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Lead Acid Battery Noise

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I am unable to find this information on google, perhaps I am not searching the right terms.

Lead acid batteries are inherently low-noise, but what happens when they are very near the end of their life cycles? Is it possible that they would become noisy (either extra johnson or 1/f noise) if they are nearly dead?
Any battery - if noisy at all - tends to get very silent towards it's end of life time. :)
so noise voltage decreases with stored charge and/or stored charge capacity?

I have never researched this. Intuitively, I'd guess that they do get noisier because their effective impedance increases as they discharge. However, if you are thinking of using this a State-Of-Charge indicator, I am guessing that by the time they get noisy, they are stone-dead, and you have discharged them way more than you should have.

I know that some battery chargers measure effective series resistance of the battery to determine SOC.

Interesting (to me) topic!
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It is not for a state of charge indicator. My reason is that I have a low-noise current amp being powered from these batteries. I notice a significant increase in output noise when the amp is powered from the wall. I measured the batteries of another, identical amp connected to identical batteries and it was extremely low noise - however, my unit is noisy. The batteries also have a very short life before requiring charge, so I am trying to determine if it is noisy batteries that are causing the extra noise that I am measuring.

I am predicting that this extra noise has a 1/f characteristic, which SORT of makes sense since there is a DC current flowing in the battery and it has some effective impedance --> 1/f noise.

The batteries are powersonic PS-1220. The datasheet (direct PDF link):
**broken link removed**

I also measured the working batteries in the identical unit directly, and they have very low noise - less than 20nV/sqrt(Hz), which is the noise floor of my measuring instrument. Connect to the wall and the batteries measure over 1 uV/sqrt(Hz) since they are charging. However, I am unable to measure the noise characteristic of my presumed-dead batteries as I no longer have access to a known-working piece of equipment that measures power spectral density. It is a long and complicated story; I am trying to prove that an old (circa 1986) dynamic signal analyzer is working by measuring a known noise source, but to measure the known source I must amplify it... and if my batteries are noisy, that's not a very good standard to be measuring to!

And it is quite an interesting topic indeed!
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Isn't that what regulators are for? I've never considered battery noise for anything because one of the first things I learned was to never trust any unregulated power source to be stable or quiet.
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The battery is likely to be 40+db "quieter" than the output of an IC Voltage Regulator Chip, even if the regulator output is bypassed with a low ESR capacitor.
I presume that the battery voltage is regulated with some low-noise technique inside the amplifier (stanford research SR570). However I also presume that the circuit is fairly dependent on battery noise quality as the amp manages to achieve noise levels of 5 fA/sqrt(Hz) (yes, femtoamps. not a typo).
There are two separate considerations: First, slow variations of the battery voltage are attenuated by the opamp's Power Supply Rejection Ratio (PSSR). White noise coming from the battery may or may not be rejected by the opamp's PSSR.
I actually posses a full schematic (with part numbers) of the entire SR570 amplifier. Its not digital so I'd have to find a scanner to show you guys...

Anyway, when running on battery power:

the batteries are fed directly to an LM2940 (10V LDO regulator) for the +10V reference and to an LM340 for the 5V reference (through some MOSFETs that are used as switches). There is an interesting circuit involving an opamp that uses the -12V battery terminal and the regulated +10V to create a -10V reference rail.

I looked up the voltage regulators and their datasheets specify their output noise voltage, which is way higher than the noise specs of the overall amplifier. So the magic must be in the amplifiers they use. The input stage uses two low-noise amps depending on the mode...AD743 (low noise spec), and the AD546, for low input-current mode.

I'm pretty sure all the important bits of the amp are inside a can on the circuit board.

Anyway, I'm not sure whats causing this excess noise. The batteries are well filtered and the regulators are higher noise than them anyway, so they would have to be very very degraded and extremely noisy to permeate into the low noise amps (which, being low noise, were probably designed for extremely good immunity from power supply variations.

I thought it was the batteries but it could be anything, since the gain on the amp is set to 1,000,000 or 10,000,000. anything that couples in just before that point...

the batteries need to be replaced anyway. if it fixes the problem, great, but if it doesnt, I'm still stuck where I am.
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