... so a high pass filter with a very low cut off frequency would just be taking away the DC component. What I'm not quite sure about is that... the cut off frequency is f=1/(2*pi*R*C). Many different combinations of R and C can give the same cut off frequency. So how do I justify choosing specifically 20K and 10uF?
Yes - having a high gain circuit with the DC component amplified to the same extent can, as you can probably imagine, cause 'offset' havoc!
As to the choice of components. As I say, 10uF capacitors are usually electrolytic, which often have a wide range of tolerance, so are not usually used where accuracy is required.
Choosing which combination of components will often come down to the range of impedance best suited to your proposed circuit. There are no hard and fast rules.
Typically, I would suggest you would probably select values to suit this kind of circuit, from within the range 1K to 100K.
Significantly lower than 1K? - filter capacitor values can start getting very large, and you start approaching the max drive capability of the opamps.
Significantly higher than 100K? -- at very high impedance, you can start to get problems with 'stray' capacitance in PCB track or strip board layouts, and leakage currents from some capacitors.
As I say, there are no 'hard' rules. Practical experiment and experience are often the best instructors here . Try a particular variation, and see how it works out!!
Sometimes, published data doesn't always help. The attached extract from an old National Semiconductors audio handbook illustrates the kind of thing I mean.
R13 is shown as 93.1K 1% resistor. R14 is a 10k variable resistor
in series with R13.
So the value can be calibrated to any value
anywhere between 93169R and 104.031R (+/- the tolerance of R14)!
No real reason to specify R13 as a '1%' resistor here, I would suggest??
But very confusing when you are first starting out, and tend to trust what you read in published data.
When I first started experimenting, especially with audio circuits, I would start from the premise: 'all resistors are 10K, until proved otherwise'. Nice 'medium' impedance to work from!
A bit simplistic perhaps, but it helped me learn quite a lot!!