How to Measure Internal Resistance of a Battery

[neilparker62]

Table of Contents
1IntroductionExperimental BriefRevised Experimental BriefTable of Measurements and Calculated ValuesRegression Analysis: Measured vs Ohm’s Law calculated...

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[nsaspook]

https://data.energizer.com/pdfs/batteryir.pdf

 

[neilparker62]

https://data.energizer.com/pdfs/batteryir.pdf

I would say the "alternate method" I suggest is similar to the dual pulse method although I am not really using a stabilization current. Since the measurement is "touch/release" with the multimeter leads, I am effectively applying a 2-3 second 'pulse' with an $\approx 50mA$ load. I have adopted the practice of measuring the battery voltage under load (first) and open circuit voltage thereafter. So as to remove "surface charge" effects. Although I'm not sure how applicable 'surface charge' is with AA batteries - seems more applicable to heavy duty lead acid batteries.

Generally I expect my "pre-pulse" open circuit voltage to correspond to my "post-pulse" open circuit voltage. 50 milli-amps is chosen to try and ensure that we specifically don't have any appreciable change in battery emf over the period of measurement. The method doesn't work for AAA batteries because they drain too quickly at 50mA.

 

[Nik_2213]

Slightly tangential, I remember measuring the internal resistance of Uni lab's wall-power via current & voltage of an incremental dummy load, a bank of 60 watt incandescent lamps.

And, yes, the Lab Tech did warn us NOT to 'just' use the resistance scale of the big Avo analogue multi-meters supplied: He'd expended half a CO2 extinguisher on that hapless perp. Even an Avo's fusing had its limits...

FWIW, when it came to wiring up two long-legged germanium transistors etc as a free-running ~1 kHz multi-vibrator, the lecturer was appalled to find I'd briskly plugged his components into my S-Dec, a palm-sized solderless breadboard. I was done before most of my fellow students had laid out their nail-bed bread-boards, never mind tinned a chunky soldering iron. I had to do mine over the traditional way. No sweat, I'd brought along several of my favourite hair-clip heat-sinks, was soon done...

He was left speechless when I mentioned that three stages made a fun 'Flip-Flap-Flop', four ran as 'two-pair', five did 'two pair plus a runt pulse' and six did 'two prials'...

 

[neilparker62]

Some recent measurements using low resistance measurement techniques described in this article.

Internal resistance: Varta AA rechargeable batteries (2100 mAhr): 47 milli ohms

Pair of battery jumper leads: 47 +- 12 milli ohms
Standard meter leads (pair) : 116 +- 12 milli ohms
Gold plated meter leads (pair): 70 +- 12 milli ohms. These are about twice as long as the other lead pairs mentioned here.
Custom designed meter leads (pair): 47 +- 12 milli ohms
Custom designed pair with 3 wires in parallel (pair): 24 +- 12 milli ohms

28 meters 10 mm^2 roofing cable for a solar power installation: 70 +- 12 milli ohms
2 meters galvanized steel wire: 426 +- 12 milli ohms.

I have requested a modification on the Major-Tech MT870 meter which should reduce the attainable resolution (currently about 24 milli ohms) by a factor of 3.

 

[ArtZ]

Hi,
Though I don't recall if I ever did this with a battery, there were times over my career when I was faced with needing to determine the internal resistance or impedance of a black box voltage source. For many cases, it is quite easy. First, measure the open circuit voltage of the source. Then, simply place a known load resistance in series with the source and monitor the load voltage. Adjust the resistance until you measure 1/2 of the open circuit voltage. The resistance that produced 1/2 of the open circuit source voltage is the internal resistance. If the internal resistance of the source is very low, it may be necessary to momentarily switch in the load repeating as the load resistance is changed to mitigate load heating or source voltage fatigue.
Art

 

[berkeman]

Adjust the resistance until you measure 1/2 of the open circuit voltage.

Modulo the current limit setting of the voltage source...

 

[neilparker62]

Hi,
Though I don't recall if I ever did this with a battery, there were times over my career when I was faced with needing to determine the internal resistance or impedance of a black box voltage source. For many cases, it is quite easy. First, measure the open circuit voltage of the source. Then, simply place a known load resistance in series with the source and monitor the load voltage. Adjust the resistance until you measure 1/2 of the open circuit voltage. The resistance that produced 1/2 of the open circuit source voltage is the internal resistance. If the internal resistance of the source is very low, it may be necessary to momentarily switch in the load repeating as the load resistance is changed to mitigate load heating or source voltage fatigue.
Art

If there's a known load voltage and resistance, circuit current can be determined. Then division of the difference between open circuit volts and load voltage - and current will give the source resistance. In the technique I described using a meter's battery test setting, this would include meter leads resistance. Therefore the latter must be deducted to obtain "true" internal resistance. Alternatively use another meter to monitor voltage directly across the battery terminals. Any voltage drop here (under load) can only be on account of internal resistance so divide that drop by current to obtain internal resistance.

Today I ran such a test on an Ansmann AA cell drawing about 170 mA through a low resistance load. When the load is disconnected, terminal volts increase by about 7 mV. Hence internal resistance of the battery is 7/170 - about 41 milli ohms.

 

[TonyStewart]

Load regulation tests effectively measure any voltage source ESR whether the load loss is 1% or 50% or 100% (short circuit pulse test) Although there is more than one effective C in batteries from double-electric charge layer effects. Thus there is more than one Time constant T1=C1*ESR1, T2=C2*ESR2 so the duration of the x% pulse must be varied to capture at least two. THe load and unload duration of current affects both measurements of the voltage drop and recovery voltage (steady state) also tells you about these distinct values.
The slope on battery CC discharge tests indicates the validity of this. Although most users just want the a quick test ESR on full capacity after steady state. ESR does rise sharply below 10~20% SoC and ESR will have a shape in BODE plots but can be estimated with different current pulse durations. Thus the value will be different from DC to 1MHz.

This is energizer's method which just uses a 100 ms load test using a heavy drain of 505 mA with preload of 5 mA. which is quick to measure but may differ from your method.

 

[DaveE]

ESR will have a shape in BODE plots but can be estimated with different current pulse durations. Thus the value will be different from DC to 1MHz.

Which is why I would choose a Frequency Response Analyzer (small signal) of some sort. But this step response test (large signal) is nice if either you don't have the FRA or if your PS requirement is based on this sort of load, which isn't uncommon.

edit: OTOH, the OP is working with just a DMM, or maybe two.

 

[neilparker62]

Load regulation tests effectively measure any voltage source ESR whether the load loss is 1% or 50% or 100% (short circuit pulse test) Although there is more than one effective C in batteries from double-electric charge layer effects. Thus there is more than one Time constant T1=C1*ESR1, T2=C2*ESR2 so the duration of the x% pulse must be varied to capture at least two. THe load and unload duration of current affects both measurements of the voltage drop and recovery voltage (steady state) also tells you about these distinct values.
The slope on battery CC discharge tests indicates the validity of this. Although most users just want the a quick test ESR on full capacity after steady state. ESR does rise sharply below 10~20% SoC and ESR will have a shape in BODE plots but can be estimated with different current pulse durations. Thus the value will be different from DC to 1MHz.

This is energizer's method which just uses a 100 ms load test using a heavy drain of 505 mA with preload of 5 mA. which is quick to measure but may differ from your method.
View attachment 325269

I see this plot in an Energiser technical bulletin which gives an example calculation leading to an ESR of 214 milli-ohms. I presume this is typical for non rechargeables ? Rechargeables (in my limited experience) are nearly an order of magnitude better. Maybe 30 to 40 milli ohms on tests I have conducted on Ansmann (2850 mA hr) cells and Varta (2100 mA hr) AA cells.

 

[neilparker62]

Which is why I would choose a Frequency Response Analyzer (small signal) of some sort. But this step response test (large signal) is nice if either you don't have the FRA or if your PS requirement is based on this sort of load, which isn't uncommon.

edit: OTOH, the OP is working with just a DMM, or maybe two.

Yes - I have two Major-Tech MT870 DVM/DMM s.

 

[TonyStewart]

I see this plot in an Energiser technical bulletin which gives an example calculation leading to an ESR of 214 milli-ohms. I presume this is typical for non rechargeables ? Rechargeables (in my limited experience) are nearly an order of magnitude better. Maybe 30 to 40 milli ohms on tests I have conducted on Ansmann (2850 mA hr) cells and Varta (2100 mA hr) AA cells.

This shows clear difference in degradation of mAh capacity with Alkalines and Lithium non-rechargeables.

Your Ansmann (2850 mA hr) and the Varta (2100 mA hr) AA cells are both NmH rechargeable and indeed have low ESR with some hybrid technology.

IMHO , if you buy in bulk. Alkaline non-rechargeables offer competitive mAh/$ economy as long as the load is not excessive drains in less than 2 days of continuous use. Otherwise with continuous drains, they degrade significantly in mAh capacity as shown above from Energizer https://data.energizer.com/pdfs/alkaline_appman.pdf