EE210 Lab 4: Superposition And Linearity Objective

EE210 Lab #4 Superposition and Linearity Objective This experiment

This experiment aims to illustrate the concept of circuit analysis using superposition. The superposition principle states that the voltage across or current through an element in a linear circuit is the algebraic sum of the voltages or currents due to each independent source acting alone. The analysis involves isolating each source by temporarily removing others—replacing voltage sources with open circuits and current sources with short circuits—and then calculating the individual contributions of each source. These individual responses are then summed to determine the total voltage or current for the circuit.

The experiment begins with simulating the circuit shown in Figure 1, which involves specific resistor values (R1 = 1 kΩ, R2 = 5.6 kΩ, R3 = 6.8 kΩ) and voltage sources. Using Multisim, the currents and voltages at points Ix, Iy, and Iz are measured when both sources are active. Then, in subsequent steps, one source is removed at a time—first removing the 15 V source to analyze the circuit in Figure 2, and then removing the 10 V source to analyze the circuit in Figure 3. The corresponding currents and voltages (denoted as Ix’, Iy’, Iz’ for the first case and Ix”, Iy”, Iz” for the second) are then recorded.

Furthermore, the project includes designing an experiment to demonstrate the property of linearity explicitly. This involves creating a circuit or setup where the response (current or voltage) is directly proportional to the input, and then verifying this proportionality through measurements. Documentation of the design process, measurement data, and analysis should be included in the report.

The final report should contain an introduction that clarifies the importance of superposition and linearity in circuit analysis, include the detailed circuits used for each step, present all measurement results, and explain how the experiments verify the principles of superposition and linearity. The conclusion should summarize findings, reaffirming the relevance of these principles for real-world circuit analysis.

This report is due by April 6 at midnight. The instructor is available for virtual meetings; students should request meeting times via email, and a Zoom link will be provided accordingly.

Paper For Above instruction

Introduction

The principles of superposition and linearity are fundamental in the analysis of electrical circuits. Superposition allows for the simplification of complex circuits with multiple independent sources by analyzing each source separately and then combining the results. Linearity ensures that the response of the circuit to scaled inputs is proportionally scaled outputs. These concepts are central to the theory and practice of electrical engineering, enabling engineers to analyze and design circuits efficiently. This report documents the application of these principles through simulation experiments using Multisim, demonstrating their validity through systematic analysis.

Methodology

The experimental setup involved simulating a circuit with resistors R1, R2, and R3 connected along with voltage sources in Multisim. The primary circuit (Figure 1) incorporated a 15 V and a 10 V source. The first step was to perform a comprehensive simulation with both sources active, measuring the currents Ix, Iy, and Iz across specified nodes. Subsequently, the sources were individually removed: first, by removing the 15 V source (Figure 2), and then the 10 V source (Figure 3), with measurements taken for the resulting currents Ix’, Iy’, Iz’ and Ix’’, Iy’’, Iz’’ respectively.

To verify superposition, the individual responses were algebraically summed and compared with the total response obtained when both sources were active. Additionally, an experiment was designed to demonstrate linearity explicitly by varying the magnitude of the input sources and observing the proportional change in circuit responses.

Results

In the initial simulation with both sources active, the measured currents were as follows: Ix, Iy, and Iz. When the 15 V source was removed, the resulting currents (Ix’, Iy’, Iz’) reflected the circuit's response to the 10 V source alone. Conversely, removing the 10 V source yielded responses (Ix’’, Iy’’, Iz’’) attributable solely to the 15 V source.

By linearly combining the responses from the two single-source simulations, the total currents were reconstructed and compared with the original combined response. The close agreement verified the superposition principle. Additionally, the linearity experiment involved increasing source voltages proportionally and documenting the corresponding proportional changes in circuit currents, confirming the linear relationship.

Discussion

The results showed that the sum of individual source responses closely matched the combined response, validating the superposition principle for this linear circuit. This confirms that circuit responses are additive in nature when sources are independent. The linearity test demonstrated that scaling input voltages results in proportional changes in current responses, thus confirming the linear behavior of the circuit components.

This experiment underscores the importance of superposition and linearity in simplifying circuit analysis, especially in complex circuits with multiple independent sources. Engineers utilize these principles to analyze systems efficiently, troubleshoot issues, and design reliable electronic devices.

Conclusion

The conducted simulations successfully verified the superposition principle and the property of linearity in a resistor network with voltage sources. Demonstrating that the total circuit response is a summation of individual responses confirms the foundational theories used extensively in electrical engineering. The linearity experiment further illustrated the proportional response characteristic, essential for predictable circuit behavior. These principles are vital tools for engineers in designing, analyzing, and interpreting electrical systems effectively.

References

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