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A lab report detailing the application of Thevenin's and Norton's theorems to find the equivalent circuits of a given circuit. The report includes theoretical calculations, simulations using PSpice, and a conclusion confirming the validity of the theorems.
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George Mason University Volgenau School of Engineering Department of Electrical and Computer Engineering
ECE 285-
1 Thevenin’s Theorem 1 1.1 Theory and Calculations............................................ 1 1.2 Simulation.................................................... 2
2 Norton’s Theorem 4 2.1 Theory and Calculations............................................ 4 2.2 Simulation.................................................... 5
3 Conclusion 5
Figure 1.1: Circuit for Lab 5
1 Thevenin’s Theorem
A. Find the theoretical Thevenin’s voltage VTh by finding the open-circuit voltage between terminals a and b for the circuit in Figure 1.1. Solution In order to find the theoretical Thevenin’s voltage VTh, we can use the redrawn circuit in Figure 1.2 and
Figure 1.2: Redrawn circuit from Figure 1.1 to find VTh
find the voltage at the terminals of R 3. The equivalent resistance in this circuit is expressed by summing the resistors R 1 , R 3 , and R 4 :
Req = 1 kΩ + 2.2 kΩ + 3 kΩ = 6.2 kΩ
Then, the current through the loop can be found by applying Ohm’s Law:
Req
≈ 1 .61 mA
Lastly, we can apply Ohm’s Law again to find the voltage across this resistor.
VTh = IR 3 = (1.61 mA)(2.2 kΩ) ≈ 3 .55 V
B. Then find the theoretical Thevenin’s resistance RTh by removing the Load Resistor. Also replace the source V 1 with its internal resistance (ideally, a short). Solution To find the theoretical Thevenin’s resistance RTh, we can use the redrawn circuit in Figure 1.3 and solve for the equivalent resistance between terminals a and b.
Rab ≡ RTh = R 2 + (R 3 ‖ (R 1 + R 4 )) + R 5 = 3 kΩ + (2.2 kΩ ‖ (1 kΩ + 3 kΩ)) + 10 kΩ ≈ 14 .4 kΩ
4 3
0
Figure 1.5: Thevenin equivalent circuit simulation
4 3 2
3k
203 .7uA
2.2k
1.482mA
1k
1.685mA
1.685mA
3k
203.7uA
10k
203.7uA
3k
1.685mA
b 0V 5.056V 7.093V
a 7.704V
Figure 1.6: Original circuit simulation
2 Norton’s Theorem
A. Calculate the Norton’s resistance RN for the circuit in Figure 1.1. How is it related to Thevenin’s resistance RTh? Solution Norton’s equivalent resistance RN is calculated using the same process as RTh, thus it is the exact same. See part B from section 1.1 for the work.
RN ≡ RTh ≈ 14 .4 kΩ
B. Also calculate the Norton’s current IN for the circuit in Figure 1.1. Solution The Norton current IN can be calculated from our previously calculated values of VTh and RTh.
VTh RTh
14 .4 kΩ
≈ 0 .247 mA
C. Draw the Norton’s equivalent circuit and calculate the voltage across the load resistor. Solution The Norton equivalent circuit is shown in Figure 2.1. As for the voltage across the load resistor, we must
4 3 2
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246.5u
3k
14.4k
Figure 2.1: Norton equivalent circuit
first calculate the equivalent resistance in the circuit.
Req = RN ‖ Rload =
14 .4 kΩ × 3 kΩ 14 .4 kΩ + 3 kΩ
≈ 2 .48 kΩ
Now, we can use Ohm’s Law to calculate the voltage across the parallel combination of everything.
V = IR ⇒ Vab = IN Req ≈ 611 mV