# Simple equivalent circuit model for batteries

So I have no knowledge about batteries and I just came across the phrase (simple equivalent circuit model (linear second order system)) when dealing with an exercise about batteries and the identification of their circuit's parameters.

My question is: Is there a specific form for the linear second order system circuit model? In other words, is there a circuit with a predefined number of resistors, capacitors that would satisfy this term? And would it be possible to determine the circuit's parameters, given the voltage, current and SoC?

Typically it's a voltage supply in parallel with an RC ladder, like this:

simulate this circuit – Schematic created using CircuitLab

Usually the values of the components (including, sometimes but not always, the voltage supply) vary with the state of charge of the battery. Generally the resistances go up as the battery discharges because the ions in the cells have to flow further to do their magic.

Sometimes the voltage source itself diminishes as the battery discharges (i.e., lithium-polymer cells or lead-acid cells).

Sometimes it does not (dry cells and NiCd cells), and any apparent voltage drop is the result of the equivalent resistances increasing with discharge.

This can all get super-complicated, and to my knowledge there isn't one exact "master model" of a electrochemical cell. Different practitioners may have different favorites, or they may have different models for different situations. You pretty much have to play it by ear, and either find an expert or gain just enough expertise to get the job at hand finished.

In general, second order circuits means you have a resistor and two energy sources, i.e., two capacitors or two inductors or the combination of one from each. I'm not sure exactly how it works for a battery equivalent circuit, but you can draw a whole bunch of different equivalent circuits using the def above and parallel/series circuits knowledge.

" And would it be possible to determine the circuits parameters given the voltage current and SoC? " -> you can just use Ohm's law to determine the impedance and hence the value of those parameters.