How can I model a charging battery using simple circuit analysis techniques?

[lasteem1]

I'm trying to understand how I could use simple circuit analysis techniques to model a charging battery in the circuit attached. The battery connected only to a power supply will want to sink up to about 1A starting out then will transition downward quickly to about 200ma. Then it will fall off slowly. Can anyone help?

 

[uart]

Model the external circuit as a Thevenins equivalent of approx 4.4 volts in series with 17 ohms.

The model of the battery is a little more tricky. You can approximate it as a state of charge (SOC) dependent voltage in series with an SOC dependent resistor.

Since the external circuit resistance will likely dominate the battery internal resistance in this circuit we don't need to worry about too much detail in modelling the resistance. Given what you said "about 1 Amp initial charge at 5 volts" we can assume it's about 1 ohm.

A very much simplified model for battery internal EMF would be linear function of SOC varying from about 3.6 volts at zero SOC up to about 4.2 volts at 100% SOC. That is,

$$E \simeq 3.6 + 0.6 \alpha$$

where $\alpha$ varies from 0 to 1 representing the SOC from 0 to 100% respectively.

Putting that all together you get (after some simple circuit theory) a very approximate model of,

$$I \simeq \frac{0.8 - 0.6 \alpha}{18}$$

BTW. This corresponds to an initial charging current of about 45mA for a discharged battery dropping down to about 10 to 12 mA when fully charged.