.. when battery is reaching 4V-4.2V then we have less than 1V to play with, (0.1V goes for the drop at the charger IC as well), so maximum current is now becomes less than 1/8=125MA so there is an increase in charge time there.
so ideally it is better to take the extra input voltage when it actually exists so I made that circuit ..
Well, now you have a problem. There is a universal charge profile for CORRECT charging of LiION. You need to check the manufacturers papers for exact
voltages and currents, but basically it goes -
Max of 1C (come 0.5C - 2C) via constant current at a max voltage eg
4.5V 4.25V (corrected mistake), then WHEN the current drops C/10, the charger must drop to constant voltage
eg 4.20V max with current limit of C/20. Generally this changeover point happens ~3.8-3.9V , at the cell, so 125mA at 4.0V is most likely TOO high.
All depends on chemistry type. If you look at the charge / energy curve of LiIONs, there's bugger all capacity to be gained after 3.8-3.9V anyway, so
VERY few designers bother to gain that extra 2-5% and RISK a failure. You can PUSH it, but you WILL SEVERELY reduce the total # cycles.
In a race pack we DO push it past the limit, and if we only get 10 cycles, we're happy, especially if it helps win a race (or gain a few positions).