Electronic – arduino – Rough Battery (9V Alkaline) Level Estimation with Analogue Reading

This seems to be very similar to Nick's schematic, was probably busy drawing it when he posted :-).

First why you can't use the N-FET on the high side: it needs a gate voltage a few volts higher than the source, and the 4.2 V is all you have, nothing higher, so that won't work.

I have a higher value for the pull-up, though a value of 100 kΩ also will do. 10 kΩ will cause an unnecessary extra current of 400 µA when you're measuring. Not the end of the world, but it's 1 resistor in both cases, so why not use a higher value.

For the MOSFETs, there are a variety of parts to choose from given the requirements are not so strict; you can consider inexpensive ones such as, e.g., Si2303 for the P-channel and BSS138 for the N-channel.

It sounds like you may have a handle on your question already, but I would like to add a couple of points about NIMH vs Alkaline.

You don't say how many watts or how many amps or milliamps your megaphone will be demanding, but the NiMH have a much lower internal resistance and so they can provide a much higher current without dropping their voltage as much as an Alkaline will. At higher loads, a Nimh will provide more power than a Alkaline; at very low loads, an Alkaline will provide more power (a very very loose generalization, but for example, an Alkaline will last forever in a remote control while the NiMH will not last as long - of course there is also the self discharge of many of the NiMH).

Also, most NiMH have a NOMINAL volatage of 1.2, but fully charged they start out at closer to 1.4 (I have measured some NiMH fully charged at 1.5) volts, and as mentioned already, hold to the 1.2 volts for most of their discharge.

The Alkalines often start closer to 1.6 volts, but quickly lose voltage as they discharge so that their average voltage through their life is about 1.2 Volts! Of course this depends on what the cut off voltage of your Megaphone is.

Don't forget that most NiMH have a very high self discharge rate and can lose 10-20% of their capacity in the first day, and 1% of their capacity per day just sitting there and are essentially completely discharged in 3 months or less! There are newer NiMH that hold 85% of their capacity over a year.

Check out http://batteryuniversity.com/learn/article/Nickel_based_batteries for more info.

As far as your 4 options, option 2 sounds like the best one. Options 3 and 4 have been discussed by others as to why they offer such poor performance.