Schematic Design Help: LED with battery charging circuit

Hoping for a few more ideas:

I’m trying to create a battery charging circuit - the battery recommends a constant voltage charge of 3.1V and I’ve already identified the appropriate device for that part.

What I’m having trouble with is designing a circuit that can indicate when the battery is charging. I must interface to a device that can have an LED on while charging (think flashlight). This leads to my expected current - 4.5mA steady state (if the light is on), up to 9.5 mA charging.

Is there a good analog way to check for a current charging differential? My other option would be to use a cheap micro-controller and a current sensor to look at the current and decide programmatically if it is charging or not.

Are there better options available for something like this?

What type of battery will be charged by this charger?

Manganese Silicone Lithium button cell battery.

Link?

Since these LiMa batteries apparently charge with a constant voltage, it seems you could simply put a resistor in series with the battery (e.g. battery cathode to GND, battery anode to resistor, other end of resistor to constant 3.1V) and feed the voltage at the battery/resistor node into a comparator.

Due to the small currents likely involved, I'd use an opamp intended for instrumentation applications to buffer the voltage at the battery/resistor node so that the input offset current doesn't affect the output. Then feed the output of that buffer into the comparator.

I did some quick Googling on LiMa batteries and the button types I hit upon work at currents of dozens to hundreds of microamperes. Apparently you're using a much bigger battery!

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