Exercise 11. The Sine Wave EXERCISE OBJECTIVE DISCUSSION OUTLINE. Relationship between a rotating phasor and a sine wave DISCUSSION


 Regina Joseph
 4 years ago
 Views:
Transcription
1 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 will lso be fmilir with the different prmeters of sine wve, such s its period, frequency, mplitude, nd instntneous vlues. You will see how to express current nd voltge in c power circuits s sine wves. You will be introduced to the concept of rms (effective) vlues nd know how to clculte the rms vlue from the mplitude of voltge or current sine wve. The hndson exercises in this mnul require you to be fmilir with the computerbsed instruments. Refer to the user guides titled Dt Acquisition nd Control System (86716E0) nd ComputerBsed Instruments for EMS (86718E0) to become fmilir with the opertion nd use of the computerbsed instruments. DISCUSSION OUTLINE The Discussion of this exercise covers the following points: Reltionship between rotting phsor nd sine wve Period nd frequency of sinusoidl voltge or current Amplitude nd instntneous vlue of sinusoidl voltge or current Effective or rootmensqure (rms) vlue nd heting cpcity Effective (rms) vlue of sinusoidl voltge or current DISCUSSION Reltionship between rotting phsor nd sine wve A direct reltionship exists between circulr motion nd sine wve. Thus, sinusoidl voltge or current cn be grphed using the verticlxis deflection s function of the ngulr position of rotting phsor. A phsor is vector hving its origin t the center (0, 0) of crtesin plne. Ech cycle of sinusoidl signl corresponds to one complete revolution (one turn) of the phsor round the circle, which is equl to 360 or 2 rdins. Figure 14 shows sine wve grphed using the verticlxis deflection s function of the ngulr position of rotting phsor. Festo Didctic
2 Ex. 11 The Sine Wve Discussion (90 ) + Voltge V or current (A) 0 rd (180 ) 225 (270 ) rd (360 ) Angulr position ( ) One complete cycle (2 rdins or 360 ) Figure 14. Sine wve grphed using the verticlxis deflection s function of the ngulr position of rotting phsor. Figure 15 shows n exmple in which phsor is rotting counterclockwise round the center of circle t constnt velocity. As the phsor is rotting, the verticl distnce between the tip of the phsor nd the horizontl xis of the circle continuously vries. A grphicl projection of the distnce vlue, on the XYplne s function of the ngulr position gives sine wve. The following cn be observed in Figure 15: Initilly, the phsor is t 0 (horizontl position), so the verticl distnce between the phsor nd the horizontl xis is null. As the phsor is rotting from 0 to 90, the verticl distnce between the tip of the phsor nd the horizontl xis grdully increses from zero to mximum positive (pek) vlue. As the phsor is rotting from 90 to 180, the verticl distnce between the tip of the phsor nd the horizontl xis grdully decreses from the mximum positive vlue to zero. As the phsor is rotting from 180 to 270, the verticl distnce between the tip of the phsor nd the horizontl xis increses from zero to mximum negtive (pek) vlue. As the phsor is rotting from 270 to 360, the verticl distnce between the tip of the phsor nd the horizontl xis decreses from the mximum negtive vlue to zero. One complete revolution of the phsor (i.e., 360 ) corresponds to one complete cycle of the sine wve. 6 Festo Didctic
3 Ex. 11 The Sine Wve Discussion Period Figure 15. Reltionship between rotting phsor nd sine wve. Festo Didctic
4 Ex. 11 The Sine Wve Discussion Period nd frequency of sinusoidl voltge or current The time required for one complete cycle of sine wve to occur is clled the period. The number of cycles tht occur in one second is clled the frequency of the sine wve. Frequency is mesured in hertz (Hz), 1 Hz being equl to 1 cycle per second. The eqution used for clculting the frequency is: (11) where is the frequency of the sine wve, expressed in hertz (Hz) or cycles per second (c/s). is the period of the sine wve, expressed in seconds (s). The period is the reciprocl of the frequency: (12) In 60 Hz c power system, the cycle of the sinusoidl voltge nd current repets itself 60 times per second. Therefore, the period of one cycle is 1/60 s 16.7 ms. In 50 Hz c power system, the cycle of the sinusoidl voltge nd current repets itself 50 times per second. Therefore, the period of one cycle is 1/50 s 20 ms. Amplitude nd instntneous vlue of sinusoidl voltge or current The eqution of sine wve is: (13) where is the instntneous vlue of the sine wve t given instnt. is the mplitude of the sine wve. is the ngulr position of the sine wve t given instnt, expressed in degrees ( ). is the ngulr velocity, expressed in rdins per second (rd/s) of the rotting phsor.. is the time, expressed in seconds (s). The mplitude is the mximum vlue reched by the sine wve during its cycle. The mximum vlue is the sme for both the positive nd negtive hlfwves of the cycle, except for the polrity which chnges from positive (+) to negtive ( ). 8 Festo Didctic
5 Ex. 11 The Sine Wve Discussion The generl eqution of sine wve cn be used to describe sinusoidl voltge mthemticlly: (14) where is the instntneous vlue of the voltge t given instnt of the cycle, expressed in volts (V). is the mplitude of the sinusoidl voltge, expressed in volts (V). For exmple, if the mplitude (mximum voltge) of the voltge is 100 V, the instntneous vlue of the voltge t ngulr position is: Figure 16 shows the voltge sine wve grph resulting from Eqution (14). + Voltge (V) Angulr position (û) Figure 16. Voltge sine wve. Similrly, the generl eqution of sine wve cn be used to describe sinusoidl current mthemticlly: (15) where is the instntneous vlue of the current t given instnt of the cycle, expressed in mperes (A). is the mplitude of the sinusoidl current, expressed in mperes (A). Festo Didctic
6 Ex. 11 The Sine Wve Discussion Effective or rootmensqure (rms) vlue nd heting cpcity The effective (rms) vlue of n c voltge is relted to the het produced by resistive element when supplied with this voltge. For exmple, consider n c voltge hving n mplitude pplied cross lod resistor. The pplied voltge cuses current to flow through the resistor, which hs the effect of incresing the resistor s temperture until it stbilizes to certin level (equilibrium temperture). The rms or effective vlue of this c voltge cn be found by pplying dc voltge cross the lod resistor, nd djusting the dc voltge until the resistor stbilizes to the equilibrium temperture previously reched with the c voltge. The vlue of this dc voltge corresponds to the rms or effective vlue of the c voltge. Effective (rms) vlue of sinusoidl voltge or current The effective (rms) vlue of sinusoidl voltge is clculted s follows: (16) Similrly, the effective (rms) vlue of sinusoidl current is clculted s follows: (17) For exmple, the effective (rms) vlue of sinusoidl voltge hving n mplitude of 100 V is 70.7 V ( V). This mens tht sinewve voltge hving n mplitude of 100 V hs the sme heting cpcity s dc voltge of 70.7 V. Figure 17 shows the rms vlue of voltge sine wve in comprison to its mplitude vlue. 10 Festo Didctic
7 Ex. 11 The Sine Wve Procedure Outline + Voltge (V) Time (s) Figure 17. Effective, or rootmensqure (rms), vlue of sinusoidl voltge. Stndrd instruments used to mesure c voltge nd current normlly indicte the effective (rms) vlue directly on their disply. The rms vlues of voltge nd current re used to clculte electricl power in c power circuits. The resoning behind rms vlues will be explined in more detil in Exercise 13. PROCEDURE OUTLINE The Procedure is divided into the following sections: Setup nd connections Mesuring voltge, current, nd frequency in n c circuit Reltionship between frequency nd period Mesuring voltge, current, nd frequency in series c circuit PROCEDURE High voltges re present in this lbortory exercise. Do not mke or modify ny bnn jck connections with the power on unless otherwise specified. Setup nd connections In this section, you will connect n c circuit contining resistor nd set up the equipment to mesure the circuit current nd voltge using the LVDACEMS softwre. You will lso determine the reltionship between the frequency of sine wve nd its period. 1. Refer to the Equipment Utiliztion Chrt in Appendix A to obtin the list of equipment required to perform this exercise. Instll the required equipment in the Worksttion. Festo Didctic
8 Ex. 11 The Sine Wve Procedure 2. Mke sure tht the min power switch on the FourQudrnt Dynmometer/ Power Supply is set to the O (off) position, then connect its Power Input to n c power outlet. Connect the Power Input of the Dt Acquisition nd Control Interfce to 24 V c power supply. Turn the 24 V c power supply on. 3. Connect the USB port of the Dt Acquisition nd Control Interfce to USB port of the host computer. Connect the USB port of the FourQudrnt Dynmometer/Power Supply to USB port of the host computer. 4. Turn the FourQudrnt Dynmometer/Power Supply on, then set the Operting Mode switch to Power Supply. This setting llows the Four Qudrnt Dynmometer/Power Supply to operte s power supply. 5. Turn the host computer on, then strt the LVDACEMS softwre. In the LVDACEMS StrtUp window, mke sure tht the Dt Acquisition nd Control Interfce nd the FourQudrnt Dynmometer/Power Supply re detected. Mke sure tht the ComputerBsed Instrumenttion function for the Dt Acquisition nd Control Interfce is vilble. Select the network voltge nd frequency tht correspond to the voltge nd frequency of your locl c power network, then click the OK button to close the LVDACEMS StrtUp window. 6. Set up the circuit shown in Figure 18. Note the symbol used to indicte vriblevoltge c source in this circuit. In order to obtin the resistnce vlue indicted next to the resistor in Figure 18, mke the necessry switch settings on the Resistive Lod. Throughout this mnul, keep in mind tht the resistnce vlues shown in the figures re equivlent resistnces. To obtin given resistnce vlue with the Resistive Lod, you my need to connect two or more resistors of resistor section in prllel s well s to interconnect resistor sections in prllel. Appendix C lists the switch settings to implement on the Resistive Lod in order to obtin vrious resistnce vlues. Use inputs I1 nd E1 of the Dt Acquisition nd Control Interfce to mesure the source current, nd the voltge cross the resistor. 12 Festo Didctic
9 Ex. 11 The Sine Wve Procedure 100 V 300 Figure 18. AC circuit contining resistor. 7. In LVDACEMS, open the FourQudrnt Dynmometer/Power Supply window, then mke the following settings: Set the Function prmeter to AC Power Source. This setting mkes the internl power source operte s n c power source (i.e., source producing sinusoidl voltge). Mke sure tht the Voltge Control prmeter is set to Knob. This llows the c power source to be controlled mnully. Set the No Lod Voltge prmeter to 100 V. This sets the nolod effective (rms) voltge of the c power source to 100 V. Set the Frequency prmeter to the frequency of your locl c power network. This mkes the frequency of the c power source equl to the frequency of your locl c power network. Leve the other prmeters set s they re. Notice tht the Sttus prmeter is set to Stopped. This indictes tht the c power source is disbled (i.e., it produces no output voltge). The c power source will be enbled in the next section of the procedure. Festo Didctic
10 Ex. 11 The Sine Wve Procedure Mesuring voltge, current, nd frequency in n c circuit In this section, you will mesure the rms vlues of the voltge nd current wveforms in the c circuit. You will then mesure the mplitude of these wveforms nd clculte the corresponding rms vlues. You will compre the mesured nd clculted rms vlues. Finlly, you will compre the shpes of the voltge nd current wveforms to confirm tht they rech their mximum nd null vlues t the sme time. 8. In the FourQudrnt Dynmometer/Power Supply window, enble the c power source (i.e., set the Sttus prmeter to Strted or click on the Strt/Stop button). The c power source now delivers power to the lod,. In this mnul, for brevity purposes, the rms vlue is implied in the denomintion of most prmeters tht re commonly mesured s rms vlues (e.g.,,,, men,, ). A complementry suffix, such s rms or mx, is dded only when extr clrity nd precision re necessry, such s in equtions, for exmple. 9. In LVDACEMS, open the Metering window. Set meters E1 nd I1 to mesure the rms vlues of the resistor voltge nd source current. When doing mesurements using either the Metering window, Oscilloscope, or Phsor Anlyzer, lwys select the continuous refresh mode. This enbles updted dt to be seen on screen t ll times. In the FourQudrnt Dynmometer/Power Supply window, redjust the vlue of the No Lod Voltge prmeter so tht the c power source voltge (indicted by meter E1 in the Metering window) is equl to 100 V. Record below the mesured vlues of the resistor voltge nd source current (meters E1 nd I1, respectively). Resistor voltge V Source current A 10. In LVDACEMS, open the Oscilloscope nd disply (input E1) nd (input I1) on chnnels 1 nd 2, respectively. If necessry, set the time bse to disply t lest two cycles of the sine wves. In the Oscilloscope settings, you cn enble the filtering option to improve the regulrity of the displyed wveforms. 14 Festo Didctic
11 Ex. 11 The Sine Wve Procedure 11. On the Oscilloscope, select the continuous refresh mode. Chnge the verticl scles so s to be ble to mesure the mplitude of the resistor voltge nd source current. Record the mesured vlues below. The rms vlue, verge vlue, nd frequency of the signls pplied to the input chnnels of the Oscilloscope re displyed below the Oscilloscope screen. To obtin n ccurte mesurement, you cn use the horizontl cursors of the Oscilloscope to mesure the mplitude of the voltge nd current. Resistor voltge V Source current A 12. Clculte the rms vlues of nd from the voltge nd current mplitudes mesured in the previous step. Resistor voltge V Source current A 13. Compre the rms vlues obtined in the previous step with the rms vlues indicted by the meters (s recorded in step 9). Are they pproximtely the sme? Yes No 14. Compre the source current wveform with the resistive lod voltge wveform. Are they both sine wves? Yes No 15. Wht is the instntneous vlue of the resistor voltge t the ngulr position 225û? Resistor voltge V 16. Do the wveforms of the resistor voltge nd source current rech the mximum positive vlue, null vlues, nd mximum negtive vlue t the sme time? Yes No When wveforms rech the mximum nd null vlues t the sme time, the wveforms re sid to be in phse, which mens there is no phse shift between them. This is covered in more detil in Exercise 12. Festo Didctic
12 Ex. 11 The Sine Wve Procedure Reltionship between frequency nd period In this section, you will determine the reltionship between the frequency nd the period of sine wve. You will do so by setting the frequency of the c power source to vrious vlues nd mesuring ech time the period of the voltge wveform. You will then clculte the frequency from ech mesured period nd compre it with the c power source frequency. 17. In the FourQudrnt Dynmometer/Power Supply window, set the Frequency prmeter to 40 Hz. This chnges the frequency of the c power source to 40 Hz. 18. Using the Oscilloscope, mesure the period of the wveform of the resistor voltge. Record the period vlue in the corresponding cell of Tble 11 below. To obtin n ccurte mesurement, use the verticl cursors of the Oscilloscope to mesure the time intervl between two points on wveform. Tble 11. Reltionship between the frequency nd period. Source frequency (Hz) Period (ms) Clculted source frequency (Hz) 19. Repet steps 17 nd 18 for ech c power source frequency indicted in Tble 11. Record your results in the corresponding cells. 20. Bsed on the mesured period vlues in Tble 11, clculte the resulting frequencies. Record your clculted source frequency vlues in the corresponding row of Tble Compre the c power source frequency vlues to your clculted source frequency vlues. Are they the sme? Yes No 22. Does this confirm the reltionship ( ) between the frequency nd period? Yes No 16 Festo Didctic
13 Ex. 11 The Sine Wve Procedure Mesuring voltge, current, nd frequency in series c circuit In this section, you will clculte the voltge nd current rms vlues in circuit contining two resistors in series. You will confirm tht Ohm s lw pplies to c power circuits by mesuring the voltge nd current rms vlues nd compring them with those you clculted. You will lso confirm Kirchhoff s lw by verifying tht. Finlly, you will verify tht both the current nd voltge wveforms re in phse with ech other. 23. In the FourQudrnt Dynmometer/Power Supply window, disble the c power source (i.e., set the Sttus prmeter to Stopped or click on the Strt/Stop button). 24. Set up the circuit shown in Figure 19. To obtin the resistor rrngement of Figure 19, mke the necessry connections nd switch settings on the Resistive Lod (refer to Appendix C if necessry). Use inputs I1, E1, E2, nd E3 of the Dt Acquisition nd Control Interfce to mesure the source current, voltge, voltge, nd source voltge respectively V 300 Figure 19. AC circuit contining two resistors connected in series. 25. Clculte the equivlent resistnce of the circuit resistors. Using Ohm s lw, you will then be ble to clculte the rms source current. Equivlent resistnce Source current A 26. Clculte the resistor voltges nd cross ech resistor by using the source current vlue obtined in the previous step. Resistor voltge = V Resistor voltge = V Festo Didctic
14 Ex. 11 The Sine Wve Procedure 27. In the FourQudrnt Dynmometer/Power Supply window, set the Frequency prmeter bck to the frequency of your locl c power network, then enble the c power source. In the FourQudrnt Dynmometer/Power Supply window, redjust the vlue of the No Lod Voltge prmeter so tht the c power source voltge (indicted by meter E3 in the Metering window) is equl to 100 V. 28. In the Metering window, set meter E2 to mesure the rms vlue of the resistor voltge. Record voltges nd nd the source current. Resistor voltge V Resistor voltge V Source current A 29. Compre voltges nd mesured in the previous step with the voltges clculted in step 26. Are they pproximtely the sme? Yes No Is the sum of the voltges cross the resistors ( equl to the source voltge? Yes No 30. Compre the source current mesured in step 28 with the source current clculted in step 25. Are they pproximtely the sme? Yes No 31. Clculte nd compre the rtio of the voltges mesured cross the resistors with the rtio of the resistor vlues. Are they pproximtely the sme? Yes No 32. From the results obtined in the previous steps, cn c circuits be solved by using the sme fundmentl rules s those used with dc circuits, which re Ohm s lw, Kirchhoff s voltge nd current lws, nd the formuls used to clculte the equivlent resistnce? Yes No 18 Festo Didctic
15 Ex. 11 The Sine Wve Conclusion 33. On the Oscilloscope, disply the voltge (input E1), voltge (input E2), nd source current (input I1) on chnnels 1, 2, nd 3, respectively. Mke sure the time bse is set so s to disply s lest two cycles of the sine wves. 34. Compre the wveforms displyed on the Oscilloscope. Do the source current wveform nd resistor voltge wveforms rech the mximum positive vlue, null vlues, nd mximum negtive vlue t the sme time, indicting tht they re in phse? Yes No 35. In the FourQudrnt Dynmometer/Power Supply window, disble the c power source. 36. Close LVDACEMS, then turn off ll the equipment. Disconnect ll leds nd return them to their storge loction. CONCLUSION In this exercise, you were introduced to the sine wve nd the wy to express sine wve using phsor rotting round the center of circle. You lerned how to clculte the different prmeters of sine wve, such s the period, the frequency, the mplitude, nd the instntneous vlue. You were introduced to the concept of rms vlue nd lerned how to clculte the rms vlue from the mplitude of sine wve. REVIEW QUESTIONS 1. A voltge sine wve hs n mplitude of 200 V. Clculte its rms vlue. 2. The period of sine wve is 0.02 s. Clculte its frequency. 3. Wht is the effect on the cycle of sine wve of incresing the frequency? Festo Didctic
16 Ex. 11 The Sine Wve Review Questions 4. Which ngulr position (in degrees s well s in rdins) on circle corresponds to the positive mximum vlue of voltge sine wve whose cycle begins t the origin? 5. Wht is the difference between the mplitude nd rms vlue of voltge sine wve? 20 Festo Didctic
The 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 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 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 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 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 informationJob Sheet 2. Variable Speed Drive Operation OBJECTIVE PROCEDURE. To install and operate a Variable Speed Drive.
Job Sheet 2 Vrible Speed Drive Opertion OBJECTIVE To instll nd operte Vrible Speed Drive. PROCEDURE Before proceeding with this job, complete the sfety check list in Appendix B. 1. On the Vrible Speed
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 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 information(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 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 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 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 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 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 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 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 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 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 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 informationNP10 DIGITAL MULTIMETER Functions and features of the multimeter:
NP10 DIGITL MULTIMETER. unctions nd fetures of the multimeter: 1000 V CT III tri requencies from 10.00...10 M. Diode mesurement nd continuity testing. HOLD mesurement. Reltive mesurement. Duty cycle (%)
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 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 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 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 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 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 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 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 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 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 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 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 informationCAL. NX15 DUODISPLAY QUARTZ
L. NX15 UOISPLY QURTZ l nlogue time disply l igitl time nd clendr l hronogrph l Tchymeter l t recll function l lrm l Illuminting light (Electroluminescent pnel) ENGLISH Illuminting light (TIME/LENR mode
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 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 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 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 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 informationSolving Simple AC Circuits Using Circuit Impedance Calculation
Exercise 41 Solving Simple AC Circuits Using Circuit Impedance Calculation EXERCISE OBJECTIVE When you have completed this exercise, you will be able to resolve simple parallel and series ac circuits
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 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 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 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 informationEnergy Harvesting TwoWay Channels With Decoding and Processing Costs
IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING, VOL., NO., MARCH 07 3 Energy Hrvesting TwoWy Chnnels With Decoding nd Processing Costs Ahmed Arf, Student Member, IEEE, Abdulrhmn Bknin, Student
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 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 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 informationProducts no longer available
echnicl dt sheet otry ctutor F2P(O) ultifunctionl rotry ctutor with emergency control for 2 nd 3 wy control bll vlve orque Nm Nominl voltge C/DC 2 V Control: odulting DC... V or vrible Position feedbck
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 informationUltra Low Cost ACCELEROMETER
Chip Scle Pckged Digitl Therml Orienttion Sensing Accelerometer MXC6226XC Document Version D Pge 1 of 13 Fetures Generl Description Fully Integrted Therml Accelerometer X/Y Axis, 8 bit, Accelertion A/D
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 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 informationUltra Low Cost ACCELEROMETER
Chip Scle Pckged Fully Integrted Therml Accelerometer MXC622xXC Rev,A 8/19/2011 Pge 1 of 13 Fetures Generl Description Fully Integrted Therml Accelerometer X/Y Axis, 8 bit, Accelertion A/D Output (± 2g)
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 informationSection 10.2 Graphing Polar Equations
Section 10.2 Grphing Polr Equtions OBJECTIVE 1: Sketching Equtions of the Form rcos, rsin, r cos r sin c nd Grphs of Polr Equtions of the Form rcos, rsin, r cos r sin c, nd where,, nd c re constnts. The
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 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 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 informationFuzzy Logic Controller for Three Phase PWM ACDC Converter
Journl of Electrotechnology, Electricl Engineering nd Mngement (2017) Vol. 1, Number 1 Clusius Scientific Press, Cnd Fuzzy Logic Controller for Three Phse PWM ACDC Converter Min Muhmmd Kml1,, Husn Ali2,b
More informationThe Discussion of this exercise covers the following points:
Exercise 1 Power Diode SinglePhase Rectifiers EXERCISE OBJECTIVE When you have completed this exercise, you will know what a diode is, and how it operates. You will be familiar with two types of circuits
More informationSafety Relay Unit. Main contacts Auxiliary contact Number of input channels Rated voltage Model Category. possible 24 VAC/VDC G9SA501.
Sfety Rely Unit The Series Offers Complete Lineup of Compct Units. Four kinds of mm wide Units re ville: A pole model, pole model, nd models with poles nd OFFdely poles, s well s Twohnd ler. Simple
More informationJUMO Wtrans B Programmable Head Transmitter with Radio Transmission
Dt Sheet 707060 Seite 1/10 JUMO Wtrns B Progrmmble Hed Trnsmitter with Rdio Trnsmission Brief description The Wtrns B hed trnsmitter with wireless dt trnsmission is used in connection with Wtrns receiver
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 informationThe Discussion of this exercise covers the following points: Phasor diagrams related to active and reactive power
Exercise 32 Apparent Power and the Power Triangle EXERCISE OBJECTIVE When you have completed this exercise, you will be familiar with phasor diagrams showing the active power, reactive power, and apparent
More informationSeries AE W PFC INDUSTRIAL POWER SUPPLY
FEATURES Progrmmle output voltge (0%~05%) Progrmmle output current (0%~05%) Universl AC input / Full rnge Constnt current limiting Optionl glol control vi RS3 Selectle +5V / 0.5A or +9V / 0.3A uxiliry
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 informationPulse Radar with FieldProgrammable Gate Array Range Compression for Real Time Displacement and Vibration Monitoring
sensors Article Pulse Rdr with FieldProgrmmble Gte Arry Rnge Compression for Rel Time Displcement nd Vibrtion Monitoring MihiLiviu Tudose 1, *, Andrei Anghel 1, Remus Ccovenu 1 nd Mihi Dtcu 1,2 1 Reserch
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 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 informationTranslate and Classify Conic Sections
TEKS 9.6 A.5.A, A.5.B, A.5.D, A.5.E Trnslte nd Clssif Conic Sections Before You grphed nd wrote equtions of conic sections. Now You will trnslte conic sections. Wh? So ou cn model motion, s in E. 49. Ke
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 informationARC DISCHARGE AND EROSION BEHAVIOR OF SILVER ELECTRIC CONTACTS BETWEEN STATIC GAP
ARC DISCHARGE AND EROSION BEHAVIOR OF SILVER ELECTRIC CONTACTS BETWEEN STATIC GAP Chung, HH. 1 Lee, RT. 2. Chiou, YC. 2 1 Deprtment of Automtion Engineering KoYun Institute of Technology 2 Deprtment
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 informationExercise 3. Phase Sequence EXERCISE OBJECTIVE DISCUSSION OUTLINE DISCUSSION. Phase sequence fundamentals
Exercise 3 Phase Sequence EXERCISE OBJECTIVE When you have completed this exercise, you will know what a phase sequence is and why it is important to know the phase sequence of a threephase power system.
More informationSpiral Tilings with Ccurves
Spirl Tilings with curves Using ombintorics to Augment Trdition hris K. Plmer 19 North Albny Avenue hicgo, Illinois, 0 chris@shdowfolds.com www.shdowfolds.com Abstrct Spirl tilings used by rtisns through
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 informationREVIEW, pages
REVIEW, pges 510 515 6.1 1. Point P(10, 4) is on the terminl rm of n ngle u in stndrd position. ) Determine the distnce of P from the origin. The distnce of P from the origin is r. r x 2 y 2 Substitute:
More informationModeling of Inverter Fed Five Phase Induction Motor using V/f Control Technique
Interntionl Journl of Current Engineering nd Technology EISSN 2277 4106, PISSN 2347 161 201INPRESSCO, All Rights Reserved Avilble t http://inpressco.com/ctegory/ijcet Reserch Article Modeling of Inverter
More informationDirect AC Generation from Solar Cell Arrays
Missouri University of Science nd Technology Scholrs' Mine UMRMEC Conference 1975 Direct AC Genertion from Solr Cell Arrys Fernndo L. Alvrdo Follow this nd dditionl works t: http://scholrsmine.mst.edu/umrmec
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 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 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 informationResolver Interface Card "OPCG1. RES" Product Specifications
Resolver Interfce Crd "OPCG1 G1RES RES" Product Specifictions Suzuk Fctory Design Dept. Dte Nme Approved Drwn 201141 Awi/Ueki Checked 201141 Y.Kto Y.Kto Drwing No. Fuji Electric Co., Ltd. SI275375
More informationFTU263. Ripple Control Receiver. Technical Data. Load Management Ripple Control
Lod Mngement Ripple Control Ripple Control Receiver FTU263 Technicl Dt The FTU263 comines the functionlity of ripple control receiver nd full clendr time switch. The FTU263 receiver is suited for opertion
More informationVector Calculus. 1 Line Integrals
Vector lculus 1 Line Integrls Mss problem. Find the mss M of very thin wire whose liner density function (the mss per unit length) is known. We model the wire by smooth curve between two points P nd Q
More informationPostprint. This is the accepted version of a paper presented at IEEE PES General Meeting.
http://www.divportl.org Postprint This is the ccepted version of pper presented t IEEE PES Generl Meeting. Cittion for the originl published pper: Mhmood, F., Hooshyr, H., Vnfretti, L. (217) Sensitivity
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 informationCS2204 DIGITAL LOGIC & STATE MACHINE DESIGN fall 2008
CS224 DIGITAL LOGIC & STATE MACHINE DESIGN fll 28 STAND ALONE XILINX PROJECT 2TO MULTIPLEXER. Gols : Lern how to develop stnd lone 2to multiplexer () Xilinx project during which the following re introduced
More informationUltima 11. Manufactured for: Pain Management Technologies. Instruction Guide
Ultim 11 Mnufctured for: Pin Mngement Technologies Instruction Guide PADS The pds tht re supplied with your Ultim 11 T.E.N.S. Unit re selfdhesive nd cn be used severl times. Skin must be llowed to brethe,
More informationElectrical data Nominal voltage AC/DC 24 V Nominal voltage frequency
echnicl dt sheet EVC24AMF Prmeterisle gloe vlve ctutor for 2wy nd 3wy gloe vlves Actuting force 2500 N Nominl voltge AC/DC 24 V Control modulting DC (0)2...10 V Vrile Nominl stroke 40 mm Actuting time
More informationMagnetic monopole field exposed by electrons
Mgnetic monopole field exposed y electrons A. Béché, R. Vn Boxem, G. Vn Tendeloo, nd J. Vereeck EMAT, University of Antwerp, Groenenorgerln 171, 22 Antwerp, Belgium Opticl xis Opticl xis Needle Smple Needle
More informationNevery electronic device, since all the semiconductor
Proceedings of Interntionl Joint Conference on Neurl Networks, Orlndo, Florid, USA, August 1217, 2007 A Selftuning for Reltime Voltge Regultion Weiming Li, XioHu Yu Abstrct In this reserch, selftuning
More informationRadar Altimeter TRANS / REC ( RADAR) APN117? Made by STC (UK) in 1966
dr ltimeter / ( ) 5826 99 954 2879 117? de by () in 1966 everse engineered 1 july 2014 ht is it his rdr trnsmitter/receiver is distnce meter or ltimeter, bsed on the principle. I don't hve n instrument
More informationPMSM Control Using a ThreePhase, SixStep 120 Modulation Inverter
Exercise 1 PMSM Control Using a ThreePhase, SixStep 120 Modulation Inverter EXERCISE OBJECTIVE When you have completed this exercise, you will be familiar with sixstep 120 modulation. You will know
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 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 informationINTRODUCTION TO TRIGONOMETRY AND ITS APPLICATIONS
CHAPTER 8 INTRODUCTION TO TRIGONOMETRY AND ITS APPLICATIONS (A) Min Concepts nd Results Trigonometric Rtios of the ngle A in tringle ABC right ngled t B re defined s: sine of A = sin A = side opposite
More informationElectrical data Nominal voltage AC/DC 24 V Nominal voltage frequency
echnicl dt sheet SR24AMF Prmeterisle rotry ctutor for ll vlves Nominl torque 20 Nm Nominl voltge AC/DC 24 V Control Modulting DC (0)2...10 V Vrile Position feedck DC 2...10 V Vrile echnicl dt Electricl
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 informationThis is a repository copy of Effect of power state on absorption cross section of personal computer components.
This is repository copy of Effect of power stte on bsorption cross section of personl computer components. White Rose Reserch Online URL for this pper: http://eprints.whiterose.c.uk/10547/ Version: Accepted
More information