Chapter 3
Analysis Techniques

m3.4 Thévenin Equivalents and Maximum Power Transfer

In the circuit of Fig. m3.4, find the Thévenin equivalent of the circuit at terminals (a,b) as seen by a load resistor R_L. Specifically:

1. Determine the open-circuit voltage V _OC that appears at terminals (a,b).
2. Determine the short-circuit current I_SC that flows through a wire connecting terminals (a,b) together.
3. Determine the Thévenin resistance.
4. Determine the maximum power P_Lmax that could be delivered by this circuit.

Use these component values: V _SRC = 10 V, R₁ = 680 Ω, R₂ = 3.3 kΩ, R₃ = 4.7 kΩ, and R₄ = 1.0 kΩ.

NI Multisim Measurements

1. Enter the circuit of Figure m3.4 into NI Multisim. Connect a resistor R_L as a load between terminals (a,b).
2. Use interactive analysis and measurement probes to determine the open-circuit voltage.
3. Use interactive analysis and measurement probes to determine the short-circuit current.
4. Run a parameter sweep to plot the load resistance power as a function of load resistance connected between terminals (a,b). Use a plot cursor to determine the value of maximum power.

These tips provide more detail about the Multisim techniques for this problem:

• Place a measurement probe on terminal b to display the load current.
• Place a measurement probe on terminal a referenced to the probe you placed on terminal b to display the voltage across the load.
• Set the load resistance to a small yet finite value such as 0.1 Ω. Run the interactive simulator to determine the short-circuit current.
• Set the load resistance to a large yet finite value such as 100 MΩ; enter this value as 100MEG rather than 100M because ”m” means ”milli” regardless of case. Run the simulator to determine the open-circuit voltage.
• Set up a Simulate → Analyses → Parameter Sweep to plot P(RL) over the range 1 Ω to 10 kΩ. Choose a linear plot type, select “DC Operating Point” for “Analysis to Sweep,” and plot 100 evenly-spaced points to create a smooth curve.
• Use the plot cursors to find the maximum value of the load power. Compare this value to the maximum power you calculated analytically.

NI myDAQ Measurements

1. Build the circuit of Figure m3.4. Calculate the Thévenin equivalent circuit from the measurements taken in the next two parts.
2. Recall that the DMM voltmeter has very high resistance and thus appears as an open circuit. Connect the voltmeter between terminals (a,b) to measure the open-circuit voltage.
3. Also recall that the DMM ammeter has very low resistance and thus appears as a short circuit. Connect the ammeter between terminals (a,b) to measure the short-circuit current.
4. Connect the variable load circuit shown in Figure 3.4a between terminals (a,b) and connect the myDAQ analog input channels to measure the overall load voltage and the voltage that appears across the shunt resistor; this latter voltage is proportional to the load current. Run the LabVIEW VI “VIPR.vi” (described below) to display the load’s voltage, current, power, and resistance. First sweep the potentiometer throughout its full range to get a sense of the overall behavior, and then collect and tabulate at least 10 measurements of load power and load resistance; adjust the potentiometer to take measurements in 1 mW steps. Also record the maximum power and associated load resistance. Finally, plot the load power as a function of load resistance.

LabVIEW “VIPR.vi” details:

• The LabVIEW VI “VIPR.vi” measures the overall load voltage on analog input channel 0 (AI0+ and AI0-) and the shunt resistor voltage on analog input channel 1 (AI1+ and AI1-). Enter the measured shunt resistance for best accuracy. “VIPR.vi” calculates the load current as the voltage on AI1 divided by the entered shunt resistance value, the load power as the product of load voltage and current, and the load resistance as the load voltage divided by the current.
• The measured current value can become somewhat noisy, and “VIPR.vi” applies a noise filter to improve your ability to read the display. The noise filter calculates the average value of all of the measurements accumulated since the last time the measured voltage changed by at least 0.01 volts. Disable the noise filter, if desired.
• “VIPR.vi” is linked at the bottom of http://decibel.ni.com/content/docs/DOC-16389. Download this source file and double-click it to open in LabVIEW; click the “Run” button to start the VI.

Further Exploration with NI myDAQ

Try this simple yet effective technique to directly measure Thévenin resistance:

1. Measure the open-circuit voltage at terminals (a,b),
2. Connect a variable resistor as the load (10 kΩ potentiometer works well for this circuit),
3. Monitor the load voltage and adjust the potentiometer until the voltage is exactly one half of the open-circuit voltage,
4. Disconnect the potentiometer from the circuit, and
5. Measure the potentiometer resistance with an ohmmeter; this value is the Thévenin resistance.

Apply this method to the circuit of this problem and compare your results to your other measurements of Thévenin resistance.

Explain why this method works. Hint: Consider a Thévenin equivalent circuit connected to a load resistor and recall what you know about voltage dividers.