# multiple feedback bandpass filter

Joined Apr 28, 2009
2
I have to design a 4 band audio equalizer using a multiple feedback bandpass filter

with given normal center frequencies (0.30kHz, 1.05 kHz, 3.7 kHz, 13 kHz)
a quality factor of 0.9 and adjustable overall voltage gain between 0.2 and 2 for each band

i used the equations f_o= 1/ (2*pi*C sqr R1*R2) and Q = 0.5 sqr R2/R1

i got resistor values of 20k for R2 and 5.1k for R1

my issue is when i plot the overall gain in pspice for each band set at 0.2 i get to high of a gain

any suggestions thanks you in advance

#### Darren Holdstock

Joined Feb 10, 2009
262
You have gain peaking because a Q of 0.9 is underdamped (Q=0.5 is critically damped). Normally in the MFB BP circuit there's another resistor forming a potdown with R1 - I have lots of info on that, but sadly very little on the (perfectly cromulent) alternative circuit you've used here. Fortunately there's google - there should be some equations linking gain peaking magnitude to Q out there somewhere. This gain peaking magnitude equation is often a scaling factor for the separate equation for passband gain when the circuit is critically damped.

#### hgmjr

Joined Jan 28, 2005
9,029
I could not help but notice that your filter is a departure from the classical multiple feedback bandpass filter topology. This may not be a significant obstacle but it could have an impact on your gain.

I have attached a couple of png files that I harvested from the Internet to illustrate my point.

What gain are you getting that you are calling too high?

hgmjr

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#### hgmjr

Joined Jan 28, 2005
9,029
I think you need to put a resistor in series with each of the potentiometers. You really don't want to allow the series resistance go all the way to zero. If you use a 1K for example, you would be able to adjust the gain of the final stage from a high of -1 all the way down to -0.091.

Are you getting a midband gain of -2 through your active filters?

hgmjr