To record bipolar EEG, you will need an EEG amplifier for each pair of electrodes that you want to calculate the potential difference between. It is important to note that you can also derive bipolar measurements from unipolar measurements. This is done in software. For example, if you are recording from sites A, B, C in unipolar you can then get the following bipolar measurements:
AB by calculating A-B
BC by calculating B-C
AC by calculating A-C
If you want to look at all possible pairs, you can calculate the combinations without repetition: n!/(r!(n-r)!) where n is the number of electrodes and r is 2.
For example, for a bipolar recording on 5 sites you would need 5!/(2!3!) = 10 EEG amplifiers. This assumes that you want to look at the potential difference between all possible combinations of electrode sites. This is the maximum number of EEG amplifiers that would be required.
Here is a reference for the number of EEG amplifiers required if you need to look at all electrode pair potential differences:
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