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The above graph shows how the combination of the front speaker's low frequency fall off and the sub woofer's high frequency fall off can cause an almost smooth response as long as the -3dB point and slope of both curves is the same. So what is needed is a low pass filter with a 12dB per octave slope and a -3dB point set to the same frequency as that of the front speakers and all should be fine!
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The above circuit diagram is of a 12dB per octave low pass filter. The resistors 'R' and capacitors 'C' control the cut off frequency and can be calculated from the equation Fc=1/(2PI x R x C) where PI=3.1415927 ish! Now there are many combinations of R and C which will give the same result so we have to be realistic here and choose sensible values for both. For my Wharfedales which have a cut off of 70Hz (have I told you that?.....) I arrived at a resistor value of 22Kohm (22,000 ohm)and a capacitor of 100nF(100 x 10^-9 F).
Putting these values in the equation gives:
Fc=1/(2 x 3.1415927 x 22000 x 100 x 100^-9)
Fc=1/(1.38 x 10^-2)
Fc=72.34Hz which is near enough.
I would suggest keeping the 100nF value for your own design and altering the resistor value to suit.
Before the low pass filter, we need a mixer/ pre-amplifier. This is accomplished by using another operational amplifier (op amp) such as the 741 as used in the filter.
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Above is the full circuit of the mixer and filter used in my sub woofer. The circuit was built on vero board but a printed circuit board could be used. I hope to include a PCB design at a later date. All that is needed now is your choice of power amplifier connected to the volume control and that's it.