QuestionQuestion

You have been asked by a sound studio, to design bandpass filters for a DJ Mixing deck that will be used to provide lighting for a rock concert.

The DJ Mixing deck will provide stage lighting that will correspond to the sound level and frequency of the music.

Using the fact that the human ear can perceive sounds from 20 Hz to 20 kHz, the specifications state that the audio frequency spectrum is to be divided into three ranges.

You are to use Passive RC filters which will be used to isolate signals for each range.

These signals will then be amplified and used to control LED lights of a particular color.

The low-frequency components (20 to 150 Hz) will control Blue LED lights, the mid-frequency components (200 Hz to 2 kHz) will control Green LED lights, and the high-frequency components (2.5 kHz to 20 kHz) will control Red LED lights.

Note that for the frequency ranges that are rejected by the filters simply means that all LED lights will be off for those frequencies.

Although the specifications call for 3 band-pass filters, you decide that you can simplify the design by using a low-pass filter with a 3dB cutoff frequency of 200 Hz for the low frequencies and a high-pass filter with a 3dB cutoff frequency of 2 kHz for the high frequencies.

Task 1

Draw the block diagram of the system you propose representing the requirements

Task 2

Using only passive RC filters,

2(a) Draw the circuit configuration for a high pass filter

2(b) Draw the circuit configuration for a low pass filter

Task 3

For the high pass filter design

3(a) Derive an expression for the transfer function showing all steps

3(b) Determine the 3 dB cut off frequency in terms of R and C

Task 4

For the low pass filter design

4(a) Derive the transfer function showing all steps

4(b) Determine the 3 dB cut off frequency

Task 5

You decide to design your bandpass filter by cascading the high pass filter and the low pass filter circuits.

5(a)

Derive an expression for the overall transfer function of the band pass filter.
Show all steps.

5(b) Determine the upper and lower 3dB cut off frequencies for the band pass filter

Task 6

Design the three filters for the DJ mixing desk by calculating the required capacitor values that will satisfy the filtering requirements as described above.

Note round all calculated capacitor values to the nearest off the shelf capacitor values available in the industry.

To simplify your work, you decide to use only 10kQ resistors for all filters.

Show all calculations.

In your final designs, present

6(a) The low pass filter circuit diagram showing all circuit values, the completed transfer function and the calculated 3dB cutoff frequency for the filter

6(b) The high pass filter circuit diagram showing all circuit values, the completed transfer function and the calculated 3dB cutoff frequency for the filter

6(c) The band pass filter circuit diagram showing all circuit values, the completed transfer function and the calculated the 3dB cutoff frequencies for the filter

Task 7

Use PSpice to simulate your three filter designs and

7(a) obtain a screen shot of each filter circuit diagram used in your simulation

7(b) obtain Bode plots showing magnitude and phase responses for each filter circuit, and

7(c) from the bode plots, obtain the 3 dB cutoff frequencies and the maximum gain of each filter design

7(d)
Compare the values obtained in 7(c) with your circuit analysis results obtained in Task 6

Task 8

Manually sketch the bode plots of all three designed filters on the same axes Note all graphs are to be carefully annotated showing all 3dB cut off frequencies and labeling of all axes.

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