lab4theveninstevens

8/4/2019 Lab4TheveninStevens

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Lab 4: Thevenin Equivalent Circuits

By:

Hanyu Li, Jing Wang, and Yang LiStevens Institute of TechnologyPrepared and Taught by the Department of Electronic and Computer EngineeringIn Academic Year 2006 Spring Semester

Purpose

The purpose of this lab is to learn how to obtain a Thevenin Equivalent circuit by making measurements of the I-V(current-voltage) characteristics at a pair of terminals.

Equipment Required

Agilent E3631A DC power supply

Agilent 34401A Digital Multimeter

5 resistor 500,1k,1.5k,2k,2.5k.

1 variable resistor.

Introduction

Any linear DC circuit as seen at a pair of terminals can be reduced to a practical voltage source (an ideal voltage sourcein series with a resistor). Thevenins theory can be found from Page 80-Page 86 in the textbook. See Figure 1.

Figure 1: Thevenin Equivalent Circuit


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Voc=VR221

2

RR

R

+= Vs (2)

Step 2:For calculation ofisc, we can transform the original circuit (Figure 2) by replacing the load R4 by a wire (please note the

difference between open circuit and short circuit) as shown in Figure. 5.

Figure 5: Circuit 1 short circuit

The problem of solving for isc can be transformed to solve for i3, since we are looking at the same loop. Hence,isc=i3

To solve for i3,. Current divider formula can be used, i.e.

isc=i3=i1*

32

2

RR

R

+(3)

Where i1 can be calculated as

i1=

32

32

1

s

321

s

RR

RRR

V

R//RR

V

++

=+

(4)

The above equation is based on Ohms law and Equivalent resistance formulas.

Step 3:The Thevenin equivalent resistance RThcan be determined from the equation (1)

RTh =v

oc

isc

Experimental ProcedureYou will build two circuits, calculate their Thevenin Equivalent circuit as seen at a pair of terminals, and then verify youranalysis through measurements.

1. Circuit 11) Obtain four different valued resistors R1=500, R2=1k, R3=1.5k, and R4=2.5k.

2) Measure and record the value of each resistor.

3) Build the circuit shown in Figure 6 on the breadboard, using the DC power supply as vs. Once you have built thecircuit, set the value ofvs to 10 V. Be sure to use the multimeter to make sure the terminal voltage produced by thepower supply is as close to 10 V as you can get it.

4) Calculate the voltage drop from a to b (across R4) using voltage division twice. Be sure to show all your work in yourlab report.


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5) Measure (and record) the voltage drop from a to b (across R4).

6) Calculate the Thevenin Equivalent circuit as seen at terminals ab without R4 present. You are calculating theThevenin Equivalent circuit as seen by R4. Be sure to show all your work in your lab report.

7) Remove R4from your circuit. Measure voc and iscat terminals ab and calculate RTh. Do your measurements agreewith your theoretical analyses?

8) Dismantle your circuit. Obtain a 1 k potentiometer (variable resistor) from the parts bin. There are several different

drawers with potentiometers. Locate the drawer with the 1 k label. Using the ohmmeter, adjust the resistance of thepotentiometer to the value of RTh you calculated in step 6.

9) Build the circuit shown in Figure 7 using the same resistor for R4, the potentiometer for RTh, and the DC powersupply for voc. Adjust the terminal voltage of the power supply to the value of voc you calculated in step 6. Be sure touse the voltmeter to check this voltage!

10) Calculate the current through R4 in Figure 7.

11) Measure the current through R4. Do the calculated and measured values agree?

12) Measure the voltage across R4. Does this value agree with your calculated value from step 4 and measured valuefrom step 5?

13) Dismantle your circuit.

R4

2.5k

R2

1k

Vs

10Vdc

R1

500

b

aR3

1.5k

Figure 6: Circuit 1

Figure 7: Thevenin Equivalent circuit connected to a load resistor


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2. Circuit 2

Vs

10Vdc

R4

2.5k

a b

R3

1.5k

R5

2k

R2

1k

R1

500

Figure 8: Circuit 2

1. Obtain five different valued resistors each with R1=500, R2=1k, R3=1.5k, R4=2.5k and R5=2k.

2. Measure and record the value of each resistor.

3. Build the circuit shown in Figure 8 on the breadboard mounted to the bench top, using the DC power supply as vs.Once you have built the circuit, set the value ofvs to 10 V. Be sure to use the multimeter to make sure the terminal

voltage of the power supply is as close to 10 V as you can get it.

4. Calculate the voltage drop from a to b (across R4) using the node voltage method. This can be done by calculatingthe node voltage. for example, Va=Vs-V1 and Vb=Vs-V3. Then the voltage drop from a to b can be calculated by Va-Vb. Be sure to show all your work in your lab report.

5. Measure (and record) the voltage drop from a to b (across R4).

6. Calculate the Thevenin Equivalent circuit as seen at terminals ab without R4 present. You are calculating theThevenin Equivalent circuit as seen by R4. Be sure to show all your work in your lab report.

7. Remove R4 from your circuit. Measure vocand isc at terminals ab and calculate RTh. Do your measurements agreewith your theoretical analyses?

8. Dismantle your circuit. Obtain a 1 k potentiometer (variable resistor). Using the ohmmeter, adjust the resistance ofthe potentiometer to the value of RTh you calculated in step 6.

9. Build the circuit shown in Figure 7 using the same resistor for R4, the potentiometer for RTh, and the DC powersupply for voc. Adjust the terminal voltage of the power supply to the value of voc you calculated in step 6. Be sure touse the voltmeter to check this voltage!

10. Calculate the current through R4 in Figure 7.

Figure 7: Thevenin Equivalent circuit connected to a load resistor

11. Measure the current through R4. Do the calculated and measured values agree?

12. Measure the voltage across R4. Does this value agree with your calculated value from step 4 and measured valuefrom step 5?

13. Dismantle your circuit.


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14. Return the resistors to the proper drawers in the parts cabinet.

3. PSpice (Optional)

Get familiar with PSpice by professor Tewksburys PSpice Tutorial. The tutorial can be downloaded from E245Homepage.Then use PSpice to simulate the four following circuits.

1. Circuit 1 with R4 present. Monitor voltage drop across R4.

2. Circuit 1 with R4 replaced with a large dummyresistor. Monitor voltage drop across Rdummy

3. Circuit 1 with R4 replaced with a wire. Monitor current through the wire.

4. Circuit 2 with R4 present. Monitor voltage drop across R4.

5. Circuit 2 with R4 replaced with a large dummyresistor. Monitor voltage drop across Rdummy

6. Circuit 2 with R4 replaced with a wire. Monitor current through the wire.Compare in detail your theoretical, measured, and simulated results.

Figure 9: Circuit 1 with nodes labeled for PSpice

4. Questions(Optional)

Answer the following questions in your lab report.

1. What is meant by the word "equivalent" in Thevenin Equivalent circuits?

2. Explain why Rdummy is needed in the PSpice simulations. Why not just take R4 out of the circuit and simulate theresulting circuit?

3. Why is it that making Rdummy "large" produces accurate simulation results? How large must Rdummy be in order toproduce accurate simulation results?

4. What is the practical value of Thevenin Equivalent circuits? Give several practical applications in which TheveninEquivalent circuits are used.

5. As you have seen, the Thevenin Equivalent of a circuit can be obtained by calculating/measuring two I-V values: vocand isc. Often, it is not practical to measure the short circuit current. Can you imagine trying to measure isc for a carbattery? Suppose you wanted to obtain the Thevenin Equivalent of a circuit by making two measurements, neither of

which involves measuring isc. You measure voc and then place a 1 k resistor across the terminals and measure thevoltage drop across the resistor. Do you have enough information from these two measurements to obtain theThevenin Equivalent circuit? Justify your answer in detail.

6. Suppose you have two boxes in front of you. One box contains a Thevenin Equivalent (voltage source inseries with aresistor) and the other box contains a Norton Equivalent (current source in parallel with a resistor). Each box has apair of terminals available for measurement. You cannot open the boxes. You may make any electrical measurementsat the terminals. You also have access to the outside surface of the boxes. Can you determine which box contains the


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Thevenin Equivalent and which box contains the Norton Equivalent? Or is it impossible to determine which circuit is inwhich box? Justify your answer in detail.

lab4theveninstevens

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