Hi
I want to make a simple, cheap method for charging this battery
https://uk.rs-online.com/web/p/coin-button-rechargeable-batteries/0422387/
Since I don't think it's going to need recharging very often, it doesn't really matter if it takes a long time. I read one can use the LM317 to provide a constant current using a single resistor, but I also want it to be safe to leave the battery connected to the charger indefinitely. How low a current do I need to achieve this?
I'm also concerned about another issue: the battery will need to be connected to the circuit it powers while charging. This circuit cannot safely tolerate a voltage higher than 3.6V but I read that the fully charged voltage of a Ni-Mh battery is higher than this. If I limit the charging voltage to 3.6V will I severely reduce the charge the battery holds?
Thank you

 

Nimh use constant current,and so the cell makes it own voltage , you can charge the cell at 10 to 50% of it's rated current, so your cell is a 16mAh that would be 1.6mA to 8 mA.

You can use a lm317 with a 150 to 750 ohms resistor .

 

Go to the Battery University or to Energizer Technical Info online and learn about Ni-MH batteries.
This battery has three tiny Ni-MH cells in series that are charged to 1.4V to 1.5V each (4.2V to 4.5V for the entire battery) at a fairly low current, then the charger circuit must sense a full charge and disconnect the over-charging or switch to a 1/30th of its mAh rating for a continuous trickle charge. A battery charger IC will do these things. All the recommended charging currents are listed on its datasheet.

Since your circuit cannot safely tolerate a voltage higher than 3.6V then charge the battery only partially, far from a full charge. The graph from Energizer shows that a battery charged to 1.2V per cell (3.6V for yours) is dead with almost no charge.

Use a higher voltage battery and a voltage regulator IC.

 

You could add in a diode in series with the battery output to reduce its voltage while charging.

Alternately, if the load current is low, you could add a resistor in series with the battery to the load and add a 3.6V clamp at the load to limit the voltage when charging.

A third option is to use a low-power 3.3V ultra low drop-out regulator such as this to isolate the high charging voltage from your load.

 

Hi
I want to make a simple, cheap method for charging this battery

Have you looked at the MAX712 IC, aimed at this kind of charger in one IC.
Max.