Hi. My previous video on this Ling Electrodynamic shaker was very popular, so I thought I'd do a follow-up video to this. I'll link it up here if you haven't seen it and down below. Highly recommend you watch it.

Explains what electrodynamic shakers are, shows you inside this thing and we have a play around with it. It's for testing. it's designed for to shake Pcbs just like this. You shake them in this direction and change your rotation this direction.

and this direction. and not just shake like this, but actually over a whole frequency. uh, span. So this one goes from a couple of Hertz.

Um, I've got this at five Hertz at the moment. You can count those if you really want to and and can go up to like, you know, many kilohertz. Um, they usually top out at around you know, 10 kilohertz. So these electrodynamic shakers are great for testing Pcbs and products and assemblies.

And you're basically testing them, uh, to see if they can survive, uh, transport. Or they might whack a satellite on here and like a really big one Because you can get ones the size of cars and trucks and you can shake a whole satellite on there to simulate you know, launch. Or you know, your space probe to simulate re-entry. Or now I'm going to show you how to set up one of these and it's all about a mathematical term called coherence.

Now, hopefully I'm not going to lose a lot of people, but it involves using once again, my very cool, uh Hp. None of this. uh, Agilent. or even keysight.

Uh rubbish. Hpr 35 668 Dynamic Signal Analyzer or Dsa And this is the bread and butter tool for the industry I used to work in. uh, the seismic industry where everything was like low frequency stuff. I mean, this thing only goes up to 100 kilohertz 50 kilohertz if you turn on two channels, right? So these things are designed for really low frequency stuff, but they go right down to Dc.

They're low noise and they're purpose designed and as you'll see, they have the mathematical capabilities to actually measure coherence, which is a fundamental concept of setting up. uh, one of these so you can buy your ten thousand dollar calibrated electrodynamic shaker. You can buy a thousand dollar, uh, accelerometer here, and then you can pay another thousand bucks to get it. Nist Traceable Calibrated.

Here's uh, the little accelerometer here and you might think, well, I've got all this calibrated gear. This is fantastic. I can just whack my accelerometer on here. I can have another one on my product Pcb that I'm shaking and Bob's your uncle.

I can just get these beautifully calibrated measurements. Couldn't be further from the truth. If you don't set up your jig properly and you and you have to do this before you take any serious measurement at all, then your measurements are absolutely useless in the industry. If you hand in a test result, uh, report and it doesn't have the coherence, uh data that I'm going to show you uh, setting up today, then they're just going to toss your report in the bin because it's absolutely all your data is absolutely worthless.

If you haven't proven that, your uh, shaker table in this particular case and your setup for the particular measurement that you're taking at the time is set up correctly. So that's what this video is about. I'm going to show you how to set this up and the importance of coherence. Now, of course, I have to mention that you don't need to do any of this that I'm talking about in this video.

If your goal is just to put your product on a shaker and then just shake the crap out of it until something fails. If that's your goal and you're not doing any quantitative measurements at all using uh, little accelerometers or bigger accelerometers like this one, then that's fine. You don't have to worry about any of this, but if you're doing any quantitative measurements, you have to do what I'm doing as a first step. Absolutely essential.

Now you can think of a dynamic signal analyzer is just like a spectrum analyzer or like an Fft analyzer. In fact, that's what they're often called Fft analyzers, but this one is specifically designed. As I said for low frequency measurement goes right down to Dc. That's where they come into their own in.

like physical measurements like this, or your physical phenomenon uh, that you're typically dealing with in, vibration and sound and other uh, you know, physical, uh type things. They're all down in the Dc to, you know, tens of kilohertz range. So this is the bit of kit that you want and it's got the mathematical functions as we'll see, so it works. Just like a spectrum analyzer.

you have frequency on the X-axis I'm actually starting from zero Hertz here and I'm going to 200 Hertz and that's what we're going to analyze today. and on the Y-axis Uh, we've got a Db volts Rms here and I'm actually feeding in a 100 Hertz Sine wave and there it is. You could just get the peak at 100 hertz. and if we feed in a sweep, you know we'll see a flat frequency response here because I've just got the source actually connected directly to the input channel one here and that's what we're seeing.

Simple, but the real advantage with a dynamic signal analyzer is all the mathematical stuff that you can actually do and you can do it when you include a second channel like this. So you'll notice that we have the options of just getting the frequency spectrum of channel one or channel two. Uh, Psd, I've shown that in another video. that's the power, spectral, uh, density.

and you can get uh time as well. so it can just work like an oscilloscope. But then you can get. Well, you can get frequency response, but you then you can get.

what's called coherence down here. And that's what this video is all about because it's so important that's related to our cross spectrum as well. And you'll notice that they're all grayed out because we don't have the second channel enabled. So if we actually go into our two channel measurement here, then we'll find that we'll actually get all of these and we can enable these.

So what we need to do is enable what's called coherence measurement here. Okay, before I freak you out with what coherence is, let me explain what we're actually trying to measure here. Now, we have a signal source here. Um, so we can generate a sine wave.

We can generate a sine sweep, which is called a periodic, uh, chirp. Or, as we're going to use here, it's going to generate a random frequency over the frequency range of interest 0 to 200 Hertz. So we've got our signal source. This is the input to our system.

This is our system here. Our shaker table is a system. We have an input, which is our signal that we're feeding in via our big power amplifier over here. But that's the input signal to this electrodynamic shaker here.

And then I'm feeding that input signal into Channel One of our Dynamic Signal Analyzer, so that we can measure the input. And you guessed it, Channel two is going to measure our output here. So our output here. Um, this comes from our accelerometer.

Now it can be. Uh, this tiny little. uh, Pcb Piezotronics Sheer accelerometer. This is designed for really small systems.

It's absolutely tiny. One of the smallest ones you get. This is actually designed to be glued onto here. This is an adhesive mount.

So we're going to put the accelerometer onto our shaker plate here. Or we could use a bigger one. In this particular case, this one's got a big ass magnet and it just boom. Um, it attaches to the plate like that.

Or you can screw them on. Uh, they're the three different types available. Geez, that's powerful. So the system we're trying to measure is the input to the shaker here, and the output from the accelerometer.

So what we're going to try and measure with our coherence here today is we're going to try and ensure that this setup that we've got this crude, pathetic set up here is, uh, ready for measurement. In that it's linear. it doesn't have any issues. It's got no noise associated with it.

It's got no other vibrational modes or anything like that. There's nothing in this system that is going to cause a problem. Then, once we set it up, our accelerometer will actually go on to our product onto our Pcb under test. For example, we want to get a quantitative measurement with the accelerometer in say, the middle of the product.

How much this board is? Uh, flex in, for example, over the vibrational frequency range, so that will be our output. But the values we get here won't be worth anything unless we know that our system itself is set up and it's coherent. So what does coherence mean? Well, it's actually a mathematical concept, and if I put up the formula, I'm probably going to freak you out. But it doesn't matter.

Don't worry about the formula whatsoever. It's a coherence is a mathematical concept that and the coherence has to do with uh, complex mathematics, which has, of course, real and imaginary parts. That's why Dsas have uh, real and imaginary Uh measurement components, and the coherence is using all sorts of other Uh measurements internally, um in the scope as well. Basically, if we've got an input to a system here, and we've got an output to a system, how much does this output signal that we're getting correlate to the input signal? Like if we're putting in a perfect sine wave into this thing, are we getting a perfect sine wave out? Basically, and it does that for every frequency element over the entire frequency range.

So basically, think of it: how much of the output is correlated to the input and you want obviously a hundred percent correlation, Because if your output signal is not one hundred percent correlated with your input signal the shake that you're putting into this thing, then obviously you've got some sort of non-linearity in your system. You've got noise in the system, you've got vibrational modes in your daggy stupid plate that I've got set up here, and I'll hopefully be able to see the difference in a minute. With that, and you want to make sure that your system is set up, because once you go to do your quantitative measurements, if you haven't done your coherence measurement and ensured that your system is completely linear and set up, then all bets are off. your data's useless.

So here's actually a coherence. uh, plot here. and this is once again over frequency 0 to 200 Hertz. And what the coherence mathematical function gives you is a value between 0 and 1.

Here, this is not like 1 volt or anything like that, right? This is basically this is a factor between zero and one, and if your factor is one up here, then you have perfect correlation. If you've got one point, zero, zero, zero, Zero Zero pops out for your coherence up here. That means at that particular frequency, we can move the cursor in the middle. There, At 100 Hertz, we have a coherence of 0.99 and that's excellent.

Basically, you know anything above like it depends on what actually it depends on what type of measurements that you're uh, trying to take. But you know, in a system like this above, 0.95 would be like considered like pretty schmick. So this is ideally what we want is a coherence value that's completely flat over the entire frequency range. But of course you can see like at 10 hertz here, it's starting to roll off and we're not worried about that.

That's just a limitation of our system here. So things in this particular system that might cause uh, your coherence not to be a perfect one like you want it at a particular frequency, you could be getting noise in your measurement. You know, you could be getting like electrical noise pickup. Uh, it could be trunk getting tribal electric noise on your Uh cables, which is basically the vibration couples uh through to the cables.

Um, and then your output signal that you get in from your accelerometer is then no longer correlated with the input signal. So it's basically uncorrelated. Noise is one of the factors that will cause your coherence to drop. Now, if you've got a really crappy shaker, this one's a particularly good one.

but it might be non-linear and that non-linearity could be in the Uh coil itself. It could be the fact that you're over driving it. Uh, it could be that, uh, you know you've got like a real dodgy plate sitting on it that's just hanging out flapping out in the breeze over here. And if you've got your accelerometer over here, then you might have a vibrational mode on this plate which causes non-linearity for example, and that will screw up your measurements.

Or you could have something that's loose on your plate and it's shaking around and things like that that will cause uncorrelated noise that's not coming from your source, it's inherent in the system and that'll cause you to drop in coherence. Another thing that'll drop the coherence is any, uh, delay in the system. If you've got any phase delay, measurement delay, or anything like that that will cause a drop in coherence as well. So let's actually assume that this is our vibration test jig that we've assembled and we want to do quantitative measurements on it.

So let's set this up and test how linear this system is. See what the coherence performance is like before we take any measurements whatsoever. Because as I said, absolutely essential to do this before taking any measurements. So what we're going to use is, we're going to use our little Um.

Icp accelerometer here and I'm going to just attach this to the plate. I'm going to be really dodgy. Okay, normally you glue these things as super glue, but I couldn't be bothered. and I think it's going to work fairly well with a bit of electrical tape.

She'll be right, and I've got it right near the actual armature over here like this. Now, these accelerometers are touchy little beasties. They actually require a constant current source in this particular one. Um, it's a couple of milliamps up to 10 milliamps.

So I'm going to put it around 5 milliamps. So I've got my constant constant current source here set up for 5 Milliamps and it requires a compliance voltage that is anywhere from 18 volts up to 30 volts if I disconnect the accelerometer. Tada, There we go. I've got to set up for a 20 volt compliance voltage.

And then when we plug in the accelerometer, we're getting a uh, this is smack in the middle of its uh nominal range. so nine volts. So this gives it the Dc Uh bias point. So we have our five milliamps coming in here and this is powering our accelerometer Now I'm tapping off that with an Ac coupling cap here at 0.5 microfarads um, Ac coupling cap which goes into our input because the inputs are not that robust and you can't actually blow them up so you don't want to be going using like high voltage, high compliance voltage sources even though this does have an Ac coupling input option and we're going to be using that.

um, like it. Yeah, I just want to be built in braces to ensure that no, no Dc is going to the input here. Okay, I've set it up for 0 to 200 hertz span here. Now You can actually do a periodic uh chirp like it's sweeping through the frequency range.

It's called a chirp, but it's basically you might know it as a frequency sweep and that's useful for some things, but we generally don't use that for this sort of test. so we're going to choose actually a random noise and you can might be able to hear that now. And that's inputting random noise over that frequency range from 0 to 200 Hertz. So then when we average our data, we take multiple samples.

We average average average. You know that you're going to get energy input at each frequency over here because it's random and eventually you'll build up a uh, waveform over frequency. Okay, so we've got our coherence measurement here. Our input: uh, we can like auto range our inputs um, so that it gets a suitable Um, select a suitable input range and I've turned on averages as well.

Let's just get an Rms average and then we'll just start like this. So it's going to now take a few seconds before it starts getting a couple of averages and then it starts displaying it. Bingo! We now have this is our coherence response over frequency and you'll see it slowly gets better as we take more samples and then it gets more samples. At each particular Uh frequency, you can see that this is actually a pretty schmick response.

The coherence is pretty darn close, uh, to one over the entire frequency range. And this is just for um, a bit of tape like this. and if we actually glued it down, we might get the smidge better. But yeah, that's not bad performance at all.

So what happens if we move our accelerometer right out to the edge? here? Let's actually do that again. We've got to restart Before we had it right on the armature here. Now it's out here flapping around in the breeze over here and oh, that's not very good is it? Look at that Really have something happening here at 100 Hertz and it's like, and it's all over the place at Even. You Know it's not just 100 Hertz.

But what's happening here is, um, our system has become non-linear because we've moved the accelerometer from right on the armature here, right out here. So we now got it. So now this is taking into account the mechanical properties of this plate. and with this plate flapping around in the breeze over here, going wiggle wiggle wiggle? Yeah, right.

it's it's causing all of this uncorrelated noise that's not coming from our signal source. it's coming from. Um, the mechanical. It might be the mechanical resonance, It might, you know, Just basically the non-linearity in the system.

Bam. Look at that. So this is horrible. So if we put, if we built this and we wanted to do some uh, quantifying measurements and our accelerometers mounted over here like this, then I if we didn't do this coherence measurement, we would have had no idea that this thing is horribly unlinear between like you know, 80 hertz and like 140 or something.

Okay, so let's run the same test again. but we'll use uh, this accelerometer. This is a Viber Metrics Inc. made in the United States of America Model 7000.

It's really old, but it still works. It's got a magnetic mount, so let's whoa, put it on there. but this one is much heavier. I mean, this weighs practically nothing, but this one is heavy as it's designed for much bigger systems, so that extra weight is going to affect the magnitude.

Here, it's going to possibly affect the mechanical mode of this plate hanging out in the breeze here. and let's start that again and see how this one performs. That's not too shabby at all, and it's going to get better and better as we build up more data there with the averages. But yep, that's a really schmick response.

Is it not? Now what happens if we move this all the way out to the end here so that that wasn't there before, was it? So if we slide that back yeah, you can see. Yeah, it is very different. So that was causing down at about 10 hertz there or something. Um, yeah, that was causing an issue.

definitely just by having it out there like that. And this is smart enough to know that if I try and measure coherence without turning averaging on, yeah, nah, you can't do that. And as I mentioned before, the coherence is actually related, uh, to the cross spectrum. and uh, they're mathematically.

they are actually different. but we can actually do a cross spectrum measurement as well and you'll notice that it's fairly linear. but we won't go into uh, cross-spectral analysis versus coherence. but suffice it to say, they are intimately related.

Pop Quiz Hotshot. We've got our nice uh response like this: It's all happening exactly what we've seen before. Now I'm going to change something. See if you can spot the difference.

Check this out. There's something horrible happening at like what? 65 hertz? there? Something like that, right? Pretty awful. You might think, oh, there's something wrong with my thing. Or if you've actually got your a second accelerometer on your Uh.

product on your actual uh, Pcb and you're getting your response. And this is what all this coherence is about. If you're getting this response, you might think that your product is doing that, but it's not. It's not your product.

It's not the jig. What has changed, Well, it's the auto range. Your input values matter because we're actually clipping. You might have seen there that we'll get in an overload on Channel 2 here, which was the accelerometer input.

Now if we put it back to auto range to range it properly. Bingo. We go back to exactly where we were before and this is the importance of coherence. There's all sorts of factors that can go into this.

It's not just the physical jig itself, the physical mounting, and everything else. You have to ensure that your entire system is set up correctly, because at the moment, we're just testing the response of this plate and You would leave a reference accelerometer on the plate, but this is just setting the system up. Then you'd add a second accelerometer onto your actual product or multiple accelerometers onto your product and you'll get your various frequency sweeps to see if they meet some you know, military, uh, Performance Vibration Standard or whatever it is, you're in the house company standards. Doesn't matter what it is, you'll get a response on here and you might see all these dips and everything else and you might think, oh, I've got some mechanical resonance in my product.

Oh, I better redesign it. Quick panic, and no, you just haven't set up your jig properly. And that's the importance of coherence here. This is why I was saying: if you don't have your coherence data with your report of your test results of your product, then it's worthless because it shows that you have not put any thought into setting up your vibrational test system and your data that you get out of your accelerometer product is absolutely worth it.

Doesn't matter how calibrated your accelerometers and charge amplifiers and your shaker electrodyname shaker is, it doesn't matter at Rats. So until now, we've been playing around with, uh, that random generator. but we can't actually do a sweep. So what I've got is an external function generator here.

I'm actually going to set it up for a 30 second sweep here from 10 Hertz to 200hz which is our frequency range of interest. There we go. It starts out slow, starts out slow, and over 30 seconds it will sweep. So let me start our acquisition.

Let's have a look. And because we're only at one frequency, it's You'll find that it's going to slowly sweep across like this, and eventually 30 seconds later it will have swept all the way across and we will actually get coherence values. Now this is showing a real interesting result. Now here we go.

It's getting 150. It's almost at 200 Hertz here. and boom. And then it can, of course, keep doing its Rms, um, averaging and what not.

But look at all these notches that we've got here. What's going on? Once again, this is a gross example of where you might get a response that you might think is coming from your product, but it's not. It's because you haven't set up your sampling system correctly, so can you guess what the problem is here? I'm gonna change something here on our signal Gen and we'll do it again. It's similar, but more frequent.

Okay, I've changed it yet again and look at this. Oh, come here. And so I actually started it a bit late there and look. we're getting this little wiggle wiggle wiggle wiggle yeah in that signal.

Check it out. Look at that. That's interesting, isn't it? What's going on here? Is this some sort of little micro resonant thing happening here? What's going on? Well, for those who are paying attention that it took a bit longer, you would have realized that I was changing the sweep time. It started out as 30 seconds.

then I increased it to 60 and you would have seen that those dropouts we got here would double in in frequency when I change from 30 to 60 seconds. So, it's a function of our record length and sample time in our Dsa compared to our sweep speed that we're actually doing this at. Um, So Yeah, this makes a huge difference in the measurement. And if you just whack your accelerometers on your product and started getting your sweep and thinking that you're getting getting the correct values because you've got your whiz being expensive, calibrated accelerometers and software and everything.

No, if you haven't set up the system correctly, you can get all sorts of wibbly, wobbly stuff that has absolutely no correlation to the product that you're actually testing. I was getting sick of the tape here, so I've actually, uh, super glued it on now. I should have done that from the start. Now, check this out.

I'm actually setting a sweep time now that is uncorrelated with the uh, anything to do with the sample rate. So 7.7 seconds sweep time. Just a random number if I start a new sample. So this is 7.7 seconds.

Uh, sweep time and you'll notice that, right? It's all over the shop. But eventually this will get better and better as we do more averages and because it's uncorrelated time wise. Then slowly we're going to build up a complete picture so you can see it there. Yeah, it's slowly building up a complete picture of this thing.

Now I'm not saying this is the the correct uh method to do it, I'm just like showing this as an example of how you can have like a sampling and other Um time correlation errors which will cause a drop in your coherence. There we go. We've almost got the the basically the full response of this thing now. so time and sampling correlation is yet and phase correlation as well as I mentioned can be another Um source of error that you can get in your measured signal that if you don't do this coherence measurement test you'll never be able to see it.

The coherence test is a definitive way to show that you've got no errors in your system or you know as few errors as possible in your system before you actually start your proper quantitative measurement. Here's another example of our error that we're getting in. You can see that the response is not that great. Here is it? It's like it's glued on.

This response is supposed to be really nice. Can you spot the error? Maybe you can hear the error. It's these damn screws rattling around. because I haven't tightened them up, tighten them back up.

Start that again and you'll see that. Our response is much nicer. We didn't get all this random noise and crap in there, which then would have gone through onto our output. Uh, signal.

All of that crap was happening because we had lucy goosey um, stuff on our set up here. And when you're setting up your system like this and getting your coherence measurements, it can matter that whether or not you've got your actual product that you want to test on your shaker table because it has extra mass. it can change the dynamic properties of the shaker, which can introduce non-linearity into your system. And look, I haven't changed anything else.

All I've done is screw on that Pcb there and we've got this huge notch here at what you know, 32 hertz or something like that, like it's terrible. And then when you go to put your accelerometer on your product here, um, you're going to get all these weird and wonderful results that you didn't expect. and you might think that you have like, a design modal mechanical problem in your product that you're actually testing. When you don't, it's your setup.

Sure, this is like an extreme example with it flapping around in the breeze, but hopefully that gives you a good example of what can happen here. So there you go. I hope you found that interesting the importance of coherence measurement. So when next time when somebody shows you their test results for their vibration, uh, tests that they've done for their product.

Oh, look at this. Ask them. hey, where's your coherence data Because it ain't worth jack unless you've set up your system properly. So there you go.

I hope you found that really interesting coherence. This is not something that you'll learn in school. Basically, you'll only learn this hands-on I guarantee you will learn about coherence The very first day you start trying to do vibration testing on everything and your results go to crap and you're wondering what the hell happens. Then you discover the world of coherence and setting up your jigs and characterizing your test jigs properly so that you know the results are going to be good.

and anytime you change anything. in fact, anytime you do a measurement, you should do a coherence test first to make sure sanity check Your results are what you expect because there's so many errors that can go into introducing non-linearity into your test system. Once you get non-linearity, your measurement output data you don't know whether or not it's real or aha imaginary. Get it real and imagine any complex.

Uh, I'm here a week Anyway, I hope you found that interesting invaluable. If you did, please give it a big a thumbs up. And as always you can discuss down below and as always Euv blog forum, all that sort of stuff and all the different channels I'm on. I'm on every platform.

Catch you next time you.