Lab Report 7222014 Experiment 5: Thévenin Equivalent Circuit

Lab Report 7222014experiment 5 Thévenin Equivalent Circuitsexperime

This laboratory report details the procedures, measurements, simulations, and analyses conducted to explore Thévenin equivalent circuits. The objective was to verify the Thévenin theorem through experimental measurements and PSpice simulations. The study involved circuits with single, dual, and combined voltage/current sources, including load testing and maximum power transfer analysis.

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The primary purpose of this experiment was to understand and verify the Thévenin theorem, which posits that any linear bilateral circuit can be simplified to an equivalent voltage source and series resistance at its terminals. This concept is fundamental in circuit theory and significantly simplifies the analysis and design of complex electrical systems.

In the first part of the experiment, the Thévenin equivalent of a circuit with a single voltage source was determined. Constructed with R1, R2, R3 each of 10 kΩ and a 6 V power supply, the measurements yielded an open-circuit voltage (Voc) of approximately 2.991 V and a short-circuit current (Isc) of 0.2016 mA. These values allowed calculation of Vth as 2.991 V and Rth as approximately 14.84 kΩ. It was emphasized that directly measuring Rth with an ohmmeter is ill-advised because such devices measure the resistance of the power supply as well as the load, leading to inaccuracies. Instead, open-circuit voltage and short-circuit current measurements provide a more accurate method for determining the Thévenin equivalent.

Simulations using PSpice replicated the experimental setup, featuring a current source sweeping from -3 mA to 3 mA. The simulation produced an I–V characteristic curve consistent with theoretical calculations and experimental measurements, confirming the validity of the Thévenin model. The data showed close agreement in Voc, Isc, and Rth values, reinforcing the theory.

Subsequently, the experiment involved injecting known currents using a +25 V source into the circuit and measuring the voltage required for different current levels. While ideal value of 2 mA could not be achieved, the measurements at 1.537 mA and 0 mA provided data points that aligned reasonably with the initial I–V curve, illustrating the linear behavior expected from a Thévenin equivalent.

The second part extended the analysis to circuits with two voltage sources. The configuration consisted of an arrangement with V1 = -5 V, V2 = 10 V, and associated resistances. The open-circuit voltage (Voc) was approximately 5.48 V, with a short-circuit current (Isc) of around 1.151 mA. Calculations yielded a Thévenin voltage (Vth) roughly equal to 5.480 V and a resistance (Rth) near 4.76 kΩ. These findings were confirmed experimentally and via simulation, demonstrating the Thévenin equivalent's accuracy.

Further testing involved connecting load resistors of 1 kΩ and 10 kΩ across the circuit's output. The resulting voltages and currents, plotted on the I–V graph, fit well within the theoretical line, with the reciprocal of the slope confirming the Thévenin resistance. The consistency between measured and predicted values verified the effectiveness of the Thévenin theorem in representing complex sources with simpler equivalent circuits.

The third section focused on circuits containing both voltage and current sources, as depicted in Figure 3a of the lab manual. Constructing this circuit with a -10 V source and resistors R1, R2, R3, measurements of open-circuit voltage and short-circuit current closely matched theoretical predictions (Vth approximately 1.89 V; Rth about 0.845 kΩ). The results affirmed the theorem's applicability to circuits with mixed sources.

The maximum power transfer point was analyzed in the fourth part. Using theoretical calculations involving voltage divider formulas, the maximum power load resistor (R_L) was estimated. Experimentally, varying R_L from 100 Ω to 10 kΩ revealed a peak power at around 1.45 kΩ, aligning well with the theoretical Rth. Measurements of voltage, current, and power at each load demonstrated the classic bell-shaped power curve, confirming the maximum power transfer theorem.

Complementing the experimental data, PSpice simulations conducted parametric sweeps of load resistance R_L, graphing power versus R_L. The simulation identified a maximum at approximately 1.45 kΩ, consistent with experimental results, further validating the theoretical analysis.

This comprehensive approach, combining empirical measurements, simulations, and theoretical calculations, underscores the robustness of Thévenin's theorem. The experiment illuminated how complex circuits can be resolutely simplified without loss of accuracy in the regimes that matter most, such as load analysis and power transfer. Practical significance arises in designing efficient power systems, ensuring maximum power delivery, and optimizing circuit performance.

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