MORGAN STATE UNIVERSITY DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING EEGR 203: INTRODUCTION TO ELECTRICAL LABORATORY Instructor: Dr. Gregory M. Wilkins Lab 4: Superposition Principle and Thevenin’s Theorem You will see this reminder in all of your labs. Please take notes and commit all you learn in each lab to memory You will need every bit of this information to complete your project !!! Introduction: The following is a statement of the principle of superposition: The value of any variable may be found as the sum of the values of that variable produced by each of the values of that variable produced by each of the excitation sources acting separately. Let’s try another: In any Linear circuit containing more than one independent source, any voltage (or current) in the circuit may be calculated as the algebraic sum of the individual voltages (or currents) caused by each independent source acting alone; i.e., with all other independent sources set at zero. Note that a voltage source is set to zero if it is replaced by a short circuit. (There is no voltage across a short regardless of the amount of current flowing, so the short continues to meet the definition of a voltage source, of a magnitude of 0.0 volts). A current source is set to zero if it is replaced by an open circuit. Recall that the definition of a current source is that it provides the same current regardless of the voltage across it. An open circuit provides zero current regardless of the voltage across it. The linearity aspect is important. In a previous lab we looked at a diode. There was a certain voltage across the diode when 10 mA was flowing through it. However, twice the voltage was not required to force 20 mA. The diode is a non-linear element, so superposition cannot be applied to a circuit containing a diode. A statement of Thevenin’s Theorem is offered: Any network consisting of (only) linear resistance and independent sources may be replaced at a given pair of nodes by an equivalent circuit consisting of a single voltage source and series resistor as illustrated in Figure 1. 1 The value of the resistor is the input resistance seen at the pair of nodes when all the independent sources are set to zero. The value of the voltage source is that seen at the open circuit terminals. Figure 1 - Thevenin Equivalent Figure 2 – Circuit for Principle of Superposition 2 Lab Procedure (Superposition): 1. Construct the circuit illustrated in Figure 2. Measure the value of resistors R1, (nominally 1.8 k), R2 (220 ) and R3 (220 ) and record in Table 1. Mount the resistors on your breadboards. The supply on the left of the Figure (10 V) is the large 6038 supply you used in previous labs. The supply on the right is either the same model or a 6236B Triple Supply. Note that the 6038 has the current limiting feature which you should use. The 6236 does not have this capability. To use the triple supply, adjust the +6 V Output to 4.5 V using the +6 V adjust control. Note that the meter switch must be in the +6 position. The voltage is available at terminals +6 and COM. Supply voltages should be set prior to connection to the circuit. 2. Measure and record the data as required in Table 1. Note that quantities V1, V2 and VR1, VR2 and VR3 are measured using the multimeter, Currents IR1, IR2 and IR3 are to be calculated using Ohms Law. Repeat this for each of the following conditions: a) Both sources on. b) With the 10 V (V1) source replaced with a short circuit and 4.5 V on. c) With the 10 V source on and the 4.5 V (V2) source replaced with a short circuit. 3. Using the values measured for R1, R2, R3, V1, and V2 calculate the theoretical values of VR1 VR2 VR3, IR1, IR2 and IR3- (This may be done outside the lab). 4. Using Table 1, briefly illustrate that the principle of superposition appears to be valid. Lab Procedure (Thevenin Equivalent): 5. Using your breadboard, set up the circuit illustrated in Figure 3. Note that the load resistor is variable; use the Heath decade boxes. Vary the value of the load resistor (Rload) from 0 to infinity, and record the voltage and current readings as indicated in Table 2. Note that one can easily take voltage and current measurements with a single multimeter. Figure 4 shows the same circuit except that the physical location of the ammeter has been relocated. Note that voltage is measured between the top and middle terminals, and current flowing in the bottom and out the middle. In the second representation the meter is configured as in a previous lab. By depressing the DC voltage, the voltage may be read and by depressing the DC current, current may be read, all without reconfiguring. 6. Plot the I-V characteristics of the circuit illustrated in Figure 3. Use the x-axis for current and the y-axis for voltage. Using the plot determine the Rthev and Vthev for the circuit of Figure 3. 3 Figure 3 – Original Network 7. Determine the Thevenin equivalent of the circuit illustrated in Figure 3. Build up such an equivalent circuit and repeat step 6. Note that the precise value of Rthev probably will not be a standard value. Try to come within 10  by connecting resistors in series. Figure 4 – Thevenin Equivalent Network Summary of Written Assignment: The written assignment is to include Table 1, Items 3 and 4, Table 2 and Items 6 and 7 (plus the extra credit). Please use this as your checklist to assure your write-up is complete. The report should also include difficulties which were encountered and a general discussion of the results. Pre-Lab: In part 3, you are asked to calculate some theoretical values based on measured values. Calculate those values based on theoretical values. 4 Table 1 Superposition Data Actual Measured Values: R1 = __________ R2 = __________ R3 = __________ V1 V2 VR1 VR2 VR3 IR1 IR2 IR3 PART A Theoretical Experiment 10.0 V 4.5 V PART B Theoretical Experiment 0.0 V 4.5 V 5 PARTC Theoretical Experiment 10.0 V 0.0 V Table 2 Thevenin Equivalent Data RLoad () 0 10 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 2000 2500 3500 4500 5000 Original Circuit ILoad VLoad (mA) (V) Thevenin Equivalent Circuit ILoad VLoad (mA) (V) 6 EEGR 203: Introduction to Electrical Laboratory Report Requirements for Lab 4 Superposition Principle and Thevenin’s Theorem Be sure to include ALL of the following information in your lab report. 1. Discuss the purpose of the lab, i.e. explain both principles listed in the title of this lab, namely the Superposition Principle and Thevenin’s Theorem 2. For the Superposition Principle, show all work which led to the theoretical values for each part, namely Part A (both sources V1 and V2 on), Part B (V1 off, V2 on), and Part C (V1 on, V2 off). Be sure to show that Superposition is upheld, making sure to adhere to the polarities and current directions indicated in class. Compare and discuss the theoretical values with the values obtained through measurement. 3. For Thevenin’s Theorem, plot the results from both the original circuit and the Thevenin equivalent circuit. Show the calculations which led to VTHEV and RTHEV. Indicate on the graphs the location and value where the graph crosses the horizontal axis, corresponding to VLOAD = 0 V (short circuit, RLOAD = 0 , and where the graph crosses the vertical axis, corresponding to ILOAD = 0 A (open circuit, RLOAD = ∞ . For the open circuit, the graph will need to be extrapolated to cross the vertical axis since the largest value of load resistance used is RLOAD = 5 kIndicate the equations of the lines plotted, which may be obtained directly by performing Kirchoff’s Voltage Law (KVL) on the Thevenin equivalent circuit. Scanned by CamScanner Scanned by CamScanner Morgan State University School of Engineering Department of Electrical and Computer Engineering Introduction to Electrical Laboratory EEGR 203.001 Dr. Gregory M. Wilkins Lab (Number): Lab Title Lab Partners: Date Submitted: Name 1: Student 1 Name 2: Student 2 Name 3: Student 3 Date (Signature) (Signature) (Signature) Introduction A brief outline of the overall purpose of the experiment including techniques being used and goals. Techniques used may be optional depending on the lab being performed. Theory This section should include information needed in order to derive the theoretical features of the experiment. All sources of information from which expressions and definitions are obtained are to be included here. If equations are used, be sure that they are numbered sequentially, beginning with Equation (1) Equipment List the model and make of equipment being used in the experiment, including the components used, such as resistors, capacitors, diodes, etc. Design Procedure If the experiment is one of a design nature (i.e., the experiment is developed by you), then this section should show the development of your circuit. The actual calculations used by you to determine the values used in your circuit must be shown. Experimental Procedure This describes all measurement techniques, the procedural steps and the test equipment used. The manufacturer’s name and the model number of each piece of test equipment should be given. This section should also include a schematic showing the circuit and how the test equipment is connected to the circuit. List ALL schematic diagrams for the circuits analyzed. Be sure to label the values of the components used and indicate the nodes at which measurements may have been made. Label schematics sequentially, beginning with the Figure 1 as listed in YOUR report. Be sure to provide a caption for the figure. For example, Figure 1: Series Resistive Network Results This section would include all theoretical and experimental data obtained by you. These can be shown in tabular form or in graph form. In either case it is necessary to clearly identify the various data obtained by you. If graphs are used the axis must be labeled showing the type of information (current, voltage, etc) as well as the units (milli amps, volts etc). If more than one plot is shown on a graph then each plot should be individually identified with captions. For example, Figure 1: Series Resistive Network OR Table 1: Voltages Measure at Node A Discussion Discuss your results in relation to how well it matched the theoretical results and any errors that may be determined by you. Conclusion Summarize your report. Briefly state what you set out to do, what you did and any conclusions that can be drawn from your results.
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