Usefulness of different TDR designs?

[David Hess]

LeCroy offers a RIS function.  I cannot discern any utility to it, but in all fairness I've not spent a lot of time trying to devise a test case.  I've not played with a Tek sampler that had the feature.

The RIS described here by LeCroy is just what Tektronix and others would call equivalent time sampling or random equivalent time sampling.  (1)  I remember finding this last time I searched on this subject.

Most certainly no one has implemented what Donoho and Candes described in a commercial product.  You cannot get a PhD by repeating someone else's work.  And failure is not an option.  If you fail you have to start over on a new project. At least that's the case at reputable schools.

I may have been thinking of what HP did in the HP 54645A/D (2) in 1997 which is about the time that I remember although this is not the application note I remember.  This is not the document I remember either.  I think HP either sent me a brochure about it at the time or I read about it in a trade magazine.

(1) It is really annoying when trying to use this if the waveform synchronizes with the sample clock; you might think that impossible but I have had it happen.  Universal counters face the same problem and may deliberately dither their timebase with noise to avoid it.

(2) Also here.

[rhb]

Thanks for the LeCroy link.  That's a much better description than the LC648DLX manual.  It also makes clear why it doesn't work very well aside from not having a relay to remove the anti-alias filter from the signal path.

What LeCroy is doing is absolutely useless so far as I have been able to tell.  My square wave pulser from Leo has a 36 ps or better rise time.  There is *no* difference in the rise time measured using RIS or regular sampling.  It's ~250 ps either way.  I was quite disappointed.  However, it may also be related to clock granularity. The LeCroy is my fastest scope other than the 11801 which is a completely different sort of beast.

Donoho did the mathematical proof of compressive sensing in 2004.  I was quite stunned when I discovered his work in 2013.  I was solving massively underdetermined inverse problems following Mallat's discussion of basis pursuit when it sank in that I'd been taught you can't do that.  So I had to find out how this could be happening.  That led me to Foucart and Rauhut and the most difficult math I've ever encountered.  One of Donoho's proofs is 15 pages!  Fortunately the other two theorems in the paper were only 2-3 sentences. Donoho has a great sense of humor, so he commented on it at the end of the first proof.

In the case of compressive sampling the wave form does not need to be repetitive.  As I understand it, the sole requirement is that the sample intervals be completely uncorrelated.  I'd love to talk to someone with the fortitude to read Foucart and Rauhut.  With Mallat as an essential prerequisite, it's a lot of work.

[David Hess]

In the case of compressive sampling the wave form does not need to be repetitive.  As I understand it, the sole requirement is that the sample intervals be completely uncorrelated.  I'd love to talk to someone with the fortitude to read Foucart and Rauhut.  With Mallat as an essential prerequisite, it's a lot of work.

That is the part I remember.  Randomizing the sample time was suppose to suppresses aliasing on single shot captures and that is sort of what the HP notes I linked claim.  The document from HP that I remember however went into a lot more detail.

[vk6zgo]

 

If it really matters you shouldn't rely on a 0.66 vop; instead, determine it from a known length of the same cable (using the TDR), preferably off the same spool or batch.

Alternatively, you can use a CW signal from a signal generator, monitoring the outgoing signal to the cable with an Oscilloscope.(Or a swept signal if you want to be fancy).
At 1/4 wavelength, an o/c far end will give you a (sharp) null in the display, and a s/c, a peak.

I tested my reel of RG58 several times this way, & the cable length always came out correct for 0.66.
Now I just use the tape measure (for that particular reel).

[rhb]

Those provide a better idea of what RIS/ETS  was about.  I was taught that ETS implied that you had to provide an external band pass filter to limit the BW to the Shannon-Nyquist limit.  I was a bit disturbed when I discovered that the EE community were not being very scrupulous  about the mathematical niceties.  My LeCroy samples at 2 GSa/s with a 1.5 GHz BW.  So everything above 500 MHz is aliased.  Gad!!!

The attached figure is from "A Mathematical  Introduction to Compressive Sensing" by Foucart and Rauhut.

The top left shows the amplitude spectrum of the signal which has 5 non-zero spectral components.  The lower left shows the time domain signal corresponding to the spectrum above it.  The dots in the lower left show the 16 sample points selected randomly.

The upper right is the result from attempting to compute the amplitude spectrum using a standard L2 norm discrete Fourier transform.  The lower right shows the spectrum *exactly* recovered using an L1 discrete Fourier transform.

When I was working on Bin Liu's minimum weighted norm regularization (Sacchi's student) I attempted to regularize data by means of an irregularly sampled discrete Fourier transform.  In my case the average sampling met the Nyquist criterion, it was simply that the samples were not regular.  The L2 norm inherent in the DFT produced a broad nasty mess for a single sine wave.  That and the realization that the process appeared to be severely dip limited led me to abandon the work.  It was a complex algorithm and would have been at least 6-9 months of full time work to implement.

To put things in slightly different terms.  The upper right figure is the results of attempting to solve Ax=y where x is a vector of Fourier coefficients using the traditional L2 (least squares) norm.  The lower right is solving the exact same problem except using an L1 (least summed absolute error) norm.

When I was at Austin in 85-89 we were so constrained by the 125K multiply-add rate of the 11/780 that serious work using an L1 norm was unthinkable.  We did occasionally use SVD and truncate the eigenvalues, but without  understanding that exact reconstruction possible in the noise free case.

The operations research people were solving L1 norm problems via linear programming, but there was no interaction between OR and seismic that I am aware of.  And in any case, the sheer volume of data we had to contend with would have made serious work impractical.    We were already contending with 5-8 day run
times for fairly simple stuff.

Compressive sensing arose out of Donoho's recognition that if you could acquire data in the traditional manner and compress it to 1% of the initial volume, you could skip the traditional acquisition step.  Candes had already proved that exact reconstruction was possible in the noise free case with fewer samples. The two of them were firing papers back and forth over the course of 2004.  Donoho was at Stanford and Candes was at CalTech.  It's really fun to watch the ideas fly back and forth.  Both are excellent writers and just reading the abstracts and introductions will give a strong sense of how things developed without delving into the complexities of the mathematics.

Have Fun!
Reg

[Per Hansson]

In a TDR, random sampling would allow the TDR to measure the reflected pulse immediately after or even before it is sent (1) but since a TDR can always generate its own pretrigger signal of whatever duration is required, random sampling is never needed.

(1) A must when doing maintenance on a TARDIS.  This explains the rarity and high price of 7T11 and 7T11A plug-ins; those who still do TARDIS maintenance can pay unearthly (Gallifreyan) prices on the Terran market and can rebid on lost auctions if they choose.

Hmm, I don't think I'm as deeply versed in Doctor Who as you are
A time machine would be useful though, will put it on my to-do list

Leo will provide 1 MHz square wave units on request for an extra 10 pounds.  I have ordered two for TDR with a DSO.

Yes having Leo's and maybe also Mr Carlson's TDR for a comparison would be nice.
Would be interesting to see how they stack up for TDR use.

[rhb]

I'm planning to play with fast edge circuits when my SD-32 arrives.

[David Hess]

Those provide a better idea of what RIS/ETS  was about.  I was taught that ETS implied that you had to provide an external band pass filter to limit the BW to the Shannon-Nyquist limit.

That sounds more like an under-sampling application where the bandwidth of the input signal must be limited to below the Nyquist frequency as oppose to a baseband application like an oscilloscope where the input bandwidth must extend to DC.

IF sampling receivers do this to extract say a 15 kHz passband from a 15 kHz IF stage using a 100 kSample/second ADC at 10.7 MHz or whatever the IF frequency is.  The right kind of sampling oscilloscope can do the same thing using an external clock.  Oddly enough, some old DSOs can do it also because they support an external clock input.  This has the effect of using the ADC as the final mixer stage.

With a Costas loop to recover the carrier, such an oscilloscope can directly demodulate AM from an IF within its bandwidth.  I think Linear Technology published an application note doing this using one of their sampling ADCs.

I was a bit disturbed when I discovered that the EE community were not being very scrupulous  about the mathematical niceties.  My LeCroy samples at 2 GSa/s with a 1.5 GHz BW.  So everything above 500 MHz is aliased.  Gad!

That sure does not seem right.  Exactly what LeCroy model DSO is it?  Typically a DSO of that caliber would deliver a real time sample rate of 2 GSamples/second but deliver 20 Gsamples/second or higher using ETS or what LeCroy called RIS in the application note I linked.

My Tektronix 2440 is like that.  The full 300 MHz bandwidth is not supported by its real time sample rate of 500 MSamples/second but the sample rate in ETS mode is 25 GSamples/second.

Hmm, I don't think I'm as deeply versed in Doctor Who as you are
A time machine would be useful though, will put it on my to-do list

One of the Tektronix 7B92A timebases I bought produced a sweep which went backwards in time.  Suggestively, it was prominently marked "Physics Department" in red ink on the side.  Unfortunately, I fixed it before considering what I had carefully enough.

[rhb]

The Shannon-Nyquist limit is the BW of the signal, not the maximum frequency.  I'll leave Shannon's paper to the interested reader.

The LeCroy in question is a DDA-125/LC684DLX.  It's 2 GSa/s on 4 channels, 4 GSa/s on 2 channels and 8 GSa/S on one channel with an external adapter to combine 2 & 3. I don't have the adapter unfortunately.

But it has a <250 ps rise time whether it is in 2 channel or 4 channel mode.  It also has 20% overshoot which is actually stated in the datasheet.  At least they are honest enough to include it.  The rise time is the same in RIS mode.

The DDA-120 doesn't need the external adapter to merge 2&3.  So it looks like a good candidate for a set of switched low pass filters with 750, 1500 and 3000 MHz corner frequencies.  And a VGA LCD to replace the CRT and provide room for the filters and SMA relays.

The DDA-125 will dither the clock to give 40 ps sample intervals and claims a measurement resolution of 5 ps.  However, I've not observed it to be useful for anything.  It certainly does not give you a faster rise time measurement unless there is some menu toggle I've not found.  I had great hopes of 11801 level performance when I bought it.  But at least I can do hysteresis plots without requiring an external analog integrator.

As far as I'm concerned, the EE sampling jargon is an egregious abuse of the English language and the mathematics put forth by Wiener and Shannon.

Sampling scopes do *not* evade the Shannon-Nyquist constraints any more than wavelets evade the time-frequency resolution limits of the Fourier transform.  A sampling scope is only sampling a very narrow range of frequencies.  One need only consider the integral transform of the sampling window to see this.

Or as I used to put it when people would breathlessly tell me that wavelets had better resolution than short window Fourier transforms, "If a statement is true in French, then it is still true correctly translated into any other language."

[ocw]

There are a number of factors influencing the use of a TDR or Frequency Domain Reflectometry (FDR) measurements.  While I have used a Tektronix 1503B and various Riser Bond TDR's to locate and then correct many cable problems, FDR's are generally replacing TDR's since they do a better job of locating most faults.  See:  https://www.anritsu.com/en-US/test-measurement/solutions/en-us/distance-to-fault

Examples of this are shown in my attachments.  I am comparing a Tektronix 1503B to a Agilent E7495A.  The best example is probably comparing an inexpensive Chinese 2M BNC to BNC RG58 cable.  The end of the cable is connected to a 6 GHz 50 ohm load.  The Tektronix TDR display indicates that it is perhaps not the best cable in the world, while the Agilent FDR display clearly demonstrates that besides the connectors being marginal, the cable is not the best quality either.

The RG214 cable comparison shows the differences when measuring a better quality cable.

Additional cables are shown on just the Agilent FDR since the differences are more easily seen on that instrument.

[rhb]

While most TDRs seem to use a square wave, if an impulse is used the energy is distributed across a very broad spectrum.

I have one of Leo's 100 ps impulse units.  The output spectrum of that is approximately a  sinc(f)**2 with the first zero at 50 GHz.  Unfortunately, a DSO with that BW is rather more expensive than an FDR.

I plan to build some pulsers in an attempt to have something capable of testing my SD-32 which at 7 ps is quite a challenge.

[FriedLogic]

 It certainly does not give you a faster rise time measurement unless there is some menu toggle I've not found.  I had great hopes of 11801 level performance when I bought it. 

Hi,

The point of RIS etc. is more to fill in the trace with actual measurements rather than a calculated interpolation, and so get around the artefacts and errors that come with it - and in the case of older scopes like that it's needed even more because the ADC's used could not sample fast enough, which was common at the time. I wouldn't have expected it to change the rise time much, except to the extent that the interpolation was wrong.
I have an old 100MHz Metrix that samples at 50MS/s, and that can get interesting....

[rhb]

I have an SD-32 sampling head in transit which should arrive on Saturday.  I am very interested in suggestions of how to produce an edge which is faster than the 7 ps rise time of the SD-32.

[David Hess]

The LeCroy in question is a DDA-125/LC684DLX.  It's 2 GSa/s on 4 channels, 4 GSa/s on 2 channels and 8 GSa/S on one channel with an external adapter to combine 2 & 3. I don't have the adapter unfortunately.

From the manual:

Repetitive signals can be acquired and stored at a Random Interleaved Sampling (RIS) rate of 10 GS/s for all models except LC564, LC584, AND  LC684 SERIES, whose RIS rate is 25 GS/s.

The DDA-125 will dither the clock to give 40 ps sample intervals and claims a measurement resolution of 5 ps.

The 40 picosecond sampling resolution in RIS mode is consistent with the given 25 GS/s sampling rate in RIS mode.  5 picoseconds probably represents the interpolated measurement resolution which is not unrealistic.

However, I've not observed it to be useful for anything.  It certainly does not give you a faster rise time measurement unless there is some menu toggle I've not found.

Why would it?  The sampling method has nothing to do with input bandwidth.

Sampling scopes do *not* evade the Shannon-Nyquist constraints any more than wavelets evade the time-frequency resolution limits of the Fourier transform.  A sampling scope is only sampling a very narrow range of frequencies.  One need only consider the integral transform of the sampling window to see this.

Sampling oscilloscopes do not act or operate as you describe.  Their bandwidth extends from DC to whatever their -3 dB point is.  The -3 dB point exists for a sampling input however it does not really have the same meaning because the frequency response curve is non-linear with a null at the reciprocal of the sampling gate time and every harmonic past that.  For this reason they do not obey the 0.35 rule but their transition time can definitely be measured or calculated based on the sampling gate width.  This actually provides an easy way to measure sampling input bandwidth; find the first null and work backwards using the sin(x)/x response; a leveled signal source is not required. (1)

One thing not commonly realized is that sampling oscilloscopes often have trigger bandwidths considerably in excess of their sampler bandwidth and their trigger bandwidth can be extended using injection locking.  Injection locking a sweep used to be pretty common.  Tektronix made normal oscilloscopes which included the same type of triggering (HF SYNC) through the 1980s for special applications.

(1) This breaks down somewhere above 20 GHz where samplers get weird.

[rhb]

Write out the acquisition equation in the time domain and then apply an analytic Fourier transform.

[David Hess]

It is irrelevant; at this point I am not convinced that you understand how sequential and random sampling work and what equivalent time sampling means.  Your LeCroy supports random equivalent time sampling (RIS in LeCroy speak) of up to 25 GS/s using real time sample rates of 2, 4, or 8 GS/s depending on the number of active channels.  This does not conflict with its 1.5 GHz of bandwidth at all except of course that it cannot capture 1.5 GHz of bandwidth with all 4 channels operating at the same time in a single shot without aliasing.  That is what RIS is for.

I am still puzzling over chapter 7 of the manual which discusses 5 picosecond timing resolution in connection with 40 picosecond sampling resolution.  I wonder if that is based on 5 picosecond resolution in the time delay counter which measures the difference between the trigger and sample clock.  Usually that is irrelevant because samples are only saved with up to 40 picosecond resolution in this case in the acquisition record and any extra resolution from the time delay counter is lost.  Maybe LeCroy is retaining the 5 picosecond timing resolution somehow outside of the acquisition record.

With the same design, Tektronix discards any extra resolution from the time delay counter.  (1) But timing resolution greater than the acquisition record resolution is still possible when measurements take the vertical signal levels into account.  That is how digital time delay counters produce timing resolution much greater than their sampling rate.  Tektronix uses something like interval arithmetic to calculate and display measurement results with the proper number of significant digits and I wish other DSO manufacturers did the same thing.

(1) Going by memory, the Tektronix 2440 TDC has a timing resolution of 0.5 picoseconds (or maybe 2.0 picoseconds) but this is obviously meaningless.  The extra resolution supports gain, offset, and perhaps linearity calibration of the TDC and I suspect LeCroy does the same thing.

[rhb]

If you want to discuss pulse generation circuits, I'm fine with that.  But I have no desire to rehash 3 semesters of grad school mathematics.  Proving the orthogonality of the Fourier basis once was quite enough for me.

If EEs want to have their own special meaning for ETS, they may do so.  But I am not interested in such abuses of language and mathematics.  Wiener, Shannon and Nyquist got it right and stated it properly.

[ocw]

My prior post showed the comparison evaluations of short transmission line jumpers as measured by my Tektronix 1503B TDR and Agilent E7495A FDR/Station Test Set.  I am more commonly evaluating lines from 100 to 2,000 feet long.  That first attached picture shows the inner and outer conductors of some slightly overheated 3 1/8" rigid line that I replaced.  There wasn't much left of the Teflon insulators near those points.

With my being more concerned about longer lines I thought that I would include views of about a 175 foot long line to a receive antenna.  It is mostly LMR400 cable although there are some shorter pieces of other cable also included.  You can see those connections much better on the E7495A FDR.  With saved measurements, you can see deterioration of connections or in the line itself.  You can also make measurements on the specific frequency or range of frequencies primarily used.  For comparison, I also included a Riser Bond 1205CX measurement as well.

[rhb]

Why is there a reflection at around 140 ft on the Tek and RB displays and not on the Agilent?

Also what is the frequency step on the Agilent?  Does the Agilent correct for transmission loss?  It certainly looks as if it is and it would be much easier to do in the frequency domain than in the time domain.

Thanks for posting these.

[ocw]

Why is there a reflection at around 140 ft on the Tek and RB displays and not on the Agilent?

You are missing the obvious.  Note what the Agilent reports at 152 feet vs. the end of the line at 176 feet.  That is what the Tek and RB report at a slightly closer length.  That is a connection point between the end of the LMR400 and the more flexible line used in the rotator loop.  Note the "noisy" return loss of that rotator loop cable.  You only see that on the Agilent.

Also what is the frequency step on the Agilent?  Does the Agilent correct for transmission loss?

As it shows on the Agilent display, I left it in the auto-frequency mode to automatically chose the best frequency range for the best length resolution.  It chose 375 - 672.485 MHz.  As the Agilent shows I selected the mostly proper LMR400 cable.  The Agilent takes the velocity factor and attenuation of the cable into account when preparing its measurements.

The receive antenna is a special one which I made for TV channel 6 through the lower half of the FM broadcast band (80 - 98 MHz).  It is a ten wide spaced element Yagi antenna almost 100 feet high.  That's why the return loss of the antenna was so high--it wasn't made for those higher measurement frequencies.  My concern was line evaluation at a higher frequency where its limitations are more obvious with greater location resolution.

[rhb]

Without readable  scales it's a bit hard to compare things.  Does the Agilent actually use a continuous sweep? 

I was actually asking about what Joel Dunsmore calls "reflection masking" rather than intrinsic cable attenuation.   In geophysics we call  the portion of the incident wave reflected at an interface transmission loss.  Physics uses the same terminology for EM.

[ocw]

The Agilent automatically places markers on the four distances with the least return loss and shows those distances and RL figures.  That obviously makes it easy to see any change in future measurements.  For the two TDR's I moved their one marker to the end of the coax.

Does the Agilent actually use a continuous sweep?

My spectrum analyzer shows that the frequency range chosen (either automatically or manually chosen) is swept continuously in frequency.

[vk6zgo]

There are a number of factors influencing the use of a TDR or Frequency Domain Reflectometry (FDR) measurements.  While I have used a Tektronix 1503B and various Riser Bond TDR's to locate and then correct many cable problems, FDR's are generally replacing TDR's since they do a better job of locating most faults.  See:  https://www.anritsu.com/en-US/test-measurement/solutions/en-us/distance-to-fault

Examples of this are shown in my attachments.  I am comparing a Tektronix 1503B to a Agilent E7495A.  The best example is probably comparing an inexpensive Chinese 2M BNC to BNC RG58 cable.  The end of the cable is connected to a 6 GHz 50 ohm load.  The Tektronix TDR display indicates that it is perhaps not the best cable in the world, while the Agilent FDR display clearly demonstrates that besides the connectors being marginal, the cable is not the best quality either.


The RG214 cable comparison shows the differences when measuring a better quality cable.

Additional cables are shown on just the Agilent FDR since the differences are more easily seen on that instrument.

I was confused by the distances in feet, not matching what I thought meant  "2metre  long" cable, not realising "2M"in this context was a part number.
I lost interest, but now I need to revisit your interesting postings.

[ocw]

I was confused by the distances in feet, not matching what I thought meant  "2metre  long" cable...

It was a 2 meter long cable being measured.  It is just that the cheap cable did not meets its velocity factor specification.

[tomato]

If EEs want to have their own special meaning for ETS, they may do so.  But I am not interested in such abuses of language and mathematics.  Wiener, Shannon and Nyquist got it right and stated it properly.

You want to discuss instruments designed by EEs on an EE forum, but you reject the conventions used by EEs with a condescending attitude?  Good luck with that approach.