ENG 100 Lab 3 Report

Passive Second-Order Filter Circuits

ENG 100, Lab 3

April 29, 2004

Thursday 1-4pm

Abstract:

The purpose of this lab was to analyze the response of a band-pass filter, while experiencing signals at a large range of frequencies. A band-pass filter is defined as a circuit, which allows signals to pass relatively unaffected in magnitude, within a series of ranges. When the signal frequency becomes too great or too small, the circuit acts as a “filter.” For the pre-lab, the transfer function of the second-order RC circuit was derived and used to theoretically calculate the amplitude and phase at varying frequencies. Once the amplitudes and phases were experimentally calculated, the two sets of data were compared and plotted.

Results:

The experimental data provided little surprise during the lab because of its consistency to the theoretical data calculated earlier. When the amplitudes and phases were plotted for comparison, the theoretical and experimental data flow on a smooth and closely matching curve, which implies a high accuracy for this experiment. The only source of concern is the experimental phase angles at the low end and high-end frequencies. The low-end phase angles can be explained very easily. It was impossible to obtain time delays for the first frequencies, due to high static, which made the calculated phase angles zero. The high-end frequencies also go to zero, which seem consistent with the definition of a band-pass filter. I can only speculate that the pre-lab calculations were inaccurate.

Part A: passive RC band-pass filter

Plot of phase (Degrees) versus frequency (Hz):

Plot of measured magnitude (dB) versus frequency (Hz):

Calculation for pre-lab amplitude and phase results for 100 Hz:

w = 2*p*100 = 628.32

VRMS = = = 0.0094

dB = 20*log (Amplitude) = 20*log (0.0094) = -40.537

phase = 90- tan-1((3wRC)/(-w2*(RC)2 + 1) = 90- tan-1(3*628.32*1500*0.00000001/

(-628.322*(1500*.00000001)2 + 1)) = 88.38

Calculation for experimental amplitude and phase results for 178 Hz:

Experimentally determined that VRMS = 0.016

dB = 20log(VRMS) = 20*log(0.016) = -35.92

Calculated phase shift = td*(-360*178) = 116.63

Measured td = -1.82 (10-3) sec.

Conclusion:

This lab should be considered a success. The theoretical and experimental amplitudes and phases were not only calculated, but closely resembled each other. Technical difficulties were a constant challenge during the lab, but were overcome with time and assistance.