What is the most accurate way to measure internal resistance of a consumer battery?

Question

The typical way to measure the internal resistance of a battery, that I've found through research, is by connecting the battery in a circuit with a resistor, measuring voltage through the battery, calculate current, measure voltage through the resistor, find the voltage drop and use kirchoff laws to calculate the remaining resistance, which would be internal resistance.

A professor mentioned that this is too inaccurate for batteries with very low internal resistances, so is there another, more accurate way to test the internal resistance of a standard battery?

Answer 1

The easiest is to use an AC current, just like a network analyzer.

You can use a switchable current sink of known value, or a resistor and a FET. Measure voltage with current on, then with current off, substract, divide by current, you get internal resistance. If you keep repeating this on/off cycle, this is equivalent to using an AC current.

An advantage of AC measurement is that you can use a capacitor to get rid of the DC, and only handle the small AC voltage. It also ignores any DC offset in the signal chain, from opamps etc. AC measurement is the most accurate method.

You can use something like this as an experiment:

^{simulate this circuit – Schematic created using CircuitLab}

Here the voltage source on the left drives an AC signal through R1 and C1 into the battery. This is AC coupled via C1.

C2 extracts the AC voltage on the battery.

Knowing AC voltage V1, once you measure the AC voltage on "OUT", battery internal resistance is easily calculated, as it forms a resistive divider with R1.

You can do this with a soundcard, or with a function generator and a multimeter. Make sure you calibrate and verify your test rig by replacing the battery with a resistor of known value, which should be of the same order of magnitude than the expected resistance to be measured.

Answer 2

The objection by your professor to the method you described is wrong. If a battery has low impedance, you just increase the load, so the difference can be better measurable.

The problem, however, is quite deeper. Batteries usually don't have a steady DC load, and often people need to know the battery reaction to impulse load. The issue is that the battery doesn't have a single "impedance" that can be used for estimation of its response to load. Every battery have a spectrum of impedances, different impedance for different frequency of loading. This topic of engineering is called "Electrochemical Impedance Spectroscopy". An example of presentation. See also this article from BatteryUniversity, with an example of "electrochemical spectrum".

So, the most accurate way to characterize internal impedance of a battery is to measure its spectrum, using, for example, the circuit suggested by peufeu.

However, this is not all. The EI-spectrum is usually collected using "small signal" applied. As Lorenzo Donati commented below, the value of impedance is not only dependent on frequency, but its is also nonlinear with amplitude of applied signal/load, which adds another dimension into complexity of the problem.

Answer 3

Internal resistance is an approximation of a complex V(I) function of a battery, so there is no "true" internal resistance value you could accurately measure in the first place. The most representative measurement you can do is the actual V(I) curve for relevant current values. If, by chance, you obtain a straight line - bingo, your battery can be accurately described by a single internal resistance value. Otherwise, you'll have to use the curve you've got to determine current and voltage values for any given load.