Lab Manual - Faculty of Engineering and Applied Science
Contents
1. For different values of resistances across terminals a b measure and record the voltage across and current through this resistor in Table 6 Use the circuit of Figure 2 Repeat 4 1 with the Th venin equivalent circuit Place the resistor that consumes the maximum power across terminal a b R5 calculated from the Prelab Measure and record the voltage and current in Table 6 Use the two different circuits as in 2 4 1 and 2 4 2 Calculate the load power for each load using your measurements and record them in Table 6 Plot the power consumed by the load resistor both circuits on the same graph as in prelab 15 Table 6 Maximum power transfer Figure 2 Measured load voltage Measured load current Load Power P W VV IL mA Load R Original Thevenin Original Th venin Original Th venin circuit circuit circuit circuit circuit circuit 100 Q 430 Q 2 2 KQ 3 0 KQ R Lab Report Session 2 2 2 1 2 2 2 2 3 1 2 4 Present all your results clearly All the completed tables must be included in the report Samples of all the calculations both for prelab and experiment must be shown clearly These should include relevant sample percent error calculations Compare the results obtained in Table 3 Does superposition hold for all the variables Comment on any error What are the principal sources of error in this experiment What are the challenges of using this2. curon cunsone vertical zero position CH1 MATH CH2 MENU MENU L MENU Number of volts per VOLTS DIV VOLTSIDIV vertical screen division D ey is set with this knob Figure 3 Main controls for the vertical amplifier the number of volts per division and the zero reference are set here 19 In order to display a signal as a function of time an internal time base generator also called a sweep generator is used to sweep the beam horizontally at a rate selected on the front panel This turns the horizontal axis of the display into a time axis MB HORIZONTAL B bp 9 Xo her sexo HORE MENU J X The number of seconds per Horizontal division is set i SET TO ZERO A SEC DIV me Dr Y o 0 74 Figure 4 Time base generator controls EXPERIMENTS On the breadboard there are is a power supply with connectors for positive and negative voltages and a common return In the available connectors this common return will be connected to an actual ground within the supply Although you cannot see it the oscilloscope and signal generator instruments also have one lead connected to this ground In this and future exercises be particularly careful when placing wires near any power contacts The power supplies and the signal generator can be easily destroyed by incorrect connections Leave the breadboard power off Use the following experiments and gain an understanding of the different f
3. Expression 20 LOG10 M v 2 MIv 1 Lance Hep Figure 2 Obtaining a decibel plot of the output input magnitude ratio in PSpice EXPERIMENT 1 Construct the circuit of Figure 1 Use the components based on the Prelab Adjust the input for 5 V peak or 10 V peak to peak sinusoidal For the source frequency varying from 10kHz to 60 kHz measure Vo and Vin for 20 different frequencies using Oscilloscope In particular carefully record the output voltages near the frequencies of interest 20 kHz and 50 kHz REPORT 1 Plot the frequency response of the circuit you have designed based on your measurements Use Excel or some other convenient software to obtain the plot Compare the experimental plot with that obtained using PSpice Discuss your results NOTE Prelab and Lab Report must be submitted at the end of the Lab Session 38
4. The name of the person must be attached to the top of each Prelab 4 Label the Prelab sections as they are in the online manual 5 Use only one side of the paper in answering the Prelab questions as well as in the experimental write up 6 Start the actual lab write up one per group after the last page of the Prelab See the write up requirements following the sample cover page in this document Put the words Lab Report at the top margin of the first page of the actual write up of the experiment 7 Label the lab report sections as they appear in the online manual 8 Staple the Cover Page individual Prelabs and a group Lab Write up in that order together in a single package 9 Graphs based on data collected in the lab may be produced manually or electronically for example using Microsoft Excel or any other convenient software 10 Submission of each lab package is required at the start of the subsequent lab Sample Cover Page Faculty of Engineering and Applied Science Memorial University of Newfoundland Engineering 3821 Lab 3821 X Title Title of Lab as it Appears in the Online Manual Names Name 1 and Student Number Name 2 and Student Number Date Date that experiment was done Lab Report Purpose Restate the purpose of the lab as found in the online manual feel free to use your own words Apparatus and Materials List in a column Be sure to give the make and model of the appar
5. branches of the circuit on the diagram submitted with your report b Determine the voltage across all the elements polarity is important c Check that your answers satisfy KCL at all nodes and KVL in all meshes d Show that the power delivered by the sources equals the power absorbed 2Q Ob Ground Figure 2 LAB SESSION The following instructions are meant to be supplemented by input from the lab teaching assistants Be sure to save all files in your directory Any of the following parts not completed during the lab period must be completed outside of lab hours Part 1 Carefully follow the step by step instructions in Chapter 1 of the PSpice manual ensuring all Libraries see Figure 5 page 4 have been added and produce the circuit in Figure 11 page 9 Use Place from top line of toolbar and then Net alias to specify node numbers specifying the node between the 12 V source and the Xkresistor as 1 and the node between the 3 K2 and 6 KQ resistors as 2 after you have drawn the circuit Once you have placed the ground which is essential to do as explained on pages 6 and 7 of the PSpice manual it is specified automatically as node 0 If you don t specify the other node numbers they are specified automatically with sometimes obscure grid numbers It is usually a little easier to refer to node numbers which are user specified Simulate the circuit and determine all the voltages and
6. current flowing in each branch of the circuit with the direction as indicated in Figure 1 Record these readings in Table 2 Table 2 Verification of Kirchhoff s Current Law KCL Figure 1 Variable Calculated values from Prelab 1 Measured values I mA I mA Is mA I mA Is mA Is mA I mA Is mA 11 Lab Report Session 1 Present all your results clearly All the completed tables must be included in the report All the calculations both for the prelab and the experiment must be shown clearly 1 1 Based on the values in Table 1 determine the sum of measured voltages with proper sign around the closed paths adga abga acda acba and bcdgb as in Figure 1 Verify that KVL is satisfied 1 2 Based on values in Table 2 determine the sum of measured currents with proper direction at nodes a b c and d of Figure 1 Verify that KCL is satisfied 13 Using the measured voltages and currents determine the power associated with each element Verify that the power delivered by the sources is equal to the power consumed by the resistors 1 4 Compare the prelab values with the measured values Show sample calculations of percentage errors for at least one current and voltage and discuss sources of error 1 5 State appropriate conclusions based on the prelab and experiment and be sure to indicate how the selection of the ground node influences the final r
7. currents Note the V I and W buttons on the toolbar which may be used to display voltages currents and power associated with various parts of the circuit Next place IPRINT VPRINT1 VPRINT2 in suitable places in the circuit of Figure 11 Refer to page 24 of the manual Be careful with the polarities they are incorrect in Figure 27 Once you highlight a device its polarity may be changed by right clicking and choosing a mirror horizontally feature etc if necessary Consider how the details in the output file View Output file relate to the node numbers IPRINT VPRINT etc Verify that the power output of the source equals the power consumed by the two resistors Part 2 Construct and solve the circuit of Figure 1 above using PSpice Be sure that you use the ground and VPRINT IPRINT parts where required here and elsewhere Part 3 Construct and solve the circuit of Figure 2 above using PSpice Part 4 Verify Example 1 page 18 of the PSpice manual that is use the PSpice software to repeat this example Part 5 Construct and simulate the circuit of Figure 27 on page 23 of the PSpice manual For source voltage varying from 0 volts to 100 volts in steps of 10 volts determine the power absorbed by the 40 ohm resistor Plot the variation of the power with the voltage on the x axis and the power on the y axis by appropriately using the Trace Add Trace menu option as explained in the manual REPORT Treat the P
8. method for a circuit containing many sources Discuss the results recorded in Table 4 and Table 5 and suggest possible applications Discuss possible applications of your discovery in Section 2 4 16 Exp 3821 3 The Oscilloscope and Function Generator PURPOSE To learn how to use an oscilloscope to observe and measure both DC and AC voltages To generate AC alternating current and DC direct current signals using a function generator To build and analyze a DC and AC voltage divider circuit To construct and examine an RC circuit To become familiar with some features of the oscilloscope EQUIPMENT e Tektronix Oscilloscope TDS 1000 e Function Generator FG 7002C e Multimeter Pre Lab Tasks Study and understand Sections 9 1 and 10 3 of Text Nilsson Riedel Draw two cycles of the voltage across a 60 Watts bulb at your home Show clearly the time in x axis and the magnitude in y axis Hint What is the maximum voltage Draw two cycles of the current through the 60 Watts bulb at your home Show clearly the time in x axis and the magnitude in y axis Draw two cycles of a square wave frequency 1 kHz and 10 kHz on a different plot Assume a 5 V amplitude Draw two cycles of a triangular wave Frequency 1 kHz and 10 kHz on a different plot Assume a 5 V amplitude Draw two cycles of a sinusoidal wave Frequency 1 kHz and 10 kHz on a different plot Assume a 5 V amplitude Draw two cycle
9. output of the function generator to Channel 1 of the oscilloscope Adjust the function generator and observe the following waveforms Make a rough sketch of the waveforms Refer to your pre lab tasks Two cycles of a square wave Frequency 1 kHz and 10 kHz 5 V amplitude Two cycles of a triangular wave Frequency 1 kHz and 10 kHz 5 V amplitude Two cycles of a sinusoidal wave Frequency 1 kHz and 10 kH2 5 V amplitude Two cycles of a sinusoidal wave Frequency 5 kHz 10 V amplitude and a DC offset of 3 Volts Adjust some control knobs on the function generator observe the waveforms and make a record of your understanding Can you relate the displays at the bottom of the screen to your signal Basic features of the oscilloscope required to complete this experiment Measure CH1 Menu Vertical Position Control Horizontal Position Control 5 buttons close to the screen these are very useful for measuring frequency amplitude etc You may have to use the Back option button 5 button frequently Trigger Menu Source CH1 FAMILIARIZATION WITH THE OSCILLOSCOPE Oscilloscope Probes The oscilloscopes used in this laboratory have been designed to measure node voltages Therefore one end of the oscilloscope probe long lead has to be connected to the ground terminal For the hot terminal of the probe always use a hook up wire to measure a voltage Do not attach the hot terminal directly to a circuit comp
10. 5 0 047 0 068 0 10 and 0 22 microfarads or whatever is available in the lab Make sure that the input voltage remains constant throughout the experiment adjust it if it does not why might the source voltage change Make R2 100 Q instead of 120 Q Why Hint Is the inductor ideal Using a DMM measure the current in the circuit Using the current measurements plot the power consumed by the load resistor R2 as a function of capacitance Comment on the results 31 REPORT Present all results including Prelab tasks clearly Show all calculations and comment on all significant results Phasor diagrams are important for this Lab Using your measurements as well as Prelab calculations verify that KVL is satisfied in the loop containing L1 C1 R2 and R3 Figure 3 Prove this using a phasor diagram Comment on any discrepancies between simulations or hand calculations and what were measured in the lab 32 Exp 3821 6 Frequency Response amp Resonance PURPOSE 1 To determine the frequency response of RC and RLC circuits 2 To study resonance is a series RLC circuit excited by a sinusoidal source INTRODUCTION The current and voltage responses in circuits containing inductors and capacitors besides resistors are frequency dependent because the impedances of the former elements vary with frequency Such circuits can be therefore used as frequency selective circuits or filters that is they respond to signals of
11. MEMORIAL UNIVERSITY OF NEWFOUNDLAND Faculty of Engineering and Applied Science Laboratory Manual for Eng 3821 Circuit Analysis 2013 Instructor E W Gill PREFACE The laboratory exercises in this manual have been designed to reinforce the concepts encountered in the course Eng 3821 Circuit Analysis They form a mandatory portion of the course and while they are valued at 10 of the overall mark unexcused missed labs will result in an incomplete grade for the course Official documentation such as a doctor s note in the case of illness is required in order to be excused from graded work Documented valid reasons for missing graded work including labs will permit the transfer of the relevant marks to either the midterm or the final examination as agreed to by the instructor and the student The specific objective of each experiment should be kept in mind throughout the laboratory session The conclusions based on the experiments and other observed phenomena must be clearly discussed in the laboratory report Before performing the experiments the students must be aware of the basic safety rules for minimizing any potential dangers Table of Contents Submission Format and Rules for Lab Reports ccssccsscesseees 2 Exp 3821 1 Circuit Analysis Using PSpicez csccsssscsssssccsssscesssscesees 6 Exp 3821 2 Circuit Analysis for Resistive Circuits ccsscscsssscssseeees 9 Exp 3821 3 The Oscil
12. NT Figure 3 Circuit for Part 2 of PreLab Prelab Part 3 Figure 4 may be considered as a circuit having a fixed load connected between terminals a and b but variable source impedance The load consists of resistor R2 and inductor L1 while the source impedance is changed by varying the capacitor values Determine the value of the capacitor for which maximum power is transferred to the load when the source voltage is 6 V peak and has a frequency of 15 kHz Determine the value of the capacitance C1 so that the overall power factor of the circuit is unity at the frequency of 15 kHz 30 1 1 2 1 R2 i AC 6 L1 2 2mH Figure 4 Circuit for Part 3 of Prelab EXPERIMENT Refer to your notes on the use of the oscilloscope The cursor feature Math Function CH1 CH2 etc will be useful for these experiments Build the circuit of Figure 3 and measure the following phasor voltages at 15 kHz with the oscilloscope Measure the phase relative to the input signal from the function generator If required seek help in making the phase measurements with the scope Compare the results of your measurement with prelab simulation and with the hand calculations Enter your experimental readings i the following table Prelab Calculation Prelab Pspice Mag 6 Angle 0 Mag 6 Angle 0 Mag 6 Angle 0 Build the circuit of Figure 4 Operate the circuit at a frequency of 15 kHz Use each of the following values for C 0 02
13. REPARATION section as a pre lab Each person in a group is required to submit the results from that section Parts 1 to 5 of the LAB SESSION are to be submitted as a single submission per group attached to the PREPARATIONS from each student of the group Exp 3821 2 Circuit Analysis for Resistive Circuits PURPOSE To understand and verify by experiment some of the basic techniques for the analysis of resistive circuits INTRODUCTION This laboratory will be covered in two sessions each of which must be submitted in the lab period one week after it is performed Review the course notes and relevant text sections covering 1 Kirchhoff s current law KCL which describes current relations at any node in a lumped network see page 6 of the text for the definition of a lumped parameter network or system 2 Kirchhoff s voltage law KVL which describes the voltage relation in any closed path in a lumped network 3 Node Voltage and Mesh Current methods of circuit analysis 4 The principle of superposition 5 Th venin s theorem 6 The maximum power transfer theorem which may be stated as maximum power is obtained at a given pair of terminals when the terminals are loaded by the Th venin resistance of the circuit SESSION 1 Node Voltage amp Mesh Current Methods PRELAB for Session 1 1 The circuit of Figure 1 contains two constant voltage sources Solve this circuit using node voltage method Determine the currents thro
14. ate the waveform so that the pulse width is half the period Use PSpice to determine the step response voltage across the resistor of the circuit Limit your transient response plot to one cycle of the source voltage Obtain the response for the following two RL combinations simply change R and repeat R 100 Q L 1 0 mH R 220 Q L 1 0 mH Le 1 2 V1 D Figure 2 RL circuit with square wave input 4 The circuit of Figure 3 is excited by a square wave voltage of 4 V as before but with a frequency of 500 Hz Using Pspice obtains the plot of the variation of the voltage across the capacitor Assume zero initial conditions Limit the response to two cycles only Do your simulations for the following two combinations R 1 5 Q L 2 2 mH C 0 1 uF R 68 Q L 2 2 mH C 0 1 pF C V Figure 3 RLC circuit with square wave input Find the frequency of the oscillations using the circuit parameters Also determine them from the plot Note that theoretically this frequency in radians second is given by fea z LC 2L 25 EXPERIMENT Note There may be minor differences in the components you use in the experiment and those you have used for prelab Preliminaries Setting up the Equipment Note Follow the steps in the experiment on the oscilloscope to take the required readings For example the cursor feature will be useful for voltage and time measurements Set the controls on the funct
15. atus if applicable For example 1 1 EZ Digital Co Ltd Multimeter Model DM 441B 2 1 GW INSTEK DC Power Supply Model GPS 3303 3 Standard Resistors 4 7 Q 18 Q 39 Q 4 X sets of leads with banana plugs and alligator clips 5 Various connecting wires Theory Give the equations used along with the meanings of their symbols For example Ohm s Law The voltage v current i and resistance R either for a circuit element or the whole circuit are related as v iR 1 and so on for example in Lab 2 you would also give the KVL KCL and power formulae Procedure In general you may simply say As per lab manual but note any modifications that you make that may have enhanced the basic procedure Label each part of the Experiment report according to the titles given in the manual Part Title of this part For example in Lab 2 you would have first Part 1 Node Voltage and Mesh Current The first sub heading should be Data Put the labelled circuit diagram if relevant at the beginning of this section Under this sub heading also put for example for lab 2 TABLE 1 Verification of Kirchhoff s Voltage Law KVL for Circuit of Figure 1 Carefully draw the table and fill it in with the measured or calculated values as required Also in the case where table entries require calculations provide sample calculations below the table That is if there are several calculations which have exactly the same for
16. ce which allows certain frequencies to pass through it while blocking or severely limiting others It is possible to design simple circuits using resistance inductance and capacitance which act as filters Here a study the frequency response of a particular RLC circuit configuration is examined PRELAB 1 Consider the circuit of Figure 1 The circuit capacitors C1 and C2 are to be chosen so that the circuit effectively transmits a 25 kHz signal and effectively blocks a 50 kHz signal e Calculate C2 The L1 and C2 parallel combination should be an open circuit at 50 kHz i e choose C2 so that the impedance of the parallel combination is infinite Calculate C1 Use the value of C2 determined above and minimize the overall impedance of the circuit at 25 kHz In PSpice simulate the circuit of Figure 1 using a sinusoidal source VSRC with AC 1 whose frequency varies from 10kHz to 60 kHz The simulation should be set up to do an AC sweep Obtain a decibel plot of IVo Vinl see Figure 2 Use the cursor features of PSpice to show the response of this circuit at the frequencies of interest 37 AC 1 Figure 1 Frequency Selective Circuit Add Traces r Simulation Output Variables m Functions or Macros Analog Operators and Functions 7 M Analog E Diaa I Voltages W Currents M Power E Nose v2 He M Alias Names Je Subeirenit Nodes 22 variables listed Full List Trace
17. different frequencies differently and can therefore be designed to pass certain frequencies to a load or other parts of the circuit and to attenuate others The study of the frequency response of a network involves the consideration of the magnitude and phase of the steady state voltages and currents as the frequency varies An integral part of such a study involves the concept of resonance a condition in which a circuit response can be maximized by adjusting either the circuit elements or the frequency of operation THEORY The resonant frequency wo of an RLC is given by 1 We The half power frequencies i e the frequencies at which the power associated with the output signal drops to one half of its maximum value for a series RLC circuit in this lab the output signal is a voltage signal taken across R are given by see diagram at end of this lab MO R R 1 2 2L 4 LC A R R 1 an 3 OC 2L 4 LC lt The half power bandwidth is given simply by BW 2 R L 0 4 33 PRELAB General Guidelines Draw schematics for the circuits indicated in Figures la and 2 Use source VSRC AC 1 Since vin 1 vo itself will give the desired response Some of the PSpice parameters are shown on the diagram Setup AC Sweep Linear and specify the frequency range as shown in Figure 1b Refer to the PSpice Supplement 1 Let the circuit of Figure la be excited by a si
18. e B 100K ye Power 10V P P AC Supply f 1KHz Probe Ground Figure 6 The AC voltage divider P P means positive peak to negative peak 150K 3 2 Repeat parts 2 2 to 2 4 for the above circuit 3 3 Use the multimeter to measure all these three voltages and compare your oscilloscope and meter readings Note The meters read rms root mean square see text values for a c signals 4 RC Circuit and Phasor Measurements 4 1 Build the RC circuit as shown below using R 100 KQ and C InF Probe A Probe B 100K F 10V P P AC a f 1KHz Ine o Probe Ground Figure 7 A simple RC Circuit 22 4 1 1 Display the source voltage and the voltage across the capacitor Note the phase of the capacitor voltage in degrees with respect to the source voltage Note the peak values of these voltages 4 1 2 Use the dual mode in your oscilloscope to get the voltage across the resistor using the suitable Math function of the oscilloscope Note the phase of the voltage in degrees across the resistor with respect to the source voltage Note the peak value of this voltage 4 1 3 Make a rough plot of these voltages 2 cycles show the quantities of interest It is necessary to use the Math function of the oscilloscope here Since this measurement can be challenging at first please get help from the TAs or Professor When you measure the phase difference note which signal is lagging or leading The analysis of t
19. eatures of the oscilloscope These will be useful whenever you use this oscilloscope It is suggested that you keep a Journal and record all the steps carefully You can use this Journal as a Users manual for this oscilloscope Basic Features Repeated Measure CH1 and CH2 Menu Vertical Position Control Horizontal Position Control 5 buttons close to the screen these are very useful to measure frequency amplitude etc You may have to use the Back option button 5 button frequently Trigger Menu Source CH1 or CH2 Measurements Some of the possible measurements that will be useful are Frequency period Mean Peak Peak RMS Minimum and Maximum 20 Cursors The cursors always appear in pairs and allow measurements to be taken by reading their values from the display readouts There are two types of cursors Voltage and Time To use cursors push the CURSOR button and set the source to the waveform on the display that you want to measure Voltage Cursors Voltage cursors appear as horizontal lines on the display and measure vertical parameters Time cursors Time cursors appear as vertical lines on the display and measure the horizontal parameters 1 DC voltage from the bread board 1 1 Connect the fixed 5 V supply to Channel 1 Measure this voltage using the oscilloscope and multimeter 1 2 Connect the variable positive supply to Channel 1 Adjust for 6 V and then for 16 V Measure these voltages usin
20. equencies of the circuit in Figure 3 Draw a phasor diagram i e for the voltage across all elements at the resonant frequency DMM 0 47 uF lOmh Vin 47Q Figure 3 Circuit for Part 3 of Prelab and Lab EXPERIMENT Refer to your notes on the Oscilloscope and use the relevant features for these experiments 1 1 Connect the circuit of Figure 1 Adjust the function generator to provide 3 V 6V peak peak supply For the source frequency varying from 60Hz to 20kHz measure Vo and vin for 12 different frequencies Use the oscilloscope or counter to measure the frequency accurately 2 1 Experimentally determine vo v as a function of frequency for the circuit of Figure 2 for values of R1 equal to 47Q Take more readings near the frequency of interest Use the DMM 3 1 For the circuit of Figure 3 apply a 3 V 6V peak peak sinusoidal source Vary the source frequency and experimentally determine the resonant frequency and half power frequencies Use the DMM to measure the current Carefully note the point of resonance and measure the magnitude and phase of all voltages source amp across all circuit elements at resonance using the oscilloscope For phasor measurements you may have to follow the procedures of Lab 5 Make sure that the source voltage is kept constant REPORT Plots Since the range of the x axis is large plot using a semi log graph 1 Draw the frequency response of the RC circuit using your measurements From you
21. ers For this course we will use OrCAD PSpice Demo 16 2 or 16 3 In the following exercises you will use PSpice to solve some simple circuits and to determine several quantities of interest PREPARATION There is no Official Pre lab to be completed and shown to the lab assistants prior to this Lab However some work as indicated immediately below should be done BEFORE the lab Read Chapters 1 2 and 3 of the manual Introduction to PSpice Using OrCAD by J W Nilsson and S A Riedel Make a directory in your M drive for all the PSpice files Complete the following two problems 1 Solve the circuit of Figure 1 below using the Mesh Current method a Determine the current magnitudes and indicate their directions for all branches of the circuit on the diagram submitted with your report b Determine the voltage across all the elements showing the correct polarities c Check that your answers satisfy KCL at all nodes and KVL in all meshes d Show that the power delivered by the sources equals the power absorbed 4Q 1Q VW VWV V 5 Q 3a 3 16Q 10Q V 12 V Ground Figure 1 2 Solve the circuit of Figure 2 below using the Node Voltage method Notice that two of the essential nodes are labelled a and b There are two other essential nodes Label the one at the top of the 12 V source c and the remaining one d where is it a Determine the current magnitudes and indicate their directions for all
22. es are exactly 20 V and 10 V after they are connected in the circuit using the DMM Measure the three currents in the circuit note the direction indicated in Figure 2 Record these reading in Table 3 Measure the voltage across each resistor in the circuit with the polarity as shown in Figure 2 Record these reading in Table 3 Turn off the power supply and remove V2 from the circuit Replace it with a short circuit Be careful not to short out the voltage source directly Why Repeat the measurement of 2 2 2 and 2 2 3 and record the result in Table 3 Turn off the power supply and return V gt to the circuit Remove V from the circuit and replace it with a short circuit Do not short out V directly Repeat the measurement of 2 2 2 and 2 2 3 and record the result in Table 3 Complete the calculation indicated in Table 3 column D 13 Table 3 Superposition in Linear Circuits Figure 2 A B C D Result by With both sources With V inactive With V inactive superposition B C Variable Measure Measure Measure Measure Prelab Prelab ment Prelab ment Prelab ment ment I mA I mA I mA Vri V Vr V Vrs V Vra V 2 3 Th venin Equivalent Connect the circuit shown in Figure 2 with both voltage sources Remove the R4 430 Q resistor from the circuit Switch on the power supply and ensure that the voltage sources are exactly 20 V and 10 V Measure
23. esults SESSION 2 Superposition Th venin Equivalent and Maximum Power Transfer PRELAB for Session 2 1 Solve the circuit of Figure 2 using the principle of superposition That is determine the currents through all the elements and voltages across all elements Record the answers in Table 3 2 Again consider the circuit of Figure 2 Determine the Th venin equivalent of the circuit with respect to the nodes a b with the resistor R4 removed Use this Th venin equivalent circuit to determine the current through the resistor R4 and the voltage across it Redraw the circuit using the Th venin equivalent Change Rg to 1 5 KQ and 2 2 KQ and calculate the current through the resistor R4 and the voltage across it using Th venin equivalent of the circuit Record the calculated values in Tables 4 and 5 3 Determine the value of a resistor R to be connected between nodes a and b Figure 2 without R4 so that it consumes the maximum power Determine the maximum power delivered to the resistor Ri 4 Consider that Ri varies from 100 Q to 3000 Q in steps of 10 ohms Plot a graph of power versus resistance i e resistor values on the x axis and power on the y axis 12 Figure 2 Circuit for Superposition Th venin Equivalent and Maximum Power Transfer LAB EXPERIMENT Session 2 2 2 Superposition 2 2 1 2 2 2 2 2 3 2 2 4 2 2 5 2 2 6 2 2 7 2 2 8 Construct the circuit of Figure 2 Ensure that the voltage sourc
24. g the oscilloscope and multimeter 1 3 Change the attenuation switch in the probe to 10X Measure 12 V Investigate the function of the probe option in the oscilloscope and note your observations 1 4 Connect the variable negative supply to Channel 1 Adjust for 6 V and then for 16 V Measure these voltages using the oscilloscope and multimeter 2 DC Voltage Divider 2 1 Build the simple circuit shown in Figure 5 and apply 10 V DC from the power supply to the circuit and then measure the amplitude of the signals at A and B with respect to ground VA is the source voltage and VB is the voltage across the 150 K resistor Probe A Probe B 100K s Power 10V DC Supply D Probe Ground 150K Figure 5 The DC voltage divider 2 2 Use the dual mode in your oscilloscope to display both signal A and B 2 3 Your oscilloscope has a math function by selecting it you can get VA VB and VA VB Measure the amplitude of this signal and verify that it is as expected 2 4 Calculate the ratio VB VA Does the answer match with what you expect based on your understanding of basic circuit concepts i e the voltage divider rule 21 3 AC Voltage Divider In the circuit of experiment 2 change the source voltage to AC sinusoidal voltage with frequency of 1 KHz and peak to peak amplitude of 10 V see Figure 6 3 1 Measure the amplitude of the signals at A and B with respect to ground Probe A Prob
25. hat obtained using PSpice Prelab and comment on the discrepancies 3 Compare the response of the RLC circuits obtained from the experiment with the PSpice simulation Discuss the differences between the types of response for the two circuits Compare the experimentally determined frequency of oscillation with the theoretical value 27 Exp 3821 5 Sinusoidal Steady State Response PURPOSE 1 To examine phasor analysis in PSpice 2 To determine the steady state response of RLC circuits using phasors 3 To study complex impedance matching and maximum power transfer for a general ac circuit INTRODUCTION The bulk of the electric power generated in power plants throughout the world and distributed to the consumers appears in the form of sinusoidal variation of voltage and current The analysis of many circuits and devices is accomplished by the techniques embodied in the sinusoidal theory The sinusoidal steady state response of circuits can be described using the concept of phasors Phasors may be represented in polar form as a magnitude and phase or equivalently in complex form i e the sum of real and imaginary parts PRELAB Here PSpice will be used to perform phasor analysis on ac circuits operating in steady state The first part of the Prelab is a tutorial that will provide a familiarization with some of the basic PSpice features necessary for such an analysis Refer to Chapter 10 of the PSpice supplement to understand Sin
26. his type of circuit will be discussed in the class 4 1 4 Measure the voltages VA and VB using multimeter and record the values 4 1 5 Verify if KVL is satisfied in the circuit based on the measured values Discuss your answer 4 2 Change the source frequency to 10 kHz 4 2 1 4 2 5 Repeat all the measurements of 4 1 1 to 4 1 5 Compare and discuss You may find this lab a little challenging but it should prove very useful in later experiments REPORT Submit a detailed record of all the procedures and results in this lab session References 1 FG 7002C Sweep Function Generator Operation Manual EZ Digital Co Ltd 2 TDS1000 and TDS2000 Series Digital Storage Oscilloscope User Manual Tektronix Inc 23 Exp 3821 4 Step Response of RL RC and RLC Circuits PURPOSE 1 To study the response of RC RL and RLC circuits when energized by an independent voltage source INTRODUCTION Many phenomena that occur in electric circuits involve or produce time dependent variables When a RC RL or RLC circuit is suddenly energized or de energized a transient phenomenon occurs which dies out as the circuit approaches the steady state operation occurs This is because of the way in which inductors and capacitors store energy and resistors dissipate the energy The nature of the transients depends on the values of R L and C as well as on how they are combined in a circuit The steady state response of the circuit which is determined b
27. hy is this the case in the experiment when it wasn t the case in PSpice Determine the time constant of the circuit Carry out the experiment for the two combinations of R and Las in the prelab Be sure that the function generator provides a 4 V peak square wave with all elements connected 3 1 Construct the circuit of Figure 3 Adjust the function generator to provide a 4 V peak 500 Hz symmetrical square wave after connecting all the elements Note that the use of this signal enables you to simulate the effect of repeatedly energizing the RLC circuit andthe waveform in the oscilloscope may be considered similar to the step response of this circuit Sketch to scale one half of the input square wave and the voltage across the capacitor Complete the 26 experiment for the two combinations of the circuit elements as in prelab For the response which is more oscillatory try to estimate the frequency of oscillation REPORT 1 Based on your experiments with the two RC circuits discuss the effect of changing R and C on the nature of the response and final value of the capacitor voltage Compare the experimental plot with that obtained using PSpice PreLab and comment on the discrepancies 2 For the experiment with the RL circuits discuss the effect of changing R and L on the nature of the response final value of the resistor voltage and final value of the current in the circuit Compare the experimentally determined time constant with t
28. ion generator to output a square wave with an amplitude of 4 V and a frequency of 100 Hz Connect the output of the function generator to channel 1 of the scope Use the time base and amplitude controls to adjust the scope display Likewise the vertical and horizontal positioning may be adjusted to move the curve Be sure to check the ground level of the scope to make sure amplitude measurements are accurate 1 1 Construct the circuit of Figure 1 Adjust the function generator to provide a 4 V peak 100 Hz symmetrical square wave Note that the use of this signal enables you to simulate the effect of repeatedly energizing the RC circuit and the waveform in the oscilloscope may be considered similar to the step response of this circuit Sketch to scale the first half of the input square wave and voltage across the capacitor Determine the time constant of the circuit by observing the waveform Repeat the measurement for the second half of the input signal Do your experiment for the following two combinations R 3 3kQ C O0 1pF R 3 3 KQ C 0 22 uF Make sure that the function generator provides a 4 V peak 100 Hz symmetrical square wave with all elements connected 2 1 Construct the circuit of Figure 2 Adjust the function generator to provide a 4 V peak 5 kHz symmetrical square wave Sketch to scale the first half of the input square wave and the voltage across the resistor You may have trouble getting the wave to look exactly square w
29. loscope and Function Generator ssscscseeeeee 17 Exp 3821 4 Step Response of RL RC and RLC Circuits cssscsesesees 24 Exp 3821 5 Sinusoidal Steady State Respomse csscccsssccssssccsssscsseeees 28 Exp 3821 6 Frequency Response and Resonance cccccccssssssscesssees 33 Exp 3821 7 Design of a Simple Filter ccscscsssscssscsscsesseeseeessesenees 37 REFERENCES 1 Electric Circuits 9 Ed W Nilsson S A Riedel Pearson Education Inc 2011 Introduction to PSpice Using OrCAD J W Nilsson S A Riedel Pearson Education Inc 2011 3 Introduction to Electrical Engineering Laboratories E B Slutsky D W Messaros Prentice Hall 1992 4 Fundamentals of Electric Circuits 4 th Ed C K Alexander M N O Sadiku McGraw Hill 2009 Acknowledgements Dr B Jeyasurya Dr J E Quaicoe Mr R Hadidi Ms Eilnaz Pashapour Submission Format and Rules for Lab Reports General 1 Use a cover page as shown following these general instructions 2 Start the Prelab immediately after the cover page EACH PERSON in the group must submit a Prelab Unless otherwise directed by the instructor in order to obtain full marks for a lab report the Prelabs for all but the first experiment must be shown to the lab Teaching Assistant before the lab starts unless otherwise indicated by the instructor for other specific labs Failure to do so will result in a maximum grade of 7 10 for that lab 3
30. m provide a single sample The other calculations will of course be completed and entered into the table but there is no need to show many calculations which are identical in form The next heading should be as required Questions Discussion and Conclusion s Label these as suited Repeat the above format for subsequent parts of the experiment This general approach should be taken in all lab write ups It may vary slightly depending on the requirements Exp 3821 1 Circuit Analysis Using PSpice PURPOSE 1 To learn the basic features of PSpice De To use PSpice in studying Basic DC Analysis Circuit Analysis involving Dependent Sources Parameter interdependencies using Sweep Analysis INTRODUCTION The rapid change in the field of electrical engineering is paralleled by programs that use the computer s increased capabilities in the solution of both traditional and novel problems With the availability of tools for computer aided circuit analysis circuits of great complexity can be designed and analyzed within a shorter time and with less effort compared to the traditional methods SPICE is a computer aided simulation program that enables the design and simulation of circuits SPICE is the acronym for a Simulation Program with Integrated Circuit Emphasis It was developed at the University of California and made available to the public in 1975 OrCAD PSpice A D from Cadence is a popular implementation for personal comput
31. nusoidal source whose frequency varies from 10Hz to 40 kHz Use PSpice to obtain a plot of Vo Vinl versus frequency In Probe set the x axis setting of the plot to log scale R1 Figure 1a RC Circuit Simulation Settings lab403 x General Analysis Include Files Libraries Stimulus Options Data Collection Probe window Analysis type AC Sweep Type A Noise Linear Start Frequency fro Options Logarithmic End Frequency faoo00 Total Points 200 General Settings Monte Carlo Worst Case Parametric Sweep Noise Analysis Temperature Sweep Save Bias Point I Enabled Gibtpot y clteae Load Bias Point Vif Source Interval m Output File Options I Include detailed bias point information for nonlinear controlled sources and semiconductors OP Figure 1b PSpice simulation profile for frequency sweeping 2 Consider the circuit of Figure 2 Let the circuit be excited by a sinusoidal source whose frequency can be varied from 100 Hz to 100 KHz Use PSpice to obtain a plot of Vo Vin versus frequency for two different values of R1 472 and 220 Q Obtain the two required plots on the same graph by creating two circuits in the same Schematics file In Probe set the x axis setting of the plot to log scale Li C1 1 2 0 47u 01 t Figure 2 RLC Series Circuit 34 3 Calculate the resonant frequency and half power fr
32. onent and never take the plastic sleeve off the probe See ground terminal plastic sleeve hot terminal N hook up wire to common ground rail Figure 1 The Oscilloscope probe 18 How the Oscilloscope Works Most of the oscilloscope screens are similar to a television screen see Figure 2 The inside is coated with phosphor which glows when struck by an electron beam But the scope we use in this lab is digital and uses an LCD instead A signal to be viewed is put into an amplifier which deflects moves the beam position vertically up and down The deflection can be time varying AC signal or constant DC signal Signals displayed on the screen can be measured numerically by counting grid divisions printed on the screen and multiplying by the amplifier settings on the control knobs i Bah echt ted prepet Horizontal grid lines one division apart Each Major division has 5 subdivisions CHI J aN lt 10 Figure 2 The oscilloscope dis divisions play there are 10 horizontal divisions and 8 vertical Familiarize yourself with the different functions of the 5 buttons close to the screen these are very useful for measuring frequency amplitude etc You may have to use the Back option button 5 button frequently The vertical and horizontal controls are briefly discussed below see Figures 3 and 4 VERTICAL TT POSITION POSITION SED SED Vv z This knob adjusts the
33. r plot determine the half power frequency and compare it with the theoretical value Compare the experimental plot with that obtained using PSpice Suggest a possible application of this circuit 2 Draw the frequency response for the series RLC circuit Compare this plot with the plot obtained by the PSpice simulation Discuss the influence of the value of the 35 resistance in the frequency response of the circuit Suggest an application for this circuit 3 Compare the resonant frequency and bandwidth of the circuit based on your experiment with that of the Prelab Compare the calculated and measured voltage phasors at resonance Discuss the nature of the circuit at resonance using a suitable phasor diagram based on your experiment 4 Discuss your understanding of the frequency response of the different circuits you have used in this laboratory session Resonance Curve For RLC Series Circuit Current i A l I I I I I I 1 l I l I l l I I I I I I I 1 i l Paul s ph o frale a nal w w 0 w Angular Frequency w rad s 36 Exp 3821 7 Design of a Simple Filter PURPOSE de To design a filter to pass a signal at a desired frequency and reject the signal at another frequency 2 To simulate this circuit in PSpice and study its frequency response 3 To experimentally verify the performance of the filter INTRODUCTION A filter is a frequency selective devi
34. s of a sinusoidal wave Frequency 5 kHz Assume a 10 V amplitude and a DC offset of 3 Volts OVERVIEW In this experiment students are introduced to both the oscilloscope scope and function generator The function generator creates a varying voltage source with different frequencies The oscilloscope will be used to measure both the AC and DC components of a waveform The oscilloscope is a voltage measuring device The oscilloscope can be used to measure the amplitude of any waveform as well as the frequency and period of a periodic waveform Before the actual experiment takes place there are few familiarization exercises to be conducted 17 FAMILIARIZATION WITH THE FUNCTION GENERATOR The function generator is capable of generating a wide variety of waveforms For this session our focus will be on sine waves square waves and triangle waves Examine the front panel and record the features different tasks that are possible of the frequency range selector the function switches the frequency dial the DC offset controls and the amplitude control Locate the main power switch for the device The best way to understand the features of the function generator is to observe the waveforms using the oscilloscope at this point note Figure 1 and related text You will do more experiments using the oscilloscope in the second section For the present we will use the oscilloscope to observe some signals from the function generator Connect the
35. s very important to use the correct value of resistance verify using the color code and the DMM For safety of the equipment and for personal safety follow the order of connecting and adjusting all devices and parts as specified Also be aware that resistors heat up over time and can be overly warm to touch Care should be taken in this regard 1 1 Construct the circuit in Figure 1 on the breadboard provided Turn on the power supply and use the DMM to measure the source voltages Within the limitations of the control knobs ensure that the voltage sources are fixed at 20 V and 25 V after they are connected to the circuit by adjusting the power supply if necessary 10 1 2 It is important to use the correct range of the DMM for the various measurements Measure the voltage across each resistor in the circuit with the polarity as indicated in Figure 1 Record these readings in Table 1 Table 1 Verification of Kirchhoff s Voltage Law KVL Figure 1 Variable Calculated values from Prelab 1 Measured values Vri V Vr V Vrs V Vra V Vrs V Vre V Vrz V Vrs V 1 3 1 4 When you use the DMM as an ammeter you have to disconnect some part of your circuit and connect the DMM in series with the element whose current you want to measure Do this carefully Before you make the connections make sure that that the power supply is turned off Measure the
36. the voltage across the open circuit terminals a b This is the Th venin equivalent voltage Record this value 2 3 1 2 3 2 in Table 4 Remove sources V and V2 and replace each source with a short circuit Measure the resistance across the open circuit terminals a b using a DMM This is the Th venin equivalent resistance Record this value in Table 4 Table 4 Th venin equivalent circuit Figure 2 Variable Calculated from Prelab Measured Th venin voltage Vin V Th venin resistance Ra Q 2 3 3 Reconnect the power supply and the 430 Q resistor R4 Measure the voltage across R4 Record the values in Table 5 14 2 3 4 Repeat step 2 3 3 for R4 resistances of 1 5 kQ and 2 2 KQ 2 3 5 Construct the Th venin equivalent circuit Adjust the source to the value of Vin determined in step 2 3 1 Use available resistors to form Rn by connecting them in series Try to get the resistor as close to the as possible to Rj Connect the 430 Q resistor to the Th venin equivalent circuit and measure the voltage across it Record the values in Table 5 2 3 6 Repeat step 3 5 for R4 resistances of 1 5kQ and 2 2 KQ Table 5 Resistor Ry voltages Figure 2 Resistor Voltage measured Voltage calculated Voltage masured in R3 in original circuit in Thevenin circuit Thevenin circuit 4300 1 5 KQ 2 2 KQ 2 4 Maximum Power Transfer 2 4 1 2 4 2 2 4 3 2 4 4 2 4 5
37. ugh all the elements and voltages across all elements Note carefully the direction of all currents and the polarity of all voltages Verify that the total power developed equals the total power absorbed Use Table 1 and Table 2 to record all your answers 2 Repeat a using the mesh current method 3 Solve the circuit of Figure 1 using PSpice Use part VPRINT1 and IPRINT Page 24 of PSpice supplement suitably From the output file make a record of the required voltages and currents Be care with polarities 4 Repeat the PSpice simulation by considering the node a in the Figure as the ground Using the output file make a record of the required voltages and currents Figure 1 Circuit for Node Voltage amp Mesh Current Methods LAB EXPERIMENT Session 1 Before you start The various functions of the Digital Multi Meter DMM and the power supply should be understood Familiarization with the different ranges for measurement purpose of the different control knobs selector switches etc is necessary Consult the Lab Technologists or TAs for help as required Note that the power supply has two variable and one fixed voltage output The variable voltage outputs will be used for the experiments It is a good practice to connect the ground of the power supply to the ground of your circuit You should be familiar with the color codes for the resistor Refer to the ENGI 1040 Lab Manual or any convenient source It i
38. ure 2 Screens for Part 1 of Prelab a Setting the PRINT 1 ANALYSIS field b Simulation Profile 29 From the PSpice gt New Simulation Profile choose AC Sweep and set the AC Sweep Type to Linear the Start Frequency and End Frequency to 15000 and the Total Points to 1 as shown in Figure 2 b The PRINT devices put their output in the file which may be viewed from the PSpice gt View Output File menu option In the above circuit the PRINT 1 has been used to establish voltage magnitude and phase It could also be used to find currents For example setting ANALYSIS value of Figure 2 a to ac I R_R1 Ip R_R1 would give the magnitude and phase of the current through resistor R1 To determine the voltage across a device using the PRINT1 values in the Output File the individual voltage on either node of the device must be subtracted For example the voltage across the inductor in Figure 1 is V2 V3 These voltages are phasors Convert the three voltages in the output file to complex numbers and show that Kirchhoff s voltage law holds for the circuit Prelab Part 2 Solve the circuit of Figure 3 and determine the phasor voltages V1 V20 V23 V30 V24 and V4o Use the source voltage as the reference phasor The ac voltage source is 6 V peak Use PSpice to verify your answers This is just the previous circuit with another branch added Note the node numbers Ignore the terminal numbers 2 1 for L1 of the inductor IPRI
39. usoidal Steady State Analysis in PSpice Prelab Part 1 In PSpice construct the circuit shown in Figure 1 The necessary steps are outlined below and some of the important screens that will be encountered are shown in Figure 2 e In the analog library parts list choose the resistors and inductor as required e From the SOURCE library choose VSRC and set the ac value to 6 The Tran and de values may be ignored or deleted e Install the ground as usual e From the SPECIAL library choose and install the PRINT1 parts at nodes 1 2 and 3 these nodes should be labelled using the Place gt Net Alias feature Double click on each of these parts and for node 1 set the ANALYSIS field to ac v 1 vp 1 where the three arguments together indicate that PSpice will return the magnitude and phase of the ac voltage of that node relative to ground See Figure 2a Repeat these labels for the PRINT1 devices at nodes 2 and 3 28 AC 6 Figure 1 Circuit for Part 1 of Prelab Orcad Capture Lite Edition Property Editor ilele a Hee oe A SSA HEAT nenamerne alalle AeA v Nen Coun _Aooy Ben ete Pen tee H SCHEMATIC1 PAGE1 PRINT1 ac 1 vpli Default PRINT1 Normal i i Indicate Magnitude Y and Phase Y in this screen a Simulation Settings acfirst General Settings _ Monte Carlo v orst Case ClParametric Sweep CIT emperature Sweep ClSave Bias Point _j Load Bias Point b Fig
40. y the external source is reached only after a transient time interval As discussed in the class the response of RLC circuits may be classified as under damped critically damped or over damped PRELAB 1 Refer to Chapter 6 and 7 of the PSpice supplement This will be useful for your prelab study 2 The circuit of Figure 1 is excited by a square wave voltage of 4 V peak or zero to peak having a frequency of 100 Hz In PSpice use VPULSE to create this voltage waveform by setting V1 to 0 and V2 to 4 For additional information on pulse waveform refer to page 100 and 101 of PSpice supplement Use a pulse width of 5 ms What is the pulse period here Use PSpice to determine the transient response voltage across the capacitor of the circuit Limit your transient response plot to one cycle of the source voltage This may be done by setting the Run to time parameter in the Edit Simulation window to be of the same length as the period of the VPULSE Obtain the response for the following two RC combinations R 3 3 KQ C 0 1 UF R 3 3 KQ C 0 22 uF Calculate the time constants using the circuit parameters Also determine them from the plots Remember the response changes by a factor of 1 e during one time constant R Vi 0 5 10 t ms Figure 1 RC circuit with square wave input 24 3 The circuit of Figure 2 is excited by a square wave voltage of 4 V zero to peak as before but now with a frequency of 5 kHz Again cre
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