Many laptop batteries have a microcontroller connected to the SMBus (therefore being a "smart" battery), which is an industry standard interface.
Placing 3Ah cells in a 2.2Ah "smart" battery would only result in getting 2.2Ah out of the 3Ah cells, because the battery microcontroller connected to the SMBus needs to be reprogrammed (if you can do it - a rarity) to fully charge 3Ah cells.
I learned this the easy way by reading the Smart Battery Data specification.
Most (if not all) higher capacity non-OEM batteries will still be able to be charged to their rated capacity is because the capacity of the battery microcontroller can be programmed (rarely, if ever by the user) from 0 to 65,535 mAh (a very long way to go before the SMBus specification needs a major revision!) and the charge rate (and various other parameters) are also programmable (again, rarely, if ever by the user) to suit the particular AC adaptor.
Placing 3Ah cells in a 2.2Ah "smart" battery would only result in getting 2.2Ah out of the 3Ah cells, because the battery microcontroller connected to the SMBus needs to be reprogrammed (if you can do it - a rarity) to fully charge 3Ah cells.
I learned this the easy way by reading the Smart Battery Data specification.
Most (if not all) higher capacity non-OEM batteries will still be able to be charged to their rated capacity is because the capacity of the battery microcontroller can be programmed (rarely, if ever by the user) from 0 to 65,535 mAh (a very long way to go before the SMBus specification needs a major revision!) and the charge rate (and various other parameters) are also programmable (again, rarely, if ever by the user) to suit the particular AC adaptor.
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