Lab 3 Thevenin Equiv

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University of Utah *

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2200

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Electrical Engineering

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Dec 6, 2023

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ECE 2200/2210 Lab 3: Thévenin Equivalent Circuits and Digital to Analog Converters Possible Points:100 Lab Equipment List:  Breadboard and wires  Resistors (560, 1k, 10k, and a few resistors of your choice)  Triple Output DC Power Supply  Digital Multimeter (DMM)  Wires with connectors on one end and alligator clips on the other  In addition, checking out a portable multimeter from the stockroom can be useful. Partnering:  Everyone must create their own lab report (fill out this document).  Everyone must build their own circuits, but you may use the same measurement equipment.  Discussions are encouraged, and you are also encouraged to answer each other’s questions!  Seek out the TA if you get stuck or need help. Lab Procedures: Welcome to Lab 3! This lab is designed to help you understand some of the circuit analysis techniques we’ve discussed in class in greater detail. Part 1: Thévenin and Norton Equivalent Circuits (53pts) Thévenin equivalent circuits are a very helpful tool for modeling complicated power supply systems in a more simple manner, simplifying circuit analysis, and generalizing system behavior. In this part of the lab, we will first be running some LTSpice simulations to measure the voltage and current across three different load resistors that are attached to a larger circuit. We will then use those results to determine the Thévenin and Norton equivalent circuits. Finally, we’ll then build the Thévenin equivalent circuit on a breadboard and take measurements using the same three load resistance values to see how well the physical Thévenin equivalent circuit compares to the simulation of the more complicated circuit. 1. LTSpice should already be installed on the CADE lab computers. As a result, it will be easiest to complete this section by first logging into one of the CADE lab computers. 2. Download the zip file of schematics from the Canvas page for the lab and unzip it . There should be three files in the same directory when you unzip it. 3. Open the provided Lab3_Equivelent.asc file in LTSpice (this is the easiest way to open the LTSpice program, rather than trying to find the program itself on the computer). This file contains a single load resistor as well as a block that represents the circuit for which we will find the Thévenin and Norton equivalent circuits. 1 UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu

ECE 2200/2210 4. For this step, you will be running the LTSpice simulation three times (one simulation for each different load resistor). Choose three resistors that you will test as loads to the circuit you just opened in LTSpice. These resistors should have values of 100 ohm, 1 Meg, and one more resistor with value in between. Also, since you’ll be testing these resistors later in measurements, make sure the resistors are values that exist in your lab kit. 5. After choosing your three resistor values, to prepare the simulation, begin by labeling the top node coming from the A port of X1. To do so, click on the “Label Net” tool from the toolbar (or press F4): In the empty field, write Va. Place the label so that the box below the letters intersects with the top node coming from A and going into R L . 6. Next, add the first resistor value. To do this, move your cursor over the R L ’s schematic symbol (not its label). Your cursor should turn into a pointing finger. Right click on the symbol and enter your first value for R L in the Resistance [ Ω ] field. Note that no units are required in LTSpice. However, do place the standard prefix, i.e. k for kilo- and Meg for mega-, after the number if needed. Don’t worry about Tolerance or Power Rating. 7. After adding your first value for R L , click the run button from the toolbar: A small window will appear providing the voltage and current values in the circuit. Record this information in the “Resistor 1” column of Table 1. Here you should include units. 8. Repeat for your other two resistor values and fill in the “Resistor 2” and “Resistor 3” columns of Table 1. Make sure one of the values is Thévenin resistance (2pts/unit = 16pts) R value Resistor 1 = __ Ω Resistor 2 = __ Ω Resistor 3 = __ Ω Open Circuit Load Short Circuit Load Voltage 0 V Current 0 A Table 1 9. Find what the voltage would be when no load resistor is present (for this, you can set R L = ∞ in LTSpice) For this, choose a significantly high value i.e. 5000Kohm. Record this value in Table 1 (i.e. fill in the missing value in the “Open Circuit Load” column). 10. Find what the current would be when the load is a short circuit (a wire, for this, you can set R L = 0 in LTSpice). Show your work below. Record this value in Table 1 (i.e. fill in the missing value in the “Short Circuit Load” column). (Caution, finding the short circuit current without knowing what the internals of a circuit are is generally a bad idea, but thankfully, we know that nothing will physically burn up in a simulation.) 2 UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu

ECE 2200/2210 11. Now that you have filled in Table 1, we will create a plot of the Table 1 voltages (y-axis) vs. the Table 1 resistances (x-axis) using MATLAB. Open MATLAB and create a new .m file. (The CADE lab computers have MATLAB installed.) 12. At the beginning of your .m file, paste and fill in the following (anything that comes after a % is a comment and is not read by MATLAB when running the program): % Fill in your name here % Date % Short description of what this code does clear; % good to clear all variables before starting close all ; % helpful to close old figures so we know % which plot is our new one 13. At the end of the MATLAB file you just created, add the following. Also fill in the resistances, voltages, and currents from Table 1: % Create an array that will hold your resistor values % separate the resistor values with a comma (e.g. [100, 200, 300]) resistance = [ ]; % ohms % Create an array that will hold your load voltage values voltage = [ ]; % Volts % Create an array that will hold your load current values current = [ ]; % mA 14. At the end of the same MATLAB file, let’s create the voltage plot. Paste in the following: % Plot the voltages vs. resistances yyaxis left ; plot(resistance, voltage, 'LineWidth' ,2); xlabel( 'Resistance (ohms)' , 'FontSize' ,14); % label the x-axis ylabel( 'Voltage (V)' , 'FontSize' , 14); % label the left-side y-axis 15. Try running your program. What do you see? If you’ve chosen load resistor values ranging from ~100 and ~1 Meg as requested, the results for the large resistor values probably dominate your plot (more than the results for the smaller resistor values). So, try instead to plot the (x-axis) resistor values on a log scale so you can see more of what is going on across all resistor values. Replace: plot(resistance, voltage, 'LineWidth' ,2); with: semilogx(resistance, voltage, 'LineWidth' ,2); 3 UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu

ECE 2200/2210 If you ever want to know what a MATLAB command is doing, you can type “help semilogx” (for example) at the command line. 16. Rerun your program and see how the plot changed. Hopefully you can see more of what is going on. 17. Now let’s add the currents to the plot. Paste in the following at the end of your .m file: % add this so the next plot will show up in the same figure hold on % Plot the currents vs. resistances yyaxis right ; semilogx(resistance, current, 'LineWidth' ,2); % label the right-side y-axis ylabel( 'Current (mA)' , 'FontSize' , 14); 18. And, we’ll add a title and a legend to the plot. Paste in the following at the end of your code: % add a title for your plot title( 'Load Voltage / Current vs Load Resistance' , 'FontSize' ,14); % add a legend legend( 'Voltage (V)' , 'Current (mA)' , 'FontSize' , 14); hold of 19. Run your program and see how the results look. Is this what you expect? 20. Lastly, let’s create a separate plot of the power dissipated by the load (as Fig. 2). Paste the following at the end of your .m file and run the program one last time. % Let's create a separate plot of the power dissipated by the load figure (2); % multiply the voltage * current to find the power % dissipated by the load % don't forget to convert the current to mA % first before multiplying! power = current.*0.001.*voltage; % plot the results semilogx(resistance,power, 'LineWidth' , 2) % add a title for your plot title( 'Power Dissipated by the Load' , 'FontSize' ,14); xlabel( 'Resistance (ohms)' , 'FontSize' ,14); ylabel( 'Power (W)' , 'FontSize' , 14); % label the right-side y-axis 21. Paste Fig. 1 below. (3pts) <put Fig. 1 from your MATLAB code here> 4 UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu

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