Theoretical Performance

The circuit design laid out in the previous post was designed on multisim and bode plots were generated in order to determine the performance of the circuit and see if it would suit the needs of our project.

The design is again shown below in the proper layout for testing. The measurement tool at the top of the design is a bode plotter which is built into multisim.

CircuitFirst

After running the bode plotter tool for this design the following plots were generated. The first plot is a phase plot while the second plot is the magnitude plot.

BodeFirstPhaseBodeFirst

As can be seen from the magnitude plot, the peak gain occurs just around 110Hz as desired for the note A. The 3dB points for the magnitude occurred at roughly 105Hz and 115Hz. Since the next two notes (E and D) occur at roughly 82Hz and 147Hz respectively, our circuit should theoretically be able to isolate our desired note to a good extent. The gain at both 82Hz and 147Hz was about 4dB while the gain at 110Hz was 20dB. The quality factor for the circuit is therefore 11.

After performing this analysis, a similar analysis was run on a second order filter of the same design. This involved essentially copying the first filter and feeding the output of the first into the input of the second. This circuit is shown below:

CircuitSecond

The bode plotter was then used to measure the new output. The phase plot and magnitude plots are both shown below:

BodeSecondPhaseBodeSecond

As can be seen in the magnitude graph, the peak appears much steeper than the first graph, as expected. However, upon further examination, it seems that a second order circuit of this type may not be as beneficial as anticipated. While the peak now has a gain of 40dB and the 3dB frequencies occurred at around 106 and 113Hz, the gain at the frequencies for the adjacent notes of E and D was now about 9dB. While this level of amplification is small compared to our desired frequency, it may make it harder to isolate the note we want. The quality factor for this circuit was 15.71 which is definitely greater than the quality factor of the first order filter.

Despite the slight increase in quality, Our team believes the single filter design will be sufficient for the purpose of this project. However, if necessary, this second order design will be revisited.

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