# Electronic – Alkaline battery noise varies with temp

analogbatteriesnoise

I had an 9V alkaline battery connected to a resistive bridge, that stepped out the voltage to several analog channels. I was testing the analog channels over temperature and when it got below 10C I noticed that the battery voltage noise went from >1uV to 10's mV. As I have always thought that batteries were a stable source I started checking my analog electronics, only to find it was the battery.

Has anybody characterized this noise or the temperature it starts at?
Where does it come from (what physical processes)?
Does this apply to all battery chemistries (Do all battery types get noisy with lower temps)?

Edit – More stuff:
This is not mechanical, a test engineer and I ruled that out. The electronics are not at the same temperature, and are not powered by the battery. The battery is a reference. There are sensors that we use that we normally take down to temperature that the analog electronics are connected to and there is no problem with noise with the regular sensor. The noise is coming from the battery

Edit – Final word:
So you don't have to read through loads of comments, I'll post the result here. When I woke up this morning I thought I would heed the council of a few users and double check the mechanical setup. I suggested that the tech look things over and redo the solder joints with leaded solder instead of the lead free. After that things worked great, I had less than 1uV noise going down in temp. So I apologize for not listening to comments about mechanical.

Considering that noise variation with temperature is a fundamental property of matter, all the things (which includes alkaline batteries) will have noise proportional to temperature. All resistances have thermal noise, and all batteries have resistance, and their noise is more or less from that internal resistance. The voltage noise of a battery (or resistor) is: $$V_{noise}=\sqrt{\frac{4hfR\Delta v}{e^{\frac{hf}{kT}} -1}}$$

where h is planck's constant, f is the frequency, R is the internal resistance of the cells or cell, ∆v is the bandwidth, k is Boltzmann's constant, and T is temperature in kelvin. As you can see, lowering the temperature lowers the noise. This is true for everything, there is nothing happening here unique to batteries. This noise is called Johnson-Nyquist noise.

As for which chemistry has the lowest noise, there is no meaningful difference in theory. In practice, Nickel-Cadmium cells have the lowest voltage noise. However, this is purely due to that chemistry also having the lowest internal resistance. As you can see from the earlier equation, lowering resistance will lower noise over all. Alkaline cells have relatively high internal resistance, so it is not surprising they would be noisier as a chemistry. Note that this means cell size is as important to the voltage noise as cell chemistry. Larger cells have lower internal resistance and therefore lower noise.

But don't take my word for it. Take NIST's. They did a study on the noise of batteries, and there are nice graphs for those curious in that paper, but after substantial measurements all the way down to the thermodynamically limited noise-floor, they concluded that battery voltage noise is essentially in agreement with the expected Johnson-Nyquist thermal noise one would expect from the cell's internal resistance.

Edit: Whoops, I forgot that the entire question was about the noise increasing once it got cold enough. A battery's internal resistance increases as it gets cold, and decreases as it gets warm. This mechanism is chemical in nature, and likely could vary between different constructions of the same chemistry. In general, temperature can increase the internal resistance a lot once you get cold enough. The internal resistance is ultimately determined by the rate the chemical reaction can occur, and the colder the battery, the slower the reaction. It's a safe bet to look at a cell or chemistry's internal resistance vs. temperature, this should give you a good idea of how warm you need to keep the cell. There is going to be a 'sweet spot' where the noise is lowest. Warmer and the temperature increases the noise more than the internal resistance decreases, colder and the internal resistance increases more than the noise decreases.

EDIT2: It looks like an alkaline cell's internal resistance doubles (or at least an AA cell) going from 20 degrees C to 10. This is far too small to account for the several orders of magnitude noise increase.

Sorry. Something weird is going on. Thermocouple effects perhaps?