Introduction During This Experiment The Class Continu 301627

Introductionduring This Experiment The Class Continued To Learn About

During this experiment, the class continued to learn about how voltage varies with frequency. This experiment explored passive filters, also known as band pass filters. The procedures involved two series RLC circuits and two parallel circuits containing an inductor, a capacitor, and two resistors.

Preliminary calculations included deriving the transfer function H(jω)=V2/V1 for the circuits, which expressed the frequency response. For the series RLC circuit, the transfer function is H(jω)=1/[1 + j((ωL/R) - (1/RCω))], with magnitude |H(jω)|=1/√[1 + ((1/R)(ωL - 1/ωC))²]. The resonant frequency ωr was calculated to be approximately 6.1 kHz, and the bandwidth was approximately 11.9 kHz. Similar calculations applied to the parallel circuit yielded comparable resonant frequency and bandwidth values.

The main procedure involved constructing the circuit with specified resistor, capacitor, and inductor values, then varying the input frequency from 10 Hz to 100 kHz while measuring the output voltage V2 with an oscilloscope. The measured magnitude of V2 was plotted against frequency, revealing a resonant frequency near 5.12 kHz, slightly lower than the theoretical 6.1 kHz. The bandwidth estimated from the experimental data was less precise due to limited data points near the peak.

Additional simulations using PSPICE verified the experimental results, showing good agreement with measured data. This procedure was repeated with different resistor values (2kΩ, 5.1kΩ, and equal resistances of 10kΩ), and in each case, the experimental resonance points were close to the theoretical predictions, emphasizing the importance of dense sampling near the resonance for accuracy.

Throughout the experiment, students practiced measurement techniques, especially using oscilloscopes, and applied mathematical models of circuit behavior. They observed that both the experimental and theoretical values deviated by approximately 16%, primarily because of insufficient data points near the peak frequency, which influenced the accuracy of bandwidth and resonance calculations.

In conclusion, the experiment demonstrated the frequency-dependent behavior of band pass filters, highlighting the critical role of precise measurements and comprehensive data collection. This experience underscored the importance of extensive data points for accurate correlation between theory and practice, preparing students for more advanced analysis in circuit design and signal processing.

Paper For Above instruction

The study of passive filters, particularly band pass filters, is fundamental in understanding how circuits manipulate signals based on frequency. This experiment provided comprehensive insights into the behavior of RLC circuits, emphasizing the importance of theoretical understanding coupled with practical measurement techniques. The primary focus was to analyze how voltage output varies as a function of frequency and to evaluate the accuracy of theoretical models against experimental results.

The theoretical foundation of the experiment was based on deriving the transfer functions for both series and parallel RLC circuits. The series RLC transfer function H(jω)=1/[1 + j((ωL/R) - (1/RCω))] indicates a frequency response where the amplitude peaks at the resonant frequency ωr. The magnitude response |H(jω)|=1/√[1 + ((1/R)(ωL - 1/ωC))²] illustrates how the output signal varies with frequency, particularly around ωr. The resonant frequency is crucial because it represents the point at which the circuit responds most strongly to input signals, which was theoretically calculated to be approximately 6.1 kHz for the specified component values, with a bandwidth near 11.9 kHz.

Experimentally, the circuits were constructed using precise resistor, capacitor, and inductor values, and the input signal’s frequency was varied systematically. Oscilloscope measurements of V2 allowed the plotting of magnitude versus frequency, revealing that the resonant frequency was approximately 5.12 kHz, indicating a deviation of about 16% from the theoretical prediction. This discrepancy primarily resulted from limited data points around the peak, emphasizing the need for dense sampling near the resonance for higher accuracy.

The use of PSPICE simulations further validated the experimental results, showing close agreement with real measurements. By employing simulation software, students could visualize the theoretical frequency response curves and understand the nuances of circuit behavior more clearly. This synergy between theoretical calculations, experimental measurement, and simulation underscored the importance of multi-faceted approaches in electrical engineering education.

Repeating the procedure with varied resistor configurations, such as R1=2kΩ, R2=20kΩ, and R1=10kΩ, R2=10kΩ, demonstrated consistent trends in resonant frequency and bandwidth. In each case, the experimental resonant point closely matched theoretical predictions when more data points were taken near the resonance peak, reinforcing the critical role of comprehensive data collection in frequency response analysis.

Throughout the experiment, students gained valuable skills in measurement techniques, including oscilloscope calibration, data recording, and analysis. They learned that insufficient data points could lead to inaccuracies in calculating bandwidth and resonance, which are essential parameters in filter design. The importance of dense data sampling near the resonance peak was emphasized, as it significantly impacts the precision of the measured and calculated values.

In conclusion, this experiment elucidated the frequency-dependent behavior of band pass filters, highlighting the importance of meticulous experimental procedures and the integration of theoretical modeling with practical implementation. It reinforced the understanding that accurate SEL (signal energy levels) measurement and dense data collection are vital for validating theoretical models against real-world circuit behavior, a crucial skill for future engineers and researchers in the signal processing domain.

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