Electronic – Avoiding electrolytic capacitors in high-pass filters with sub-Hz cut-off

The -3dB point is your cutoff frequency. It's just standard practice to define it that way. In order to find what your values should be, I'd go with equal element implementation (it's simpler, and you can correct for gain with a simple gain stage later if you need to). Choose R1=R2, C1=C2, and pick a value for either R or C. This yields the following formula for the cutoff frequency: $$f_0=\frac{1}{2\pi RC}$$ I generally choose a value of C initially, as it's easier to find or make a resistor with a strange value, whereas it's more difficult with capacitors. So, set your cutoff frequency equal to f0, and solve for R.

Here's an example: let's say I want a LPF with f0=250 Hz. I'll choose C to be 0.1 micro and solve for R. $$250=\frac{1}{2\pi RC} \rightarrow 250=\frac{1}{2\pi R(0.1x10^{-6})}\rightarrow R\approx6400\Omega.$$

From there, all you need to do is implement your circuit. Once you know what your value for R is supposed to be, you can use a dual-channel potentiometer that has the correct resistance within it's range in place of the two resistors (for the above example, something like a 10k ohm potentiometer would do the trick). This will allow you to change your cutoff frequency, since it's based upon both R and C.

Edit: As Matt Young suggested in the comments, adding a resistor in series with the potentiometer will set the maximum cutoff, and prevent shorts. It's an excellent addition to the circuit, and will keep some sanity when adding the potentiometers.

It looks like both filter sections are designed with the -3dB point at the same frequency, or very close together, so this filter is doing what it should.

In the crossover region, both sections contribute to the output, so it is higher than either alone. The slight peax at the crossover frequency would be 3dB if both signals were in phase(so they added coherently), so presumably they aren't. EDIT : apparently the small separation between -3dB points, rather than phase, accounts for this peak being less than 3dB.

For a classic design without that bulge, read up on the Linkwitz-Riley crossover, commonly used in loudspeakers where you want HPF and LPF outputs to sum to unity.

I don't know what you were expecting but if you wanted a notch you'd have to separate the -3dB frequencies, then the depth of notch will depend how far apart they are, and it won't be a deep notch.

If you wanted a deep notch, one approach is the Twin-T filter which can be made as narrow as you want.

Or start by specifying the frequency, notch width (at -3dB), and notch depth you want, and research filter design techniques to meet that specification.