ECEN 214 - Equivalent Networks and Superposition

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Texas A&M University *

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216

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Electrical Engineering

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Jan 9, 2024

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ECEN 214 - Equivalent Networks and Superposition Lab Number: 3 Section Number: 516 Student’s Name: Aneek Roy, Kelvin Su Lab Measurement Date: 2/06/23 Due Date: 2/27/23 TA: Farid Naghavi

Objectives: The lab involves building two DC circuits to experimentally test circuit solving techniques such as Thévenin's equivalent circuit and the superposition principle. The first procedure is to verify Thévenin's equivalent circuit and the second is to verify the superposition principle and its application conditions. The lab also involves learning how SPICE can be used to model a circuit. Procedure: In task 1, the instructions ask to construct the circuit shown in Figure 3.3 below using batteries and a variable voltage source. Three measurements are to be taken using a voltmeter. First, the voltage is measured across the 1kΩ resistor and recorded. Next, the 3V source is removed and replaced with a short circuit and the voltage is measured across the 1kΩ resistor and record it. Finally, the 3V source is put back and the 4V source is removed and replaced with a short circuit and the voltage is measured across the 1kΩ resistor and recorded. For task 2, repeat the instructions in task 1 with the only addition of a diode(1N4148). This is to check the superposition principle validity for a non-linear device. Data Tables: Parameter Measured Calculated % difference SPICE % difference (SPICE to measured) VL -0.273 -0.2654 2.79% -0.2655 2.75% VL1 0.285 0.2909 1.99% 0.2909 2.07% VL2 -0.563 -0.5564 1.19% -0.5564 1.17%

VL1+VL2 -0.278 -0.2655 4.66% 0.2655 4.50% Table for Task #1 Parameter Measured Calculated % difference SPICE % difference (SPICE to measured VL -2.80E-06 -2.521E-06 11.07% -2.521E-06 11.07% VL 1 0.1469 0.1614 8.98% 0.1614 8.98% VL2 -2.70E-06 -2.522E-06 7.06% -2.522E-06 7.06% VL1+VL2 0.1469 0.1614 8.98% 0.2655 8.98% Table for Task #2 Sample Calculations: For Task 1, the only relevant equations relate to the superposition principle. These would be the equations below. At V1 with V2 shorted (V1 - 4) / 5.1 kΩ + (V1) / 2kΩ + (V1 - V2) / 1kΩ = 0 At V2 with V1 shorted (V2 - V1) / 1 kΩ + (V2) / 5.1kΩ + (V2) / 2kΩ = 0 For Task 2, the principle of superposition only applies to a linear system with resistors and voltage/current sources. The diode is a non-linear device that does not obey Ohm’s Law, because the current flowing through a diode does not increase linearly with voltage. The equation used for task 2 was V T = V L1 + V L2

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Discussion: The superposition principle states that the response in any linear circuit is the sum of the responses caused by each individual source acting alone. This principle works with certain circuits that are linear and have a linear relationship between the input and output. In other words, for a circuit to obey the superposition principle, the output must be directly proportional to the input. In a linear circuit, the current and voltage at any point in the circuit are proportional to the voltage or current applied at the input. Therefore, by using superposition, we can break down the circuit into smaller parts where each individual source is applied and solve for the response caused by each source. Then, we can sum the individual responses to get the total response. However, the superposition principle only works with circuits that are linear and have no dependent sources or nonlinear elements like diodes and transistors. If the circuit contains nonlinear components or dependent sources, the principle may not be valid, and other circuit analysis techniques must be used to analyze the circuit. In task 1, the principle of superposition does apply. This can be proven by finding the voltage drop across the 1000Ω resistor with both V1 and V2 combined, and then find the voltage drop for V1 and V2 separately. If the sum of the separate V1 and V2 voltage drops is equal to the voltage drop when V1 and V2 are combined, then the principle of superposition holds. In our case it can be seen in table one, the values are roughly the same when they are measured together, or when adding them up separately. In task 2, the principle of superposition does not apply to the circuit with the diode in it, because the sum of the voltage drops across the 1000Ω resistor with only V1 active and only V2 active does not equal the value when they are measured with both of them active. This is due to the fact that the diode is a non-linear element in the circuit. The superposition principle only applies to linear circuits. A diode is a non-linear element because diodes have polarity, and due to that the current cannot flow in the reverse direction Conclusion: This lab focused on the concepts of Thévenin equivalent circuits, superposition, and diodes. It taught the applications of superposition principle and how it can be used correctly with linear circuits. It also teaches how diodes work and how they affect circuits making them non-linear, causing the superposition principle to not work.