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For my university project I'm trying to flatten out my bass frequencies while keeping the other frequencies intact. (The idea is to first amplify a part of the input signal and input this signal into the system.) This is because of the bass lacking 11 dB from 20 Hz to 32 Hz, after that a -40dB/decade rolloff is needed till 75 Hz. So this means a second order low-pass filter was needed (since our system cuts off all frequencies below 20 Hz and above 40kHz). Also the rest of the frequencies must remain and therefore a summing amp was needed to amplify the low frequncy signal and keep the rest of the signal. So this is the design I came up with:

My Design However, there is this weird dip which I can't really explain. (I was thinking of feedback from one of the op-amps, but not really sure about that)

Plot of the frequncy respons of my design The green line is the total response and the blue line is the filter, which seems to act normal. So how can I either fix my design or can someone help me with a new design which meets the requirements?

So, here is a graph which shows our frequency response: Frequency Response The lower blue line is our response, the upper blue one can be ignored but the orange one is the transfer we thought was needed to compensate our lacking bass. However later we heard from our instructor that the peak could be a result of the measuring program we used and thus a simple second order LPF would be needed.

Edit: Thanks to everyone for the help! I decided to stick to an second order filter, but I added an all pass filter to the design, as seen below: New design However, during testing the design didn't work as simulated. At 20khz it gave (not really sure if this was the exact value because we were short on time) approximately 0.1V RMS on the output with 0.5V as input. At 20Hz however it gave 0.35V. So it looks like it's amplifying, but not as expected. I was thinking of maybe a dead (or two) opamp(s), is there anything else I could check? (Solder joints are triple checked and the opamps (Lm741 and lm742) are recommended for 15v but we decided to use 10.4 V with a voltage division since our psu can deliver 21V unloaded but loaded 19V)

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    \$\begingroup\$ You have overlooked the results of phase shift in your filter. Consider what will happen, for instance, if the filter puts out some amplitude, but with 180 degrees of phase shift. Can you say, "Destructive interference"? I knew you could. \$\endgroup\$ – WhatRoughBeast Jan 13 '18 at 22:24
  • \$\begingroup\$ You made a mistake. 'HPF' should be 'LPF', because you have a DC input, and it is built as a low pass filter. The roll-off is set by C1, C2, R1, R2. The green line response is from R3 partially bypassing your low-pass filter. U2 is just a summing node. Re-think what you are doing. \$\endgroup\$ – Sparky256 Jan 13 '18 at 23:23
  • \$\begingroup\$ Damn, thanks WhatRoughBeast! I indeed overlooked phase shift as a possible explanation, however I'm still not sure how to fix the problem. The main problem is that we firstly tried to only keep the filter non-active (the rest of the circuit remained more or less the same), but after simulations we saw that the filter used (non-active second order butterworth filter) didn't really work as expected at the frequencies needed (as we later read in our book). So therefore we thought an active filter would be necessary. We also tested this circuit with a first order filter, which did worked fine. \$\endgroup\$ – Jeremy van Wieringen Jan 14 '18 at 0:12
  • \$\begingroup\$ Indeed Sparky, HPF should be named LPF. That was just a typo. The 100kOhm resistor from the source to the summer was intentional. The idea was that the lower frequencies of the signal would pass through the filter so it could be amplified (since the resistance to the summer is smaller (although I could reduce the resistances of the filter but this gives the problem of having the components we're bound to)). The higher frequencies couldn't pass to the summer, so they have to go through the resistor. And this had to give us in theory amplified bass, but keeping the highs from being filtered out. \$\endgroup\$ – Jeremy van Wieringen Jan 14 '18 at 0:26
  • \$\begingroup\$ Why is your bass 'lacking' 11dB, and why does it matter? \$\endgroup\$ – Bruce Abbott Jan 14 '18 at 5:04
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You need to define an overall error tolerance in almost every active filter design.

If less then 1dB you will probably need a higher order Bessel LPF perhaps 4th order but staggered breakpoints.

Or you will need a 1/2 octave graphic equalizer... But warning, excessive Q in any filter can make impulse sounds loose punch. For bass the word "muddy" fits , like the kick drum impulse. Therefore low Q filters are preferred and some amplitude error tolerance is a necessity.

Otherwise improving the subwoofer is the optimal method.

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    \$\begingroup\$ Why do I need a 4th order LPF, while our roll-off should be -40dB? And what do you exactly mean with staggered breakpoints? Also, I thought it would help if I put a frequency response graph in the answer to show what my group wants to achieve. \$\endgroup\$ – Jeremy van Wieringen Jan 14 '18 at 12:36
  • \$\begingroup\$ I stated why. read again. If the ripple error is < 1 db.. since the range is 1 octave 35 to 70hz 1db in 12dB slope is reasonable for a 2nd order filter. 0.5dB is not possible to have the slope and low error, so a higher order filter is needed. Again you MUST define an acceptable amplitude error. then explore better filters like Gaussian, Bessel etc. \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Jan 14 '18 at 14:50
  • \$\begingroup\$ Unfortunately I cannot really give an acceptable amplitude error since my manual just states that "as flat as possible". Also, this project ends with a contest which group has the best acoustic transfer. \$\endgroup\$ – Jeremy van Wieringen Jan 14 '18 at 22:55
  • \$\begingroup\$ ok then 1dB error is possible as you have done with 2nd order LPF and maybe <0.5 dB with 4th order, but 1dB error is hardly noticeable. If you want a 4th order 35Hz Bessel Filter go to TI and get their free Windows software or try 30nF for C1 and compare error \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Jan 14 '18 at 23:07
  • \$\begingroup\$ So I stuck with the second order filter but added an all pass filter to the side which would let the normal signal through (will put it as an edit to the question). However, during testing the design didn't work as simulated. At 20khz it gave (not really sure if this was the exact value because we were short on time) approximately 0.1V RMS on the output with 0.5V as input. At 20Hz however it gave 0.35V. So it looks like it's amplifying, but not as expected. I was thinking of maybe a dead opamp, is there anything else I could check? (Solder joints are triple checked) \$\endgroup\$ – Jeremy van Wieringen Jan 16 '18 at 17:27

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