Electrical – Center Frequency Shift Bandpass Filter

What you are asking is very difficult. The problem is that you are asking for a constant bandwidth, rather than a constant Q (that is, frequency divided by bandwidth). A 50 Hz bandwidth at 50 Hz is easy - 50 Hz at 5 KHz is very narrow. The sort of circuits you've been looking at are hard to do at very narrow bandwidths due to sensitivity, where the exact bandwidth gets very sensitive to the exact (less than 1%) values of the components you use.

Furthermore, narrow filters are usually intended to have a sharp cutoff at all frequencies away from the center. A simple filter of the sort you link to is called a second-order filter, and for frequencies much away from center the cutoff is quite gradual. You can get around this by specifying higher-order filters, but each of these must be adjusted at the same time by the right amount, and the separate responses tend to interact to produce weird frequency responses.

You have not specified how you intend to change the center frequency. Do you want to use a knob on a front panel, or a voltage? If the former, if you're willing to stick to a 2nd-order filter (the simplest kind), you can get get ganged pots, where 2 resistors are connected to one shaft, and this may possibly do you, although I doubt it.

If you want electronic control, and especially if you want narrow filter response such as 50 Hz at 5 KHz, I suggest you look into switched capacitor filters. Linear Technology and TI both produce compact solutions. LT has an app note http://cds.linear.com/docs/en/application-note/an40f.pdf which is a good place to start.

Most importantly, do some more research on exactly what filter responses mean. Do you need Butterworth response, Bessel or Chebyshev? What order filter do you need? Until you understand the implications of your requirements, it will be hard for you to select the right filter.

Your design is a very basic and might work but since it has no feedback it is not so predictable in how it will behave in practice.

The "proper" engineer's way of designing this is by use of feedback. You basically make a crude amplifier with a high gain and enough bandwidth and use feedback to get the gain you actually want.

Unfortunately this design procedure is not something which can be explained in a few sentences. I learned this in a course which took several days and included a design assignment.

I found a University course here that should explain this method, that's 70 slides to get you started ;-)

If this is too much of a stretch in the time you have then just remember this and come back whenever a more challenging amplifier design task pops up.

Another option altogether would be to use an opamp in a feedback configuration. If you want to know more about opamp circuit design look here: Opamps for everyone