Hi in my previous video reviewing this one, Gigahertz Siglent STS 5000 series oscilloscope I made a little bit of an oopsie in the noise measurement compared to the Road & Schwarz one over here which I was just comparing the input channel noise of the two and only a couple of people actually spotted the mistake. So let's see if you can actually spot it Now of course, to measure noise on a waveform, there's two ways you can specify it. You can specify the peak to peak noise or the Rms noise. and usually like most people will probably use the Rms noise you could.

You know it depends how you want to do it. per peak to peak you can see like all these little Peaks in there and if we stop that you could actually potentially see like little tiny spikes in there that's can contribute to the peak to peak noise and that really is not hugely relevant in a lot of cases. That's why often the Rms noise will be is a better measure when you're comparing like two different oscilloscopes in this particular case and of course the Rms value. We've got the statistics here.

I'll run that again. The mean value of our Rms is about 94 93 micro volts. So you would say that this signal scope has an input noise of in on this particular range on the 1 millivolt range with 2 Meg of memory at 1 microsecond per division with the bandwidth which is actually 200 mega Hertz It's not 1 gigahertz because on the lower 1 milli volt per division of 500 micro volts per Division range, you don't get the full bandwidth out of it. It's a bit of a trap for young players.

you only get a more limited bandwidth on this siglent scope anyway. so we're at 200 megahertz bandwidth. All those settings about 94 micro volts. where's the road and Schwartz over here if we go over and have a look the same settings.

I've got 1 millivolt per division I've got 1 microsecond per division I've got 2.5 g examples. So roughly the same amount of memory, but our RMS noise is mien is about 323 microvolts. so you might think this road in Schwartz is much worse than the signal sequence. much better than Rohde Schwarz, but that's not the case.

I've made an oopsie here and this is what happens when Dave doesn't engage his brain when he's shooting videos and it could easily happen. and I didn't I knew this, but I just I goofed it in the video. So let's look at it. So pause the video now and see if you can figure out why.

the road and Schwartz are a mess. Noise is much higher then the Sigler it is. It's an important and subtle point that makes a huge difference. Alright, did you guess it? Did you get it? Did you get it? Well I'll tell you all about it and look in here.

you'll see that you can see C 1. It means channel 1 that is right in the center there and that would be our ground point. and you can see there's a slight little DC offset there. and that is a problem because if you're measuring RMS with a DC offset by definition, Root Mean Squared does not take out that DC offset.

It's going to include that DC offset Value Said, that's why there's a small amount of DC offset. Look, it's a 1 millivolt per division. It's only a couple hundred micro volts, right? It's it's down. It's almost bugger-all but it makes gonna make a huge difference and it's going to add on and contribute to that mean value.

And you might think aha, Dave dummy, It's because you've got DC coupling if your input. Well let's go in to AC coupling. Oh Turn my channel off. it's going to come on.

Give me my menu. There you go AC Coupling The statistics have reset themselves, but it's still there. It hasn't removed that DC offset cuz that DC offset is actually after the input AC coupling cap. which is when you select AC mode.

Here there's a relay in there, either a mechanical or electronic relay that will switch in an AC coupling capacitor. So the DC offset is actually after that AC coupling cap. It's residual within the input amplifiers and it'll vary with temperature and time and everything else. So if we made wait another hour or something that DC offset might drift up and you can see that the siglent over here just so happens to have at this particular time, it could drift I Don't know.

Hardly any DC offset. maybe Aa and maybe it's a width of a paper over ground there. So this one has a slight, probably a slight DC offset value, but it's not really contributing to that noise. Not nearly as much as I Rode and Schwartz.

So that's why. aha, we're getting that high mean value. But there's actually a measurement on these oscilloscopes that we should use instead of RMS. Let's have a look all right.

So our AC coupling didn't fix it, but we actually have a different type of measurement from RMS. It's still RMS but it's not RMS I'll get into it. Let's press the measurement button and go up and have a look. and of course we can.

We've got our volts peak-to-peak at the moment and RMS and we can choose a many different types. So let's get a third measurement here and we can choose the type here and we can go in and have a look at the moment. We're using Peter peak and we're using RMS but there's one chord standard deviation and you can I Love the Road in Schwartzy because it actually shows you the actual formula. and in this particular case, you can see that this standard deviation formula is almost identical to this our the formula that we get for RMS here root means squared, which is the square root.

Went on and the sum from 1 to N and the square of the values. Anyway, this is not going to be a maths lesson anyway. let standard deviation is very similar. Okay, except it's 1 on n minus 1.

It's the same Raincy summing the same values, except it's instead of XK Here it's XK minus the mean value of X and it's got the square in there as well. so it's actually subtracting out effectively the DC value. So what this standard deviation is is not to be confused with a graph of standard deviation. You know, the bell curve and all that sort of stuff.

It, Let's not go into it. This formula here is actually what's called a sample standard Deviation not to be confused with a population standard deviation. and I won't going to the differences because then we have to get into a whole maths lesson and I really hate maths. It's Anyway, this standard deviation is also called AC RMS.

So it's It's exactly the same as the RMS, but instead of including DC values, it actually simply removes any You can think of it as removing the DC offset or having an AC coupled RMS value. But instead of physically decoupling with an AC capacity in here, it does it in the formula. It does it in the software. It removes that DC value.

So if we select our standard deviation bingo, we're gonna. let's reset our stats. There we go. And bingo.

we now have our mean value of about of the standard deviation and the standard deviation is actually a square root of the variance. But once again, oh you math nerds, go and go for broke down in the comments: oh I won't try and explain it but the mean value is now 96 micro volts practically identical to the Sickle. And in fact, because this is a higher bandwidth scope, this is actually 350 megahertz because you do actually on the 1 millivolt per division range on the road and switch, you get the full 350 megahertz bandwidth. There's no limitation like there is on the siglent.

so this is actually a better result because as a rule for the higher bandwidth you have the more inherent noise you're gonna get. It's it's just a function. Once again, there's lots of advanced math behind that and in theory and we won't go into it but a wider bandwidth. So technically this is a lower noise scope for a given bandwidth than the siglent.

There you go: I Simply forgot that there was this DC I'll set up there I didn't notice it dull and I know I should've cuz it's really obvious and also I should have known if I was in gay my brain that 330 micro volts. well look at the look at the actual level just you know a mark white. Use your mark one eyeball and compare the thickness of that line to the one over here on the siglent and you can see that there. You know there are practically identical really.

in fact, the signal. It might look a bit thicker, but you know it's like slightly. there's nothing in it. So yeah, if I was thinking I would have gone well, it's obviously 337 micro volts can't be correct value for the RMS.

So uh, oops, there's a DC offset in there are I should be using the standard deviation or AC RMS. So let that be a lesson to you. you should be using AC RMS when you're doing these types and noise measurements where you need to remove any residual DC offset. So let's go back to the Sieglin here and see if the siglent has the AC RMS as it's often called Sometimes it's not called standard deviation, it'll just be called AC RMS.

So let's go into the type here and yes, it does. standard deviation. There it is. It's also for art, both the RMS value here and for the standard deviation value they have also what's called cycle RMS and cycle standard deviation.

That's if you want to measure it over the one cycle on your screen. But of course we don't have a cycle here. We're not inputting a sinusoidal or other repetitive waveform. we're measuring noise.

So the cycle standard deviation of cycle RMS just won't work. and it just won't give you anything. so we can put standard deviation. So if we get rid of that, bingo, We now have our standard deviation here and it's actually um, smaller.

So there you go. If we're doing now, we're doing an A be a true A/b comparison. The mean is about 65 micro volts so the C colon is actually lower. But as I said, the Rona Schwartz is higher bandwidth so you could probably run the numbers there and kinda let's just call them pretty equivalent in terms of noise floor.

But if you really wanted to do it properly, well, let's go into our channel menu here and let's get we can set the bandwidth on both of them to 20 Meg Okay, so now I've got 20 megahertz band and you can see that it's much lower noise. The mean is now 38 micro volts on the siglent and in the road and Schwartz what are we got? 44 micro volts? There you go. So actually the Rhone Schwartz is a bit higher noise for the 2004 the fixed 20 megahertz bandwidth there. And curiously, of course, you've got the standard deviation of the standard deviation there.

That's confusing and we won't go into the details anyway. but just remember the standard deviation you'll find in the measurement menu like this: see your press measurement and bingo and you can go into the type and the type of measurement. That thing, if it says standard deviation on your particular scope, just remember it's AC RMS. That's the best way to remember it because it's functionally what it is.

So the best way to think of that is the standard deviation is basically the spread in the numbers of the AC RMS value. if that makes sense. Maybe you know. if you've got a better way to explain it, leave it in the comments down below, please.

Okay, so a better example of this is if we actually put in a real signal. In this case, I've got a 1 megahertz sine wave here I'm on one volt peak-to-peak and I'm actually feeding in from my generator. up here. you can see on my generator there 2 volts RMS and we've got a 2 volt DC offset.

So let's just reset the statistics there. That's the thick fur I Can talk hardly so you can see our ground point over here is actually shifted up where one volts per division. So 1 volt, 2 volts you can see there's a 2 volt DC offset here. The waveform has been shifted up that DC by a 2 volts DC there.

and if you have a look at the RMS value here, then let's reset our statistics to make sure I've got it right. and look at the mean value. it's 2.8 1 volts RMS So of course we know we're only feeding in 2 volts RMS from our signal generator. It's giving us an error.

Well, in this particular case, it's not an error because we've chosen the RMS measurement which by definition of RMS includes the DC. But you can see if we choose our standard deviation measurement which is as I said, AC RMS it removes that DC offset there without having to AC couple. Remember, we're still DC coupled on our input, so we've seen our offset like that. but we're effectively AC coupling the signal in software.

so it gives us almost precisely our two partner our two volts. RMS They're 1.9 eight volts near enough, well within spec. by the way, you can often now remove these residual DC offsets by actually our self calibrating the oscilloscope and I'm just running through the self alignment process at the moment with the road and Schwartz here. So like if you move your scope to say like a much different temperature environment or something like that, you know you go from a 20 degree lab and then you go use it outside of zero Degree You know if you really want the best accuracy, you should probably do a re self calibration and Bingo.

Sure enough, after the calibration, the RMS value now is 84 micro volts. you can see that there's basically no DC offset anymore. So yeah, I just hadn't self calibrated the scope, self calibrate yours. It's worth it.

And if we actually compare this to our multimeter here and we're a regular AC mode, I've had to reduce the frequency down to one kilohertz for the bandwidth of the meter here, but you can see that we're precisely 2 volts. RMS because the AC on your multimeter actually physically does AC coupling. so it removes that DC offset. You only get that standard effectively.

it's doing that standard deviation measurement. and if you want to include like a Rms measurement, that's not true RMS that's actually what's called AC plus DC mode. So DC plus AC if you do that. Bingo! 2.8 so you can see it's identical 2.8 there and the standard deviation.

and let's go back. If we actually go to DC, it'll be 2 volts like that because that is the DC offset. It's measuring the DC offset. So there you go.

Let's just say comparison with the multimeter more to me can do the same thing. But don't confuse DC plus AC mode with true RMS because true RMS means it's just measuring the RMS value will be correct for any wave shape be it a triangle wave or whatever, or some weird convoluted waveform. and depending on the crest factor. But let's not go into that.

True RMS means it's valid for the RMS values of valid for any wave shape. any waveform shape not just sinusoidal, but you want DC plus AC if you want to include that DC offset. So which one is more relevant, the RMS that includes the DC value DC plus AC or your AC RMS value. Well, it depends on your particular application.

There's no right or wrong. They're both valid. It's just depends on what what your application is really. So there you go.

That's a bit of a little trap for young players and it's important to realize the difference between AC RMS and RMS. So have a play around with your scope. Let us know what your particular scope is, Because as I said, it may not be called standard deviation. It could be called AC RMS.

And usually and often they won't call the likes a DC RMS. They'll just call it RMS because by definition of the formula, it's going to include DC. But standard deviation could be called AC RMS on your particular scope or let us know if your scope doesn't have it at all. So anyway, I hope you found that interesting.

And if you did, please give it a big thumbs up. And as always, discuss in the comments down below or over in the Eevblog forum. Catch you next time.