Two Tone Test with Scope and SA

[mawyatt]

What you are overlooking is that the IMD terms are coherent. If you combine two coherent terms in phase the level on the spectrum analyser goes up 6dB with respect to the power of each tone and not 3dB.

I'm not sure I need equations to prove this as this should be common knowledge.

You have made the common mistake of just doubling the power. The power goes up by 6dB in the in-phase/coherent case which is a multiplication of four not two.

Put the numbers in to my earlier equation for the case where the IMD terms are at the same level. This is when d = 0.  You should get 6.02dB as the answer (not 3.01dB).

Nothing overlooked, the two signal generators are NOT coherent, as shown in just about every app note anywhere these source are completely independent sources. The IMD products are computed a 2F1-F2 and 2F2-F1, where F1 and F2 are completely independent sources, so the common mistake is yours

Best,

[G0HZU]

Wow, just wow... this is taking much longer than it should...

Have a look at page 13 of this white paper from Rohde and Schwarz

https://scdn.rohde-schwarz.com/ur/pws/dl_downloads/dl_application/application_notes/1ma219/1MA219_2e_IM_Distortion.pdf

If you think they are as clueless as me you could also look at page 21 of this article from Keysight.

https://www.testunlimited.com/pdf/an/5980-3079EN.pdf

They use the same equation as me. The same equation I've been using for decades.

Nothing overlooked, the two signal generators are NOT coherent, as shown in just about every app note anywhere these source are completely independent sources

You simply aren't listening to what I'm saying. The generated distortion terms are coherent in both stages. That's the point I'm trying to make.

[mawyatt]

A good practical example would be to take two identical 12dB gain amplifiers and put them in series with an attenuator in between them that has 12dB attenuation. So you end up with the same 12dB gain of a single amplifier. Then compare the narrowband IMD level of this arrangement to the IMD seen on a single 12dB gain amplifier with no attenuator. Note that this analysis assumes a perfect measuring tool. Or you could consider the second amplifier stage to be the limiting factor of the measurement tool if you like.

For a narrowband system the IMD of the first and and the second amplifier usually sums in phase so the IMD levels for the two amplifiers in series will usually be about 6dB worse (higher in level) compared to the case where you just measure a single amplifier on its own with no attenuation.

This is because the two IMD terms sum together in phase so you get twice the voltage (four times the power) hence a 6dB increase in IMD level seen with the dual amplifier setup.

Well this won't work as you state either!! The two identical 12dB gain amplifiers the second "sees" the IMD of the 1st attenuated by the 12dB attenuator, however the source signal level will be the same for the 2nd, so the net result will NOT be twice IMD level as you claim, but slightly more IMD than a single amp.

Please note that typical amplifiers and most circuits the IMD grows faster than the input signal level grows, so in your example the 1st and 2nd amplifier would have the same IMD if the second one had the 12dB attenuator input, but the 1st would have the IMD also attenuated by 12dB, so the 2nd would see an input with the same signal level as the 1st and the 1st IMD attenuated by 12dB, thus likely not much additional overall IMD.

Anyway, this is why noise is usually determined by the first stages and linearity by the later stages in well designed systems, and from the posts shown here the new SDS2000X HD is a very well designed data acquisition system disguised as a scope

Best,

[G0HZU]

A good practical example would be to take two identical 12dB gain amplifiers and put them in series with an attenuator in between them that has 12dB attenuation. So you end up with the same 12dB gain of a single amplifier. Then compare the narrowband IMD level of this arrangement to the IMD seen on a single 12dB gain amplifier with no attenuator. Note that this analysis assumes a perfect measuring tool. Or you could consider the second amplifier stage to be the limiting factor of the measurement tool if you like.

For a narrowband system the IMD of the first and and the second amplifier usually sums in phase so the IMD levels for the two amplifiers in series will usually be about 6dB worse (higher in level) compared to the case where you just measure a single amplifier on its own with no attenuation.

This is because the two IMD terms sum together in phase so you get twice the voltage (four times the power) hence a 6dB increase in IMD level seen with the dual amplifier setup.

Well this won't work as you state either!! The two identical 12dB gain amplifiers the second "sees" the IMD of the 1st attenuated by the 12dB attenuator, however the source signal level will be the same for the 2nd, so the net result will NOT be twice IMD level as you claim, but slightly more IMD than a single amp.

Please note that typical amplifiers and most circuits the IMD grows faster than the input signal level grows, so in your example the 1st and 2nd amplifier would have the same IMD if the second one had the 12dB attenuator input, but the 1st would have the IMD also attenuated by 12dB, so the 2nd would see an input with the same signal level as the 1st and the 1st IMD attenuated by 12dB, thus likely not much additional overall IMD.

Anyway, this is why noise is usually determined by the first stages and linearity by the later stages in well designed systems, and from the posts shown here the new SDS2000X HD is a very well designed data acquisition system disguised as a scope

Best,

If you won't take my word for it then read the app notes I linked to in post #109 written by R&S and Keysight. There is a graph there if it helps. The graph shows that the IMD level rises 6dB when the IMD level in stage 1 is the same as the IMD in stage 2. The two identical amplifiers in series (with an attenuator between them) is a neat way to demonstrate this. It can be demonstrated on a decent RF simulator or you can do the tests on a pair of real amplifiers and use a decent spectrum analyser. I've demonstrated both methods in the past. The result is usually very close to a 6dB increase. This assumes the IMD terms generated in each stage are in phase so they sum and this gives a 6dB boost.

See the blue curve below. It shows a 6dB boost just as I told you it would.

[SilverSolder]

Are you saying that if we have two signal generators running, and we are able to change the phase between them, we should see a difference in the result?

[G0HZU]

No, what matters is the relative phase of the distortion term from stage 1 delivered to stage 2 with respect to the phase of the distortion term generated in stage 2. The theory and equations are at their best when the distortion terms are very low in amplitude compared to the amplitude of the test tones.


Note that mawyatt could maybe take a look at the graph in my earlier post and see that his calculation of <1dB uncertainty when there is a 10dB difference in IMD is wrong and my calculation of 2.4dB was correct. The blue curve shows about 2.4dB error at a 10dB difference.

[mawyatt]

Wow, just wow... this is taking much longer than it should...

Have a look at page 13 of this white paper from Rohde and Schwarz

https://scdn.rohde-schwarz.com/ur/pws/dl_downloads/dl_application/application_notes/1ma219/1MA219_2e_IM_Distortion.pdf

If you think they are as clueless as me you could also look at page 21 of this article from Keysight.

https://www.testunlimited.com/pdf/an/5980-3079EN.pdf

They use the same equation as me. The same equation I've been using for decades.

Nothing overlooked, the two signal generators are NOT coherent, as shown in just about every app note anywhere these source are completely independent sources

You simply aren't listening to what I'm saying. The generated distortion terms are coherent in both stages. That's the point I'm trying to make.

Agree it's taking too long, and I'm listening very well thank you!!

These are good references for a swept SA and assumes a separate DUT is being evaluated and measured by the SA. Whereas the DSO under discussion here are FFT based and the actual DUT is themself being measured, so effectively DSO measuring themselves. These references also state the signal sources are coherent, whereas we've stated all along they are not coherent, and as such can use the RSS approach which assumes incoherent signals. With coherent vs. incoherent signals this is likely the source of the 3dB difference we are discussing, and maybe even the swept SA vs FFT based analysis. Also suspect if the 2 Tone IMD beat waveform were analyzed exactly over a integer number of complete cycles which might be difficult with a conventional SA, then the results might converge to a similar value.

Here's a couple papers on IMD for ADCs, and this is actually what's being discussed regarding the Two Tone Test, that and the scope input.

https://www.analog.com/media/en/training-seminars/tutorials/mt-012.pdf

https://www.ti.com/lit/an/slyt090/slyt090.pdf?ts=1655216827186

This one discusses placement of the two tones so the IMD products fall within the FFT frequency bins.

https://pdfserv.maximintegrated.com/en/an/AN728.pdf

Anyway, interesting discussions.

Best,

[mawyatt]

A good practical example would be to take two identical 12dB gain amplifiers and put them in series with an attenuator in between them that has 12dB attenuation.

For a narrowband system the IMD of the first and and the second amplifier usually sums in phase so the IMD levels for the two amplifiers in series will usually be about 6dB worse (higher in level) compared to the case where you just measure a single amplifier on its own with no attenuation.

This is because the two IMD terms sum together in phase so you get twice the voltage (four times the power) hence a 6dB increase in IMD level seen with the dual amplifier setup.

A) With the attenuator the total IMD should be just slightly more than the IMD of the second amp since this distortion products of the 1st are attenuated by 12 dB.

B) But what would the IMD be if the single amp had the same gain (read twice) as both amps in series wo the attenuator, 6dB worse maybe??

If you won't take my word for it then read the app notes I linked to in post #109 written by R&S and Keysight. There is a graph there if it helps. The graph shows that the IMD level rises 6dB when the IMD level in stage 1 is the same as the IMD in stage 2. The two identical amplifiers in series (with an attenuator between them) is a neat way to demonstrate this. It can be demonstrated on a decent RF simulator or you can do the tests on a pair of real amplifiers and use a decent spectrum analyser. I've demonstrated both methods in the past. The result is usually very close to a 6dB increase. This assumes the IMD terms generated in each stage are in phase so they sum and this gives a 6dB boost.

See the blue curve below. It shows a 6dB boost just as I told you it would.

Yes, saw the graph and it clearly states coherent input sources, not incoherent sources as we've stated all along as this is the basis for utilizing RSS as stated.

Edit: Added here

Figure 2–17
Amplitude Uncertainty
due to Two Coherent 8.00 CW Tone Adding 6.00 Together

Best

[nctnico]

What matters here is the relative phase of a small IMD term generated in stage 1 (and this IMD tone is then amplified by stage 2) vs the phase of the IMD term actually generated in stage 2 from the two main test tones.

If the phase of these is not the same then there will be some cancellation in stage 2. Do you understand it now?

After reading your other posts: what you are saying is that the measurement uncertainty depends on whether the intermodulation products of various devices in the chain are in phase or not? For two identical amplifiers the assumption is that the intermodulation products are in phase and thus -worst case- add up (no matter whether the input signal is a single tone or multiple tones).

Edit: better wording

[G0HZU]

In the case of a DSO I guess a lot depends on the signal handling performance of every stage of the analogue front end before it gets into the digital domain. All these stages can generate IMD ahead of the ADC.

The same applies to a spectrum analyser. Often it's the front end that defines the IMD performance.

A) With the attenuator the total IMD should be just slightly more than the IMD of the second amp since this distortion products of the 1st are attenuated by 12 dB.

I'm confused why you come to this conclusion. This is for a classic two tone IMD test. The 12dB attenuation is offset by the 12dB gain of the first stage. So the second stage is being driven by a signal that now has (say) -60dBc IMD. The second stage will amplify these IMD terms by about 12dB but it will also generate coherent -60dBc IMD terms of its own at a similar level at the output. These two mechanisms are usually in phase so the IMD terms will appear 6dB worse for the dual amplifier compared to the single amplifier case.

The single amplifier is being fed the same amplitude drive level but there are no IMD terms in the drive signal. So it just generates IMD3 terms close to that predicted by the datasheet for that drive level. The dual amplifier will have IMD terms 6dB higher.

[G0HZU]

See the attached video showing a dual stage amplifier vs a single stage amp. Each amp has 13.1dB gain and there is a 13.1dB attenuator between them. The IMD3 terms are -57dBc for the dual amplifier.



When the second stage and the attenuator is removed then the IMD levels drop to about -63dBc. This is only a simulation so not exactly conclusive but I have done similar tests on a pair of 'real' and identical ERA-1SM test amplifiers. These produce about 12.2dB gain so I did the test with a 12.2dB attenuator in between them for the dual amplifier scenario. The IMD change was very close to 6dB when I changed to a single amplifier with no attenuator. It was within about 0.3dB of 6dB.

[2N3055]

In the case of a DSO I guess a lot depends on the signal handling performance of every stage of the analogue front end before it gets into the digital domain. All these stages can generate IMD ahead of the ADC.

The same applies to a spectrum analyser. Often it's the front end that defines the IMD performance.

A) With the attenuator the total IMD should be just slightly more than the IMD of the second amp since this distortion products of the 1st are attenuated by 12 dB.

I'm confused why you come to this conclusion. This is for a classic two tone IMD test. The 12dB attenuation is offset by the 12dB gain of the first stage. So the second stage is being driven by a signal that now has (say) -60dBc IMD. The second stage will amplify these IMD terms by about 12dB but it will also generate coherent -60dBc IMD terms of its own at a similar level at the output. These two mechanisms are usually in phase so the IMD terms will appear 6dB worse for the dual amplifier compared to the single amplifier case.

The single amplifier is being fed the same amplitude drive level but there are no IMD terms in the drive signal. So it just generates IMD3 terms close to that predicted by the datasheet for that drive level. The dual amplifier will have IMD terms 6dB higher.

You keep repeating same things and mentioning first stage and second stage and spectrum analysers.

What does it have to do with two tone performance of oscilloscope in question?
How do you map your statements to that?

So plainly, if you feed two-tone into scope input like Mike did (noncoherent two tones) and get some IM distortion (whatever the number) isn't that IM distortion of the scope.

He is not trying to measure any external DUT. He is simply trying to characterize the scope internal IM distortion.

What am I missing here?

[G0HZU]

You can think of the two tone source itself as the first stage. I got the impression the IMD performance of this was unknown.

Normally, a high performance two tone source will use two sources separated by a high isolation (linear) combiner and there will be lowpass filters in place as well.

[G0HZU]

You can also experiment with the type of resistive combiner. It's often risky to use a classic delta or star resistive combiner as these have limited port to port isolation. I've built and used alternative resistive combiners that offer higher port isolation at the expense of some loss in the combiner. The alternative is to add attenuators before the combiner.

[tautech]

You can think of the two tone source itself as the first stage. I got the impression the IMD performance of this was unknown.

Normally, a high performance two tone source will use two sources separated by a high isolation (linear) combiner and there will be lowpass filters in place as well.

Mostly the 2 tone sources in this thread have been created in SDG models with their 2ch wave combine feature although I don't remember now if the very early one in this thread I did for Mike had locked phasing however I don't think that was needed or even a requirement from Mike.



Anyways, riveting discussion that we can all learn something from. 

[mawyatt]

Think the issue boils down to whether the various contributors of Two Tone IMD in an DSO & signal sources can be determined by the RSS method which assumes incoherent signals, or not, which assumes coherent signals. This is where the 3dB difference arrises I believe.

Anyway, as long as the methods for DSO Two Tone IMD evaluations are the same, then the results can at least be compared wrt each other, and in either case the actual 2 Tone IMD of the new SDS2000X HD is impressive as has been shown.

Best,

[mawyatt]

Mostly the 2 tone sources in this thread have been created in SDG models with their 2ch wave combine feature although I don't remember now if the very early one in this thread I did for Mike had locked phasing however I don't think that was needed or even a requirement from Mike.

Anyways, riveting discussion that we can all learn something from. 

Don't recall details either, was this plot from the SDG2042X AWG? Recall something about hearing AWG relays click when the wave combine function is active and brings up the question as to how and where this waveform combining takes place?

Anyway, speaks highly of the SDS2000X HD. Do you know if the front end section of the SDS2000X HD & ADC are the same as the SDS6000 series 12bit ADC version sold only in China, or the one for LeCroy?

Agree, very interesting discussions!!

Best,

[mawyatt]

.....
He is not trying to measure any external DUT. He is simply trying to characterize the scope internal IM distortion.

What am I missing here?

Don't think you are missing anything, spot on to what reviving this thread is about!!

Best,

[tautech]

Mostly the 2 tone sources in this thread have been created in SDG models with their 2ch wave combine feature although I don't remember now if the very early one in this thread I did for Mike had locked phasing however I don't think that was needed or even a requirement from Mike.

Anyways, riveting discussion that we can all learn something from. 

Don't recall details either, was this plot from the SDG2042X AWG? Recall something about hearing AWG relays click when the wave combine function is active and brings up the question as to how and where this waveform combining takes place?

Yes, SDG2042X it was and don't you too have one now ?

Anyway, speaks highly of the SDS2000X HD. Do you know if the front end section of the SDS2000X HD & ADC are the same as the SDS6000 series 12bit ADC version sold only in China, or the one for LeCroy?

Have no idea Mike, maybe 2N3055 or Performa01 can help you with this one....that's if their NDA lets them. 

I suppose I should do a 2 tone with my SDS6204A however with what I have here 200 MHz is the current limit of toys available.

[mawyatt]

Yes, SDG2042X it was and don't you too have one now ?

Yes, have a SDG6022X also (needed the higher frequency waveforms).

I suppose I should do a 2 tone with my SDS6204A however with what I have here 200 MHz is the current limit of toys available.

Would be interesting to see how good this SDS6204A is, I'm sure others are interested as well.

Best,

[rf-loop]

Anyway, speaks highly of the SDS2000X HD. Do you know if the front end section of the SDS2000X HD & ADC are the same as the SDS6000 series 12bit ADC version sold only in China, or the one for LeCroy?

Have no idea Mike, maybe 2N3055 or Performa01 can help you with this one....that's if their NDA lets them. 

due to NDA and so on...

But why even need for answer this just anything more than read from public data sheets and rest can know if think even bit. Answer to this question is obvious.

SDS6204 H12 Pro and SDS6204 H12 Pro what is up to 2GHz/1GHz  front end vs SDS2000X HD 500MHz front end... no, they are not equal aka same.

And even more, then in question there was "& ADC".  How it can even think if they are same.   
Example 6k H12 Pro models have 5GSa/s 12bit ADC's
2GHz models have one for every channel. 1GHz models and below have shared ADC's, one for two cannel  so that these have 5GSa / 2,5GSa/s
 
Then very different animal...
2kXHD have two 2GSa/s 12bit ADC's shared one for two channels so 2GSa / 1GSa/s.
No need any deep knowledge. It can read just from data sheet. 
And these SDS2kXHD ADC's are "perhaps" normal industrial models what who ever can buy from several different vendors.
No need Sherlock Holmes to quess what they are.

Naturally front ends are more or less close relatives. No one is so stupid that start every time from empty board. Development and design of something new is a continuous and cumulative, but also self-correcting learning process

[G0HZU]

If it helps I have an early/old Tek spectrum analyser here that has a digital IF. When used down at below 40MHz it is effectively a 40MHz baseband scope sampling at 102.4MHz but the display is trapped in the frequency domain. This is not a swept analyser, it samples the input and generates an FFT just like a scope.

If I inject two clean tones I can generate IMD in this analyser at about -83dBc if I drive it towards FSD of the ADC. If I then deliberately sum in a 'pre-distortion' tone at the source input at -83dBc at one of the IMD3 frequencies and then rotate the phase of this the analyser shows the expected behaviour where the displayed IMD3 term rises 6dB to -77dBc when the IMD3 terms are in phase and the IMD3 term vanishes on the FFT display when the phases cancel. This shows that the equal IMD of the source can cause summing at up to 6dB on the display and it can also cause cancelling although significant cancelling is highly unlikely to happen as I'd expect the source IMD terms to normally be in phase.

[Performa01]

Everything said by our RF-guru G0HZU should be taken seriously. Up to now, he mainly talked about the (close to) +6 dB boost for the distortion products in case of two clearly (and inevitably) corelated distortion sources, but of course this assumes zero phase shift, hence zero runtime – or at least test signals whose wavelengths are long compared to the physical dimensions of the test setup. Once the distance between distortion sources happens to be half the wavelength, we get phase inversion and instead of a boost, the distortion components will cancel out.

EDIT: Doh! Nobody notified me of my mistake. Of course the runtime is almost irrelevant, since the distortion products in question are almost the same frequency as the test signals!

In my test, the frequency was 450 MHz and half its wavelength is about 33 cm. While it is highly unlikely that such massive distances will occur between potential distortion sources within the DSO frontend, it would be perfectly possible that an odd multiple of this distance exists (as electrical length) between the external generator and any non-linear stage within the DSO. As a consequence, there is indeed a chance of cancelling out distortion products in this scenario.

My claim that I cannot guarantee the IMD performance of the test tones to be better than -74 dBc came from the fact, that I’ve measured this with my SA. It’s pure coincidence that the measurement result with the DSO was about the same. Since I don’t happen to own a R&S FSEA30 boat anchor with 110 dB third order dynamic range, I could not know whether I hit the limit of the generator or the analyzer. With two 10 dB pads for the external power combiner, hence a total isolation of 26 dB, any IMD products should be killed reliably. Now I could indeed measure an IMD of at least -85 dBc and can be confident that my source will be vastly better than this, when it already measured as -74 dBc IMD with only 6 dB isolation.

With the 10 dB pads in place, I cannot maintain a 0 dBm signal anymore. Even though I could have used about -3 dBm, I voted for repeating the test with a signal level of -10 dBm. This totally changes the scope settings and its internal nonlinear transfer curves.

Originally, I had 0 dBm signals at 500 mV/div. This means that there is an internal 20 dB attenuator active, and the PGA (Programmable Gain Amplifier) might have to deliver about 6 dB of gain. For an equivalent setting at -10 dBm, I would have to set the channel gain to 160 mV/div. With this, the attenuator is still in place, but the PGA now is at 16 dB gain, which might cause more distortion. In general, I think that the PGA might be the main source of nonlinearity in a wide bandwidth scope frontend, whereas the unity gain input buffer as well as the ADC should be rather benign in this regard.

Look at the attached screenshot for -10 dBm at 160 mV/div. The IMD isn’t quite as good, but it still happens to be another sweet spot:

SDS2504X HD_IMD_160mV_C450MHz_O200kHz_-10dBm

We can also try to replicate our former sweet spot without the internal 20 dB attenuator. For this, we need a -20 dBm test signal at 50 mV/div, see third screenshot:

SDS2504X HD_IMD_50mV_C450MHz_O200kHz_-20dBm

With this setup, we can be confident that the generator signal is way better than that, so we need not speculate where the distortion comes from.

[tautech]

I suppose I should do a 2 tone with my SDS6204A however with what I have here 200 MHz is the current limit of toys available.

Would be interesting to see how good this SDS6204A is, I'm sure others are interested as well.

Okay so I had a little play, SDS6204A running 500 Mpts fixed Mem depth with 189 & 190 MHz 0dB tones from SDG6022X.
All except the last were at 4 Mpts and last was at 8 Mpts FFT with some averaging.
Ref levels +5dB and -40dB.....most of which is visible in menus or OSD.

[mawyatt]

If it helps I have an early/old Tek spectrum analyser here that has a digital IF. When used down at below 40MHz it is effectively a 40MHz baseband scope sampling at 102.4MHz but the display is trapped in the frequency domain. This is not a swept analyser, it samples the input and generates an FFT just like a scope.

If I inject two clean tones I can generate IMD in this analyser at about -83dBc if I drive it towards FSD of the ADC. If I then deliberately sum in a 'pre-distortion' tone at the source input at -83dBc at one of the IMD3 frequencies and then rotate the phase of this the analyser shows the expected behaviour where the displayed IMD3 term rises 6dB to -77dBc when the IMD3 terms are in phase and the IMD3 term vanishes on the FFT display when the phases cancel. This shows that the equal IMD of the source can cause summing at up to 6dB on the display and it can also cause cancelling although significant cancelling is highly unlikely to happen as I'd expect the source IMD terms to normally be in phase.

Think your test show we can't use the RSS method to evaluate/estimate/separate DSO sources of IMD as it can potentially introduce a 3dB optimistic result because of correlation.  Thanks for taking the effort for this testing.

Best,