Analog Devices' Matt Duff describes how to convert spectral noise density (nanoVolts per root Hertz) into RMS noise (microVolts rms)
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Calculating Spectral Noise Density to RMS Noise Hi, my name is Matt Duff, I’m an applications engineer covering precision amplifiers, and today I want to talk to you about converting spectral noise density to RMS noise. So when you look at a data sheet, typically you’ll see on the sheet looks something like this, so say voltage noise density add up to your frequency and it will say something about the hertz and that is the spectral noise density. Typically also on a data sheet in the typical performance section, you’re going to see a curve like this and if you look, you’ll notice that this point in the data sheet under the sheet table corresponds with the point on the curve in the typical performance curve. So this point goes in hertz at one kilohertz is right here on the curve as well. Now what we’re going to talk about today is how to convert this information into our RMS noise which can be useful at looking at the noise of the whole system and I would encourage you also to look at another video we have where we convert RMS noise to peak to peak noise. So how do we go about doing this? Well what we need to first know is what is our frequency of our system, so let’s assume for an example if the frequency of our system is 10 kilohertz, I’m going to draw a line right here and what we want to do is we want to integrate under this total area of the curve so we want to know is the energy all along here. Now what you can do is you can go and you can look at this little piece, integrate, look at this little piece, integrate, look at this little piece, integrate, and be very accurate. That’s very time intensive so I’ve drawn up here this equation of how you would go about doing this. But again this is something that most people don’t do because you do have to go and look at the data sheet and pick out each number out of this graph. So what most folks do is we’re just going to approximate. We’re going to say that this area is going to look like a box, we’re going to draw a box, and we’re just going to do this area. And you might say, look at all this extra that we’re leaving here, we’re going to get really bad answer because we’re leaving off with all this energy. Well actually if you remember we got a lot of rhythmic scale here and so because we have a lot of rhythmic scale this amount of energy is quite small compared to the amount of energy here. So it's really a pretty good approximation as long as we’re operating—as long as our cut off is in the white noise area of the curve, as long as we’re not trying to do some sort of approximation way over here. So now that we have our box, what do we do? Well now it's pretty simple, so instead of this complicated equation all we have to do is we take our spectral density and we multiply it by the square root of our frequency. So if we say this is 40 megahertz here and this is 10 kilohertz, we just multiply it by that so it's pretty easy. So if you want to be a little more accurate, one thing to remember is that in most systems you don’t have a ice brick wall filter here where you pass everything to your cut off frequency and then everything else is blocked. Typically in a normal system you’ve got filter and that filter looks something like this. So it comes down here and it comes up here, so you chop off a little bit of frequency content here but most you let through a lot of extra noise content here and so you have to account for this. And depending upon your filter, it's a lot more content through, so I’ve drawn up on this pad here different filter types so you can notice that a one pull filter is going through so a brick wall filter as you can see the brick wall filter has ideal case one and for a one pull filter you let 57% more through so you would also block by a 1.57 and as you go to higher and higher order of filters you get closer and closer to this ideal one. Now I have drawn up stuff for a butter works filter, note that for a shabby shack or for a vessel you have different values
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