That takes an I and Q source with better accuracy (both phase and amplitude) than you want in the result; an oscilloscope sample, with two channels, is the ubiquitous and available box for this job.
A synthesized I and Q (data synthesis, not signals) would work, but only sees ONE component, and a real signal has some finite frequency spread to consider.
Practically, it doesn't; the phase is indeterminate when the signal is low or down in the noise, and the statistical weight function (in previous post) knocks it out. Things like 'the ends of the acquisition' are broadband noise, not peaked at one frequency. No peak amplitude means no statistical weight. You can also just ignore data below a threshold, with similar effect.
Excuse me?? What exactly was "awful" about them?
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Of course! The best of relationships have their ups and downs. Why haven't you fixed it? They're readily accessible repair-wise, not like those Chinese things John's always banging on about.
I'll have to look that one up; not familiar with it.
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The secondary-emission versions had terrible contrast and the tubes didn't last. The storage mesh ones looked better (well, better contrast but fuzzier traces) but the writing rate was terrible.
Neither allowed multiple simultaneous event storage, which is what you need to debug many transient bugs.
The scan conversion tube things cost more than a Cadillac and were gigantic. Just one trace. I have one of the tubes around here somewhere, in a gigantic mu-metal pipe shield. Bernard will still sell you one; he has a stash of old tubes.
A $350 Rigol scope can capture two signals simultaneously at 100 MHz bandwidth and 1 G samples/second, with infinite storage, sharp color traces, after-the-fact measurement cursors, USB image capture, and computer interfaces for test automation.
My bench scope is the 4-channel 500 MHz version, even better.
No analog scope could ever store that.
-- John Larkin Highland Technology, Inc lunatic fringe electronics
The difference is that the convolution h*g has transform HG whereas the correlation h star g has transform H G^* (the complex conjugate). A self-convolution has a complex-valued transform, whereas an autocorrelation is a purely real, even function of both time and frequency.
But the FFT does not in general give correct samples of the true continuous-time transform even in the band-limited case. The function has to be periodic in the sample length.
Also as I said above, correlation methods give "unexpected results" for the phase shift between waveforms with different shapes, e.g. VCO and reference in a PLL, so it's far from a general method. It would be seriously irritating to be scoping a phase-frequency detector and having the scope tell you that the phase was servoing around -37 degrees, for arbitrary values of 37.
The edge-triggering method doesn't have that problem, and if it's good enough to keep the waveform stable on the screen, it's good enough to measure phase to scope-level accuracy. Fancy scopes have fancier triggering algorithms--they don't use LM710s any more.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net https://hobbs-eo.com
Not if you only have, say, 1.5 periods in the sample.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net https://hobbs-eo.com
Oh, really? Mine's 44 years old and still going strong - and it's not the only one left, far from it! And the contrast on mine is just fine. Setting the controls to get a perfect image for the particular event under examination does take some fine tweaking, I'll grant you that much, but the more you do it the quicker it comes.
I do also have a high-end Tek DSO for that sort of stuff, but I have to read the FM every time I switch it on, which is no fun at all. In fact it typically takes me several minutes just to find the 'on' switch.
transient-digitizer.html
Woah! How did we suddenly get from "We want to measure the phase shift of a pair of sine waves in the roughly audio sort of range" straight to
7GHz picosecond stuff?? That's a drastic change of spec! You should be in politics, mate! :-DTotally irrelevant to your original question: "We want to measure the phase shift of a pair of sine waves in the roughly audio sort of range."
Will that scope of yours still be alive and kicking in 44 years' time? I think we all know the answer to that. ;-> :P
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While I'll agree about the awfulness of analogue storage scopes, I'll note that some had dual /beams/. Hence you could capture two simultaneous events without having to resort to alt/chop scans.
True; a good sample of something that repeats would be a thousand points, covering thirty points per cycle and thirty cycles. Analyzing the lowet and highest FFT frequencies would be unnecessary, just snip a suitable bandpass from the midrange and ignore DC and the Nyquist wall and environs.
At 1.5 periods, the zero-crossing would be the only good option, and things like curve-fitting would actually make sense. But, the phase resolution is unlikely to be better than sample time granularity when doing that, and it'd be better to fall back on Lissajous-like analysis (which amounts to finding a time-shift that minimizes the A(T) versus B(T + tau) plot's enclosed area).
I always prefer the FFT solution when the signal is narrowband, because there's a lot of white-hoise rejection, and S/N improvement means better precision. Zero-crossing can't help but absorb all the noise in the nearest datapoint.
Absolutly on topic. An interfaced digital scope is the easiest way to automate the phase measurement.
Most of our Tek analog scopes have died. I don't think any of our digital scopes have ever failed.
The digital scopes keep getting better and cheaper, and I wouldn't expect one to be interesting 44 years from now. But they's probably still work.
A 7000-series scope with minimal plugins originally cost as much as a nice car. A far superior Rigol now costs as much as a midrange bicycle.
Tek and Keysight are now selling their own scopes in the $25K to $1M range, and rebranding Chinese stuff on the low end.
-- John Larkin Highland Technology, Inc lunatic fringe electronics
I remember the Tek dual-beam scopes. The power supply was a separate box that you parked in the bottom of the cart. I can lift my 4-channel
500 MHz Rigol with two fingers.The guys out at Lawrence Livermore had some custom 4-beam scopes. Racks and racks of them, with cameras.
-- John Larkin Highland Technology, Inc lunatic fringe electronics
A 4 GHz sample rate would be fine to analyze KHz sine waves... roughly a million samples per cycle. Besides, Dr Shannon said that you can reconstruct a perfect replica of a signal if it was sampled above the Nyquist rate.
Curve fitting around the zero crossings can get time resolution way below the sample period. It also takes out noise and amplitude quantization errors.
If we know the sine frequency, and the scope sample rate (both of which which we do) then all you need is one cycle worth of samples. You can effectively then glue copies onto both ends of the sampled waveform and make it look like an infinitely long acquisition.
If curve fitting, all you need is one rising edge on each waveform.
1.5 cycles of acquisition would be fine in my case.Unless you filter or curve-fit, both of which include multiple points.
-- John Larkin Highland Technology, Inc lunatic fringe electronics
There were others, e.g. a Telequipment DM63 which is light and as portable as a Tek 465.
In that case a couple of BNC leads could also hold it off the bench :)
Are they scopes or periscopes?
I didn't understand that until a local friend pointed me to .
Thanks. O(N*log(N)) is better than O(N^2). Maybe one day I'll understand Phil's response too.
We have a need for this in decoding signals from a Watson-Watt DF receiver. The current designer planned to use Schmidt triggers, and caused a discussion about the noise problems tat has.
Clifford Heath.
Tek sold the Telequipment scopes in the USA for a while. I had one. It was horrible.
No problems so far.
And not a couple of BNCs, usually 4 or 5.
That's a great Ikea workbench, but they don't make it any more.
In that pic, there are cameras (real film cameras, not Polaroids) hung on each scope. Maybe they were 8-beam, not four; It's been a while since I got the tour.
They also had air-turbine spinning-mirror cams that exposed a circular strip of film, to get time-series images of their shots. They would spin up a bunch of those and just wait until they all accidentally sync'd up, then they fired their gadget.
Snapping one-time waveforms was tough in those days. Now we just digitize things.
-- John Larkin Highland Technology, Inc lunatic fringe electronics
Streak cameras still rule for the fastest stuff. Streak cameras have some modest gain, as well, which is helpful--light has to be pretty bright to get many photons in a picosecond.
I almost persuaded IBM to get me a streak camera scope for my tunnel junction work, but it was almost $100k, so I had to settle for a Tek TDS
7704A (7 GHz, 20 GS/s). Of course that runs an out-of-maintenance version of Windows, so I wouldn't dare attach it to a LAN nowadays.Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
yeah, but... the fit will see five points, near the zero crossing, and the FFT will be using 500 points. Go big when you can. The prize is an order of magnitude better signal/noise.
But the correlation method is worthless for general waveforms. For instance, the correlation of two rectangle waves has large flat regions, and the zero crossings are not 180 degrees apart. Which gives you the relative phase?
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
My candidate algorithm used FFT and calculated phases then averaged. The averaging has a funny statistical weight, though: any low-amplitude frequency channels have large phase noise. If you have a known frequency of interest, full correlation is more work than window-and-average,
The weighted average is kind of a least-squares fit, giving only the 'm' of the 'mX +b' formula that comes from line fitting.
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