@Gyro Thank you so much for your patience and support
we are doing a small college project with Al-ion battery. We have build the cell and now looking for charging it.
We are also planning to build a crude version of BMS with over/under charge protection using one tl431 circuit (I do have few question regarding it as well, but planning to do that as a separate thread). The CC/CV supply is for the charging of this cell, where voltage is around 2-3 volts and current draw should be restricted to 0.1milliA to 0.5milliA.
This is just the first trial test where we are basically following a trial and error method for different cell chemistry and charging voltage and later figuring out the efficient values for each. Also, just want to let you know that we are taking all the precarious for a fire. However Al-ion being non explosive, we are pretty much safe in doing these experiments (or I would say at least so far )
this is the setup. hope this gives the complete picture, which I should have explained at the beginning. Sorry for the confusion
Ah, ok. That sounds interesting.
In that case, voltage accuracy sounds like the most important characteristic - with current accuracy not far behind.
If you are in the experimental cell chemistry stage, then something like an LM317 with decent resolution adjustment pot and a load resistor on it's output to shunt away most of the quiescent current might be an option. Followed by a protective resistor and current meter?
It sounds that you need good monitoring of the battery's charge characteristics so I assume that there will need to be a uA/mA meter in series with the charging supply. If so, it will be necessary to account it's voltage burden. A high impedance voltmeter too, but that won't involve significant loading.
Your BMS also sounds as if it might have leakage current issues which could preventing accurate monitoring of the amount of charge going into the battery.
Sorry, the above isn't a solution (either), just some random thoughts related to the application.
EDIT: Sorry, from @exe's post, the LM317(l) might not be a suitable candidate (although a resistor might be used to shunt away the quiescent current as I mentioned above). You want to avoid this resistor draining the cell if the regulator voltage drops though - maybe a series diode, with voltage measurement taking place after the diode.