# EEVblog #528 - Opamp Input Noise Voltage Tutorial

Jun 08, 2021hi welcome to friday fundamentals today we're going to take a look at op amp

### voltage

## noise

now this can be a big can of worms so i'll just open it up a bit today and let's take a look at one of the most confusing parameters in an op amp datasheet and that is#### input

## noise

### voltage

density and noise voltage important if you didn't know well you know by now that any op amp is going to have inherent noise in it just like all the components and all the wires and everything else has inherent noise and the op amp is no different and that's what we're going to see now we're not going to see anything around the nose of the circuit resistor and other components and things like that what is inherent in the op amp and to do that we're going to start by taking a look at a typical data sheet now let's take a look at the OP oh seven an op amp of typical precision not particularly low noise but it's one of the candy precision devices now it has a h parameter it's called#### input

voltage noise and that's the noise effectively on the input and the units are very easy it's microvolts peak to pico and it's called e N or our VN depending on the datasheet it might be called something else but it's just typical labels for him and he knows the figure might look familiar and it's pretty easy to understand ok ok in In the case of the Oppo 7, we have a peak-to-peak input noise of 0.35 microvolts, so if we have a voltage follower like this with a gainer we're going to get output noise or inherent noise in our op amp in our complete amp here from that zero point three five micro volts peak to peak really easy to understand but there's a problem take a look at the conditions where that value is measured and it's actually zero point to one Hertz to 10 Hertz and with it you may be familiar with this from the power specs for example they may specify the output noise of your lab bench power supply over a typical 20 megahertz dth bandwidth well, in this case it's a very small low frequency bandwidth and we'll find out why later it doesn't make sense 1 Hertz to 10 Hertz and that's typically how they measure it they have the op amp here it may have some may or may not have some gain and the input will be grounded everything will be shielded of course and then we'll have a non point 1 Hertz to 10 Hertz band pass filter we'll have some more gain there because we're talking low signal levels which will go into an oscilloscope and can measure that value and give you a peak to peak or peak to peak signal and also give you a look at this as well in the it does in most data sheets also l e will give you a typical waveform, again that's bandwidth limited to zero point 1 to 10 Hertz very limited frequency range so you're fine if you're operating in that frequency range in your fantastic circuit you've got this real world figure here you get it it's easy it's a peak max voltage and you know what your system noise is going to be at least just you for the op amp very simple but what if you really want to typically operate over a range higher frequency?Going into something a little more complicated called input noise voltage density, you'll notice it's exactly the same, but they added this word density and if we go back to the datasheet and look at some typical figures for the oppo 7 what do we get? Look you can see the conditions there are three different values and these are called the point frequency values in this case we have 10 Hertz 100 Hertz and 1 kilohertz and we have different figures for ten point three ten and nine point six respectively and you'll notice how it is a little higher at lower frequencies and that's important we'll get to that in a minute but it uses these weird units that confuse a lot of people and it's nanovolts per root hertz and here it is again it's labeled exactly the same ee + VN exactly the same but instead of microvolts peak to peak we now have a value in nanovolts per root hertz what does that mean in a nutshell its spectral density i.e. the noise density over a specific spectrum or frequency range just like our input voltage noise was measured from the 1 Hertz point down to 10 Hertz you need these this unit here really needs a frequency range over which it will be valid so Otherwise, it doesn't make sense. now the confusing part about these units of nano volts per root hertz is you do well what kind of units is that good it's just voltage is what you know even though it's called nano volts per root it hurts the part/root hertz just specify that it's defined over a range of frequency because this is the spectral density now so basically it's just a voltage that's all there is now the datasheet for example for this one at a specific frequency has say 10 nano volts per root hertz, now it's very important to understand that this is not divided by root hertz, it's divided by root hertz and it's actually a reference to a hertz, so that's 10 nano volts for every 1 hertz of bandwidth and that's the key to understanding this so if you only have a 1 Hertz bandwidth then your noise will be the square root of 1 Hertz which is the same 10 nanovolts but you know that typically you won't operate in families of a Hertz, so let's look at the width of b it goes from one kilohertz and the formula is f max - f min that's a bit tricky but it's basically the bandwidth you operate with so if you operate the circuit that operates from zero hertz down to one kilohertz then you have a bandwidth of one kilohertz minus zero is one kilohertz 10 nano volts multiplied by the square root of 1 kilohertz gives you a final value of 316 nano volts easy that's the amount of RMS noise by the way this is all RMS noise in your op amp inherent in your op amp just like this value up here was microvolts but pitta peak was specified t this I'm here nano volts per root hertz specified in RMS so you can see that the higher frequency range you operate in, the more noise it will have because it is multiplied by the square root of the frequency if we operate above 10 kilohertz there is going to be a bigger noise once again, our 100 kilohertz or a mega hertz, the next important thing that should be nder is what is called referred input noise or equivalent input noise, you will see that these terms are different types of terminology but it means that this is the noise at the IMP, the equivalent noise at the input of the op amp, which means that always multiplied by the op amp gain, in this case we only got a gain of 1, so in the case of this hiccup 7, 316 nano volts RMS at the input, same 316 nano volts RMS noise at the output , pretty low noise but if you suddenly get a gain of a thousand one V equals a thousand bingo you've gone from 316 nano volts to 316 micro volts or 0.3 milli volts much higher noise now if you remember I said that this was rms, so how do you possibly make it a more useful peak-to-peak value in your system? talk here is white noise or purely random noise that has your typical Gaussian response like this and we won't go into the types of noise to a great extent but it does have that Gaussian response now I've drawn a voltage here I've rotated the axes are like this so positive and negative voltage noise can always be equally positive and negative it doesn't just go positive and it's basically the maximum value so this is just a typical voltage spike like this over time as you can see you know the noise is completely random and what these maximum values will be here this is where you get into that Sigma probability term now if we look at the value of plus or minus 3 Sigma basically which is we have 99.9 percent confidence or close to that the peak to peak noise is going to be within that specific value so the Three Sigma value is what you get that's a typical quoted figure so manufacturers can typically def Starting the rms to p2p conversion using a multiplier of x 6 or x 6 dot six six dot six will give you a 99.9 percent chance that the noise will be within a given range, but it is not a guarantee, as a point one percent chance may be outside of that range and well it's up to you as a system designer to determine what probability you need but that's a good ballpark so multiply that value by about six or six point six so in our example of a mil gain here what's our output noise for this op oh seven with 10 nano volts per root Hertz specified ok it's going to output it's going to be 316 microvolts RMS about 2 point 1 millivolt speaking to the max with a good level of confidence and that's going to be your output noise only because your op amp doesn't take into account any other components or any other part of your circuit, so it's really quite easy to tell. nder once you know just multiply that figure by the square root of your bandwidth and you'll get your output noise in rms very simple but yeah there's more let's dig a little deeper open you can worm just a little more and yeah hold on to your hat we're going to get into a graph of noise voltage versus frequency on dual log axes so we've got our root nanovolts per hertz here versus frequency and like I said log axes that's important so 10 Hertz hundred Hertz and it's not linear rise equal with frequency 10 hundred 1k and then it's your typical log axes that you should be familiar with so the black line there is our noise voltage and you'll find that this typically finds this curve at the datasheet as well and it will always be in this particular form and this is where the kicker comes in with all this op amp voltage noise that effectively we have two different types of noise in our ro op amp and effectively divide into difference Different parts of the frequency spectrum, the highest frequency, say from around 10 Hertz or a hundred Hertz up, will typically be the Gaussian white noise that we showed earlier and indeed what we are using there for our input noise voltage density is our white noise. noise up there, but all op amps, regardless of type, are going to have this characteristic response that builds up in the low frequencies and this is called noise 1 at F, so white noise dominates at the higher frequencies.

Noise 1 in F dominates at the lower frequencies. you usually know around 10 hertz or so or that figure that's why our input voltage noise here peak to peak was specified in that 10 hertz range because you're really looking at noise 1 at F it's stuff of low frequency while our voltage density is looking at higher frequency noise here and yeah they are two different things so when we were actually calculating this input noise the noise density here for a range of 0 to 1 kilohertz we were actually including this bottom part down here, but because the frequency range that we were working in because their logarithmic axes is so large that you can just ignore this extreme end and you know we can stick to the ballpark numbers that we got here for our noise voltage density over the entire frequency range and we won't go into specific details of the types of noise because there are quite a few different types but suffice to say that e White noise and high frequency stuff is made up of a combination of shot noise and thermal or junction noise or johnson noise as you may have heard it called and F noise is also known as pink noise and that's because of what which is called flicker noise, but it's usually called 1 in F-noise and that's the trap with components you can't escape if the noise is inherent in nature there's absolutely nothing you can do about it there are things you can doing in the manufacturing process of your devices to reduce t increases flicker noise but you're pretty much going to control it in that low frequency range so you might think these op amps are less noisy on dc well that not the case as you can see they get much noisier in DC their lower noise at the higher frequencies doesn't make sense but hey a lot of things in physics don't make sense the next thing we know we're talking spooky action ranged noise that are now Gaussian white noise like gunshot and thermal noise. a uniform power density what that means is it's going to be the same value regardless of frequency and that's why we have a flat light there for that but one on the F noise is not a uniform power density so that's basically we get a flat straight line like that but it has a specific slope of 3 dB per octave but we won't go into the details and this all goes back to why our input noise voltage density was specified in the datasheet at three particular frequencies one kilohertz one hundred hertz and ten Hertz is such that you can make comparisons to other op amps of how this noise changes and how well it works over a frequency range like that because if you see a big change, say, between one hundred Hertzand ten Hertz into one op amp and there's hardly any difference for another op amp then you know that that second op amp with the same figure up to ten Hertz is going to be a better aperture and that's basically a deal breaker that the corner frequency we have there determines effectively how good your op amp is indeed is the lower the corner frequency the better your op amp and that's the one you'll probably pick all things being equal and as always with datasheets specialists in marketing are going to rig the numbers to give you the best profit possible so be careful you have to go there and look at the grass look at the individual data and compare op amps and actually it can be quite difficult to compare op amps just from from the datasheets. its not that easy so you have to be careful and know how to style it in your system and you'll also note in the datasheet that that's an identical noise spec for current so your input noise current density and input noise current and we won't go into that that's the current at the input of the op amp so right now as I said we're just looking at the voltage scenario but hey if you have a significant input count you need to take the input current noise into your count as well in those really low noise circuits critical but the same kind of fundamental theory applies and yes it will all add to voltage noise too so you have to be careful and by the time you pretty much build the circuit it usually works usually the external components will dominate its circuit more than the op amp itself but hey that's why they specify these things because many critical applications have to get the lowest noise op amp possible and that's what it's all about t frequency range remember how much noise density within that 1 Hertz window and when you extrapolate these two lines here to get that corner frequency crossover point where they intersect if you extrapolate down, so we have 10 Hertz there's 20 Hertz so it's somewhere in there let's say around 15 Hertz is our corner frequency for this example we've drawn here so that 15 Hertz point is the point where the value of white noise is equal to the zero F-noise value and of course if you add them together let's say it's a 10 then as shown then you don't get 10 plus 10 of course you get 10 times the square root of 2 , so you get about 14 point 1, so there you have it, it probably took a little longer than me.

It was expected and there's a lot more detail here as well, but suffice to say your basic op amp is like this if you're working from DC if everything is DC coupled your full bandwidth is from DC to 1 kilohertz for example, effectively what does you have to take into account these tw or different types and noises and you have to add them up and when you add noises together it's actually the root of the sum of the squares so it's a square root of this noise here squared plus this noise here squared and you have to add together and that gives you total noise but as we said from the beginning this is just the noise inherent in the op amp itself it doesn't include the resistors here which of course have that Johnson thermal noise that you may be familiar with. with that classic equation, the higher the resistive value, the more thermal noise you'll get on the resistor and all sorts of other things in your circuit, so it can get really tricky, but I hope you've found that it's pretty easy to understand. what nanovolts per root hertz is and how to calculate its noise very simple this is a bit more detailed than how it actually works but let's see if we can exactly measure this graph on the bench and what tool do you use to measure the input n noise voltage of something like that as a good op-amp you use a dynamic signal analyzer or DSA which is seen in the previous videos and this is my HP 35 double 600 a DSA goes from DC to about one hundred kilohertz perfect to characterize the scene, the noise F and the power spectral density of noise in something like an op-amp or any other circuit, is the tool of choice, but unfortunately this 35 double 608 isn't exactly the best performer in the world, its noise floor isn't. cool by itself so that's what we do first we'll just measure the noise floor of this unit with a 50 ohm terminator on the input of course on channel 1 here and see what we get but it's not going to be that hot shock, but it should be good enough to at least allow us to see the differences between the different types of op amps, so I'll just briefly explain how to set up a dynamic signal analyzer to measure the power spectral density in a signal. low voltage like this now when you first convert By default here we have our frequency spectrum like this it's showing our frequency spectrum from zero hertz here to one hundred 2.4 kilohertz and we're just looking at channel one so that there is a span, the length of the record is three points. nine milliseconds for each of them and on our axis and here we have DB volts RMS here we go it's doing its automatic calibration and we have to figure out that it knows around those one hundred and thirty minus one hundred and thirty one DB volts RMS marks the first thing we have to to do because we're measuring low levels of signal go to input so I selected the input button on the front and then piped a range at the moment it's autoranging we really don't want we want to just fix it and this thing , I'm pressing the up/down arrow keys and as you can see there goes channel one range the highest gain range or lowest voltage range you have is minus hunt and minus fifty one DB volts RMS and that's equivalent to I think about a peak of four millivolts or so the next thing we want to do is turn on some averaging so I'm going to hit the averaging button on the front and then we want to turn on ar the average that way because otherwise we'll just let you know we want to smooth the alignment see what happens when you turn on the average there it's set to 10 I'm going to change that to the number of averages there and go to input a hundred averages so now when you hit the start button and we start our acquisition there we go it's already giving us a bit of a plot and we can already see that we're getting a result here is our pretty flat line with the big F noise following on the bottom but why not?

It doesn't look good on the board because we haven't plotted the frequency on a log graph but it's a linear graph it's a linear axis sorry we have to go to the input here set it up and make sure we have a couple from DC here we want to go all the way to DC to change that to a log graph we hit the scale button on the border and here's the x axis there it's currently set to linear we'll change it to log and bingo look we're just getting started to get exactly the answer that now the reason there aren't a lot of data points here because it has to do with the number of lines in the FFT response of this thing now we have a full range here of 102 point 4 kilohertz and this instrument at particular only has 400 lines of resolution so if you divide 102 point 4 kilohertz by 400 you'll get if we move our marker here you'll notice that each step can only measure at those frequency points there so it's very coarse there of course and you'll see find that the lowest step is going to be 1/4 hundredth of 102 point 4 kilo Hertz so 102 point 4 K divided by 400 there we go gives us 256 Hertz where our marker is all the way there what is that X market there is 256 Hertz so it can only jump in 256 Hertz steps because that's all the FFT resolution we have there and of course that really shows up when you have the logarithmic X axes like that doesn't really it appeared on the linear because then it would be advancing in 400 even linear increments across the screen now if i press the measurement data button on the front panel here we are in what is called diet board just normal frequency spectrum mode more correctly known as linear spectrum mode and that gives us a voltage response here and as we saw before DB volts RMS there - 123 and if we plug it into the calculator - 123 and then divide it because it's in dB remember if you want to conve rt it into a voltage so we divide it by 20 and then we take the inverse logarithm of that and we have 708 nanovolts but what that means doesn't really mean anything because that's not our power spectral density so hit the scale button on the front and we will see the vertical units that we have.

I have here DB volts RMS right now and as you see there is no option for that voltage per root hertz because we are in linear spectrum mode we are not in a do it we are not actually calculating power spectrum density but that's not means that this graph is not correct because actually the shape of this graph is absolutely direct to what we will get at the peak and density of the power spectrum, except our units up here are not correct where DB volts RMS instead of that voltage per /root Hertz so how do we get it right?

How do we convert it right? We can do it manually when we do all the calculations ourselves to convert between linear spectrum and power spectrum density but we don't need to do that what we can do is go into the press the measurement data on the front this will do it for us that's what these dynamic signal analyzers are designed to measure this noise specifically and there's the PSD mode or power spectrum density bingo to go to power spectrum density you'll notice the graph hasn't changed at all d normally when you switch modes it scales things back but it hasn't the graph has stayed exactly the same but look what we have now it's got a little asterisk next to it here and those asterisks mean there's volts RMS /root Hertz and if we go back that's exactly what we want exactly what we saw on the board and if we go back to measurement sorry the scale here in our units des verticals we'll see because now we're in power spectrum density mode here i have options root of hertz volts rms squared DB volts rms/roots hurts or volts per root hertz that's what we want volts well we want nano volts but volts per root hertz is the same it will scale for us so see bingo above what we have now now what and that value there at 10 kilohertz close to 10 kilohertz is now changed and calculated to be 28 eetu the -9 now is now of course nano volts per root hertz bingo we now have our DSA to check its own performance because we remember we've got a 50 ohm terminator on the front and there it is that's what it is after a hundred averages down here over that well on the time when the full range from zero to one hundred and two kilohertz so you can see this instrument that you know is worse than a basic, you know, op oh seven op-amp 28 nano volts per root Hertz and, like mo we saw in the datasheet before just a basic seven is around you know at a spot frequency in this case ten kilos just go up to one I think but yeah you know because it's flat it will be exactly the same I had a figure of around 10 nanovolts per root of hertz, so this thing isn't good enough to measure the performance of an op oh seven in the normal way. do, although you could actually use this instrument the way you normally would, is to use an external amplifier designed with extremely low noise to amplify noise before it enters this instrument, so use this instrument you already got raise it so you get it well above the noise floor of this instrument and then you can tell if you have 100 times gain then you can just change the units to compensate for that and you can measure the performance of an op or seven now if we bring the slider all the way to the corner frequency down there again we're very thick because we're measuring the entire hundred and two kilohertz bandwidth as it tells us that the corner frequency is about one kilohertz but I know that that will not be the case we want. what you need to do is change the span so we get more detail on this in a cooler and instead of just three fucking data points and that's easy just hit the frequency button on the front you can see these DSA they're designed specifically for these types of measurements that are optimized for this that's what they're designed for anyway we can go to intervals like this hit the interval button and then we can type say good night let's do 1000 Hertz will do a range of kilohertz and then done.

On reboot you can see that it automatically reboots and it will do the RMS it takes longer of course because it's lower frequency so it takes a quarter of a second per record length like that but there you have it this actually It's fallen off the screen, so I think we've done something with our scale.input there so if we hit our scale button there we can auto scale that and bang that will align it like this and look at that look at that now we can when that cursor now we can put it to a kilohertz there you go so it's in a kilohertz there and we're getting a value of about 31 nano volts per root hertz that's some background noise from this thing like I said not very spectacular actually I want to invest in this take a look at the op amps used on this and other components and see if I can really use the modern drop in high output op amps to really boost the performance of this thing so I'll leave that for a future video which you can see is essentially flat and starts to go up a bit there you can see it start to rise so you can see why we are effectively measuring the noise of the input noise from the input section or the op amps of input inside this particular instrument so we would get exactly the same result if we were measuring an external op amp effectively so the kilohertz value here will be slightly lower than the hundred hertz value which again , it will be lower than the value of ten hertz. here and that's why you have those three point values in the data sheet, one kilohertz, one hundred hertz and then ten hertz here and of course that will be a continuation basically completely flat to the hundred kilohertz that we saw last time , but it looks practically starting to get me wrong at a little less than two hundred Hertz there I have put it at one hundred and sixty Hertz for a reason because we are going to the technical sheet of this HP DSA and here it is taken directly from the user manual in the -51 range DB volts that is the highest gain range we have a 50 ohm source impedance we have 16 rms averaging ok we've done 100 you'll notice it doesn't specify anything below 160 Hertz you have that range from one hundred and sixty Hertz to one kilohertz: 130 DB volts per Hertz, and of course, if you want, you have to convert that to power spectrum density, which we can do. we've just done with the instrument itself so there you go that's why they have a hundred and sixty hertz figure on there because its performance really starts below a hundred and sixty hertz you know it really starts to get a little bit how you it's going and one thing I want you to take note of close to fifty hertz there you'll notice we're not getting any fifty hertz pickup at all and of course this lab is just swimming in the fifty hertz mains frequency because as we saw in tearing this thing down it's amazingly well shiel ded and we only have a 50 ohm terminator in the front but I also think we'll see when we try to measure a practical circuit we'll get at least 50 hertz pickup it's almost inevitable it's ok so let's take a note after a hundred averages at our one kilohertz marker frequency because that's a value we can get from the datasheet for some amplified operational res.

We're getting thirty-one point three nanovolts per root hertz, so that's the basic noise floor of our DSA here. and of course to measure noise levels like this you need a Faraday cage you need a shielded box one of these absolutely fantastic die cast alloy boxes so the industry standard way of measuring these things is a little breadboard with am teal oh seven two in and now i have two 9 volt batteries if you look at the datasheet the voltage is the noise for these for all these chips it's usually specified at say plus or minus 15 volts or sort of a max rail it will be close enough plus minus nine now of course once you put the lid on this sucker there is no way anything will ever get in there.

We have our good BNC there. We are going to protect a coaxial cable up to the entrance. Bob is your uncle and of course you want to. to use internal batteries in the case you don't want to use an external power supply or any sort of switching power supply or anything like that batteries are the only way to go and you'll notice no I don't need any decoupling there enough good because we have the low impedance battery directly and this thing is not going to oscillate so we have our box connected to the TL zero seven two now I chose the TL o seven two because it's not a particularly low noise op amp at about eighteen nano volts per hertz root to that one kilohertz figure straight from the datasheet because it's not designed for noise it just has the one kilohertz figure you really know it's not that good I don't really specify it in depth but here we go so that is the noise floor of or your DSA, let's press Start and we'll use the exact same parameters that we set before, remember that 31.3 nanovolts per r uta hurt now of course that's below so the noise and what we're trying to measure here of this TL o-72 is below the noise level of this DSA but remember they summit together, so we should see a spike there let's hit start and go and woohoo look at that one at F the noise has gone off scale there and look at that bump.

What frequency do you think 50 Hertz is? Blast where we're picking up our 50 Hertz. It's not through the box, it's through the shield of the coaxial cable. That's the only place you can get in. I don't know. This is an rg59 cable or something I'm not aware of just a cheap one I had lying around so yeah you're really on par with shirako axes and the shield a box we have in our 50 hertz van but anyway look what that we've almost got a hundred averages there we go we've gone up from thirty one point three nanovolts per hertz path to thirty eight point zero to eight thirty eight nano volts per hertz path to one kilohertz so it's increased about seven nano volts per path Hertz and what value we should have expected well 31.3 nano volts per path hurts the base noise floor we had there we're going to square that remember the formula we had on the board and then we have some of the squares so we have to add the value from the data sheet typically 18 nano volts per route Hertz to one kilohertz so yeah let's square that and then get the square root we should get about thirty six point one and we get thirty at and eight point one in thirty eight so you know close enough we could see a difference with that TLO seven two now we're going to get one that's even worse forty two nano volts per root Hertz is a tail oh six - that's a surprise absolute I put it there let's press start and there we go oh-ho we still get our 50 hertz of course horrible one in F the noise went off scale here but there we go ah it's huge now look at that in the order of you know 75 no no volts per hertz root they all drop there we go after 100 the average is 68 point one is correct I don't know they are what is 31 at point three squared which is the background noise of our DSA plus the nominal 42 of the sheet of data and then we can't get that and then we do the square root of what we expected to be around fifty-two point three and we're well above that so one isn't working too well it really is an old chip though trust on me, it's like 25 to years or something let me check the date code there's actually no date code on that but this is like I had it since I was a kid and it was actually D soldered off a plate so it's old and shocking but still lets us show the difference of what a shitty op amp can do and how you can measure it and now i've put up an ad for analog devices 71 - there's the identical r18 nanovolts per hurt from our tail oh seven o ne so let's give that one a bill and see what we get we still get our big 50 Hertz but there we go we're getting yeah some forty something not much different than what we got with the tail oh seven two and as i said if we really wanted to measure the performance of these op amps.

You would have to use an external amplifier here. You'd have to design it right, and ironically you need an incredibly low noise amplifier to measure low noise. to measure state-of-the-art op amps well, you'll be very careful how you turn the input amps and we could still easily measure it once we know some gain in that box. the noise level there and being able to correctly measure the absolute performance of the op amps but anyway I hope you found it interesting that we were able to see the differences between some pants ah there and if I put a really dumb op amp in there we would have actually seen it fall to prett It's a lot like mush this particular DSA so there you have it if you want to discuss it hop over to

## eevblog

4 and I hope you liked the video and if so then give it a big round of applause so I caught you next time, wait, hang up.I found in any double v 3 for op amp really a good low noise audio op amp I think they even use a couple of them here from what I saw on the schematic anyway and not on the front end I don't think but of all modes somewhere here and that has a noise figure of nano volts per root of Hertz so let's give it a count and there we go yeah we're still picking up our 50 Hertz but again we haven't gotten off the mark scale here and there. Come on, we're not, we have almost exactly the same background noise that we got with the instrument itself, what was it? so bingo there you go there's a good quality op amp for you there it is 33 point seven for the record beautiful catch you next time you you

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