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# Curriculum and Labs for Engineering Education

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## myDAQ mini-lab: Thevenin Equivalent I – Source transformations

Course Linkage: Linear Circuit Analysis >> Thevenin Equivalents; Source Transformations

Measurement Techniques: ELVISmx DMM (voltmeter, ammeter, ohmmeter)

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### Introduction

Overview: Two circuits may be quite different from each other in terms of topology and complexity and yet behave identically at a pair of terminals. “Behavior” refers specifically to the voltage and current associated with the terminal pair when other devices connect to the two circuits. The simplest circuit that is equivalent to another more complex circuit is called the Thevenin equivalent circuit; it contains only a single voltage source and a single resistor.

Objectives: In this mini-lab you will:

• Measure terminal behavior in terms of open-circuit voltage and short-circuit current
• Measure terminal with a visual indicator (light emitting diode, or LED)
• Apply source transformations and resistor reductions to reduce a circuit to its Thevenin equivalent

### Equipment

• NI myDAQ
• Connecting wire
• Texas Instruments (TI) TL072 op amp or similar device
• Resistors, ¼-W 5% carbon film: 1.5K (three), 1.0K (two), and 4.7K
• 10K potentiometer
• LED (light emitting diodes)

### Deliverables

• Submit your work in the form of a homework set problem or lab notebook entry according to the requirements of your instructor
• Submit your work for each underlined boldface item, and clearly label the item with its section letter and task number

### A. Experience circuit terminal behavior by measurement

1. Draw the three circuits shown in Figure 1. Only two of the circuits are equivalent at terminals A-B; your task is to determine which two:
2. Before you construct the circuit, set up the ELVISmx DMM as an ohmmeter and measure and record the resistance of each resistor.
3. Construct the circuit of Figure 2 with myDAQ and a breadboard; see Figure 3 for the recommended layout and Figure 4 for the myDAQ connections:
4. Connect the LED between terminals A-B on Circuit A (reverse the LED polarity if it does not light). Repeat for Circuits B and C.
5. Respond: Which pair of circuits produces the same LED intensity? How does the intensity of the third circuit compare?
6. Set up the ELVISmx DMM as a voltmeter. Measure and record the “open-circuit” voltage between the terminals A-B for each circuit, i.e., the voltage that appears when nothing connects between the terminals.
7. Set up the ELVISmx DMM as an ammeter – remember to change the red probe to the DMM “A” input. Measure and record the “short-circuit” current between the terminals A-B for each circuit, i.e., the current that flows when a wire connects the terminals together. Remember that the ammeter has very low resistance and amounts to a wire with a measuring device attached.
8. Respond: Based on your measurements, which circuits are equivalent?

The following video shows some expected results for this section:

### B. Learn the underlying principles

The following video tutorial introduces source transformations and resistor reductions as a circuit analysis technique to determine the Thevenin equivalent of a given circuit:

Learn two techniques to measure the Thevenin resistance:

### C. Connect the principles to your measurements:

1. Change resistor R5 in Circuit B to 4.7K on your breadboard; draw this new circuit and call it Circuit D.
2. Determine the Thevenin equivalent of this modified circuit at terminals A-B by applying source transformations and resistor reductions.
3. Measure and record the open-circuit voltage and the short-circuit current for Circuit D; calculate the Thevenin resistance from these measurements.
4. Connect the 10K potentiometer between the terminals A-B.
5. Set up the DMM voltmeter to measure the voltage across the potentiometer. Connect the DMM probes permanently to the terminals A (red) and B (black) to save effort. Use probe clips if you them available, or coil a wire around the probe tip with one end of the wire long enough to connect into the breadboard.
TIP: Wrap the wire around the probe tip to form a coil, remove the coil and bend it slightly, and place it back on the coil (bending the coil ensures a snug fit).
6. Adjust the potentiometer until the DMM voltmeter shows exactly half the open-circuit voltage you measured in Step 3.
7. Disconnect the potentiometer from Circuit D (leave it in the breadboard, but ensure that at least one wire connection to Circuit D is removed).
8. Set up the DMM as an ohmmeter; measure and record the resistance of the potentiometer.
9. Compare the three values of Thevenin resistance you produced in this section (one from circuit analysis and two from measurements).

The following video demonstrates the measurement technique for this section on the unmodified Circuit B: