I'm trying to figure out how to prevent over-charging a single AA battery off of a 1.5V / 200mA solar cell.
I guess this comes down to asking how to determine whether or not a battery is fully charged.
Also, which type of battery would be better for trying to keep a single battery alive for 3-4 months via trickle charging and a ~5mA pull? NiCd?
Charging NiMH batteries is usually done using the so-called Delta-V charging method. There are ready-made ICs for that (LTC4010, MAX713, etc.) but probably they won't work with the power coming directly from that solar cell.
Basically there is no simpler reliable charging method for NiMH, though in some applications it's possible to charge an NiMH battery with a constant and very low current (< 0.1C). The battery won't blow up but it will not reach its specified cycle count either.
There is a small drop in the terminal voltage when a NiCd (and NiMH) cell is fully charged; it's larger with a NiCd cell and is easier to detect. I'd use an MCU like a small PIC or AVR with an ADC to detect the negative delta voltage (remove the charging voltage periodically) and terminate the charge. I've heard of people connecting small solar cells directly to NiCd cells, but with a solar cell capable of 200 mA you need to take some precautions. I'd boost the 1.5V to something like 3V, to make things easier, and provide a suitable supply to the MCU. You'd need an MCU with a 12-bit ADC to detect the voltage dip with an NiMH cell. Here is a useful app note.
There are also energy harvesting techniques that can be used, here are some typical devices. I've experimented with the EH300 and it works OK.
