# Refining the Design - Empirical Analysis

A project log for Graphic Equalizer

A 3-band audio equalizer!

Grant Giesbrecht 09/15/2018 at 18:420 Comments

Low Range

I measured the cutoff frequency (fc) of the bass channel by feeding a DC signal from my function generator into the circuit and setting the gain to 20dB, then slowly increasing the frequency until the output drops to .707x the amplitude at DC. This is the half-power point and the frequency at which this occurs is the cutoff frequency. I measured fc=2,36 kHz.

As expected, increasing C2 resulted in a lower cutoff frequency. Replacing C2 with a 22nF capacitor dropped fc to 737 Hz. When connecting the circuit to small speakers, however, I noticed that the higher cutoff frequency low-band sounded better. All-to-common cheap & small speakers have great difficulty with low tones, and thus the higher low frequency cutoff sounded better. The 737 Hz cutoff made the music sound dulled. If I ever build a model with more than 3 bands, this lower fc channel could be a wonderful addition.

I played around with feeding different frequency waveforms into the equalizer and examining how the filter effected them. Just as expected, the low channel effected the low frequencies much more strongly. It wasn't quite as stark as I had expected, but listening to output through speakers, you could easily notice the difference in effect between the high and low frequencies.

Mid Range

To measure the cutoff frequencies (there will be two because it is a bandpass filter), I changed the frequency until I found the frequency at which gain peak. I then shifted the frequency above & below this peak frequency until I measured V = .707*Vpeak. I measured:

 Frequency (C3 = 22nF) Frequency (C3 = 10nF) Cutoff Frequency - High 3,33 kHz 3,99 kHz Peak Frequency 1,61 kHz 2,6 kHz Cutoff Frequency - Low 707 kHz 1,55 kHz

I replaced the 22nF C3 with a 10nF cap to raise fc. The results are displayed in the above table. I decided to keep the original 22nF value for C3 because the 10nF cap made the mid band perform very similarly to the high band.

High Range

To measure the cutoff frequency I used the same technique detailed for the low band, except a high frequency (100s of kHz to 1MHz) signal was used in place of a DC signal. I measured fc to be 2,653 kHz. I tried replacing the 4,7nF C4 with a 3,3nF cap for a higher fc. I measured fc=4,336 kHz after this modification.

When connected to speakers, it was clear that the higher fc was too harsh and tinny. The 3,3nF range could perhaps be used in a model with more than 3 bands, but not here.

There is still interference from radio stations, but perhaps eliminating the parasitic capacitances and inductances inherent with solderless breadboards is responsible and a proper PCB will fix this problem. I will know after creating a legitimate, PCB-based, prototype.