I'm attempting to build a simple circuit that will apply a constant voltage to a Lithium-Ion battery. If the applied voltage is greater than the battery, it should source current at a constant voltage, if the applied voltage is less than the battery, it should sink current at a constant voltage.
The circuit I've tried so far is attached in the image(s) below. I like this circuit because it allows me to control the voltage applied just by dialing a pot. It works well for sourcing current (image 1), however, as soon as the applied voltage drops below that of the battery, it flattens out (image 2). That is to say, the circuit cannot sink current at constant voltage.
I would like to build a circuit that can do both, as indicated by the cartoon graph in image 3. I would like to get behavior indicated by the dashed curve.
Does anyone have any suggestions for this?