22c+314+Lab+3

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2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3: Maximal power transfer © 2022 Alexander Ganago Page 1 of 21 Last printed 9/18/22 5:47:00 PM File: 22c 314 Lab 3 0918.docx EECS 314: Labs in your backpack and in the lab room Lab 3: Maximal transfer of power from the source to the load resistor Electric power is one of the main reasons why we study electrical engineering. We need to know how to transfer electric power from the source to its load, and how to optimize this transfer. Lab 3 includes two tasks: 1. Verify whether Thevenin theorem, which greatly simplifies the calculations of power transfer, applies to the circuit with 4 resistors, with which we are familiar from Lab 2. 2. Verify whether the Volt-Amp characteristics of HP E3631A power supply allow us to calculate and optimize the transfer of its power to individual load resistors. The first task is closely related to our theoretical study of Thevenin theorem in HW p5, which is focused on the same circuit. The optimal learning combines theory and hands-on practice: o While you are doing the theoretical calculations in HW p5, keep at hand your portable instruments AD2 and DMM, and your circuit built on the solderless prototyping board. o When you have completed a step in calculations (for instance, found the Thevenin equivalent voltage or the Thevenin equivalent resistance), do the measurements of the same, and compare the result of your theoretical calculations with your data. o Do not expect a perfect agreement between the calculated and the measured values, because the actual resistances differ from their nominal values. At the same time, any difference beyond 10% indicates an error either in the circuit building or in the calculations. This is an effective exercise in critical thinking, which prepares you for the practice of real good engineering in any field. o This file is written to help you organize your study in this optimal way. Another helpful tool is the Rubrics file for your Lab report For the second aspect – the study of maximal power, which can be transferred from a power supply to its load resistors, in the Pre-Lab you will do only calculations, which prepare you for the In-Lab measurements with industry-grade instruments. Table of contents Page The necessary background Application of Thevenin theorem to the circuit with 4 fixed resistors 2 The maximal power, which can be transferred from HP E3631A power supply to individual load resistors 4 Pre-Lab Application of Thevenin theorem to the circuit with 4 fixed resistors 8 The maximal power, which can be transferred from HP E3631A power supply to individual load resistors 11 In-Lab Application of Thevenin theorem to the circuit with a variable load resistor 13 The maximal power, which can be transferred from HP E3631A power supply to individual load resistors 16

2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3: Maximal power transfer © 2022 Alexander Ganago Page 2 of 21 Last printed 9/18/22 5:47:00 PM File: 22c 314 Lab 3 0918.docx The necessary background, and an overview of Lab 3 experiments 1. Application of Thevenin theorem to the circuit with 4 resistors, with which we are familiar from Lab 2 The circuit, which we studied in Lab 2 and HW p3, is repeated in panel a of Lab 3 Figure 1. The same circuit is redrawn in panel b to show that resistor R4 can be considered as the load, to which the electric power is transferred from the rest of the circuit (source Vs and resistors R1, R2, and R3) to the left of the terminals a, b . Then, according to Thevenin theorem, the circuit to the left of the terminals a, b (see panel b) can be mentally replaced with its Thevenin equivalent circuit (panel c), which includes only one resistor ! ! in series with one voltage source " ! . The circuit of Lab 2 includes one voltage source and 4 resistors. (a) The circuit of Lab 2 can be redrawn in the following way: Here, # " is the load resistor # # , which can be varied. (b) (c) Lab 3 Figure 1. The same circuit, which we studied in Lab 2 (panel a), can be presented in a different way (panel b); this idea leads us to the replacement of the original circuit with its Thevenin equivalent circuit (panel c). This replacement greatly simplifies the calculations of o the voltage " $ applied to the load resistor ! $ = ! % ; o the current % $ through this resistor, and o the power & $ absorbed by the load resistor ! $ = ! % . The diagrams in panels a and b of Lab 3 Figure 1 do not look the same. How do we know whether they represent the same circuit? To answer this question, analyze every connection of each circuit, and find out whether they match. For example: o The positive terminal of voltage source " & is connected to resistor ! ' . This is true for both circuits in panels a and b of Lab 3 Figure 1. o The negative terminal of voltage source " & is connected to resistors ! ( and ! % . Again, this is true for both circuits in panels a and b of Lab 3 Figure 1.

2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3: Maximal power transfer © 2022 Alexander Ganago Page 3 of 21 Last printed 9/18/22 5:47:00 PM File: 22c 314 Lab 3 0918.docx The meaning of Lab 3 Figure 1, b is that the circuit with the source " & and three resistors ! ' , ! ( , ! ) (to the left of the terminals a and b) can be considered as a source of power, while resistor ! % is considered as the load, to which the power from the source is transferred. The deeper meaning of Lab 3 Figure 1 is that the source of power to the left of the terminals a, b , can be replaced with its Thevenin equivalent circuit , that is one voltage source " ! and only one resistor ! ! . This replacement greatly simplifies the calculations of power transfer. Note the distinctions between the original circuit (panels a, b of Lab 3 Figure 1) and its Thevenin equivalent circuit (panel c of Lab 3 Figure 1): o In the Thevenin equivalent circuit the voltage " ! is distinct from the source voltage " & in the original circuit. o Also, the Thevenin equivalent resistance ! ! is distinct from any of the resistances ! ' , ! ( , ! ) in the original circuit. Despite these distinctions, both the original circuit and its equivalent circuit transfer the same amount of power to the same load resistors. The simple modifications of the original circuit, which are shown in Lab 3 Figure 2, allow us to measure and/or calculate the parameters " ! and ! ! of the Thevenin equivalent circuit. (a) (b) Lab 3 Figure 2. Thevenin equivalent voltage " ! equals the open-circuit voltage " *+ , which is measured when the load resistor is disconnected from the original circuit. Thevenin equivalent resistance ! ! equals the resistance between terminals a, b, which is measured when the voltage source " & is removed and replaced with a short circuit or a probe wire. Overview of Pre-Lab step One o In HW p5, you will calculate the parameters " ! and ! ! of the Thevenin equivalent circuit. o For the Pre-Lab, you will do the measurements of " ! and ! ! according to Figure 3-2. o Compare the results of your measurements with the results of your calculations in HW p5. o If you found a disagreement, find your error and repeat your measurements. o If your data and your calculations agree, restore the original circuit of Lab 3 Figure 1, a, b.

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2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3: Maximal power transfer © 2022 Alexander Ganago Page 4 of 21 Last printed 9/18/22 5:47:00 PM File: 22c 314 Lab 3 0918.docx Overview of Pre-Lab step Two o Use the parameters " ! and ! ! of the Thevenin equivalent circuit to calculate the voltage " $' applied to the load resistor ! $' = ! % = 220 + and the voltage " $( applied to the load resistor ! $( = ! % , = 2000 + = 2 ,+ . o Note that you have calculated the voltage applied to resistor ! $ = ! % = 220 + in HW p3, and you have measured this voltage in Lab 2. o Make sure that you measure the same voltage now. o Compare these results with your calculations based on the Thevenin equivalent parameters. o On your prototyping board, replace the resistor ! % = 220 + with ! % , = 2000 + = 2 ,+ (you collected it at the end of In-Lab 2 work); measure the voltage applied to this resistor. o Compare the results of your measurement with the results of your calculation. The completion of these two steps indicates that the Thevenin theorem applies to your circuit. Then, in the Lab room , you will use two 33461A DMMs to measure both the voltage " $ and the current % $ at the same time, with a variable resistor (10 kΩ potentiometer) as the load. Thus, you will obtain more data to verify the validity of Thevenin theorem for your circuit.

2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3: Maximal power transfer © 2022 Alexander Ganago Page 5 of 21 Last printed 9/18/22 5:47:00 PM File: 22c 314 Lab 3 0918.docx 2. The maximal power, which can be transferred from HP E3631A power supply to individual load resistors Lab 3 Figure 3 , panel a, shows the Volt-Amp characteristics of the circuit models for sources of electric power, which we use in theoretical calculations. The plots in panels b, c, d of this Figure outline the limits of output voltage and output current for 3 output terminals of E3631A triple power supply. Pay attention to the choice of the axes on the plots in Lab 3 Figure 3: Voltage is on the vertical axis. (a) (b) (c) (d) Lab 3 Figure 3. Volt-Amp characteristics of the circuit models are shown in panel a. Any real power supply has strict limits for the output voltage and for the output current: see panels b, c, d. Within the shaded areas, any combinations of output voltage and of the output current can be obtained. The simplistic models for independent voltage and current sources in panel a of Lab 3 Figure 3 do not set any limits for the output power: their straight I-V lines can be continued endlessly.

2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3: Maximal power transfer © 2022 Alexander Ganago Page 6 of 21 Last printed 9/18/22 5:47:00 PM File: 22c 314 Lab 3 0918.docx On the contrary, any real power supply sets strict limits on the output voltage and current, as shown with the shaded areas in panels b, c, d. Beyond these limits, the operation is unsafe, and therefore, not allowed. According to Ohm’s law, the Volt-Amp characteristic of any load resistor is a straight line, which starts at the {" = 0; % = 0} point. Lab 3 Figure 4, panels b, c, emphasize two different scenarios of how the power supply limits the maximal power for different load resistors. (a) (b) (c) Lab 3 Figure 4. In the default Constant Voltage (CV) mode, a power supply operates similar to the circuit model of an independent voltage source (see Lab 3 Figure 3 panel a). Namely, within its safe operation limit % *-! ≤ % ./0 , the power supply maintains the output voltage " $ , chosen by the user, at any output current % $ = " $ ! $ 1 , which is determined by the load resistor ! $ . As soon as the current % $ reaches % ./0 , the power supply automatically switches into Constant Current (CC) mode, which is a safety feature. The slanted straight lines in panels b, c of Lab 3 Figure 3 are the volt-amp characteristics of the load resistors, according to Ohm’s law. With this choice of axes (voltage on the vertical, current on the horizontal), the slope of a straight line for load resistor ! $ is directly proportional to ! $ . Note that the maximal power, which the power supply can deliver to a load resistor, is achieved when ! $, ./0 3*456 = " ./0 % ./0 1 . For any other load, the power is below the maximal possible. The default operation mode of a traditional power supply is Constant Voltage (CV). In this mode, the user sets the desired output voltage " $ (from the front panel or via computer control),

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2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3: Maximal power transfer © 2022 Alexander Ganago Page 7 of 21 Last printed 9/18/22 5:47:00 PM File: 22c 314 Lab 3 0918.docx and the output current % $ = " $ ! $ 1 is determined by the resistance ! $ of the load. This is similar to the expected operation of an independent voltage source. The power supply operates in its default CV mode only if both the output current and the output voltage remain within the safe operation limits. These safe operation are shown with the shaded rectangles In Lab 3 Figure 3, panels b, c, d, and in Lab 3 Figure 4. The output voltage and the output current cannot be increased endlessly. For any real power supply and any load resistor ! $ either " ./0 or % ./0 will limit their growth. Specifically: o If the load resistance is high ! $ ≥ " ./0 % ./0 1 then the limit to the growth is set by the maximal safe voltage " ./0 . In this default Constant Voltage (CV) mode , the current % $ through the load resistor ! $ is determined by Ohm’s law: % $ = " $ ! $ 1 . This scenario is shown in Lab 3 Figure 4 panel b. The power supply operates in the CV mode, and indicates this mode on its front panel. In this CV mode, the maximal power, which can be absorbed by the load resistor # # , equals 3 #, 789 (;<) = 4 789 > # # 5 . o If the load resistance is low ! $ < " ./0 % ./0 1 then " ./0 cannot be reached, because the maximal safe current % ./0 would be reached at a lower voltage. When the output current % $ reaches % ./0 , the power supply automatically switches into its Constant Current (CC) mode and indicates this mode on the front panel. In this mode, the voltage " $ applied to the load resistor ! $ is determined by Ohm’s law: " $ = % ./0 ∙ ! $ . The power supply keeps operating in its CC mode, that is provides the output current % ./0 and output voltage " $ = % ./0 ∙ ! $ , until the current through its terminals is reduced below % ./0 . In this CC mode, the maximal power, which can be absorbed by the load resistor # # , equals 3 #, 789 (;;) = 8 789 > ∙ # # . The most important subtlety is that Constant Current mode is not the same as one might expect from an independent current source: the power supply does not keep the output current at any arbitrary value % *-! ≤ % ./0 ; it only maintains the output current at its maximal safe limit % ./0 . Learning about these limitations and these modes of operation will help you to correctly choose the power supply for your future projects. For example, you will not expect that a power supply, which is rated at 30 W (such as E3631A) will indeed deliver any power within 30 W to any of your particular loads. o In the Pre-Lab, you will do calculations for two load resistors, and show your results for the 6V and 25V output terminals of E3631A (panels b, c of Lab 3 Figure 3) with sketches similar to those in Lab 3 Figure 4 panels b and c. o In the lab room, you will actually measure the output voltages and output currents of E3631A at two terminals (6 V and 25 V) of this power supply. o In the Lab report, you will compare your data with your theoretical predictions and with the explanations above.

2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3: Maximal power transfer © 2022 Alexander Ganago Page 8 of 21 Last printed 9/18/22 5:47:00 PM File: 22c 314 Lab 3 0918.docx The Pre-Lab Application of Thevenin theorem to the circuit with 4 fixed resistors First of all, make sure that the diagrams in panels a, b of Figure 3-1 show the same circuit. o Continue the reasoning of page 2 of this file for the remaining two nodes in your circuit. o Write your reasoning and your conclusion on a separate page to get credit. If the diagrams are indeed describing the same circuit, it means that you do not have to rearrange the connections within your circuit for the following measurements. However, you will need to prepare the terminals of your circuit in order to determine " ! and ! ! . Prepare for measurements: o AD2 and portable DMM o Your prototyping board with the circuit, which you used in Lab 2 o Additional resistor ! % , = 2000 + = 2 ,+ o Probe wires. o Make sure that your circuit on the prototyping board is not damaged or altered. o Take a photograph of your circuit for into your Lab report (and/or the Rubrics file) o Fill Table 3.1 for the nodes, as they are shown on your photograph. Refer to the diagram: Table 3.1 The nodes on your prototyping board If you use bus lines (for 1, 10, etc.), explain. o Do NOT connect AD2 to your circuit. o Instead, insert a probe wire (short circuit) between nodes 1 and 10. o Remove resistor R4. o Use portable DMM to measure ! ! – the resistance between nodes 7 and 8. o Write the result in Table 3.2 on the following page. Compare with your result obtained in HW p5. Lab 3 Figure 5. The nodes on a prototyping board are numbered: refer to Table 3.1. Node # Row # Column 1 2 3 4 5 6 7 8 9 10

2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3: Maximal power transfer © 2022 Alexander Ganago Page 9 of 21 Last printed 9/18/22 5:47:00 PM File: 22c 314 Lab 3 0918.docx Table 3.2 The measured and calculated Thevenin equivalent resistance The measured resistance, Ω The calculated resistance, Ω % difference % :;<<=>=?@= = A=BCD>=: − FBG@DGBH=: FBG@DGBH=: × 100% o Disconnect the portable DMM. Turn it OFF. o Disconnect the probe wire, which you inserted between the nodes where the voltage source should be connected. o Start using your AD2. o Refer to the pinout below. Lab 3 Figure 6. Pinout of AD2 ribbon cable. 630 e 636 . Tot 1 . 04 %

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2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3: Maximal power transfer © 2022 Alexander Ganago Page 10 of 21 Last printed 9/18/22 5:47:00 PM File: 22c 314 Lab 3 0918.docx o Connect V+ and V- to the nodes where the voltage source should be connected to your circuit. Apply +3 V and –3 V. o Measure with Voltmeter Channel 1 the supply voltage (should be near 6 V). o Adjust the Supply settings if needed, to obtain 6 V with better accuracy. o Measure with Voltmeter Channel 2 the voltage at nodes 7, 8 (in your Table 3.1). o If nothing (except for Voltmeter ) is connected between these nodes, the measured voltage is Open Circuit voltage, which equals Thevenin voltage. o Write the results of your measurements in Table 3.3. o Compare with your calculations in HW p5. Table 3.3 The measured and calculated Thevenin equivalent voltage The measured source voltage The measured Thevenin voltage The calculated Thevenin voltage % difference o Write a brief conclusion on the agreement / disagreement between your data and your theoretical results for " ! and ! ! . o Use the Thevenin circuit diagram (Lab 3 Figure 1, panel c) and the measured parameters: o " ! and ! ! from Tables 3.2 and 3.3 above. o ! $ - the actual resistance R4 (220 Ω nominal), which you measured in the previous Lab. Calculate the expected voltage across load resistor R4. To get credit, show your work, and provide a specific reference to your previous Lab report where you measured R4. o Write your result in Table 3.4. Table 3.4 The measured and calculated voltages across two load resistors The measured voltage " $ The calculated voltage " $ % difference Load resistor R4 (nominal, 220 Ω) Load resistor R4’ (nominal, 2 kΩ) o Write a brief conclusion on whether Thevenin theorem is valid for your circuit, and with what accuracy. o Explain whether the predictions based on the circuit diagram in Figure 3-1, panel c, and the measured " ! and ! ! correctly predict the voltage " $ across these two load resistors. (If they do, then the power absorbed by these resistors is also predicted correctly.) The Pre-Lab is continued on the following page. 6 . 033V / . 15 SU 1 . 180 2 . 1 % VI = UT : Be 4 6 : 226 I - 1 . 2 V & + R2 636 7 + 220 - 1 . 7 % Wi = 1 , 188 3 . SV Very . 2000 = 3 490 . 29 % 4 - ⊥ y Too

2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3: Maximal power transfer © 2022 Alexander Ganago Page 11 of 21 Last printed 9/18/22 5:47:00 PM File: 22c 314 Lab 3 0918.docx The Pre-Lab, continued The maximal power, which can be transferred from HP power supply E3631A to individual load resistors For the measurements in the lab room, you will use large resistors: see Lab 3 Figure 5. Lab Figure 7. Each of these large resistors (nearly 2 inches, or 50 mm long) is rated at 6.2 Ω and 10 W maximal safe power. o Use the equations for power absorption by resistors & = " ( ! = % ( ∙ ! Calculate: o The maximal current % ./0 , which a power supply can safely push through each of these resistors. o The maximal voltage " ./0 , which a power supply can safely appl to each of these resistors. Show your work on a separate page. Write your results in Table 3.5. Table 3.5 Maximal safe currents and voltages for the resistors, which are shown in Figure 3.5. Equivalent resistance Maximal safe total power Maximal safe current % ./0 , amps Maximal safe voltage " ./0 , volts One resistor Two resistors in parallel

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2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3: Maximal power transfer © 2022 Alexander Ganago Page 12 of 21 Last printed 9/18/22 5:47:00 PM File: 22c 314 Lab 3 0918.docx o On the diagrams in Lab 3 Figure 8 below, draw volt-amp lines for these load resistors, assuming that they are connected either to 6V or to 25V terminals of E3631A. In the Lab room, you will do the measurements, which will provide data points for these plots in your Lab report. Lab 3 Figure 8. The shaded rectangles show the possible voltages and currents at the terminals of E3631A. For each of the terminals, do the following: o Plot the straight line based on Ohm’s law for each of the resistors. o Clearly show whether this straight line reaches the maximal safe voltage " ./0 (as in Lab 3 Figure 4 panel b) or the maximal safe current % ./0 (as in Lab 3 Figure 4 panel c). o Clearly mark {FD>>=?H; "KGHBL=} of the point, at which either % ./0 or " ./0 is reached. You need to mark 4 points total. End of the Pre-Lab

2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3: Maximal power transfer © 2022 Alexander Ganago Page 13 of 21 Last printed 9/18/22 5:47:00 PM File: 22c 314 Lab 3 0918.docx In-Lab Application of Thevenin theorem to the circuit with 3 fixed resistors and a variable load resistor Your first goal is to connect the circuit, which you used in the Pre-Lab, to a variable load resistor ! $ (a part of potentiometer with total nominal resistance ! 3 = 10 ,+ ), and measure both the current % $ through this load resistor and the voltage " $ across this load resistor: Lab 3 Figure 9. (a) Lab 3 Figure 9. Panel (a) shows the circuit diagram. Panel (b) shows one of the possible connections of the potentiometer and test / measurement instruments to the circuit on a prototyping board. (b)

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2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3 : Maximal power transfer © 2022 Alexander Ganago Page 1 of 10 Last printed 9/18/22 5:25:00 PM File: 22c Lab 3 report rubrics 0918.docx Rubrics for Lab 3 report (if you choose to type your report using the tables below, rename your file: include your last name and the Lab report number, such as “Hopkins Lab 3”) Student’s name _________________________ Uniqname ________________ Last, First Lab section # ____ Date of In-Lab work _________________ Lab instructor’s name ______________________________ Pre-Lab Is the Thevenin theorem valid for the circuit with 4 fixed resistors? The circuit of Lab 2 includes one voltage source and 4 resistors. (a) The circuit of Lab 2 can be redrawn in the following way: Here, ! ! is the load resistor ! " , which can be varied. (b) The panels a (with 2 specially labeled nodes) and b of Lab 3 Figure 1 are repeated here for your convenience. (2 points) These diagrams look different; you have to explain whether they represent the same connections on the circuit board. Consider 2 nodes, which are labeled on the circuit diagram above. Write a brief explanation for each of these nodes.

2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3 : Maximal power transfer © 2022 Alexander Ganago Page 2 of 10 Last printed 9/18/22 5:25:00 PM File: 22c Lab 3 report rubrics 0918.docx Pre-Lab, continued (10 points) o Include a photograph of your circuit on the prototyping board. o Fill Table 3.1 below. Table 3.1 The nodes on your prototyping board If you use bus lines (for 1, 10, etc.), explain. o Measure " # – the resistance between nodes 7 and 8, as explained in Lab 3 manual. o Write the result in Table 3.2. Compare with your result obtained in HW p5. Table 3.2 (4 points) The measured and calculated Thevenin equivalent resistance The measured resistance, Ω The calculated resistance, Ω % difference % %&’’()(*+( = -(./0)(% − 2.3+03.4(% 2.3+03.4(% × 100% o Measure 8 # – the Open-Circuit voltage, which equals the Thevenin equivalent voltage, as explained in Lab 3 manual. o Write the result in Table 3.3. Compare with your result obtained in HW p5. Table 3.3 (4 points) The measured and calculated Thevenin equivalent voltage The measured source voltage The measured Thevenin voltage The calculated Thevenin voltage % difference Node # Row # Column 1 2 3 4 5 6 7 8 9 10

2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3 : Maximal power transfer © 2022 Alexander Ganago Page 3 of 10 Last printed 9/18/22 5:25:00 PM File: 22c Lab 3 report rubrics 0918.docx Pre-Lab, continued Measure the voltages 8 $ , which are applied to two load resistors: " $% = 220 : , and " $& = 2000 : = 2 ;: . Follow the instructions in Lab 3 manual. Fill Table 3.4. Table 3.4 (4 points) The measured and calculated voltages across two load resistors The measured voltage 8 $ The calculated voltage 8 $ % difference Load resistor R4 (nominal, 220 Ω) Load resistor R4’ (nominal, 2 kΩ) Write a brief conclusion on whether Thevenin theorem is valid for your circuit, and with what accuracy. Especially, the agreement between calculate and measured values of 8 $& would mean that Thevenin theorem is valid for your circuit. Briefly discuss whether this is true. The rubrics for Pre-Lab 3 are continued on the following page.

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2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3 : Maximal power transfer © 2022 Alexander Ganago Page 4 of 10 Last printed 9/18/22 5:25:00 PM File: 22c Lab 3 report rubrics 0918.docx Maximal power calculations for two load resistors and their connections to E3631A Table 3.5 (5 points) Maximal safe currents and voltages for the resistors, which are shown in Figure 3.5. Equivalent resistance Maximal safe total power Maximal safe current < '() , amps Maximal safe voltage 8 '() , volts One resistor Two resistors in parallel Volt-Amp plots (6 points) On the diagrams below, draw volt-amp lines for these load resistors, assuming that they are connected either to 6V or to 25V terminals of E3631A. In the Lab room, you will do the measurements, which will provide data points for these plots in your Lab report. This is the end of rubrics for Pre-Lab 3. = = = The total score for Pre-Lab 3 equals 35 points.

2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3 : Maximal power transfer © 2022 Alexander Ganago Page 5 of 10 Last printed 9/18/22 5:25:00 PM File: 22c Lab 3 report rubrics 0918.docx In-Lab Preparations for measurements of power transfer to variable load resistor (10 kΩ potentiometer) (3 points for correct drawing)

2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3 : Maximal power transfer © 2022 Alexander Ganago Page 6 of 10 Last printed 9/18/22 5:25:00 PM File: 22c Lab 3 report rubrics 0918.docx In-Lab, continued Power transfer to variable load resistor (10 kΩ pot): data, theory, and their comparison Table 3.6. The voltage = " and the current > " at various positions of the potentiometer’s tap (20 points) The expected = " The measured = " (within 0.1 V of the expected) The position of the potentiometer’s tap in cm (within 0.5 cm) The measured > " (units!) Load resistance ! " , ohms (calculated) Absorbed power ? " , mW (calculated) The lowest possible 0.5 V 1.0 V 1.5 V 2.0 V 2.5 V 3.0 V 3.5 V The highest possible For Lab 3 report EXCEL plot for comparison of the theory and your data (10 points) In the Lab report, insert the EXCEL plot, which shows the calculated power absorbed by the load (HW p5 #13) as a curve, and the results of your measurements (from Table 3.6 above) as clearly marked data points: enlarge the size of markers from 5 (default) to 15. Briefly discuss the agreement or disagreement between your theoretical results and your data.

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2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3 : Maximal power transfer © 2022 Alexander Ganago Page 7 of 10 Last printed 9/18/22 5:25:00 PM File: 22c Lab 3 report rubrics 0918.docx In-Lab, continued Power transfer from E3631A power supply to its load resistors Lab 3 Figure 7, repeated for your convenience Each of these large resistors (nearly 2 inches, or 50 mm long) is rated at 6.2 Ω and 10 W maximal safe power. Table 3.7. (3 points) The measured resistances of large resistors Expected resistance, Ω Measured resistance, Ω % difference (measured – expected) A single resistor 6.2 Ω A pair of resistors in parallel 6 . 399 3 . ' & 3 . 16S

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2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3 : Maximal power transfer © 2022 Alexander Ganago Page 8 of 10 Last printed 9/18/22 5:25:00 PM File: 22c Lab 3 report rubrics 0918.docx In-Lab, continued Power transfer from E3631A power supply to its load resistors, continued Table 3.8. (10 points) Measurements with E3631A, 6V output Expected voltage, V Measured voltage, V Measured current, A Mode of operation CC or CV Calculated absorbed power, W Agreement with Pre-Lab? A single resistor 3 V 6 V A pair of resistors in parallel 3 V 6 V Table 3.9. (10 points) Measurements with E3631A, 25V output Expected voltage, V Measured voltage, V Measured current, A Mode of operation CC or CV Calculated absorbed power, W Agreement with Pre-Lab? A single resistor 5 V MAX POSSIBLE A pair of resistors in parallel 5 V MAX POSSIBLE

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2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3 : Maximal power transfer © 2022 Alexander Ganago Page 9 of 10 Last printed 9/18/22 5:25:00 PM File: 22c Lab 3 report rubrics 0918.docx For Lab 3 report (6 points) Power transfer from E3631A power supply to its load resistors, continued Lab 3 Figure 8. The shaded rectangles show the possible voltages and currents at the terminals of E3631A. For each of the terminals, you have done the following in the Pre-Lab: o Plot the straight line based on Ohm’s law for each of the resistors. o Clearly show whether this straight line reaches the maximal safe voltage 8 '() (as in Lab 3 Figure 4 panel b) or the maximal safe current < '() (as in Lab 3 Figure 4 panel c). o Clearly mark {20))(*4; 8B34.C(} of the point, at which either < '() or 8 '() is reached. You need to mark 4 points total. For the Lab report, add the points based on your data in Tables 3.8 and 3.9. Discuss the agreement or disagreement between your expectations (Pre-Lab) and your data.

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2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3 : Maximal power transfer © 2022 Alexander Ganago Page 10 of 10 Last printed 9/18/22 5:25:00 PM File: 22c Lab 3 report rubrics 0918.docx For Lab 3 report (3 points) Write brief conclusions: 1. What was interesting or unexpected in Lab 3? 2. Has this Lab helped you to understand the theory, especially, Thevenin theorem? 3. What is still unclear? – or What could be improved in this Lab assignment?

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2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3: Maximal power transfer © 2022 Alexander Ganago Page 14 of 21 Last printed 9/18/22 5:47:00 PM File: 22c 314 Lab 3 0918.docx For measurements, you will need two 34461A DMMs at the same time. Unless you have both on your bench, prepare to team up with your classmates at the neighboring bench. If needed, ask your Lab instructor for advice on how to team up. Turn On the bench instruments: o HP E3631A power supply o Both Keysight 34461A DMMs. In your team, you’ve got 2 or 4 circuits built in the previous Labs and used for the Pre-Lab. Choose one of these circuits for measurements. If needed, ask your Lab instructor for advice. o Get cables with banana plugs: o Two 3-ft-long cables to connect your circuit to the power supply on the same desk. o Two 3-ft-long cables to connect your circuit to the DMM on the same desk. o Two 6-ft-long cables to connect your circuit to the DMM on the neighboring desk. You will be using one of these DMMs as voltmeter to measure " $ , the other as ammeter to measure % $ , at the same time for each ! $ setting. From the ratio " $ % $ 1 you will calculate the load resistance ! $ ; from the product " $ ∙ % $ , you will calculate the power & $ absorbed by this load. o Get 10 kΩ linear potentiometer: you’ll use it as a variable load resistor: Lab 3 Figure 10. Lab 3 Figure 10. The 10 kΩ linear potentiometer, which you use in this Lab, is mounted on a wooden board next to a ruler, for your convenience. It has 3 cables with banana plugs, color coded. The resistance between Black and Green cables can be varied from near 0 to 10 kΩ by moving the tap. The tap is the bright rectangle above the ruler on the photo, and the arrow on the circuit symbol. The resistance between the end connectors Black and Red cables is fixed at 10 kΩ. You will connect all cables to your circuit, using probe wires: o E3631A and the potentiometer – with banana plugs and alligator clips. o 34461A DMMs – with mini-grabbers (see Lab 3 Figure 12 ). MAKE SURE THAT ALLIGATOR CLIPS DO NOT TOUCH EACH OTHER. o Spread the alligator clips as far from each other as possible: see Lab 3 Figure 9.

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2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3: Maximal power transfer © 2022 Alexander Ganago Page 15 of 21 Last printed 9/18/22 5:47:00 PM File: 22c 314 Lab 3 0918.docx o Avoid moving the alligator clips during measurements. o On Lab 3 Figure 11 , draw the connections for the circuit, which you are about to build. Lab 3 Figure 11. Draw the connections, which you are going to build. o Get your Lab instructor’s approval of your drawing.

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2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3: Maximal power transfer © 2022 Alexander Ganago Page 16 of 21 Last printed 9/18/22 5:47:00 PM File: 22c 314 Lab 3 0918.docx Lab 3 Figure 12. Insulated mini-grabbers provide a better alternative to bare alligator clips. For this experiment, all 34461A DMMs are equipped with cables with mini-grabbers. o Refer to previous Lab manuals if you do not remember the subtleties of o building connections on the prototyping board, and of o the setting of DMMs into the particular modes of operation. o Connect the +6 V and –6 V cables to the 6V terminals of the power supply E3631A. o Get your Lab instructor’s approval BEFORE you apply the voltage from E3631A. o On E3631A, use 6V terminals; set 6.00 V; apply to your circuit. o Verify with 34461A as voltmeter that the applied voltage is as close to 6.00 V as possible. o For doing this, pull the cables with mini-grabbers from 34461A voltmeter. o Use cables with banana plugs: connect the voltmeter to 6V terminals of E3631A. o Adjust the setting of E3631A if needed to achieve 6.00 " ± 0.01 " . o Disconnect 34461A from E3631A. o Restore the connection of 34461A voltmeter to your circuit. Measure the voltage 4 # and the current 8 # at 9 positions of the potentiometer’s tap, as listed in Table 3.6. Write your data in Table 3.6. o Achieve each expected value of 4 # within 0.1 V margin. o Fill the shaded columns of the table if you have time. Ask your Lab instructor for advice. Do not hurry to do all calculations: you will need them only for your Lab report.

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2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3: Maximal power transfer © 2022 Alexander Ganago Page 17 of 21 Last printed 9/18/22 5:47:00 PM File: 22c 314 Lab 3 0918.docx Table 3.6. ( The shaded columns may be completed at the end of the Lab section or later) The voltage 4 # and the current 8 # at various positions of the potentiometer’s tap The expected 4 # The measured 4 # (within 0.1 V of the expected) The position of the potentiometer’s tap in cm (within 0.5 cm) The measured 8 # (units!) Load resistance # # , ohms (calculated) Absorbed power 3 # , mW (calculated) The lowest possible 0.5 V 1.0 V 1.5 V 2.0 V 2.5 V 3.0 V 3.5 V The highest possible Comments, based on teaching experience The minimal possible resistance of some of these potentiometers is ~1 Ω; it is higher in others. Therefore, some student teams could not reach < 0.5 V. o If the minimal possible voltage, which you can read is >0.5 V, verify that the rest of your circuit (besides the potentiometer) is built correctly. o For this verification, disconnect the potentiometer; replace it with a piece of probe wire. o If you read 0 V ± 0.1 V with a probe wire, your circuit is correct. o Restore your circuit: disconnect the probe wire; connect the potentiometer. o Do the measurements. o If you still read > 0.5 V with a probe wire, find your mistake and measure again. o Show your data in Table 3.6 to your Lab instructor for approval. o Per approval of your Lab instructor, press E3631A Output On/Off button: disconnect the power from your circuit. Keep your circuit on the prototyping board. o Disconnect all cables from your circuit. o Share the data among all teammates. Make sure that each teammate has all information needed for the Lab report. Exchange your contact information if your teammates need it. o Return the potentiometer to the box, from which you took it. o The In-Lab assignment is continued on the next page.

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2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3: Maximal power transfer © 2022 Alexander Ganago Page 18 of 21 Last printed 9/18/22 5:47:00 PM File: 22c 314 Lab 3 0918.docx In-Lab, continued The maximal power, which can be transferred from HP E3631A power supply to individual load resistors In this part, you will be working in teams of 2, using the instruments on one workbench. Get large resistors, shown in Lab 3 Figure 7 , which is repeated below for your convenience. o Each team needs both a single resistor and a pair of resistors connected in parallel. Lab 3 Figure 7, repeated for your convenience Each of these large resistors (nearly 2 inches, or 50 mm long) is rated at 6.2 Ω and 10 W maximal safe power. o Use 34461A DMM on your bench to measure their resistances. o Write your results in Table 3.7. Table 3.7. The measured resistances of large resistors Expected resistance, Ω Measured resistance, Ω % difference (measured – expected) A single resistor 6.2 Ω A pair of resistors in parallel o Disconnect 34461A from the resistors. o Turn Off 34461A. o Connect the single resistor to E3631A, 6V output. o Simply grab its connectors with the alligator clips.

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2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3: Maximal power transfer © 2022 Alexander Ganago Page 19 of 21 Last printed 9/18/22 5:47:00 PM File: 22c 314 Lab 3 0918.docx o MAKE SURE THAT ALLIGATOR CLIPS DO NOT TOUCH EACH OTHER. o Push the Output On/Off button on E3631A. Apply 3 " ± 0.1 " to the single resistor. o Read the current from the front panel of E3631A. o Read the E3631A display: determine whether it is operating in the CV or CC mode. o Record your data in Table 3.8. Table 3.8. Measurements with E3631A, 6V output Expected voltage, V Measured voltage, V Measured current, A Mode of operation CC or CV Calculated absorbed power, W Agreement with Pre-Lab? A single resistor 3 V 6 V A pair of resistors in parallel 3 V 6 V o Continue to fill the entire Table 3.8. o Make sure to set Output Off before you change the connections. o Unplug the cables from 6V output; plug them in 25V output (between +25V and COM ). o Proceed with the measurements as explained above. Fill in Table 3.9. o If the power supply switches into CC mode, reduce the voltage to achieve CV mode. Write the value of the achieved voltage in the MAX POSSIBLE row of Table 3.9. Comment based on the teaching experience As discussed in the Pre-Lab, it may not be possible to reach 5 V with 2 resistors in parallel. Then, record the data at the maximal voltage that you can reach. Table 3.9. Measurements with E3631A, 25V output Expected voltage, V Measured voltage, V Measured current, A Mode of operation CC or CV Calculated absorbed power, W Agreement with Pre-Lab? A single resistor 5 V MAX POSSIBLE A pair of resistors in parallel 5 V MAX POSSIBLE

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2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3: Maximal power transfer © 2022 Alexander Ganago Page 20 of 21 Last printed 9/18/22 5:47:00 PM File: 22c 314 Lab 3 0918.docx o Ask your Lab instructor for the approval of your data. o Set Output Off on E3631A. o Turn Off all instruments. o Return all cables to their racks (pay attention to the color and to the length). o Return the large resistors to where you obtained them. = = = For the future Lab s, you will need capacitors, inductors, 2 kΩ resistor, and a small 10kΩ potentiometer (see Lab 3 Figure 10 on the following page). o Ask your Lab instructor for advice on where to get them. o Measure and record the actual resistance of 2 kΩ resistor: ______________ kΩ. Capacitors and inductors are labeled with numbers and letters. o On large capacitors, the labels are explicit, such as “47 µF 50 V” o On small components, there is no space for explicit labels; 3-digit code is used instead. Capacitors are labeled in picofarads. Q RS = QT ?@> S . o Typical 3-digit labels are “101”, “102”, and “103”. o The first two digits refer to the numerical value; the 3 rd digit is the power of 10. o Simply speaking, the 3 rd digit shows how many zeroes you have to add at the end. o For instance, “101” means 10 × 10 ' = 10 ( UV = 100 UV o Similarly, “103” means 10 × 10 ) = 10 % UV = 10 ?V = 0.01 µV o If this seems confusing, refresh your learning of the SI units. I expect every student to get one of the following: o 1 nF capacitor (the label reads “102”) o 10 nF capacitor (the label reads “103”) o 100 pF capacitor (the label reads “101”) Inductors are labeled in µH. Q µX = QT ?A X . The convention of labeling is the same. o For instance, “102” means 10 × 10 ( = 10 ) µY = 1 ZY o Similarly, “103” means 10 × 10 ) = 10 % µY = 10 ZY = 0.01 Y I expect every student to get one of the following: o 1 mH inductor (the label reads “102”) o 10 mH inductor (the label reads “103”) o 10 kΩ potentiometer (see Lab 3 Figure 10 on the following page). o Plug all components listed above into your prototyping board. o Keep on the board all resistors from Lab 3.

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2022 Fall EECS 314 Labs with AD2 and Keysight instruments Lab 3: Maximal power transfer © 2022 Alexander Ganago Page 21 of 21 Last printed 9/18/22 5:47:00 PM File: 22c 314 Lab 3 0918.docx Lab 3 Figure 10. In the following Labs you will use small potentiometers, which can be plugged into a solderless prototyping board: the distance between their pins perfectly matches the distance between the holes in the board. The potentiometer above is connected to nodes 3, 4, 5 in column e. The middle pin 4e is connected to the potentiometer’s tap. The tap is moved by rotating the wheel either with your fingertips or with a flat screwdriver. If a potentiometer’s pin is bent, gently straighten it out with small pliers. If a potentiometer’s pin is broken off, put this potentiometer into a SHARPS container, and get a replacement. This is the end of In-Lab work. Now, clean up your bench. Leaving a messy workspace = 25% off both Lab reports. Thanks for your efforts!

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