Introduction to Thevenin S Theorem and Maximum Power Transfer

EE 442 Laboratory Experiment 3

Introduction to Thevenin’s Theorem and Maximum Power Transfer

EE 442

Lab Experiment No. 3

1/22/2007

Introduction to Thevenin’s Theorem and Maximum Power Transfer

I.INTRODUCTION

The purpose of this experiment is to study the principle of Thevenin’s Theorem. Thevenin’s Theorem will be explored by numerically analyzing a particular circuit in the preliminary part of this experiment. This same circuit will then be experimentally examined in the laboratory. Corresponding calculated and measured circuit response values will be compared. A secondary purpose of this experiment is to use the Thevenin equivalent circuit to study the principle of maximum power transfer.

We will demonstrate the validity of Thevenin’s Theorem in the laboratory by applying it to the circuit shown in Figure 1.

Figure 1 Circuit used to study Thevenin’s Theorem

II.PRELAB EXERCISES

1. Use either the node voltage or the mesh current methods to find the value of the load current, iL, through the 10 kΩ resistor, RL, as shown in Figure 1. Also find the value of the load voltage, vL. Record your results below.

iL = ______

vL = ______

1. Find the Thevenin equivalent circuit of the network to the left of terminals A-B in Figure 1. Record the open circuit voltage and the Thevenin resistance below.

vOC = ______

Rt = ______

III.LABORATORY EXPERIMENTS

Figure 2 Laboratory version of the circuit in Figure 1

1. With the DC supply turned off, construct the circuit shown in Figure 2 to the left of terminals A-B.

1. Energize the DC supply and set it at 30 Volts.

1. Measure the open circuit voltage between terminals A-B and record below. Compare this value with the open circuit voltage determined analytically in step 2 of the preliminary exercise.

vOC = ______

1. The short circuit current between terminals A-B can be measured by connecting an ammeter across terminals A-B. It is assumed that the internal resistance of the ammeter is low enough that it appears as a short circuit to the circuit between terminals A-B. Record the measured value of the short circuit current below.

iSC = ______

1. On the basis of the data recorded in steps 3 and 4, the Thevenin equivalent circuit can be derived. Calculate the Thevenin equivalent resistance, Rt, and record below. Compare this experimentally derived equivalent circuit with the one obtained by circuit analysis in step 2 of the preliminary part of this experiment.

Rt = ______

1. Before performing step 7, do the following. Turn off the 30 VDC supply. Disconnect the two leads connected to the DC supply terminals. Connect these two leads together, creating a short circuit. This procedure replaces the 30 V source with its ideal internal resistance of zero ohms. The 30 V source is now “suppressed.” An open circuit should exist between terminals A-B. Use an ohmmeter to measure the Thevenin equivalent resistance, Rt, at terminals A-B. Compare this value with the results of step 5. Remember, an ohmmeter should never be used to measure resistance of an energized circuit.

1. The next step is to measure the load current, iL, and the load voltage, vL, of the circuit in Figure 2. To perform the first of these tasks, connect the 10 kΩ load resistor in series with an ammeter and measure iL. Measure the voltage drop across RL. Record the values of iL and vL below and compare them with step 1 of the preliminary exercise.

iL = ______

vL = ______

1. Turn off the DC voltage source and dismantle the circuit. Now construct the circuit shown in Figure 3. Adjust the DC supply to the value of vOC found in step 2 of the preliminary exercise. Use the resistor value found in step 2 of the preliminary exercise for the value of Rt.

Figure 3 Thevenin Equivalent of the circuit in Figure 2

1. Using the DMM, measure the open circuit voltage of this circuit at terminals A-B. Record this value below and compare with the results of step 3 of the experimental exercise. This measurement verifies the equivalence of the two circuits (Figures 2 and 3) under open circuit loading conditions. Note that RL is infinitely large and iL is zero in this case.

vOC = ______

1. Using an ammeter, measure the short circuit current of this circuit between terminals A-B. Record below and compare with the results of step 4 of this experiment. This measurement verifies the equivalence of the two circuits (Figures 2 and 3) under short circuit loading conditions. Note that vL = 0 in this case.

iSC = ______

1. Next connect the 10 kΩ load resistor between the terminals of the circuit in Figure 3. Measure iL and record below. Also measure vL with the DMM and record below. Compare these values with the results of step 6 of this experiment. These measurements verify the equivalence of the two circuits under “in-between” loading conditions.

iL = ______

vL = ______

1. This concludes the study of Thevenin’s Theorem. The next part of this experiment will use the Thevenin equivalent circuit to experimentally study the concept of maximum power transfer.

Figure 4 Circuit to study maximum power transfer

1. The circuit of Figure 4 is the same as that in Figure 3, except that in Figure 4, RL is a variable resistance. The Thevenin equivalent portion of this circuit can be interpreted as representing the terminal equivalent of a more complicated circuit such as a DC power supply or a generator.

Consider a hypothetical problem which requires solving for the current iL through a given value of RL. The direct solution of the original circuit could involve a lot of work to obtain iL. An alternative solution would be to find the Thevenin equivalent of the original circuit, then solve for iL using the resultant simple series circuit. This technique would also certainly take a lot of work, perhaps more work than just solving the circuit outright. However, if the value of iL for a range of RL values is desired, a lot of work will be required to find the Thevenin equivalent, but finding iL for subsequent values of RL would require solving only the simple Thevenin equivalent circuits.

1. For the last part of this experiment, we want to examine the power delivered from the supply to the load and determine what load resistor value will dissipate the most power. What value of Rt should result in maximum power dissipation in RL?

RL = ______

1. Calculate the maximum power dissipated in RL.

PL = ______

1. Assemble the circuit of Figure 4. The values of vOC and Rt are the same as those used for the circuit of Figure 3. Use the decade resistance box for RL since RL will take on a range of values. For each value of RL given in the table below, measure iL and vL and record in the spaces provided. Calculate the corresponding value of power, PL, dissipated in RL, and record. Make a note of which value of RL gives rise to maximum power dissipation. Plot PL vs. RL on the attached grid (Page 7).

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