Hi Coincidentally, I've had two people recently contact me about a what is essentially the same problem to do with measuring things using coaxial cable like this. and the example was that they were trying to check the output signal level of their high frequency function dinner like this: Rygel DG 4162 can go up to 160 megahertz you know, quite a nice function generator and they'll using their oscilloscope which had a better bandwidth than this. of course, in this case, it's the Rygel Dias 2000 Series 200 megahertz that's got enough bandwidth using a nice short piece of coaxial cable like this, you know, excellent, capable of nice high performance Rg-58 Coax and they tried to measure the amplitude across the frequency. and look what happens.

We'll start at 1 megahertz here for example, and you will notice that the our peak to peak voltage over here is being displayed and currently about 1.06 volts. And if we wind that frequency up one megahertz steps at a time here, then you'll see that it's You know, it's pretty constant. We're at 28 megahertz now, but it's starting to drop a bit 980 odd millivolts or there abouts and if we keep going up, we're back to a volt. Okay, you know you don't expect it to be completely ruler flat over the frequency response of course, and the specs will tell you that.

But if we keep going, for example, look now we're getting 960 950, its drop in 920. Well look, we're under 900. What's going on here? Something strange at about 87 megahertz or there abouts 9 830. That's just.

look, it's crazy and if we go up in frequency, continue to go up 114 megahertz, our voltage is actually going back up and it's going all over the place and right up to 160 there. You can see that if I sweep it quickly, it sort of goes. It undulates up and down a little bit like that. Why is it so? And of course you wouldn't expect there to be anything wrong here as well if it was like that lost from the coax cable.

Of course, if you look at the data sheet for a coax cable, you'll find that its loss does actually increase with frequency of course, and fair enough, but in this case, we saw the signal actually unlike, actually undulate, go down, and then undulate back up at a higher frequency. So it wasn't like it was consistently rolling off or dropping in amplitude with frequency. So there's something else at play here, and it gets even stranger. Let me show you something really weird.

look: I've got the same output here I Got a B and C T adapter here, driving through exactly the same coax, exactly the same length of both Rg58 going into both channels of Elroy Go scope here. We're at four megahertz, so a low frequency and you can see that the two waveforms are identical there. Okay, now watch what happens if we increase the frequency. Not only do we get that drastic drop again, we're but we're down to six hundred and something millivolts now.

by the way. I've been using that convulse peak to peak and the function G Any stable one volt peak-to-peak over the entire range and you notice that look, look at that. The signals are get in different. So you can be forgiven for thinking that there's something wrong with the ROI Goal 2000 scope on that second channel for example.

But we're getting a whole bunch of issues here. We're getting a output amplitude which seems to change over frequency you expect it for a function Jen They're not rule a flat, but shouldn't be nearly as much as what we saw they're not even close and we're also getting amplitude differences between the two channels. Well, let's try another oscilloscope. Hopefully won't get any complaints about this one.

500 megahertz Agilent 3000 series scope and absolute beauty. Exactly the same set up both channels going in here and as you can see, there we go, they're both the same amplitude. Let's wind the wick up and see what we get. Let's change the horizontal a bit there.

25 megahertz. It's all looking good, but our amplitude has dropped a 600 millivolts peak to peak. That's way out of spec for this Rygel scope. Let's see if we get the amplitude difference between channels.

We do. look at that. Bingo! What's going on here And look. we've just got two pieces of work.

Pretty good performance Co Action Coax should easily be able to do it short path or going in using B and C s. Everything's hunky-dory and no, it has nothing to do with the 50 ohm output impedance mode. for example here: output Impedance high impedance Note: Look makes no difference whatsoever, of course. So what's going on here? So pause the video and see if you can figure out what's going on here.

I'll tell you after the break. Well, I hope you're able to figure it out. The answer is. well, the answer is actually really quite complex.

But what it basically boils down to is the fact that this is the wrong technique for doing a simple measurement like this. You can't just use coax cable unterminated on the input here. And no, there's nothing wrong with this function generator. It is.

it meets its Peck and it is pretty ruler flat. You know, within 0.4 DB or something over the frequency range to prove it. I'm going to disconnect my turnoff channel to here I'm going to use my Agilent 500 megahertz probe here. We'll have to change the volts per division and I'm using a coax cable adapter on here like this.

so let's plug that in. Let's wind that up and our amplitude look is gone back to 960 millivolts there. So if we wind that over the write down, we're at 7 megahertz now, right? So we are looking at 1.06 volts. So if we now change at 1.0 718 megahertz, we're still hovering around that one volt mark and we're still within the spec.

I Think's about plus minus 0.1 volts for a 1 volt signal a 960. You know it's not bad. It's gone at sixty one megahertz. Everything you know, 950 millivolts.

so it's gone back up to a volt. Okay, so it's certainly flat within that spec. or a little bit over. maybe a small.

No, it's not I think it's a yeah. Anyway, 160 megahertz. As you can see, there's very little difference there, and that is the correct way to do it. Not using an ordinary piece of coax like this.

Well, you can, but you have to terminate them. Okay to prove that. I'm back to my coax setup here: I'm going to set my input impedance 250 ohms. and if your scope doesn't have that, you can just use a 50 Ohm in line Terminator Oren or another T piece like this with a 50 Ohm terminator like that just hanging off it if you like There we go.

Both got 50 Ohm inputs, so let's now look at those. Okay, so we've got both channels like that. that's a one mega. It's there.

Okay, but of course we're going to be low in amplitude. Okay, because we got the 50 Ohm. In fact, we're double 50 ohm terminated here. So normally it would be half that one volt that was shown there.

Or if we turn on our where is it now 50 ohm output impedance that just basically corrects the output amplitude on here so we can go to amplitude and we can go one volt peak-to-peak and ordinarily should give us one volt peak-to-peak if we only had one output terminated like that. And we do. There we go one volt peak-to-peak but because we're double terminating that, well our amplitude is going to drop. But what I want to show you is the fact that this thing here we go, let's have a look.

Okay, we've got both waveforms there. Okay, we've got one megahertz. Let's wind the frequency up here and you'll notice that it's yeah, 675 millivolts and you'll notice that it's not going to change much and we're not going to see any of that amplitude difference between channels that we got before. There's a slight phase difference between channels.

that's okay, but look, there's no amplitude difference as we go up like we saw before. So it's all about the Terminator getting the correct termination when you're using these 50 ohm coaxial. and the reason we didn't get it when we were using this times 10 probe and I've done a video on oscilloscope pros before is because it's got that 9 Meg input resistor there which effectively takes away the capacitance. err.

anyway. I Won't go into the details, but that is the correct method to use because it does. You don't need to terminate the other end in this case like you do with a direct coax cable here. and if you're curious to know why I Said there's a phase difference was okay between the channels, it's because look, they're not actually the same length coax, they're slightly different.

Only a smidge in there. but that makes a big difference on the scope. I'll show you how you can correct for that. Now you'll notice that 160 megahertz there.

and if you zoom right in. Okay, then you can see the phase difference between there. and that is just the length. That that slight length difference like a centimeter or two between those cables.

and this is actually why oscilloscopes have a probe, skew function or a delay function. I have whatever they want to call it. This is to correct and calibrate your art probes for exactly the same delay time. and it really matters.

When you get you know two really high frequencies alternate. You know, high-frequency oscilloscopes, you know in the many hundreds of megahertz as we see here or into the gigahertz range. then your probes skew. We've added minus 262 Pico seconds of skew there to correct for that difference.

So we've basically got a length difference there. a 262 Pico seconds. Let's see if we can actually measure the exact difference and see that on the datasheet and actually get and see if that value actually calculates out. And there you go.

That's the difference in our length about 45 millimeters and the datasheet value for this I Don't have the exact one, but a it's going to be near enough. Let's take five point, oh, five nanoseconds per meter propagation delay and forty five millimeters our differential in length. There we're going to equal about 227 Pico seconds a delay difference between those two channels and what do we get on the scope? We have to correct around about 262 or there abouts. So there you go.

it works out. So with those two similar Co axes and if you don't terminate the inputs like on this Rygel scope here, look what happens I mean we're at around about 35 megahertz and not only can the amplitude change, but then the phase can drastically change as well. and then they can swap over and do weird ass stuff like that at a particular frequency that is going to change with the impedance of the coaxial using the length of the coax and the reflection and the load being reflected as well. Yes, this is all transmission line stuff.

So when you start playing around with transmission lines which coax cables are at, What? any any transmission line at high frequency and you don't terminate the things correctly, you can end up with all sorts of weird phase and amplitude adding and subtracting and standing ways which we won't go a huge amount into. But look, even though we're not terminating these inputs here, there's no 50 ohm termination at all. So it's not a simple 50 ohm termination issue. if I disconnect channel to look at, look the amplitude of channel 1 actually dropped, and then if I take another piece of coax like this and whack that in series with that one.

So I've doubled the length of one of them. Whoa, dude, look at that and it gets even more weird. Look at this right: I'm canal correctly terminating my scope in 50 Ohms, There it is. So we get in our very nice you know, 1 volt peak-to-peak exactly as we expect.

and look what happens if I just whack on a piece of coax like this. There's nothing on the other end of it. There's nothing up my sleeve. Boom.

It vanished. Our signal vanished. Whoa. and that's at 57 megahertz.

Now if I change the frequency, let's go back down to this frequency here. you'll notice it makes a hardly any difference at all. That's because the not the transmission line effects. the reflections are subtracting from going back, reflecting off this end and then subtracting at the input here to the scope so your signal at your oscilloscope can actually vanish if you're not probing things properly and terminating things properly.

Now, one way to demonstrate this is to instead of using a sine wave, use a square wave I'm just using the output of the Rygar function Jen So it's not incredibly sharp, but as you know, a square wave edge like that generates a whole bunch of you know harmonic frequencies. So watch what happens if we take this same coax cable. Look, you know it's pretty nice edge there. It's all compensated very nicely because it's terminated in our 50 ohm impedance.

Let's add on just this empty bit of coax like this and see what see what happens. Look at that we've got what it, what is causing that? Well, all of the frequencies and the phase, and depending on upon the length of the coax, the the signal has been reflected from the unterminated end of this coax, reflected back along the coax, and it's subtracted from our signal here. So it's been subtracted at the input of the oscilloscope at that particular frequency and phase. whereas at this point here, it's actually added up, so that can be the difference and that's going to change if I change the length of the coax and you'll notice that change.

Even if I just add a little tiny barrel adapter like that to it. Look at that, you see it goes. It moves back at just a tiny smidgen. So if we add another coax which is exactly the same length about two feet or whatever, look at that.

BAM Everything changes because the length of our stub here and I'll just give you a very quick whiteboard explanation of what's happening here. Now you know that the a square waiver by your Fourier theory is made up of or can be thought of or for practical purposes is made up of a fundamental frequency plus all of the odd harmonics at low, a diminishing, diminishing amplitudes. And when you add up all these sine waves, it gives you a square wave. So a square wave has many different frequencies contained in it, and for a transmission line, that's a big deal.

So what we've got here is our signal generator. Okay, we're going through the first bit of coax, but it doesn't matter. We're basically talking about the signal on the 50 ohm load at the oscilloscope. So our silla scope is actually measuring these two points here.

Okay, across our load. But then we've got that extra bit of coax hanging off that stub. and because it's open, it's not terminated properly. We're going to get reflections back.

Now, the signal here. Set this. got the square wave in red. Okay, it's made up of all these different frequencies, so if it's a 1 megahertz signal, we're going to have all of the odd harmonics in there.

3 megahertz, 5 megahertz, 7 megahertz, and so on down in diminishing amplitude. Now, when all of these frequencies travel along this coax and then get reflected back, some of them are going to be in-phase some of them are going to be out of phase, and they're going to have different delays. and this is a no-no in theory as group delay and phase delay, and I won't go into the details of it. But suffice it to say that pretty much any medium that your signal travels through bed, air, coax, or whatever, these different frequencies are going to have slightly different or can have slightly different delays and phases based on the frequency content.

So take for example, this three Megahertz. Let's just assume that that one is going to be fed back, it will reflected back in phase and I've shown this here and it is reflected back and because it's in phase, it adds up. It adds to the existing and amplitude signal at one megahertz here. So that is why in blue Here your signal rises like that as we saw on the scope.

But say your next harmonic or a different harmonic here at five megahertz that may come back out of phase due to phase delay in group delay and that sort of stuff. and then if it's out of phase, it can actually subtract from your existing signal there. So that's why you can end up with that little weird sort of you know pedestal thing on your waveform and so on and so on. For all the different frequencies, depending on your type of load, the coax, the length, and the all sorts of properties of the coax, you can end up with all sorts of weird and wonderful waveforms reflected back like this.

So that explains the square wave part of it. But what's happening with the sine wave? Well, it's exactly the same thing because of our group delay and phase delay. Even if you've got one pure sine wave at one frequency, so there's no other frequency content at all, no harmonics, you still that a one signal can still get reflected back or will be reflected back off the open end of the coax. but it could come back at a different phase depending on the frequency.

And if it's big enough, your signal can vanish, which is what we saw on the scope before, or practically vanish. Or it can double. It can actually increase or decrease in amplitude depending on the frequency, and we saw that. and we can see that there's another good example for that.

Again, I'll show you. Okay, Now what I've got here is exactly the same coax we've been using before, from the signal generator, unterminated at the input here. Okay, so our signal that we're sending from the function Gen is going to get reflected back because this isn't terminated properly. Back to here.

and and you might think well, we should always get the same value out of the function generator output here because it's a nice low impedance. It's driving this coax. Why would the signal output here change? You can understand how it changes at the end here, but watch this. So I'll get my oscilloscope probe which is on Channel 2 here so that'll be the blue waveform and we'll plug that in over here.

So now we can see the different waveforms and let's wind up the frequency and see what we get here. So watch this if we go. Start at one megahertz. Everything's fine, right? Both waveforms are all nice nicely.

In phase, they're not a problem. Okay, and exactly the same amplitude is exactly what you'd expect. But you wind that frequency up and let's see what happens here. Look, it starts to get out of phase.

This reflected signal back from the coax like this is now arriving back here out of phase and you can see the amplitude is changing. So if we increase that you can see the amplitude goes down on this reflected signal here. that blue signal there and it's out of phase. and if we get to we're up to 42 mega Hertz at the moment.

Hey that's a good number I like that. but look, we get to there and that's about 47 megahertz Just so happens to be the frequency where the minimum value. We hit the minimum value at our input over here. So and if we keep going up in frequency, you'll notice that it goes back up and it comes back in phase.

But look at that. so that's a great example of how your signal gets reflected back from the coax and can actually cancel right at the output of your function generator here. So getting back to the original question and point of this video: why does that waveform there range in amplitude that we measure on the scope here from the output of the function generator, changing amplitude when we change the frequency like this, Well, you'll notice that the yellow one is increasing in amplitude as the blue waveform. that reflective waveform is going to get into a minimum.

So you'll notice that the yellow one reaches a peak there when the blue one is the lowest and that is because the signal is being reflected back off the Sun terminating input here coming all the way back. Add in to that and it's going to continue to reflect back and forth like this. and it's basically at the input here that we're measuring with the scope that is going to get added when the when we have the most amount of reflection. So when there's the most amount of reflection here, you're going to get the maximum value.

That blue waveform is a minimum. Where was that frequency at forty seven megahertz or something? When that blue wave forms a minimum, the yellow one measured here, the input to the oscilloscope will be at its maximum value. and that is why using a piece of coax is the wrong way to do it. Unless you actually terminate it or you actually use a high frequency times 10 oscilloscope probe and plug that straight in because you're not going to get any transmission line reflection issues.

So by using this times 10 probe or using a properly terminated 50 ohm coaxial, you're going to be able to measure that is the correct way to measure the true output amplitude over frequency of your function generator here or anything else. So anyway, that was longer than I wanted it to be. but I hope you found that interesting. and why simply connecting your function generator to your oscilloscope with a piece of Co action might think that's a good thing.

You're doing the right thing, but you're not technically and you know if you wanna anything at any sort of high frequency than where the wavelength is good fraction of the length of the Co. Actually going to get problems like this, you're going to get group delay and phase delay and reflections and all sorts of things. So if you're doing this sort of thing, make sure you use your proper times 10 probe at times one probe isn't going to do it. You need a times 10 probe that is designed to actually measure that so that you don't need to return 8 your input here or you terminate the scope properly.

In the case of the Rygel DG 4000 series here and similar other function gens its output amplitude specification specified in 250 ohm load. so you have to actually terminate it in 50 load truely to meet the spec. but in this case, if you do actually want to measure its open load flatness, output voltage, then you've got to use this Times 10 probe. So there you go I Hope you found that very interesting and it's fun to play around with this sort of stuff.

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