Thevenin and Norton Equivalent Circuits: Lab Report for ECE 285 at George Mason University, Summaries of Law

Download Thevenin and Norton Equivalent Circuits: Lab Report for ECE 285 at George Mason University and more Summaries Law in PDF only on Docsity! George Mason University Volgenau School of Engineering Department of Electrical and Computer Engineering Lab 5 Report ECE 285-202 Alexander Ing 2020-04-07 Contents 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 1.1 Theory and Calculations 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 R3. The equivalent resistance in this circuit is expressed by summing the resistors R1, R3, and R4: 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: I = V R ⇒ I = 10 V Req ≈ 1.61 mA Lastly, we can apply Ohm’s Law again to find the voltage across this resistor. VTh = IR3 = (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 V1 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 = R2 + (R3 ‖ (R1 + R4)) + R5 = 3 kΩ + (2.2 kΩ ‖ (1 kΩ + 3 kΩ)) + 10 kΩ ≈ 14.4 kΩ 1 2 Norton’s Theorem 2.1 Theory and Calculations 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. IN = VTh RTh = 3.55 V 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 5 5 4 4 3 3 2 2 1 1 D D C C B B A A 0 Title Size Document Number Rev Date: Sheet of <Doc> <RevCo <Title> A 1 1Tuesday, April 07, 2020 I_N 246.5u LOAD 3k R_N 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 = INReq ≈ 611 mV 4 2.2 Simulation D. Simulate the Norton’s circuit in PSpice and present the results for voltage across the load resistor. Solution The simulated Norton equivalent is shown in Figure 2.2. Note that the voltage Vab is the exact same as 5 5 4 4 3 3 2 2 1 1 D D C C B B A A 0 Title Size Document Number Rev Date: Sheet of <Doc> <RevCo <Title> A 1 1Tuesday, April 07, 2020 LOAD 3k 204.0uA I_N 246.5u 246.5uA R_N 14.4k 42.50uA 612.0mV a b 0V 0V 612.0mV Figure 2.2: Simulated Norton equivalent circuit the theoretical voltage calculated in part C above as well as the simulated original circuit in Figure 1.6. 3 Conclusion This lab proved the Thevenin and Norton equivalent circuit theorems. This was done by using the respective theorems to calculate an equivalent circuit that should produce the same voltage across and current through a load resistor, which it did in the calculations. Furthermore, this was verified by simulating the equivalent circuits in PSpice, which produced the same results. Since the results were all consistent, we can conclude that both the Thevenin and Norton equivalent circuit theorems are true. 5