Lab 3: Equivalent Resistance

Lab 5:Thevenin Equivalent

Purpose:

To demonstrate equivalent circuits using computer simulations and actual circuits.Students should gain additional experience using computer simulations tools.

Equipment and Components:

1) Prototyping board, Multimeter, Power supply

2) Resistors: 5.1 kΩ, 13 kΩ, 20 kΩ, 24 kΩ, 43 kΩ, 56 kΩ, 120 kΩ, and othersdepending upon your design

Procedure:

1. Calculation:

Using the circuit shown in Figure1, calculate the Thevenin and Norton equivalent circuit.

1)To find RTH, First transform the lower half of the bridge using ∆-to-Y transformation (see HW5 (Lab 4)). Then use the technique shown in 4.11 (figs. 4.52 & 4.53) to simplify and find RTH.

2)To find VTH, use ∆-to-Y transformation as above then add resistances in series. Remember that the resistances can be added if they share the same current (regardless of which node of the voltage source they are connected).

Fig. 1: Bridge Circuit

1. Simulation:

Use Multisim (or LTSpice) to determine the Thevenin and Norton equivalent circuits using the two

different methods described below. Include output from your simulation inyou lab book.

1)To find VTH, we need to evaluate the open circuit voltage between terminals A&B. Add a very big resistor (e.g.1E12) between terminals A and B (SPICE simulator cannot handle floating nodes) to represent an open and find the voltage. Make sure to ground terminal B. You can use .op analysis and note the voltage difference between A&B or you can place probe on terminal A and run transient analysis.

2)To find RTH, suppress the 6 V power supply (replace it with a short aka wire[1]) and apply a test 1 V test voltage source. Using probe, determine the current IT flowing into the circuit. RTH=1 V/ IT.

Q: Do the simulated values match the calculated values?

1. Experiment:

Create the circuit shown in Figure 1 on the breadboard.

1)Measuring VTH is simple: just use the multimeter (set to voltage mode) and probe the terminals A & B. This is the open circuit voltage (since multimeter has very large resistance in the voltage mode).

2)To measure RTH let’s try following three methods:

a)Disconnect the voltage source and replace it with a short. Now put multimeter in resistance mode and simply measure the resistance between terminals A&B. This resistance is RTH.

b)Reconnect the voltage source. Change the multimeter setting to the current mode. Place it in series between terminals A&B (always power down the circuit before making any modifications or you will blow the fuse). Now measure the short circuit current (ISC). RTH=VTH (as measured above)/ISC.

c)Replace the voltage source with a short. Use test voltage = 1 V between terminals A&B. Place the multimeter in series between the voltage source and the circuit (e.g. between terminal A and positive node of the voltage source). Measure the test current that flows into the circuit. Calculate the effective resistance of the circuit.RTH=1 V/ IT.

Q: Do the measured values of RTH in a),b),and c) match?

Q: Do the calculated, simulated and measured values of VTH and RTH match?

Create a table in your lab book enlisting calculated, simulated, and measured values of VTH and RTH.

Table 5.1

Conclusion

Compare the calculated value, simulated values, and all measured values.

How do thevarious methods for measuring RTHcompare?

Which method was simplest andmost accurate?

[1]Remember that voltage source is replaced with a short and current sources are replaced with an open as these are the ideal conditions.