Lab 3.docx

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Texas A&M University *

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214

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Electrical Engineering

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Jan 9, 2024

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ECEN 214 - Lab Report Lab Number: 3 Lab Title: Equivalent Network and Superposition Purpose and Goals: The main purpose of this lab is to work on verifying Thevenin’s equivalent circuit and superposition principle. Superposition can be used with a linear circuit that has multiple independent sources to it by individually solving each source independently from each other. We also dived deeper into using SPICE in the lab and running simulations with it to verify our values. ● Verify if the circuit solving techniques Thevenin’s equivalent circuit applies to real-world circuits ● Verify if the superposition principle applies to real-world concepts and under what conditions. Procedure: For this lab, the needed materials are a variety of resistors, a diode, as well as two voltage sources. The two voltage sources in this lab will consist of a 3V source (two AA batteries in series) and a 4V source. This lab is broken up into two sections. For the first section, you will need to construct the circuit below.

Figure 1: Testing Superposition with a circuit without a diode. Once this circuit has been created, measure the voltage across the 1000 ohm resistor and record the voltage. Remove the 3V voltage source and remember to connect the circuit and measure the voltage across the 1000 ohm resistor again with only the 4V source present. Place the 3V voltage source back into the circuit and remove the 4V voltage source. Take the measured voltage across the 100 ohm resistor and record this data. For the second part of this lab, add a 1N4148 diode into the circuit and repeat the same steps taken before. Remember to record the voltage across the 1000 ohm resistor into the notebook. Figure 2: Testing Superposition with the diode in the circuit. Data Tables: Task #1: (V1 = 3.991 V and V2 = 3.354 V)

Parameters Measured (V) Calculated (V) % difference SPICE (V) % difference (Spice to Measured) 𝑉 𝐿 0.341 0.265 25.1% -0.265 15.9% 𝑉 𝐿,1 -0.288 -0.291 1.04% 0.291 1.04% 𝑉 𝐿,2 0.628 0.556 11.7% 0.556 12.2% + 𝑉 𝐿,1 𝑉 𝐿,2 0.340 0.265 24.8% 0.847 85% Table 1: Measured values over the 1000 Ohm resistor when both sources are present, when only the 3V source is present, and when only the 4V source is present. These measurements occurred when all circuit elements were linear. Task #2: With 1N4148 diode Parameter Measured (V) Calculated (V) Spice % Error 𝑉 𝐿 0 0 0 0 𝑉 𝐿,1 0.151 0.110 0.161 27.2% 𝑉 𝐿,2 0 0 0 0 + 𝑉 𝐿,1 𝑉 𝐿,2 0.151 0.110 0.161 27.2% Table 2: Measured values over the 1000 Ohm resistor when both sources are present, when only the 3V source is present, and when only the 4V source is present. These measurements occurred when one of the circuit's elements were non-linear(diode was included). Data Plots: Measured (V) v.s. Calculated (V)

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Figure 3: This graph shows the data points for VL, VL1, VL2, and VL1 + VL2. The important point is around 0.34 V in the X-axis. Although hard to see, both data points for VL and VL1+VL2 are right on top of each other. This means that the superposition principle applied to this circuit. Measured v.s. Calculated Figure 4: This graph shows the data points for VL, VL1, VL2, and VL1 + VL2. The important points are at 0V and 0.15V on the x-axis. These two points represent VL and VL1+VL2. By being at different points, it means that the superposition principle does not apply as they are not equal due to the non-linear element.

Calculations: Percent Difference Equation: - Percent Difference = * 100 | 𝑉 1 +𝑉 2 | 𝑉 1 + 𝑉 2 2 - Where is the measured voltage and is the calculated voltage. This 𝑉 1 𝑉 2 equation is used to measure the difference in percentage between the two related voltages. Percent Error Equation: - Percent Error = * 100 | 𝑉 𝐴 +𝑉 𝐸 | 𝑉 𝐸 - Where is the actual voltage measured and is the expected or 𝑉 𝐴 𝑉 𝐸 calculated voltage. This equation is used to express the difference between the expected voltage and the measured voltage in percentage. Discussion: Superposition theorem states that in a linear circuit where there are multiple sources, the voltage across or through the element in the linear circuit would equal the sum of the voltages across or currents through the element for each source considered independent of each other. The Superposition theorem applies to Task #1 because all elements in the circuit are linear, where there is a linear relationship between voltage and current. The Superposition theorem doesn’t apply to Task #2 because a diode is a non-linear element, meaning there is not a linear relationship between current and voltage. Due to how a diode works, current can easily flow through one direction but is restricted in another direction; it causes the relationship between voltage and current to be non-linear. This can be shown in our data when we analyze the table under Task #2. When comparing the magnitudes of and there is a major difference in the 𝑉 𝐿,1 𝑉 𝐿,2 voltage drop across the 1kΩ resistor. Although the change in voltage source value decreased slightly, it ended up causing the resistor to either experience some current or no current at all. Thus the relationship between the voltage and current is non-linear in this case for the diode. The reason why resistors are linear elements is because the current going through the resistor is proportional to the voltage across the resistor. Diodes are non-linear because the current value is also dependent on the direction of the current flow through the diode. Thus the relationship between voltage and current are non-linear. Conclusion: This lab helped us understand how the concept of superposition applies. This was done by including a linear and non-linear element into the circuit and applying the superposition

principle while taking measurements. From the data collected in Tables 1 and 2, we were able to conclude that superposition is only valid when the circuit includes only linear elements. This lab also helped us understand a little bit about how diodes work and how they are non-linear elements. Using Thevenin’s equivalent circuit in the first task helped us understand how to simplify circuits. Both goals were therefore accomplished in this lab. Signatures:

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