Lab 4 Maximum Power Transfer PDF

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ENEE 3518 EXPERIMENT #4 MAXIMUM POWER TRANSFER THEOREM Purpose: The purpose of this laboratory experiment is to observe and verify the Maximum Power Transfer Theorem in both a simple series resistive circuit and in a more complicated multi-source resistive circuit. Theory: In the design of practical electrical circuits and systems, it is often of great interest to know . This is the basis for a very important relationship in circuit theory called the Maximum Power Transfer Theorem. From elementary DC circuit theory, the Maximum Power Transfer Theorem states that the maximum power transfer from a circuit to a resistive load will occur only when the value of the load resistance is exactly equal to the Thevenin equivalent resistance of the circuit as seen from the load resistor terminals. Therefore, application of the Maximum Power Transfer Theorem requires familiarity with the definition and practical application of Thevenin’s Theorem in circuit analysis. Equipment Used: Agilent E3615A and E3630A DC power supplies Agilent 34401Digital Multimeter Resistors (various) 10 KΩ Potentiometer (variable resistor marked 103) Procedure: PART A: 1. Obtain the 5.1 kΩ resistor and a 10 kΩ potentiometer (R0) that you need to build the circuit shown in Figure 1 Before building the circuit, use the Agilent 34401 Digital Multimeter to accurately measure the value of your resistor. Record its value in Table 1 because it will be needed in your theoretical calculations.

5.1 kΩ

Figure 1. Circuit used in Part A. 1

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Table 1: Resistance and Voltage Values

2. Build the circuit shown in Figure 1 on your breadboard. Remember to make sure each pin of the potentiometer is in a separate horizontal row of your breadboard. Adjust one of your DC power supplies to 5V. Use the digital multimeter to get an accurate voltage reading. Record the exact value of your voltage source on Table 1. It will be needed in your theoretical calculations. 3. Now vary the potentiometer from its minimum resistance value to its maximum resistance value in small increments, and use the digital multimeter to take an accurate reading of the output voltage V0 at each increment. After each voltage reading, temporarily remove the potentiometer from the circuit and use the digital multimeter to take an accurate reading of the potentiometer’s resistance value. Be sure to replace the potentiometer back exactly the same way on the breadboard. Alternately, you can simply remove the connection between the 5.1 kΩ resistor and the potentiometer and measure the potentiometer resistance on the breadboard without removal. This is a slow process so be patient in your approach with this technique. At the end of this handout, there is a table entitled “Recorded and Calculated Values for the Circuit of Figure 1 (Part A)” and is provided for your convenience. Use this table to record your readings in Part A. Hint: Take readings for the minimum and maximum voltages first, by putting the potentiometer all the way to its minimum resistance value and then all the way to its maximum resistance value. Then take additional readings equally spaced in between. . Remember that the point of this experiment is to find the value of the potentiometer at which maximum power transfer from the circuit occurs, so try to get a reading as close to that value as possible. Compute and record the power being dissipated by the potentiometer for each pair of measured voltage and resistance values. Recall that this power is calculated as the voltage squared divided by the resistance. For your lab report on Part A, perform the following tasks. Include all results (neatly typed) in your report. a) Calculate the theoretical values of the voltage V0 and power at the potentiometer. b) Include a table with the list of measured and calculated values in addition to Table 1. c) Generate a plot of the potentiometer voltage V0 versus the potentiometer’s resistance. d) Create a plot of the power dissipated by the potentiometer versus the 2

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potentiometer’s resistance. e) Determine from your measurements what value of potentiometer resistance R0 results in a maximum power transfer from the circuit. f) Using the measured resistance and voltage source values, calculate the theoretical value of resistance R0 for which maximum power transfer from the circuit should occur. Compute the percent error between this value and the measured value. PART B: 1. Obtain the resistors you will need to build the circuit shown in Figure 2. Before building the circuit, use the digital multimeter to accurately measure the actual values of your resistors. Record these resistor values in Table 2. They will be needed in your theoretical calculations.

1 kΩ

1 kΩ

+ 10 V

5V 1 kΩ

─

Figure 2. Resistive Circuit for Part B.

Table 2: Measured Resistance Values for Part B Measured Value of R1

Measured Value of R2

Measured Value of R3

Measured Value of R4

Measured Value of R5

2. Carefully build the circuit shown in Figure 2 on your breadboard. Adjust the DC power

supplies to as close to 5 V and 10 V as you can, using the digital multimeter to get accurate readings. Record the exact values of your voltage sources on Table 3. They will be needed in your theoretical calculations.

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Table 3: Measured Voltage Values for Part B

3. Repeat the procedure and measurements as done in Step 3 of Part A for this particular circuit. At the end of this handout, there is a table entitled “Recorded and Calculated Values for the Circuit of Fig. 2 (Part B)” and is provided for your convenience. You may use this table to record your readings. For your lab report on Part B, perform the following tasks: a) Calculate the theoretical values for the voltage and power at the potentiometer (you can use mesh or node analysis). b) List the measured and calculated values on a table (typed) along with Tables 2 and 3. c) Generate a plot of the potentiometer voltage V0 versus the potentiometer’s resistance, R0, and a plot of the power absorbed by the potentiometer versus the potentiometer’s resistance, R0. You can use Matlab, but Excel will work as well for these simple calculations. Include your code in your report. d) Determine from your measurements what value of the potentiometer resistance, R0, results in a maximum power transfer to the load. e) Using the resistance and voltage source values measured in steps 1 and 2, calculate the theoretical value of resistance R0, for which maximum power transfer from the circuit will occur. Compute the percent error between this value and the measured value.

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Recorded and Calculated Values for the Circuit of Fig. 1 (Part A) Measured V0 (Volts)

Measured R0 (Ω)

Calculated P0 (Watts)

Min =

Max =

Recorded and Calculated Values for the Circuit of Fig. 2 (Part B) Measured V0 (Volts) Min =

Measured R0 (Ω)

Calculated P0 (Watts)

Max =

5

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