filtering of audio signalsGrand Valley State UniversityThe Padnos School of EngineeringFILTERING OF AUDIO SIGNALSEGR 345 Lab ExperimentJoel OostdykJoshua HoekstraDate preformed: November 30, 1999Fall 1999Objective:To build and test a filter for an audio system.Theory:Simple filters, using op-amps and off the shelf components such as resistors and capacitors, can be built. Figure 1 shows a band pass filter. This filter will pass frequencies near a central frequency determined by the resistor and capacitor values. By changing the values, the overall gain of the amplifier or the tuned frequency can also be changed.Figure 1 - A band pass filterIn order to determine the gain of the band pass filter, the circuit must be analyzed. Applying a nodal analysis at node A and B yields Equation (1) and Equation (2). 0211sCVVRVVAoAi( 1 ) 0112sCVVRVVbabo( 2 )Using basic properties of an op-amp and solving Equation (1) for Va and substituting intoEquation (2) yields Equation (3) below:A B112212112111110sCsCRVsCsCRVVRsCRVVooooi( 3 )Therefore, solving for the gain yields Equation (4):sCRsCRCCsRRsCRRRVVio112121221121111(4)Converting the gain to decibel values and graphing against frequency produces a graph similar to the one in Figure 2.Figure 2 - gain (dB) vs. frequencyEquipment:- CADET trainer GVSU EGR 7-93- Tektronix TM5006 #31012- Tektronix 2232 oscilloscope #31659- 8050A Digital Multimeter #31085- 10X probe EGR EC-11- 741 Op-amp- 2x 1-F capacitors- 3x 1k- resistorsProcedure:1. The circuit in Figure 1 was set up, and a small speaker was connected to the output ofthe amplifier.2. A sinusoidal input from a variable frequency source was applied and the oscilloscope was used to compare the amplitudes and the phase difference.Results: The Bode plots for the theoretical and actual gain and phase angle are shown in Figure (3), (4) and (5) below:Figure 3 - Theoretical Bode plot for the modeled gainFigure 4 - Actual gain plot11030.01 0.1 1 10 100 110311041105110611071108110911010110111101220010000290dBn180n1 10123.162 103freqnGain (dB)-35.00-30.00-25.00-20.00-15.00-10.00-5.000.00100 1000 10000Frequency (Hz)Gain (dB)Figure 5 - Phase angle plotWhen the output voltage from the circuit was connected to the speaker in the CADET, it was observed that the lowest audible frequency was approximately 20Hz, while the highest audible frequency was approximately 16KHz. These results make sense because the theoretical audible range is from 10Hz to 16KHz. The experimental lowest audible frequency was higher because of the limitations of the speaker used. Below 20Hz input, the speaker simply output a monotone buzzing.The maximum gains of the actual and theoretical models vary by about 6dB. Causes of this error could be traced to the inexact resistors, capacitors, additional resistance in the wires used, and possible inaccuracies of the op-amp.Conclusion:In this lab a band pass filter was constructed. The circuit was analyzed to determine how the gain and phase angle changed with frequency. This circuit was then connected to speaker to show how the human hearing is logarithmic. By observation, it was noted thatthe loudest sounds were produced from a frequency ranging between 1000Hz and 3000Hz, which agrees with the theoretical Bode plot.Phase Angle-300.0-250.0-200.0-150.0-100.0-50.00.010 100 1000 10000Frequency (Hz)Phase Angle
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