FACULTY OF ENGINEERING

LAB SHEET

CIRCUIT THEORY

EEL1166

TRIMESTER 1 (2017/2018)

CK1-Thevenin’s Theorem and Superposition Theorem

*Note: Students are advised to read through this lab sheet before doing experiment. Your performance, teamwork effort, and learning attitude will count towards the marks.

Marking scheme is given at the end of the labsheet.

Experiment CK1: Thevenin’s Theorem and Superposition Theorem

1.0 Objective

To verify the Thevenin’s theorem by using circuit theory experiment board. To verify Superposition theorem.

2.0 Introduction

Thevenin’s Theorem is a very useful and frequently used theorem in circuit analysis. To verify Thevenin’s Theorem, consider a load resistor RL (or load impedance ZL) that is connected to a “black box” as shown in Figure 1. The black box can contain any combination of the circuit elements. Thevenin’s Theorem states that in so far as the load resistor RL (or load impedance ZL) is concerned, the black box can be represented by a series combination of an ideal voltage source, VTH, and a resistor, RTH (or impedance ZTH). VTH is known as the Thevenin equivalent voltage source. Its value can be found by measuring the open-circuit voltage between terminals X and Y when the resistor RL is removed. RTH is called the Thevenin equivalent resistance and ZTH is called the Thevenin equivalent impedance. By measuring the short-circuit current ISC flowing through a wire that connects X to Y, the value of RTH (or ZTH) can be calculated as the ratio of VTH over ISC. When calculating the Thevenin equivalent impedance, the phasor values are to be used.

The series combination of VTH and RTH (or ZTH) is the equivalent circuit of the black box. By equivalent, it means the voltage across and current through any circuit element that is connected between terminals X and Y of the black box will be the same as the case when that circuit element is connected in series with RTH (or ZTH) and VTH. The theorem is valid provided that the circuit inside the “black box” is linear. The load resistor RL (or load impedance ZL) however, may not be linear.

Blackbox

V OC =V TH ISC =V TH /R TH

+-

R TH

V THR L

X

Y

Blackbox

X

Y

Blackbox

X

Y

R L

X

Y

Figure 1: Thevenin equivalent circuit

Another important theorem for circuit analysis is the Superposition Theorem. For a linear circuit, the total effect of several causes acting simultaneously is equal to the sum of the effects of individual causes acting one at a time. For example, consider the circuit in Figure 2. The current Ix can be found by calculating the current I1 due to the 3V voltage

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source alone, and the current I2 due to the 2A current source alone, and then taking the sum of I1 and I2. For a more complicated circuit, the effect of each individual source can be determined one at a time by turning off all the other sources. A voltage source is turned off by replacing it by a short circuit, while a current source is turned off by replacing it by an open-circuit.

2 A+-

4

3 V

+-3 V 2 A

Ix

I1 I2

6

4 4

6 6

Figure 2: Illustration of Superposition Theorem

3.0 Apparatus for the experiments

“Circuit Theory” experiment boardDC Power SupplyDual-trace OscilloscopeFunction GeneratorDigital MultimeterConnecting wires

4.0 Procedures

4.1 Verification of Thevenin’s Theorem

1. Construct the circuit shown in Figure 3(a) by connecting T2 to T3, T6 to T7, T16 to T17, T14 to T15, T8 to T11, and T12 to T13 on the experimental board using connection wires. Set the DC Power Supply to 3V; connect the positive terminal to P1, and the negative terminal to P2. (Be careful when inserting and removing connections from the board. Do not damage the board. Avoid using unnecessarily long wires that may introduce noise into the circuit.)

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Figure 3: Thevenin equivalent circuit

2. Using a voltmeter/multimeter, measure the voltage VL between T8 and T13. This is the output voltage across the resistor R4 (Consider R4 as the load resistor RL).

3. Remove the connections of T8-T11 and T12-T13.

4. Measure the voltage between T8 and T13. This open-circuit voltage is the Thevenin equivalent voltage VTH.

5. Set the multimeter to function as a milli-ammeter. Connect the meter between T8 and T13. The milli-ammeter acts as a short-circuit from T8 to T13 and measure the short-circuit current ISC at the same time.

6. Calculate the Thevenin equivalent resistance RTH = VTH/ISC. Is the value equal to 11 k?

7. Set the DC Power Supply to a value equal to VTH. Remove the connections of T16-T17 and T14-T15.

8. Construct the circuit shown in Figure 3(b) by connecting T2 to T4 and T5 to T7.

9. Set the multimeter to function as a voltmeter. Measure the voltage between T8 and T13. Is the reading equal to VTH?

10. Use the multimeter as a milli-ammeter. Measure the short-circuit current from T8 to T13. Is the value equal to ISC measured in Step 5?

11. Connect T8 to T11 and T12 to T13. Measure the voltage across T8 and T13. Is the reading equal to that measured in Step 2?

4.2 Verification of Superposition Theorem

1. Remove all the wires from the experiment board.

2. Set both CH1 and CH2 of the oscilloscope to DC coupling (AC/GND/DC switch in the DC position). Set the vertical sensitivity to 2 V/div for both CH1 and CH2.(Make sure the INTENSITY of the displayed waveforms is not too high, which can burn the screen material of the oscilloscope).

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3. Set “VERT MODE” to “DUAL”, “SOURCE” to “CH1”, “COUPLING” to “AUTO”.

4. Set the function generator for a 10 kHz sine wave, with 2V amplitude (4V peak to peak). Check the waveform using the oscilloscope.(Never short circuit the output, which may burn the output stage of the function generator).

5. Connect the sine wave signal to terminals P5 - P6 (grounded at P6).

6. Set the DC Power Supply to 3V; connect the positive terminal to P1, and the negative terminal to P2.

7. Construct the circuit shown in Figure 4.

8. Connect a probe from CH1 of the oscilloscope to P3 - P6 (grounded at P6).

9. Connect the second probe from CH2 to P4 - P6 (grounded at P6).

R322 k

R422 k

P3 P4

3V

R111 k

~P6 P5+-

CH1 CH2

C10.1 F

2 sin t

Figure 4: Experimental set-up for verifying Superposition Theorem

10. Sketch the waveforms displayed on the oscilloscope and label the traces (CH1 and CH2).

11. Remove the DC Power supply connections from P1 and P2.

12. Short-circuit T1 to T18 with a wire. The circuit should look like that shown in Figure 5(a).

13. Sketch the waveforms displayed on the oscilloscope and label the traces (CH1 and CH2).

14. Remove the Function generator connections from P5 and P6.

15. Remove the short-circuit at T1 - T18, and do short-circuit T12 to T13 with a wire.

16. Connect the DC Power supply positive terminal to P1, and the negative terminal to P2. The circuit should look like that shown in Figure 5(b).

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P1

P2

17. Measure the voltage at P3, and the voltage at P4, using the oscilloscope. Sketch the oscilloscope display and label the traces (CH1 and CH2).

(a) (b)

R322 k

R422 k

P3 P4R1

11 k

~P6 P5+-

CH1 CH2

C10.1 F

R322 k

R422 k

P3 P4

3V

R111 k

P6 P5

CH1 CH2

C10.1 F

Figure 5: Analysis using Superposition Theorem

5.0 Results

5

P1

P2

P1

P2

5.1 Verification of Thevenin’s theorem

(a) Results based on the measurements on the circuit in Figure 3(a)

Before removing the load resistor R4:

Voltage across the load resistor, VL = ________

After removing load resistor R4:

Open circuit voltage, VTH, between T8 and T13 = ________

Short circuit current, ISC, from T8 to T13 = ________

Thevenin equivalent resistance RTH = VTH/ISC = ________

(b) Results based on the measurements on the circuit in Figure 3(b)

Before connecting the load resistor R4:

Open circuit voltage between T8 and T13 = ________

Short circuit current from T8 to T13 = ________

After connecting the load resistor R4:

Voltage across the load resistor = ________

(c) Theoretical analysis of the circuit in Figure 3(a)Theoretical calculation of the Thevenin equivalent voltage:

Theoretical calculation of the Thevenin equivalent resistance:

Draw the Thevenin equivalent circuit. Assume that now you have a load resistor RL of 11 kΩ connected between the terminals of your Thevenin equivalent circuit. Calculate the voltage across the load resistor.

5.2 Verification of Superposition Theorem

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(a) Results based on the measurements on the circuit in Figure 4Sketch the waveforms at CH1 and CH2.

(b) Results based on the measurements on the circuit in Figure 5(a)Sketch the waveforms at CH1 and CH2.

Write a mathematical expression for each of these waveforms. For a sinusoidal voltage waveform with zero mean value, find the peak value Vm and the period of the waveform T (in seconds). The angular frequency (in rad s-1) can be calculated using = 2/T. The mathematical expression is then V = Vm sin t.

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For voltage on CH1, peak value = ________

period of waveform = ________

angular frequency of waveform = ________

VCH1a = ________________

For voltage on CH2, peak value = ________

period of waveform = ________

angular frequency of waveform = ________

VCH2a = ________________

(c) Results based on the measurements on the circuit in Figure 5(b)Sketch the waveforms at CH1 and CH2.

Write a mathematical expression for each of these waveforms. For a constant waveform, the mathematical expression is just equal to the value of the waveform.

VCH1b = ________________

VCH2b = ________________

(d) Theoretical analysis using Superposition Theorem

Using Superposition Theorem, add the waveforms in parts (b) and (c) to obtain the total waveform caused by the two sources (one ac source and one dc source).

VCH1,total = ________________________________

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VCH2,total = ________________________________

Compare the graphs in part (d) with the graphs in part (a).

Questions and discussion:1- What is Superposition theorem?

…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

2- How do you apply the superposition of independent sources?…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

3- How do you deactivate the voltage and the current sources to do superposition? ……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

4- Mention in details the three steps to construct a Thevenin equivalent circuit.……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

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5- State briefly what you have learned from this experiment.……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

Marking Scheme

Lab (5%)

Assessment Components

Details

Hands-On & Efforts (2%)

The hands-on capability of the students and their efforts during the lab sessions will be assessed.

Lab Report (3%) Each student will have to submit his/her lab discussion sheet and recorded experimental data on the same day of performing the lab experiments.

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