Noise in single vs dual supply

[ricko_uk]

Hi,
using an instrumentation amplifier (or any amplifiers) and assuming in the specific application it can be connected to single or dual supply, which is better to keep supply noise to a minimum? Single supply or dual supply?
Does dual supply introduce more noise?
Whichever it is, could you please explain also why?
Thanks

[unitedatoms]

I tried to calculate noise for two variants of supply. It looks like dual supply with uncorrelated voltage noise has small advantage. Consider single supply 10v with 10mv noise VS dual 5v/5v and 5mv noise each. The square root of sum of squares will be 7.07mv which is less than 10mv.

Problem is that ripple of supplies is usually correlated. But references can have broadband noise in frequencies higher than ripples. So may be it is still a valid advantage.

[ricko_uk]

Thank you Unitedatoms,
two questions:
1) in my application it is slightly different from what you suggested. The option I have is 0 to 5V or -5V to +5V. What would it be in that case?
2) in your example you assume that in the split supply you have half the noise. Why do you assume that? Would it not be the same noise for each rail (whether 0-10 or +/-5V?

Thank you

[gbaddeley]

With dual supplies, referenced to 0V, the noise in +5 and -5 will be uncorrelated, meaning the noise sum is less than their peak-to-peak sum. Read up on noise theory. Generally noise is not a design consideration for single vs dual supplies as the inst amp’s PS rejection will contribute  lower noise than from other sources.

[unitedatoms]

With single 5 VS dual 5+5, the noise is X VS X*1.4142. So choose single supply.
I assumed that single VS dual is for identical voltage span. If you double the span, then noise is proportionally grows as square root of sum of squares.

I also assumed that noise amount is proportional to supply voltage, to give a fair comparison. No other reasons, just to make example simpler.

[David Hess]

Blueskull posted what I was going to post.  Correlated noise in the bipolar supply can be rejected more effectively by the power supply rejection instead of the common mode rejection.  Tracking supplies have advantages in low noise circuits which can take advantage of this.

Note that the power supply rejection curves shown in datasheets may actually be common mode rejection or open loop gain if the wrong test circuit was used.