic Anlog Idel Op Amps
3 The Noninverting Op Amp The noninverting op mp hs the input signl connected to its noninverting input, thus its input source sees n infinite impednce. There is no input offset voltge becuse V OS = V E = 0, hence the negtive input must be t the sme voltge s the positive input. The op mp output drives current into until the negtive input is t the voltge,. This ction cuses to pper cross. The voltge divider rule is used with being the input to the voltge divider, nd being the output of the voltge divider. Since no current cn flow into either op mp led, use of the voltge divider rule is llowed. Eqution 1 is written with the id of the voltge divider rule, nd lgebric mnipultion yields eqution 2 in the form for gin prmeter. VE Figure 1. The Noninverting Op Amp (1) 1 (2) When becomes very lrge with respect to, / 0 nd eqution 2 reduces to eqution 3. 1 Under these conditions = 1 nd the circuit becomes unity gin buffer. is usully deleted to chieve the sme results, nd when is deleted, cn lso be deleted ( must be shorted when it is deleted). When nd re deleted, the op mp output is connected to its inverting input with wire. Some op mps re selfdestructive when is left out of the circuit, so is used in mny buffer designs. When is included in buffer circuit, its function is to protect the inverting input from n over voltge, nd it cn hve lmost ny vlue (20k is often used). cn never be left out of the circuit in current feedbck mplifier design becuse determines stbility in current feedbck mplifiers. Notice tht the gin is only function of the feedbck nd gin resistors, so the feedbck hs ccomplished its function of mking the gin independent of the op mp prmeters. The gin is djusted by vrying the rtio of the resistors. The ctul resistor vlues re determined by the impednce levels tht the designer wnts to estblish. If = 10K nd = 10K the gin is two s shown in eqution 2, nd if = 100K nd = 100K the gin is still two. The impednce levels of 10 K or 100 K determine the current drin, the effect stry cpcitnce will hve, nd few other points. The impednce level does not set the gin; the rtio of / does. (3) Understnding Bsic Anlog Idel Op Amps 3
4 The Inverting Op Amp The noninverting input of the inverting op mp circuit is grounded. One ssumption we mde is tht the input error voltge is zero, so the feedbck keeps inverting the input of the op mp t virtul ground (not ctul ground but cting like ground). The current flow in the input leds is ssumed to be zero, hence the current flowing through equls the current flowing through. Using Kirchoff s lw, we write eqution 4. Algebric mnipultion gives us eqution 5. I1 IB I2 VE IB Figure 2. The Inverting Op Amp I 1 I 2 (4) Notice tht the gin is only function of the feedbck nd gin resistors, so the feedbck hs ccomplished its function of mking the gin independent of the op mp prmeters. The ctul resistor vlues re determined by the impednce levels tht the designer wnts to estblish. If =10K nd =10K the gin is minus one s shown in eqution 5, nd if =100K nd =100K the gin is still minus one. The impednce levels of 10K or 100K determine the current drin, the effect stry cpcitnce will hve, nd few other points, but the impednce level does not set the gin; the rtio of / does. One finl note; the output signl is the input signl mplified nd inverted. The input impednce is set by becuse the inverting input led is held t virtul ground. The Adder An dder circuit cn be mde by connecting more inputs to the inverting op mp. The opposite end of the resistor connected to the inverting input is held t virtul ground by the feedbck; therefore, dding new inputs does not ffect the response of the existing inputs. (5) V1 V2 VN R1 R2 RN Figure 3. The Adder Circuit Superposition is used to clculte the output voltges resulting from ech input, nd the output voltges re dded lgebriclly to obtin the totl output voltge. Eqution 6 is the output eqution when V 1 nd V 2 re grounded. Equtions 7 nd 8 re the other superposition equtions, nd the finl result is given in eqution 9. 4 Understnding Bsic Anlog Idel Op Amps
5 N R N V N (6) 1 V 1 2 V 2. V 1 V 2 R N V N. (7) (8) (9) The Differentil Amplifier The differentil mplifier circuit mplifies the difference between signls pplied to the inputs. Superposition is used to clculte the output voltge resulting from ech input voltge, nd then the two output voltges re dded to rrive t the finl output voltge. V1 R1 R2 V V V2 R3 R4 Figure 4. The Differentil Amplifier The op mp input voltge resulting from the input source, V 1, is clculted in equtions 10 nd 11. The voltge divider rule is used to clculte the voltge, V, nd the noninverting gin eqution (eqution 2) is used to clculte the noninverting output voltge, 1. V V 1 1 V (G ) V 1.. The inverting gin (eqution 5) is used to clculte the stge gin for 2 in eqution 12. These inverting nd noninverting gins re dded in eqution V 2.. (12) (10) (11) V 1.. V 2 (13) When = nd =, eqution 13 reduces to eqution 14.. V1 V 2. (14) Understnding Bsic Anlog Idel Op Amps 5
6 It is now obvious tht the differentil signl, (V 1 V 2 ), is multiplied by the stge gin, so the nme differentil mplifier suits the circuit. Becuse it only mplifies the differentil portion of the input signl, it rejects the commonmode portion of the input signl. A commonmode signl is illustrted in Figure 5. Becuse the differentil mplifier strips off or rejects the commonmode signl, this circuit configurtion is often employed to strip dc or injected commonmode noise off signl. V1 VCM V2 Figure 5. Differentil Amplifier With CommonMode Input Signl The disdvntge of this circuit is tht the two input impednces cnnot be mtched when it functions s differentil mplifier, thus there re two nd three op mp versions of this circuit specilly designed for high performnce pplictions requiring mtched input impednces. Complex Feedbck Networks When complex feedbck networks re put into the feedbck loop, the circuits get hrder to nlyze becuse the gin equtions cn not be used. The usul technique is to write node or loop equtions, nd to solve these equtions. Becuse component is grounded, superposition is not of ny use, but Thevenin s theorem usully cn be used s is shown in the exmple problem given below. Sometimes it is desirble to hve low resistnce pth to ground in the feedbck loop. Stndrd inverting op mps cn not do this when the driving circuit sets the input resistor vlue, nd the gin specifiction sets the feedbck resistor vlue. Inserting T network in the feedbck loop yields degree of freedom tht enbles both specifictions to be met with low dc resistnce pth in the feedbck loop. X R1 R2 Y R4 Figure 6. T Network in Feedbck Loop Brek the circuit t point X Y, stnd on the terminls looking into, nd clculte the Thevenin equivlent voltge s shown in eqution 15. The Thevenin equivlent impednce is clculted in eqution Understnding Bsic Anlog Idel Op Amps
7 V TH R TH (15) (16) Replce the output circuit with the Thevenin equivlent circuit s shown in Figure 7, nd clculte the gin with the id of the inverting gin eqution s shown in eqution 17. R1 R2 RTH VTH Figure 7. Thevenin s Theorem Applied to T Network Substituting the Thevenin equivlents into eqution 17 yields eqution 18. V TH R TH R TH... R3... (17) (18) Algebric mnipultion yields eqution 19. (19) Specifictions for the circuit you re required to build re n inverting mplifier with n input resistnce of 10K ( = 10K), gin of 100, nd feedbck resistnce of 20K or less. The inverting op mp circuit cn not meet these specifictions becuse must equl 1000K. Inserting T network with = = 10K nd = 485K does meet the specifictions. Video Amplifiers Video signls contin high frequencies, nd they use coxil cble to trnsmit nd receive signls. The cble connecting these circuits hs chrcteristic impednce of 75 Ω. To prevent reflections, which cuse distortion nd ghosting, the input nd output circuit impednces must mtch the 75 Ω cble. Mtching the input impednce is simple for noninverting mplifier becuse its input impednce is very high; just mke R IN = 75 Ω. nd cn be selected s very high vlues, in the kω rnge, so tht they hve miniml ffect on the impednce of the input or output circuit. A mtching resistor, R M, is plced in series with the op mp output to rise its output impednce to 75 Ω; terminting resistor, R T, is plced t the input of the next stge to mtch the cble. Understnding Bsic Anlog Idel Op Amps 7
8 RIN RM RT Figure 8. Video Amplifier The mtching nd terminting resistors re equl in vlue, nd they form voltge divider of 1/2 becuse R T is not loded. Very often is selected equl to so tht the op mp gin equls two. Then the system gin, which is the op mp gin multiplied by the divider gin, is equl to one (2 1/2 = 1). Cpcitors Cpcitors re key component in circuit designer s tool kit, thus short discussion on evluting their ffect on circuit performnce is in order. Cpcitors hve n impednce of X C = 1 (2πfC). Note tht when the frequency is zero the cpcitive impednce (lso known s rectnce) is infinite, nd tht when the frequency is infinite the cpcitive impednce is zero. These endpoints re derived from the finl vlue theorem, nd they re used to get rough ide of the ffect of cpcitor. When cpcitor is used with resistor, they form wht is clled brekpoint. Without going into complicted mth, just ccept tht the brek frequency occurs t f = 1/(2π RC) nd the gin is 3 db t the brek frequency. CF Figure 9. LowPss Filter The low pss filter circuit hs cpcitor in prllel with the feedbck resistor. The gin for the low pss filter is given in eqution 20. X C At very low frequencies X C, so domintes the prllel combintion in eqution 20, nd the cpcitor hs no effect. The gin t low frequencies is /. At very high frequencies X C 0, so the feedbck resistor is shorted out, thus reducing the circuit gin to zero. At the frequency where X C = the gin is reduced to hlf or 3 db becuse equl impednces in prllel equl hlf the vlue of either impednce. Connecting the cpcitor in prllel with where it hs the opposite effect mkes high pss filter. Eqution 21 gives the eqution for the high pss filter. (20) 8 Understnding Bsic Anlog Idel Op Amps
9 CG Figure 10. HighPss Filter 1 X C (21) At very low frequencies X C, so domintes the prllel combintion in eqution 21, nd the cpcitor hs no effect. The gin t low frequencies is 1 /. At very high frequencies X C 0, so the gin setting resistor is shorted out thus incresing the circuit gin to mximum. This simple technique is used to predict the form of circuit trnsfer function rpidly. Better nlysis techniques re presented in more dvnced ppliction notes for those pplictions requiring more precision. Conclusions When the proper ssumptions re mde, the nlysis of op mp circuits is strightforwrd. These ssumptions, which include zero input current, zero input offset voltge, nd infinite gin, re not n unrelistic ssumption becuse the new op mps mke them true in mny pplictions. When the signl is comprised of low frequencies, the gin ssumption is vlid becuse op mps hve very high gin t low frequencies. When CMOS op mps re used, the input current is in the femto mp rnge; close enough to zero for most pplictions. Lser trimmed input circuits reduce the input offset voltge to few micro volts; close enough to zero for most pplictions. The idel op mp is becoming rel; especilly for undemnding pplictions. The mth required for idel op mp nlysis is not rigorous, thus most people should be ble to nlyze simple op mp circuits. The more dvnced pplictions require complex op mp circuits, but there re mny of these shown in the pplictions literture. Grb TI op mp nd hve fun. Understnding Bsic Anlog Idel Op Amps 9
10 IMPORTANT NOTICE Texs Instruments nd its subsidiries (TI) reserve the right to mke chnges to their products or to discontinue ny product or service without notice, nd dvise customers to obtin the ltest version of relevnt informtion to verify, before plcing orders, tht informtion being relied on is current nd complete. All products re sold subject to the terms nd conditions of sle supplied t the time of order cknowledgment, including those pertining to wrrnty, ptent infringement, nd limittion of libility. TI wrrnts performnce of its semiconductor products to the specifictions pplicble t the time of sle in ccordnce with TI s stndrd wrrnty. Testing nd other qulity control techniques re utilized to the extent TI deems necessry to support this wrrnty. Specific testing of ll prmeters of ech device is not necessrily performed, except those mndted by government requirements. Customers re responsible for their pplictions using TI components. In order to minimize risks ssocited with the customer s pplictions, dequte design nd operting sfegurds must be provided by the customer to minimize inherent or procedurl hzrds. TI ssumes no libility for pplictions ssistnce or customer product design. TI does not wrrnt or represent tht ny license, either express or implied, is grnted under ny ptent right, copyright, msk work right, or other intellectul property right of TI covering or relting to ny combintion, mchine, or process in which such semiconductor products or services might be or re used. TI s publiction of informtion regrding ny third prty s products or services does not constitute TI s pprovl, wrrnty or endorsement thereof. Copyright 2000, Texs Instruments Incorported
(CATALYST GROUP) B"sic Electric"l Engineering
(CATALYST GROUP) B"sic Electric"l Engineering 1. Kirchhoff s current l"w st"tes th"t (") net current flow "t the junction is positive (b) Hebr"ic sum of the currents meeting "t the junction is zero (c)
More informationExperiment 3: NonIdeal Operational Amplifiers
Experiment 3: NonIdel Opertionl Amplifiers Fll 2009 Equivlent Circuits The bsic ssumptions for n idel opertionl mplifier re n infinite differentil gin ( d ), n infinite input resistnce (R i ), zero output
More informationApplication Note. Differential Amplifier
Appliction Note AN367 Differentil Amplifier Author: Dve n Ess Associted Project: Yes Associted Prt Fmily: CY8C9x66, CY8C7x43, CY8C4x3A PSoC Designer ersion: 4. SP3 Abstrct For mny sensing pplictions, desirble
More informationExperiment 3: NonIdeal Operational Amplifiers
Experiment 3: NonIdel Opertionl Amplifiers 9/11/06 Equivlent Circuits The bsic ssumptions for n idel opertionl mplifier re n infinite differentil gin ( d ), n infinite input resistnce (R i ), zero output
More informationCHAPTER 2 LITERATURE STUDY
CHAPTER LITERATURE STUDY. Introduction Multipliction involves two bsic opertions: the genertion of the prtil products nd their ccumultion. Therefore, there re two possible wys to speed up the multipliction:
More informationEET 438a Automatic Control Systems Technology Laboratory 5 Control of a Separately Excited DC Machine
EE 438 Automtic Control Systems echnology bortory 5 Control of Seprtely Excited DC Mchine Objective: Apply proportionl controller to n electromechnicl system nd observe the effects tht feedbck control
More informationHomework #1 due Monday at 6pm. White drop box in Student Lounge on the second floor of Cory. Tuesday labs cancelled next week
Announcements Homework #1 due Mondy t 6pm White drop ox in Student Lounge on the second floor of Cory Tuesdy ls cncelled next week Attend your other l slot Books on reserve in Bechtel Hmley, 2 nd nd 3
More informationKirchhoff s Rules. Kirchhoff s Laws. Kirchhoff s Rules. Kirchhoff s Laws. Practice. Understanding SPH4UW. Kirchhoff s Voltage Rule (KVR):
SPH4UW Kirchhoff s ules Kirchhoff s oltge ule (K): Sum of voltge drops round loop is zero. Kirchhoff s Lws Kirchhoff s Current ule (KC): Current going in equls current coming out. Kirchhoff s ules etween
More informationLab 8. Speed Control of a D.C. motor. The Motor Drive
Lb 8. Speed Control of D.C. motor The Motor Drive Motor Speed Control Project 1. Generte PWM wveform 2. Amplify the wveform to drive the motor 3. Mesure motor speed 4. Mesure motor prmeters 5. Control
More informationCHAPTER 3 AMPLIFIER DESIGN TECHNIQUES
CHAPTER 3 AMPLIFIER DEIGN TECHNIQUE 3.0 Introduction olidstte microwve mplifiers ply n importnt role in communiction where it hs different pplictions, including low noise, high gin, nd high power mplifiers.
More informationREVIEW QUESTIONS. Figure For Review Question Figure For Review Question Figure For Review Question 10.2.
HAPTE 0 Sinusoidl StedyStte Anlysis 42 EVIEW QUESTIONS 0. The voltge cross the cpcitor in Fig. 0.43 is: () 5 0 V () 7.07 45 V (c) 7.07 45 V (d) 5 45 V Ω 0.5 efer to the circuit in Fig. 0.47 nd oserve
More information5 I. T cu2. T use in modem computing systems, it is desirable to. A Comparison of HalfBridge Resonant Converter Topologies
74 EEE TRANSACTONS ON POER ELECTRONCS, VOL. 3, NO. 2, APRL 988 A Comprison of HlfBridge Resonnt Converter Topologies AbstrctThe hlfbridge seriesresonnt, prllelresonnt, nd combintion seriesprllel
More informationModule 9. DC Machines. Version 2 EE IIT, Kharagpur
Module 9 DC Mchines Version EE IIT, Khrgpur esson 40 osses, Efficiency nd Testing of D.C. Mchines Version EE IIT, Khrgpur Contents 40 osses, efficiency nd testing of D.C. mchines (esson40) 4 40.1 Gols
More information& Y Connected resistors, Light emitting diode.
& Y Connected resistors, Light emitting diode. Experiment # 02 Ojectives: To get some hndson experience with the physicl instruments. To investigte the equivlent resistors, nd Y connected resistors, nd
More informationEngineering: Elec 3509 Electronics II Instructor: Prof. Calvin Plett,
Engineering: Elec 3509 Electronics II Instructor: Prof. Clvin Plett, emil cp@doe.crleton.c Objective: To study the principles, design nd nlysis of nlog electronic circuits. Description: In this course,
More informationSimulation of Transformer Based ZSource Inverter to Obtain High Voltage Boost Ability
Interntionl Journl of cience, Engineering nd Technology Reserch (IJETR), olume 4, Issue 1, October 15 imultion of Trnsformer Bsed Zource Inverter to Obtin High oltge Boost Ability A.hnmugpriy 1, M.Ishwry
More informationUniversity of North CarolinaCharlotte Department of Electrical and Computer Engineering ECGR 4143/5195 Electrical Machinery Fall 2009
Problem 1: Using DC Mchine University o North CrolinChrlotte Deprtment o Electricl nd Computer Engineering ECGR 4143/5195 Electricl Mchinery Fll 2009 Problem Set 4 Due: Thursdy October 8 Suggested Reding:
More informationThreePhase Synchronous Machines The synchronous machine can be used to operate as: 1. Synchronous motors 2. Synchronous generators (Alternator)
ThreePhse Synchronous Mchines The synchronous mchine cn be used to operte s: 1. Synchronous motors 2. Synchronous genertors (Alterntor) Synchronous genertor is lso referred to s lterntor since it genertes
More informationDiscontinued AN6262N, AN6263N. (planed maintenance type, maintenance type, planed discontinued typed, discontinued type)
ICs for Cssette, Cssette Deck ANN, ANN Puse Detection s of Rdio Cssette, Cssette Deck Overview The ANN nd the ANN re the puse detection integrted circuits which select the progrm on the cssette tpe. In
More informationV O = a(v I  V B ) (EQ. 10) V B = V O Z 1 / (Z 1 + Z 2 ), I B = 0 (EQ. 11) V O = av I  az 1 V O / (Z 1 + Z 2 ) (EQ. 12)
APPLICATION NOTE Feedbck, Op Amps nd AN9415 Rev. 3.00 Introduction There re mny benefits [1] which result from the use of feedbck in electronic circuits, but the drwbcks re the incresed complexity of the
More informationLecture 20. Intro to line integrals. Dan Nichols MATH 233, Spring 2018 University of Massachusetts.
Lecture 2 Intro to line integrls Dn Nichols nichols@mth.umss.edu MATH 233, Spring 218 University of Msschusetts April 12, 218 (2) onservtive vector fields We wnt to determine if F P (x, y), Q(x, y) is
More informationSynchronous Machine Parameter Measurement
Synchronous Mchine Prmeter Mesurement 1 Synchronous Mchine Prmeter Mesurement Introduction Wound field synchronous mchines re mostly used for power genertion but lso re well suited for motor pplictions
More informationA Novel Back EMF Zero Crossing Detection of Brushless DC Motor Based on PWM
A ovel Bck EMF Zero Crossing Detection of Brushless DC Motor Bsed on PWM Zhu Bopeng Wei Hifeng School of Electricl nd Informtion, Jingsu niversity of Science nd Technology, Zhenjing 1003 Chin) Abstrct:
More informationExercise 11. The Sine Wave EXERCISE OBJECTIVE DISCUSSION OUTLINE. Relationship between a rotating phasor and a sine wave DISCUSSION
Exercise 11 The Sine Wve EXERCISE OBJECTIVE When you hve completed this exercise, you will be fmilir with the notion of sine wve nd how it cn be expressed s phsor rotting round the center of circle. You
More informationExperiment 3: The research of Thevenin theorem
Experiment 3: The reserch of Thevenin theorem 1. Purpose ) Vlidte Thevenin theorem; ) Mster the methods to mesure the equivlent prmeters of liner twoterminl ctive. c) Study the conditions of the mximum
More informationSynchronous Generator Line Synchronization
Synchronous Genertor Line Synchroniztion 1 Synchronous Genertor Line Synchroniztion Introduction One issue in power genertion is synchronous genertor strting. Typiclly, synchronous genertor is connected
More informationCompared to generators DC MOTORS. Back e.m.f. Back e.m.f. Example. Example. The construction of a d.c. motor is the same as a d.c. generator.
Compred to genertors DC MOTORS Prepred by Engr. JP Timol Reference: Electricl nd Electronic Principles nd Technology The construction of d.c. motor is the sme s d.c. genertor. the generted e.m.f. is less
More informationMEASURE THE CHARACTERISTIC CURVES RELEVANT TO AN NPN TRANSISTOR
Electricity Electronics Bipolr Trnsistors MEASURE THE HARATERISTI URVES RELEVANT TO AN NPN TRANSISTOR Mesure the input chrcteristic, i.e. the bse current IB s function of the bse emitter voltge UBE. Mesure
More informationSynchronous Machine Parameter Measurement
Synchronous Mchine Prmeter Mesurement 1 Synchronous Mchine Prmeter Mesurement Introduction Wound field synchronous mchines re mostly used for power genertion but lso re well suited for motor pplictions
More informationCS 135: Computer Architecture I. Boolean Algebra. Basic Logic Gates
Bsic Logic Gtes : Computer Architecture I Boolen Algebr Instructor: Prof. Bhgi Nrhri Dept. of Computer Science Course URL: www.ses.gwu.edu/~bhgiweb/cs35/ Digitl Logic Circuits We sw how we cn build the
More informationA Development of EarthingResistanceEstimation Instrument
A Development of ErthingResistnceEstimtion Instrument HITOSHI KIJIMA Abstrct:  Whenever erth construction work is done, the implnted number nd depth of electrodes hve to be estimted in order to obtin
More informationSection 17.2: Line Integrals. 1 Objectives. 2 Assignments. 3 Maple Commands. 1. Compute line integrals in IR 2 and IR Read Section 17.
Section 7.: Line Integrls Objectives. ompute line integrls in IR nd IR 3. Assignments. Red Section 7.. Problems:,5,9,,3,7,,4 3. hllenge: 6,3,37 4. Red Section 7.3 3 Mple ommnds Mple cn ctully evlute line
More informationAlternatingCurrent Circuits
chpter 33 AlterntingCurrent Circuits 33.1 AC Sources 33.2 esistors in n AC Circuit 33.3 Inductors in n AC Circuit 33.4 Cpcitors in n AC Circuit 33.5 The LC Series Circuit 33.6 Power in n AC Circuit 33.7
More informationExperiment 8 Series DC Motor (II)
Ojectives To control the speed of loded series dc motor y chnging rmture voltge. To control the speed of loded series dc motor y dding resistnce in prllel with the rmture circuit. To control the speed
More informationSection 16.3 Double Integrals over General Regions
Section 6.3 Double Integrls over Generl egions Not ever region is rectngle In the lst two sections we considered the problem of integrting function of two vribles over rectngle. This sitution however is
More informationMAXIMUM FLOWS IN FUZZY NETWORKS WITH FUNNELSHAPED NODES
MAXIMUM FLOWS IN FUZZY NETWORKS WITH FUNNELSHAPED NODES Romn V. Tyshchuk Informtion Systems Deprtment, AMI corportion, Donetsk, Ukrine Emil: rt_science@hotmil.com 1 INTRODUCTION During the considertion
More informationPassive and Active DC Breakers in the Three GorgesChangzhou HVDC Project
Pssive nd Active DC Brekers in the Three GorgesChngzhou HVDC Project Dg Andersson, Dr, nd Anders Henriksson, B.Sc.E.E, ABB, Sweden explined below) re AbstrctA new type of DC breker, bsed on stndrd SF
More informationTYPE N AND ON CARRIER REPEATERSREPEATERED NIA HIGHLOW TRANSISTORIZED REPEATER CONTENTS PAGE 1. GENERAL This section describes the physical and
BELL SYSTEM PRACTCES Plnt Series SECTON 3624 1 2 1 ssue 2, December 1969 AT&TCo Stndrd TYPE N AND ON CARRER REPEATERSREPEATERED HGHFREQUENCY LNE DESCRPTONTYPE NA HGHLOW TRANSSTORZED REPEATER CONTENTS
More informationExponentialHyperbolic Model for Actual Operating Conditions of Three Phase Arc Furnaces
Americn Journl of Applied Sciences 6 (8): 15391547, 2009 ISSN 15469239 2009 Science Publictions ExponentilHyperbolic Model for Actul Operting Conditions of Three Phse Arc Furnces 1 Mhdi Bnejd, 2 RhmtAllh
More informationAlgorithms for Memory Hierarchies Lecture 14
Algorithms for emory Hierrchies Lecture 4 Lecturer: Nodri Sitchinv Scribe: ichel Hmnn Prllelism nd Cche Obliviousness The combintion of prllelism nd cche obliviousness is n ongoing topic of reserch, in
More informationMETHOD OF LOCATION USING SIGNALS OF UNKNOWN ORIGIN. Inventor: Brian L. Baskin
METHOD OF LOCATION USING SIGNALS OF UNKNOWN ORIGIN Inventor: Brin L. Bskin 1 ABSTRACT The present invention encompsses method of loction comprising: using plurlity of signl trnsceivers to receive one or
More informationEE Controls Lab #2: Implementing StateTransition Logic on a PLC
Objective: EE 44  Controls Lb #2: Implementing Stternsition Logic on PLC ssuming tht speed is not of essence, PLC's cn be used to implement stte trnsition logic. he dvntge of using PLC over using hrdwre
More informationElectronic Circuits I  Tutorial 03 Diode Applications I
Electronic Circuits I  Tutoril 03 Diode Applictions I 1 / 9  T & F # Question 1 A diode cn conduct current in two directions with equl ese. F 2 When reversebised, diode idelly ppers s short. F 3 A
More informationThe Discussion of this exercise covers the following points:
Exercise 4 Bttery Chrging Methods EXERCISE OBJECTIVE When you hve completed this exercise, you will be fmilir with the different chrging methods nd chrgecontrol techniques commonly used when chrging NiMI
More informationEngineer To Engineer Note
Engineer To Engineer Note EE68 Technicl Notes on using Anlog Devices' DSP components nd development tools Contct our technicl support by phone: (800) ANALOGD or emil: dsp.support@nlog.com Or visit our
More informationExample. Check that the Jacobian of the transformation to spherical coordinates is
lss, given on Feb 3, 2, for Mth 3, Winter 2 Recll tht the fctor which ppers in chnge of vrible formul when integrting is the Jcobin, which is the determinnt of mtrix of first order prtil derivtives. Exmple.
More informationMath Circles Finite Automata Question Sheet 3 (Solutions)
Mth Circles Finite Automt Question Sheet 3 (Solutions) Nickols Rollick nrollick@uwterloo.c Novemer 2, 28 Note: These solutions my give you the nswers to ll the prolems, ut they usully won t tell you how
More informationABB STOTZKONTAKT. ABB ibus EIB Current Module SM/S Intelligent Installation Systems. User Manual SM/S In = 16 A AC Un = 230 V AC
User Mnul ntelligent nstlltion Systems A B 1 2 3 4 5 6 7 8 30 ma 30 ma n = AC Un = 230 V AC 30 ma 9 10 11 12 C ABB STOTZKONTAKT Appliction Softwre Current Vlue Threshold/1 Contents Pge 1 Device Chrcteristics...
More informationEngineertoEngineer Note
EngineertoEngineer Note EE297 Technicl notes on using Anlog Devices DSPs, processors nd development tools Visit our Web resources http://www.nlog.com/eenotes nd http://www.nlog.com/processors or emil
More informationStudent Book SERIES. Patterns and Algebra. Name
E Student Book 3 + 7 5 + 5 Nme Contents Series E Topic Ptterns nd functions (pp. ) identifying nd creting ptterns skip counting completing nd descriing ptterns predicting repeting ptterns predicting growing
More information10.4 AREAS AND LENGTHS IN POLAR COORDINATES
65 CHAPTER PARAMETRIC EQUATINS AND PLAR CRDINATES.4 AREAS AND LENGTHS IN PLAR CRDINATES In this section we develop the formul for the re of region whose oundry is given y polr eqution. We need to use the
More informationNetwork Theorems. Objectives 9.1 INTRODUCTION 9.2 SUPERPOSITION THEOREM
M09_BOYL3605_13_S_C09.indd Pge 359 24/11/14 1:59 PM f403 /204/PH01893/9780133923605_BOYLSTAD/BOYLSTAD_NTRO_CRCUT_ANALYSS13_S_978013... Network Theorems Ojectives Become fmilir with the superposition theorem
More informationTUTORIAL Electric Machine Modeling
TUTORIAL Electric Mchine Modeling October 206 Electric Mchine Modeling One cn crete electric chine odels using the bsic unction blocks in PSIM. In this tutoril, we will illustrte how to crete the odel
More informationMultibeam antennas in a broadband wireless access system
Multiem ntenns in rodnd wireless ccess system Ulrik Engström, Mrtin Johnsson, nders Derneryd nd jörn Johnnisson ntenn Reserch Center Ericsson Reserch Ericsson SE4 84 Mölndl Sweden Emil: ulrik.engstrom@ericsson.com,
More informationPB735 HD DP. Industrial Line. Automatic punch and bind machine for books and calendars
PB735 HD DP Automtic punch nd bind mchine for books nd clendrs A further step for the utomtion of double loop binding. A clever nd flexible mchine ble to punch nd bind in line up to 9/16. Using the best
More informationSection Thyristor converter driven DC motor drive
Section.3  Thyristor converter driven DC motor drive.3.1 Introduction Controllble ACDC converters using thyristors re perhps the most efficient nd most robust power converters for use in DC motor drives.
More informationFirst Round Solutions Grades 4, 5, and 6
First Round Solutions Grdes 4, 5, nd 1) There re four bsic rectngles not mde up of smller ones There re three more rectngles mde up of two smller ones ech, two rectngles mde up of three smller ones ech,
More informationEngineertoEngineer Note
EngineertoEngineer Note EE236 Technicl notes on using Anlog Devices DSPs, processors nd development tools Contct our technicl support t dsp.support@nlog.com nd t dsptools.support@nlog.com Or visit our
More informationPassive and Active Hybrid Integrated EMI Filters
Pssive nd Active Hybrid Integrted EMI Filters J. Biel, A. Wirthmueller, R. Wespe, M.. Heldwein, J. W. Kolr Power Electronic Systems bortory Swiss Federl Institute of Technology Zurich, Switzerlnd Emil:
More informationPolar Coordinates. July 30, 2014
Polr Coordintes July 3, 4 Sometimes it is more helpful to look t point in the xyplne not in terms of how fr it is horizontlly nd verticlly (this would men looking t the Crtesin, or rectngulr, coordintes
More informationMOS Transistors. Silicon Lattice
rin n Width W chnnel ptype (doped) sustrte MO Trnsistors n Gte Length L O 2 (insultor) ource Conductor (poly) rin rin Gte nmo trnsistor Gte ource pmo trnsistor licon sustrte doped with impurities dding
More informationLECTURE 9: QUADRATIC RESIDUES AND THE LAW OF QUADRATIC RECIPROCITY
LECTURE 9: QUADRATIC RESIDUES AND THE LAW OF QUADRATIC RECIPROCITY 1. Bsic roerties of qudrtic residues We now investigte residues with secil roerties of lgebric tye. Definition 1.1. (i) When (, m) 1 nd
More information9.4. ; 65. A family of curves has polar equations. ; 66. The astronomer Giovanni Cassini ( ) studied the family of curves with polar equations
54 CHAPTER 9 PARAMETRIC EQUATINS AND PLAR CRDINATES 49. r, 5. r sin 3, 5 54 Find the points on the given curve where the tngent line is horizontl or verticl. 5. r 3 cos 5. r e 53. r cos 54. r sin 55. Show
More informationSection 2.2 PWM converter driven DC motor drives
Section 2.2 PWM converter driven DC motor drives 2.2.1 Introduction Controlled power supply for electric drives re obtined mostly by converting the mins AC supply. Power electronic converter circuits employing
More information2005 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media,
005 IEEE. Personl use of this mteril is permitted. Permission from IEEE must be obtined for ll other uses, in ny current or future medi, including reprinting/republishing this mteril for dvertising or
More informationDetermine currents I 1 to I 3 in the circuit of Fig. P2.14. Solution: For the loop containing the 18V source, I 1 = 0.
Prolem.14 Determine currents 1 to 3 in the circuit of Fig. P.14. 1 A 18 V Ω 3 A 1 8 Ω 1 Ω 7 Ω 4 Ω 3 Figure P.14: Circuit for Prolem.14. For the loop contining the 18V source, Hence, 1 = 1.5 A. KCL t node
More informationMixed CMOS PTL Adders
Anis do XXVI Congresso d SBC WCOMPA l I Workshop de Computção e Aplicções 14 20 de julho de 2006 Cmpo Grnde, MS Mixed CMOS PTL Adders Déor Mott, Reginldo d N. Tvres Engenhri em Sistems Digitis Universidde
More information2N6071A/B Series. Sensitive Gate Triacs. Silicon Bidirectional Thyristors TRIACS 4.0 A RMS, V
Preferred Device Sensitive Gte Trics Silicon Bidirectionl Thyristors Designed primrily for fullwve AC control pplictions, such s light dimmers, motor controls, heting controls nd power supplies; or wherever
More informationSoft switched DCDC PWM Converters
Soft switched DCDC PWM Converters Mr.M. Prthp Rju (), Dr. A. Jy Lkshmi () Abstrct This pper presents n upgrded soft switching technique zero current trnsition (ZCT), which gives better turn off chrcteristics
More informationDirect Current Circuits. Chapter Outline Electromotive Force 28.2 Resistors in Series and in Parallel 28.3 Kirchhoff s Rules 28.
P U Z Z L E R If ll these pplinces were operting t one time, circuit reker would proly e tripped, preventing potentilly dngerous sitution. Wht cuses circuit reker to trip when too mny electricl devices
More informationLecture 16: Four Quadrant operation of DC Drive (or) TYPE E Four Quadrant chopper Fed Drive: Operation
Lecture 16: Four Qudrnt opertion of DC Drive (or) TYPE E Four Qudrnt chopper Fed Drive: Opertion The rmture current I is either positive or negtive (flow in to or wy from rmture) the rmture voltge is lso
More informationECE 274 Digital Logic. Digital Design. Datapath Components Shifters, Comparators, Counters, Multipliers Digital Design
ECE 27 Digitl Logic Shifters, Comprtors, Counters, Multipliers Digitl Design..7 Digitl Design Chpter : Slides to ccompny the textbook Digitl Design, First Edition, by Frnk Vhid, John Wiley nd Sons Publishers,
More information(1) Nonlinear system
Liner vs. nonliner systems in impednce mesurements I INTRODUCTION Electrochemicl Impednce Spectroscopy (EIS) is n interesting tool devoted to the study of liner systems. However, electrochemicl systems
More informationHigh Speed OnChip Interconnects: Trade offs in Passive Termination
High Speed OnChip Interconnects: Trde offs in Pssive Termintion Rj Prihr University of Rochester, NY, USA prihr@ece.rochester.edu Abstrct In this pper, severl pssive termintion schemes for high speed
More informationDomination and Independence on Square Chessboard
Engineering nd Technology Journl Vol. 5, Prt, No. 1, 017 A.A. Omrn Deprtment of Mthemtics, College of Eduction for Pure Science, University of bylon, bylon, Irq pure.hmed.omrn@uobby lon.edu.iq Domintion
More informationDataflow Language Model. DataFlow Models. Applications of Dataflow. Dataflow Languages. Kahn process networks. A Kahn Process (1)
The slides contin revisited mterils from: Peter Mrwedel, TU Dortmund Lothr Thiele, ETH Zurich Frnk Vhid, University of liforni, Riverside Dtflow Lnguge Model Drsticlly different wy of looking t computtion:
More informationGalvanic Isolation System for Multiple Gate Drivers with Inductive Power Transfer
Glvnic Isoltion System for Multiple Gte Drivers with Inductive Power Trnsfer Drive of Threephse inverter Keisuke Kusk, Mskzu Kto Dept. of Energy nd Environment Science Ngok University of Technology Ngok,
More informationInvestigation of Ground Frequency Characteristics
Journl of Electromgnetic Anlysis nd Applictions, 03, 5, 337 http://dx.doi.org/0.436/jem.03.58050 Published Online August 03 (http://www.scirp.org/journl/jem) Mohmed Nyel Electricl Engineering Deprtment,
More informationThe computer simulation of communication for PLC systems
The computer simultion of communiction for PLC systems Jiri Misurec Milos Orgon Dept. of Telecommunictions Fculty of Electricl Engineering nd Communiction Brno University of Technology Purkynov 8 6 00
More informationArray chip resistors size ARC241/ARC242 ARV241/ARV242
Arry chip resistors FEATURES 4 0603 sized resistors in one 1206sized pckge Reduced reel exchnge time Low ssembly costs Reduced PCB re Reduced size of finl equipment Higher component nd equipment relibility.
More informationA COMPARISON OF CIRCUIT IMPLEMENTATIONS FROM A SECURITY PERSPECTIVE
A COMPARISON OF CIRCUIT IMPLEMENTATIONS FROM A SECURITY PERSPECTIVE Mster Thesis Division of Electronic Devices Deprtment of Electricl Engineering Linköping University y Timmy Sundström LITHISYEX05/3698SE
More informationNEW METHOD FOR THE STATE EVALUATION OF THE ZEROSEQUENCE SYSTEM
TX it NEW METHOD FOR THE STATE EVALUATION OF THE ZEROSEQUENCE SYSTEM Gernot DRUML A. Eberle GmbH Germny g.druml@ieee.org Olf SEIFERT Dresden University of Technology Germny seifert@ieeh.et.tudresden.de
More informationREVIEW QUESTIONS. Figure 2.63 For Review Question 2.6. Figure 2.64 For Review Question The reciprocal of resistance is:
EVIEW QUESTIONS 2.1 The reciprocl of resistnce is: () voltge () current (c) conductnce (d) couloms 2.2 An electric heter drws 10 A from 120V line. The resistnce of the heter is: () 1200 () 120 (c) 12
More informationStudy on SLT calibration method of 2port waveguide DUT
Interntionl Conference on Advnced Electronic cience nd Technology (AET 206) tudy on LT clibrtion method of 2port wveguide DUT Wenqing Luo, Anyong Hu, Ki Liu nd Xi Chen chool of Electronics nd Informtion
More informationDESIGN OF CONTINUOUS LAG COMPENSATORS
DESIGN OF CONTINUOUS LAG COMPENSATORS J. Pulusová, L. Körösi, M. Dúbrvská Institute of Robotics nd Cybernetics, Slovk University of Technology, Fculty of Electricl Engineering nd Informtion Technology
More informationLow noise SQUID simulator with large dynamic range of up to eight flux quanta
Low noise SQUID simultor with lrge dynmic rnge of up to eight flux qunt A. Mrtinez*, J. Flokstr, C. Rillo**, L.A. Angurel**, L.M. Grci** nd H.J.M. ter Brke Twente University of Technology, Deprtment of
More informationMesh and Node Equations: More Circuits Containing Dependent Sources
Mesh nd Node Equtions: More Circuits Contining Dependent Sources Introduction The circuits in this set of problems ech contin single dependent source. These circuits cn be nlyzed using mesh eqution or
More informationDP4T RF CMOS Switch: A Better Option to Replace the SPDT Switch and DPDT Switch
Send Orders of Reprints t reprints@enthmscience.org 244 Recent Ptents on Electricl & Electronic Engineering 2012, 5, 244248 DP4T RF CMOS Switch: A Better Option to Replce the SPDT Switch nd DPDT Switch
More informationModeling of Conduction and Switching Losses in ThreePhase Asymmetric MultiLevel Cascaded Inverter
Proceedings of the 5th WEA nt. onf. on Power ystems nd Electromgnetic omptibility, orfu, Greece, August 2325, 2005 (pp176181) Modeling of onduction nd witching Losses in ThreePhse Asymmetric MultiLevel
More informationSOLVING TRIANGLES USING THE SINE AND COSINE RULES
Mthemtics Revision Guides  Solving Generl Tringles  Sine nd Cosine Rules Pge 1 of 17 M.K. HOME TUITION Mthemtics Revision Guides Level: GCSE Higher Tier SOLVING TRIANGLES USING THE SINE AND COSINE RULES
More informationGeometric quantities for polar curves
Roerto s Notes on Integrl Clculus Chpter 5: Bsic pplictions of integrtion Section 10 Geometric quntities for polr curves Wht you need to know lredy: How to use integrls to compute res nd lengths of regions
More information2N6071A/B Series. Silicon Bidirectional Thyristors TRIACS 4.0 A RMS, V
Preferred Device Sensitive Gte Trics Silicon Bidirectionl Thyristors Designed primrily for full wve AC control pplictions, such s light dimmers, motor controls, heting controls nd power supplies; or wherever
More informationInnovative plate solutions for flexographic printing. nyloflex printing plates
Innovtive plte solutions for flexogrphic printing nyloflex printing pltes nyloflex Printing Pltes Unique nd comprehensive expertise in flexogrphic printing Printing pltes from Flint Group to meet every
More informationDesign Reference SLOD006A
Design Reference September 2001 Advanced Analog Products SLOD006A IMPORTANT NOTICE Texas Instruments Incorporated and its subsidiaries (TI) reserve the right to make corrections, modifications, enhancements,
More information252 Calibration of Dipole Antennas
2 Reserch nd Development of Clibrtion Technology 252 Clibrtion of Dipole Antenns Iwo NISHIYAMA, Kojiro SAKAI, Tsutomu SUGIYAMA, Kouichi SBATA, nd Ktsumi FUJII This pper describes clibrtion method of
More informationPrecision Dual Difet OPERATIONAL AMPLIFIER
OP Precision Dual Difet OPERTIONL MPLIFIER FETURES VERY LOW NOISE: nv/ Hz at khz LOW V OS : µv max LOW DRIFT: µv/ C max LOW I B : p max FST SETTLING TIME: µs to.% UNITYGIN STBLE PPLICTIONS DT CQUISITION
More informationHighlights. Opto Proximity Switches. Introduction. Opto proximity switches fast and accurate sensing with light and laser PXO100
Opto proximity switches fst nd ccurte sensing with light nd lser Configurtor A configurtor for opticl proximity switches is vilble in the A&D Mll. Bsed on the technicl fetures required, the desired product
More informationTriangles and parallelograms of equal area in an ellipse
1 Tringles nd prllelogrms of equl re in n ellipse Roert Buonpstore nd Thoms J Osler Mthemtics Deprtment RownUniversity Glssoro, NJ 0808 USA uonp0@studentsrownedu osler@rownedu Introduction In the pper
More informationJoanna Towler, Roading Engineer, Professional Services, NZTA National Office Dave Bates, Operations Manager, NZTA National Office
. TECHNICA MEMOANDM To Cc repred By Endorsed By NZTA Network Mngement Consultnts nd Contrctors NZTA egionl Opertions Mngers nd Are Mngers Dve Btes, Opertions Mnger, NZTA Ntionl Office Jonn Towler, oding
More informationRobustness Analysis of Pulse Width Modulation Control of Motor Speed
Proceedings of the World Congress on Engineering nd Computer Science 2007 WCECS 2007, October 2426, 2007, Sn Frncisco, USA obustness Anlysis of Pulse Width Modultion Control of Motor Speed Wei Zhn Abstrct
More information