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How do you make an HP/LP by using only 1cap, 1resistor and a DPDT?

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Sorry for triple posting but of course the opamp that is biased at half the supply voltage because it has a single polarity supply has a DC output at half the supply voltage.
 
The RC is the lowpass filter. The opamp at its output is simply a buffer with no voltage gain.

Your new Sallen and Key circuit uses the opamp for positive feedback to boost the response of the second-order filter at the cutoff frequency. The one shown is a Bessel filter but the frequency is calculated for a Butterworth filter and the Bessel needs a "fudge factor" of 0.9 for the resistors.

The capacitor is calculated with the common phrase "one over two pi fR".
 
Thats for calculating the capacitor for the freq. response, how is that relevant to the first cap on the left?

And how do I fix the buffer on the opamp?
 
Your first lowpass filter was a simple series resistor and capacitor to ground first-order filter. The opamp on its output does nothing in the filter but it acts like a buffer at the output of the filter.

Your second lowpass filter is a more complex one because it is a second-order filter with two RC networks for double the filtering of the first circuit. Its opamp is part of the filter because it supplies positive feedback to boost the response at the cutoff frequency which makes the filter have a flat response up to the cutoff frequency then a sharp drop at frequencies above. It is a Bessel filter but a Butterworth filter has the flattest response.
 
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FilterPro is a free, very useful active filter design tool.
 
Single-Supply Sallen Key Bessel Low Pass Filter
I see how this circuit works a lot better then the previous one, but I'm having an issue with finding proper values for the cap and resistor that are practical.
Also, how do I control the freq. response on this filter?
By "control the freq. response" do you mean being able to adjust the frequency response of the filter on the fly? That's difficult to do for most active-filters with greater than a single-pole response unless it's a digital filter.

One exception is a Biquad active filter which can have it's frequency adjusted with a ganged dual-pot (Rf1 and Rf2). It's Q (bandwidth) is controlled by a different set of resistors, so the center frequency and bandwidth can be adjusted independently. Such a filter also has simultaneous HP, LP, and BP outputs, thus one filter meets your requirements for both a HP and LP response.
 
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@crutcshow
Yes, that's exactly what I'm trying to do.
But I see now that changing the freq. response on these active filters are not that easy, and I'm trying to go for a simple one pot solution.
I think I'll just find a way to use the non-inverting linear filter.
 
A Butterworth active filter has the flattest response and a sharp drop past the cutoff frequency. In a Sallen and Key circuit the resistors and capacitors can have equal values if the gain of the opamp is set to 1.6 with two resistors (33k and 56k). Then a dual pot can be used to adjust the cutoff frequency.
 
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