There's lots information out there that almost answers this for me, but I'm having trouble with the synaptic leap.
First-time poster, BTW:

Goal: with ideally one component, a capacitor that I can experiment with after the theory is figured out, create an HPF inside the instrument. Assuming that the electronics within the instrument is very simple, a pickup and a volume pot, how do I calculate the desired capacitance? The capacitor would be placed directly between the volume pot and the instrument jack. Almost there...

In a simple High Pass Filter, a capacitor may be placed between the voltage source and the load. The cutoff frequency is f = 1/(2 * pi * R*C). I want a cutoff at 50Hz, so far so good, but what is the load (R) in this case? I'm assuming that the preamp constitutes the load. The specs of the preamp state an input impedence of 2.2Mohms.

If so, my calculation is 1.45nF = 1/(50Hz * 2pi * 2.2Mohms). Intuitively I would expect a larger cap, so I assume my assumptions are wrong. Checking a different preamp with an input imp of 500k ohms, I get 6.37nF, which is still in the same ballpark.

As a follow up question, what might I do to this design to create a steeper slope at that cutoff, like 24db/oct?

Thanks in advance!

 

No single component is going to give you the performance you want. Steeper rolloffs, such as 24 dB/octave requires multiple poles in the transfer function. Multiple poles means multiple components. Ideally, when you have a specification in mind, you work from that specification to a design. You seldom, if ever, start with a design, and try to make it fit your requirements. That is the road to perdition -- in design terms.

 

What is the purpose of your HPF in the bass guitar?
Normally you want to pass low frequencies and block the higher frequencies.

 

What is the purpose of your HPF in the bass guitar?
Normally you want to pass low frequencies and block the higher frequencies.

The instrument will create some lower frequencies that are practically impossible for the speakers to reproduce, creating "mud". Also, these lower frequencies, when fed a bunch of power, have a tendency to destroy speakers. An HPF can be used elsewhere in the signal chain as well, to eliminate noise caused by other components, but placing an HPF upstream saves other components from the bother of processing those frequencies to begin with.

You are correct, that typically a bassist will want to first filter out highs, but that's why it's really easy to find a simple solution to that problem in the form of a tone-pot. Since the low pass solution involves a cap and a pot, I thought maybe a high pass solution may avail itself simply as well.

 

No single component is going to give you the performance you want. Steeper rolloffs, such as 24 dB/octave requires multiple poles in the transfer function. Multiple poles means multiple components. Ideally, when you have a specification in mind, you work from that specification to a design. You seldom, if ever, start with a design, and try to make it fit your requirements. That is the road to perdition -- in design terms.

Appreciate the feedback. The word "ideally" I put at the front of my post is my way of saying "If I was rich and ruled the world, I would want...". The thrust of my question comes from the common existence of a low pass, where a single capacitor sends the higher freqencies to ground while the lower frequencies move on to the load*, and the apparently simple equation involved in a high pass. I suspect I'm not putting the right numbers into the equation, particularly when it comes to the R.

The 24db/oct performance is also a mere wish. The real question is, how much roll off would I get, given the most minimal design, and then what steps/components would be needed to move in the direction of my desired performance?

If I understand the theory a little better, I can deal with whatever tradeoffs I encounter.

*BTW: I assume just about everyone here knows this stuff. I'm spelling it out so you can detect my shortcomings. I am clearly quite new to this.

 

but what is the load (R) in this case? I'm assuming that the preamp constitutes the load. The specs of the preamp state an input impedence of 2.2Mohms.

If you put a capacitor in series with that resistance than the calculated capacitance for a HP 50Hz rolloff is 1.45nF, as you calculated.

A single RC filter will give a rolloff of 6dB/octave.

If you use two capacitors and two resistors you could get 12dB/octave, but it would not give a sharp rolloff around the corner frequency.
However that may be adequate for your purposes.
Below is the LTspice simulation of such a 2-pole HP filter with a -3dB rolloff at ≈50Hz.
Note the RC values on the left are 1/10th the value of those on the right to minimize interaction between the two RC filters.



To get a better filter you would need to add an op amp in an active-filter configuration.
One op amp can give a good 3-pole filter with an 18db/octave rolloff.
Here's a reference that calculates the values for such a filter.
Edit: Below is the simulated output of a 3-pole 50Hz HP active filter for comparison:

 

See