paraphrase

In this experiment the Thevenin, Norton, and the Superposition theorems were reviewed. These procedures were practiced by hand and measurements were taken with the multimeter to verify the calculations. The students also built each circuit in PSPICE and compared the values it gave them with their calculated and measured values.

Equipment Used:

Type Model Serial No. Calibration Date

DC Power Supply

Digital Multimeter CDM250

Parts Used:

QTY Component Value Type

Resistors

Software Used:

MS Office 2010, SPICE

Theory:

Thevenins theorem: order to obtain Voc remove an external part of the circuit and compute the voltage between the open-loop terminals. Then remove all sources and compute the resistance, also known as Rth.

Nortons theorem: The general procedure of obtaining Isc and Rth is to remove a part of the circuit and replace it with a short to evaluate the current.

Maximum Power Theorem: The Theorem states that for the load resistor will dissipate the maximum power when its value is equal to the Thevenin resistance.

Superposition Theorem: In any linear resistive circuit containing two or more independent sources, the current through or voltage across any element is equal to the algebraic sum of the currents or voltage produced independently by each source.

Procedure and Results:

Preliminary Calculations:

1. For Figure 6.4 the task was to find the Thevenin and Norton equivalents to the left of a-b.

Figure 6.4

To do this, the students shorted the voltage source and simplified the resistors to find Rth. Then mesh analysis was used to find Isc and Voc.

Results: Rth = 1.94 Ω, Isc = 1.1 mA and Voc = 2.13 V

2. In the circuit shown in Figure 6.5, the value of R was found that results in the maximum power being delivered to R. This was done by using the maximum power transfer theorem.

Figure 6.5

In this circuit, R = Rth. To find R, the students simplified the resistors after removing R and shorting the voltage source. It was found that R = 2.72 kΩ.

3. For Figure 6.6, superposition was needed to find V1 and V2.

Figure 6.6

The 10 volt source was removed and nodal analysis was used to find V1’ = 2.17 V. Then the 5 volt source was removed and nodal analysis was used to find V1’’ = 1.30 V. Adding them together showed that V1 = 3.47 V. Using the same procedure to find V2’ and V2’’, it was found that -8.70 V + 2.17 V = V2 = -6.53 V.

Main Procedure:

1. First, the students constructed Figure 6.4 on our bread board and measured the voltage Vab. This showed that Vab = 1.53V.

2. Removing the 3.3 kΩ resistor and measured Voc, it was found that Voc = 2.11 V. This matches the calculated value.

3. Next, a short circuit was placed between the a-b terminals and the current, Isc, was found flowing through this circuit. The measured value of Isc = 1.10 mA agrees with the calculated value.

4. The next task was to remove the 10 volt source and replace it with a short circuit. Using the multimeter to measure Rth to the left of a-b, it was found that Rth = 1.90 kΩ. This shows that the calculations were done correctly.

5. Then, the measured Voc and Rth values were used to construct the Thevenin equivalent of the circuit to the left of a-b. This showed that Vab = 1.34 V, which is very close to the measured value in step 1.

6. Next, the circuit from Figure 6.5 was constructed and several values of R ranging from 100Ω to 10kΩ, were each connected. Using the resistance values and the measured voltage enabled the class to calculate the power and then construct a plot of P versus R.

7. Next, the circuit shown in Figure 6.6 was built and measured. This showed that V1 = 3.49 V and V2 = -6.53 V.

8. Removing the 5 volt source and replacing it with a short circuit gave V’1 = 1.31 V and V’2 = 8.71 V.

9. Putting the 5 volt source back in place and replacing the 10 volt source with a short circuit showed that V1’’ = 2.18 V and V2’’ = 2.18 V.

10. Adding the results from steps 8 and 9 produced the calculated values of V1 and V2. This verified the principle of superposition.

11. Next, the circuit from Figure 6.4 was built in PSPICE. This PSPICE circuit was used it to calculate Vab. This was compared with the measured results from step 1.

12. Then PSPICE was used to find Voc and Isc for Figure 6.4.

It was found that Isc = 1.098 mA and Voc = 2.128 V.

13. Next, circuit 6.5 was built in PSPICE and the calculated value of R was plugged in. Then a new simulation was set up to measure the value of V. This showed that V=2.104 V, which matches the value of V in the preliminary calculations.

14. The last step was to do the same thing for circuit 6.6. The circuit was constructed in PSPICE and it was confirmed that the calculations matched the PSPICE measurements. This gave V1=3.487V and V2=-6.513V. These both agree with the results from the preliminary calculations.

Conclusion:

Throughout this experiment, it was confirmed that the Thevinin, Norton and Superposition theorems really work. The class furthered their experience in building circuits and taking measurements both on a protoboard and in PSPICE. This will help the class in future experiments and careers.

Power vs. Resistance

Resistor (ohms)

Power (Watts)