# Measuring band-limited noise coming from an amplifier

I have a strain gauge amplifier and from my analysis, it will produce a low level of white noise above approximately 1kHz i.e. the power spectral density is flat above 1kHz.

If I measure the output noise with a reasonably decent meter Agilent 34401A it gives me a reading of around 0.4mV RMS. The meter has a bandwidth that is flat to 300kHz and possibly extends to significantly past 1MHz.

I'm only interested in the noise in the spectrum DC to 50kHz so, I could build a battery powered 8th order low pass filter to measure that noise or maybe (and this is the crux of the question), I could make a single order low pass filter (a resistor and capacitor) and utilize what I know about that filter's equivalent noise bandwidth.

Given that I wish to know the noise over a DC-50kHz bandwidth (and that I expect the noise to be spectrally flat above about 1kHz), does it seem unreasonable to make my simple RC low pass filter have a bandwidth that is: -

$\dfrac{2}{\pi}\times 50kHz$ = 31.83kHz

I now the measure the noise with the filter (previously 0.4mV RMS without the filter) and it almost halves - this I like (of course) but am I making some really stupid error to convince myself something is better than it actually is? I'm quite happy to expect a filter of low nth order to have a significantly higher ENB but does this work in reverse?

A link to a reputable source on this would be great.

You're fine, although you will be introducing some errors, but as you point out in a spectrally flat PSD this should be minimal or even ideally zero. In your linked to derivation of noise bandwidth, the implicit assumption is that the noise spectrum is flat. So you are safe.

BTW, there is a EE.SE version of the noise bandwidth question here.

For really detailed analysis I use a Spectrum analyzer (which you may not have) as they are the ultimate low noise instrument available besides just having that handy V vs. Frequency thing going.

• I was going to suggest a spectrum analyzer also, but all the SA's I've used have problems dealing with frequencies near DC, and here we're looking for noise in the DC to 30 kHz band. – The Photon Sep 25 '14 at 16:49
• @ThePhoton fair enough, and the lower frequency SA's are the useless (for this work) FFT types, the key is that unobtainium based low noise mixer. – placeholder Sep 25 '14 at 17:51
• I appreciate the link for the derivation but I was hoping for a link that described this method as applied to measuring the noise output from a target amplifier - got a customer who might need to be persuaded that we are delivering contractually what we said we would. – Andy aka Sep 25 '14 at 18:07
• @Andyaka the reason for the link is have an internal reference as apposed to an external link. – placeholder Sep 25 '14 at 18:53
• @placeholder sorry I don't understand your comment. What I'd appreciate is some paper somewhere that describes this method as being applicable to testing the noise output from an amplifier system. I know it makes sense given the constraints but I don't think my customer would see the linked answer as applying to a method of testing the amplifier we will deliver to him. Maybe I missed something? – Andy aka Sep 25 '14 at 19:11

OK as you know 50kHz is in the opamp sweet spot. So there's no problem building a active filter. The battery may not be needed. If you are worried about power supply noise, then gain up the signal first, and add capacitor multiplier's to the supplies.

What sort of accuracy are you looking for? At the 10% level it's not too hard, at 1% you need to sweat the details.

So the ENBW of a filter assumes that the input is flat out to infinite frequency. If there is some roll-off not from the filter but from something up stream then there is some error in your ENBW number. That error is worse for a one-pole RC, since there's more gain left out at the higher frequencies. More poles rolls it off faster, so there is less HF error. But your multi-pole filter is not perfect, and you may have to measure it's transfer function.

I do know that for a 2-pole lowpass you need the input flat out to about ten times the corner frequency for a 1% error. (I can provide the math details, from the manual for this.)

As far as reputable sources, there are some ENBW number's in AoE. (the active filter chapter I think)

• I don't understand "opamp sweet spot". I also don't understand "add capacitor multiplier's to the supplies" – Andy aka Sep 29 '14 at 10:15
• @Andyaka, Oh sorry, Well kilohertz (~1kHz to ~100kHz) is a nice range for opamps noise wise. There's not much 1/f stuff and you've still got plenty of gain. (So you can keep the BW high and avoid complications in the ENBW. The capacitance multiplier, en.wikipedia.org/wiki/Capacitance_multiplier, is great for getting rid of PS noise. At low freq the opamps have nice PSRR, but not so good at higher freq's. And that where the cap-mult shines. (Try one, you may like it.) – George Herold Sep 29 '14 at 12:10