Does a capacitor charges smooth, or in stairs?

[StillTrying]

Are you viewing the open circuit end of the cable rather than the driven end, I don't know why your first step is so high in Reply#49.

[RoGeorge]

OK  These are with a Tek 11801 & 20 GHz SD-24 sampling head.  I fed the coax stub through a 150 ohm resistor.

10-12 ft coax

(Attachment Link)

50 cm



16 cm

(Attachment Link)

(sorry about the burred image.  I didn't notice it until I posted it)

(Attachment Link)

The 250 mV step has a <20 ps rise time.  The only thing changing is the travel time and the capacitance.  As the coax has approximately the same capacitance per foot, the number of steps stays constant and the only thing that changes is the time delay for each step.  If I expand the vertical scale a lot I can count about 13 steps before the steps fall below the noise and quantization.

Q.E.D.
Quod erat demonstrandum. 
It has been shown.

Have Fun!
Reg

Wow, the cleanest stair-steps reflections I have ever seen!   

Can you repeat the experiment with a real life capacitor, too, to see if the stair-steps on a capacitor are as visible as the ones seen on the coax cable, please?

Not sure what type and value of a capacitor will be the most advantageous for the experiment, maybe one with large physical dimensions, and with the plates rolled in a cylinder, rather than a tantalum or a MLCC.

[rhb]

Are you viewing the open circuit end of the cable rather than the driven end, I don't know why your first step is so high in Reply#49.

This is the reflected signal seen at the driven end.  The other end of the cable is open.  So each step is a 2 way trip down the cable and back to the source end.  Without the resistor it would be two big steps. This is the corner of the 2nd big step produced by an open circuit line.   Take a look at my "Testing RF connectors and cable"  thread.  There are lots of examples of various tests there.

RoGeorge, Let me think about how to make a test that is not obscured by other artifacts.  As the line length gets short things start getting complicated by parasitic inductance.

If I double the resistance it should double the time constant and the number of steps.  I think that a 1500 ohm resistor and the same piece of RG402 as my last photo would be the best.  That should show >100 steps and still be resolvable.

Have Fun!
Reg

[rhb]

I don't think any capacitors are designed to be constant impedance. Certainly rolled foil capacitors cannot be as the diameter is constantly changing.  So both the capacitance and inductance per turn is changing constantly from one end to the other.  In addition there is inductive and capacitive coupling from layer to layer.

The changing impedance is going to produce  a continuous series of small reflection events rather than large discrete events at the ends.    That will tend to make the response look like a piece wise linear approximation to an exponential rather than a stairstep approximation and thus very difficult to show clearly.  The stairstep is the result of the derivative of the impedance being zero except at the ends.

A flat microstrip transmission line of trapezoidal shape would be the simplest way to demonstrate the effect of changing impedance along the transmission line.

The point here is that the exponential is a series of small steps once one takes the finite dimensions of the capacitor into account.  And in the limit as the size becomes infinitesimal, it becomes an exponential.

It's probably easier to calculate the response of a hypothetical capacitor than to measure the effect in a real one.

Reg

[T3sl4co1l]

Like I said, the electrical length of a typical film or ceramic capacitor is so short, and the impedance so low, that you'll be lucky to observe anything, even with a ps scale generator and scope.

Tim

[eti]

Capacitors are incredibly versatile; they can charge on stairs, in hallways... basically anywhere.

[rhb]

Just for grins I tried a 750 ohm series resistor.  The impedance mismatch between the source and the resistor became so large that it rings like mad between the source and the resistor.  Bear in mind that this is a thru hole metal film resistor, so it also has significant inductance at 20 GHz.

The first photo is the full step response:



The second is a detail from the 2nd step showing the effect of the reflections during the RC constant:



As you can see, there are a lot more steps visible because I increased the RC constant by 5x.

As has been pointed out, the impedance of a capacitor is generally low, though not at all frequencies.  This is why high gain stages need to have the electrolytic caps bypassed by a small ceramic to prevent oscillation.  It would well nigh impossible to match a capacitor from DC to 20 GHz unless it was made from a very good piece of coaxial cable as in my examples.

The next step for these two resistors is to examine them with the nanoVNA.

In general, capacitors do not resemble transmission lines and therefore do not behave the same way.  They can be accurately described in terms of transmission line theory, but they won't *look* like a transmission line capacitor.

I'd like to add that these sorts of tests are wildly sensitive to the connection make up and often not easily repeatable.

Have Fun!
Reg

[StillTrying]

Are you viewing the open circuit end of the cable rather than the driven end, I don't know why your first step is so high in Reply#49.

This is the reflected signal seen at the driven end.

If I simulate a 40cm 50R cable driven by 150R I still can't see where your very large first step comes from, it's about 4 times higher than what would fit anywhere.

[rhb]

Read an app note about sampling scopes and step responses.  The open end produces a reflection of +1.  So you see the initial step and then a 2nd step.  A short produces a reflection of -1, so you see a step up and then down to form a single pulse.

The latter was the way short pulses were created for many years using a coax stub and a mercury wetted relay.

Reg

[StillTrying]

Your very large first steps must be due to probing the wrong end of the 150R, Pulse_Out rather than Driven_End, of the cable.

[rhb]

There is *nothing* wrong.  Take a look at the photo of the short piece of RG402 with no connector at the end.  That's the circuit.  It's a series resistor and capacitor using transmission line for the capacitor.  There isn't any place to connect the sampling head at the far end of that short piece of RG402.  If it were connected there wouldn't be a +1 reflection coefficient and thus no stairstep.

The signal is a 250 mV, 200 kHz square wave with a <20 ps rise time.  The sampling head has a <15 ps rise time.    Look at the time scales.

The SD-24 head generates a square wave and displays the outgoing and reflected signal appearing on the input.  The first big step is the outgoing pulse.  The 2nd big step is the reflected pulse from the open circuit at the end of the transmission line.  The staircase is a bit of rounding of the edge of the open circuit reflected step as the signal bounces in *just* the coax.  The large steps are the delays in the sampling head circuit getting to the 3.5 mm input connector and back.

This is basic time domain reflectometry with a high end instrument designed specifically for the task.  As I suggested before, find an app note on TDR.  It will be quite educational.  I've had more fun with the 11801 & SD-24 than any other instrument I've bought (except guitars and harmonicas ;-)

Have Fun!
Reg

[Labrat101]

RoGeorge
  Wow, the cleanest stair-steps reflections I have ever seen!   

You are all chasing a Rabbit down a Hole.
Sending a pulse or a signal down a coax ,
50 ohm or what ever.  That is not terminated the signal has to go some were .. so it will go backwards.  Echo . So there will be a reflection.
There will be a time difference.  There fore you will see steps .  SWR will not be 1:1 on any open Transmission line .
  Pulse . or Square wave . is made up of all waves . and hence it will break down back to a sine.
  There is only one true wave form and it a sine ..  That why light can't go round corners .without
Reflections  call what every you like but its the same.
It's like ripping water when a ripple gets to an edge it bounces back.  Whether you see it or not it's there..  And there is never a square wave in Water .. or light etc. etc.
Only thing at the bottom of a Rabbit hole is ...    €¥)^(¿

Also Notice How the original Author Who Himself said it was Only practical on paper.
 As for all Us Nerds . including myself . .
 Paper theories are very good as long as they stay in the right place . 
  You can always work it out with a pencil ... but taking medicine will also work ..  

 PS.  one nanosecond light travels about 0.3 meters measure the distance between the steps
     and you will find the refection point in your coax . or the the dialectic failure point .
     if the coax is perfect with no defects it will give you the length of the coax being tested.
     A tape measure would also work without the complications.
      This Method is good for finding bad connections in long data lines and has a high accuracy
      to locate the damage section of cable and repair it . used it myself to find bad broken  transmission line .. . but it does not prove that a Capacitor charges in steps .
   it like a saying a fish does not breath air . No it removes it from the water (H20.)

   Still a large Rabbit Hole ..

[rhb]

I received a Rigol DS1202Z-E today.

First the full step response using one of Leo Bodnar's <40 ps 10 MHz square wave generators and a 50 ohm thru termination.



Then a vertical zoom on the upper edge of the step:



What's really significant here is that Rigol is dithering the sampling clock and the jitter is under 100 ps so it shows a <100 ps step quite clearly.

That in turn implies that the AFE has a *real* BW of 3.5 GHz!!!

Have Fun!
Reg

[StillTrying]

The steps are 1ns apart so it's just some sampling thing. What's it triggering on 12 screens away.

This Siglent pseudo ETS DOTS mode shown by rf-loop looks interesting.

https://www.eevblog.com/forum/testgear/siglent-1104x-e-or-2204x-e/msg2118325/#msg2118325

I don't know if it still works with 500MSa/s on a fast edge.

[rhb]

If the sampling is dithered at 100 ps intervals, then the result is *exactly* what one would get of an AFE with >1.75 GHz BW and no anti-alias filter. 

Whether that is the case or it is some mundane programming error is unknown at present.  But it very much looks to be sample time dithering rather than a programming error.  I do *not* get the same result from my DS1102E with the same setup.

rf-loop's post is  meaningless.  There is no indication of the actual input waveform.  I'm using a *well* vetted signal source.  My <40 ps pulser came with a CSA803A & 40 GHz SD-30 sampling head step response plot showing a 37 ps rise time.  I can easily feed the <20 ps 11801 calibrator  pulse to the Rigol.  It won't change the result.  I've used the Bodnar step generator to test my  1 GHz Tek 7104 analog scope.  And it shows a <350 ps rise time.

In short, I have a wide range of hammers from an ounce or so to 30 pounds.  So I can beat on things rather hard.  Naturally I don't smack electronics test gear with a 30 pound stone boat, but I have the electronic equivalents.

Please look at my posts to the thread RoGeorge started.  The 11801 & SD-24 were *very* expensive kit in the early 1990's.  If you think those are erroneous you need to try harder.

Have Fun!
Reg

[StillTrying]

That in turn implies that the AFE has a *real* BW of 3.5 GHz!!!

To me the <100ps rise times imply timing errors rather than a 3.5GHz AFE in a £400 scope.

I've estimated where the trigger XY point is in comparison to the visible screen. for your 1ns steps capture.

[rhb]

I was playing with the pulser feeding a tee and coax this morning.  There is something odd going on with the vertical settings. Here it is with the trigger  on screen.  So it is *not* related to the trigger position.



I'm going to feed the SD-24 to the AFE and look at the TDR response.  That should establish whether it's ringing in the input transmission line or some artifact of the DSO implementation.

BTW My calculation was wrong.  The pixels are at about 100 ps spacing.  So the calculation should have been 0.35/200 ps.

My Keysight 33622A has a spec of <1 ps jitter, so if I set up a low amplitude square wave and use the external trigger input I should be able to measure the DSO timebase jitter.


Have Fun!
Reg

[RoGeorge]

That wave shape is so weird because of 3 things:

- DSP processing on the oscilloscope side - they applied all kind of filters to make the image look good, including non causal filters (e.g. Fourier transform can not be applied to causal signals, therefore it should NOT be used for real time signals, Fourier produces "artifacts" because the resulting spectrum is non causal) - might seem like gibberish talk, but this is how it works.  For example, the downwards peak, seen just before the signal starts to raise, is fake.  There is no reason for why a signal will first go down before going up, that dip before the signal goes up must be the result of non-causal filters (or other kind of non causal digital processing messing with the samples), that sort of "premonition" artifacts can never to be seen in physical systems, like in an analog oscilloscope.  Our physical world is causal.
- jitter (phase noise) in the oscilloscope's clock
- in Rigol, the triggering moment is detected in software

Reducing the delay between the triggering point and the piece of shown waveform on the display helps reducing the jitter in the final image (for a given phase noise, the jitter accumulates in time).

LATER EDIT:
------------------
One more thing, the 0.35 factor to determine the ratio between raise time and bandwidth of the oscilloscope, it is NOT true any more for digital oscilloscope.  That formula is valid only for analogue oscilloscopes, with analog filters and normal roll of (analog filters are always causal).  With DSP filters, waveshape corrections are made non-causal (in anticipation of a signal or an edge that is yet to come), and that 0.35 formula is now unrelated with the raise time shown in the "fake" waveform.

The Rigol screen capture speaks for itself how fake that signal is.

In this Q&A from Tektronix,  the factor is 0.45 and is valid for the kind of DSP they apply, but in general, the coefficient depends of the filters, and since DSP filters can be of any kind, the formula is not valid any more:  https://www.tek.com/support/faqs/how-bandwidth-related-rise-time-oscilloscopes

In short, a low range digital oscilloscope, like a Rigol DS1202Z-E, can not deal correctly with that kind of signal, and is in no way a match for the performance of a high end 20GHz Tektronix SD-24 analog sampling head.

[Labrat101]

That in turn implies that the AFE has a *real* BW of 3.5 GHz!!!

To me the <100ps rise times imply timing errors rather than a 3.5GHz AFE in a £400 scope.

I've estimated where the trigger point is in comparison to the visible screen.

(Attachment Link)

I have to agree your trigger is off the screen . and that is an acquisition error or the scope is set up wrong.

RNS

[rhb]

The trigger point is shown in the figure in reply #67 and is on the screen.

The use of zero phase, non-causal filters in DSOs is a major complaint of mine.  It's not the proper filter.  Moreover, the correct interpolation filter is *not* a sinc(t).  The correct filter is the minimum phase impulse response of the actual anti-alias filter used.  To avoid excessive ringing the corner frequency for the anti-alias filter should be  no more than 67% of Nyquist and for really good step response 50% of Nyquist.

The "Scope wars" thread will measure jitter among many other things.  I'm going to show what they are doing wrong and how it should be done.  The failure of a DSO to produce analog scope trace quality is a design failure.  It is not inherent in the scope being digital.  It's driven by the desire of sales and marketing to advertise a scope as having twice the BW it would have if it had a decent step response.  And the naive buyers who don't know enough about the Fourier transform to realize they are being swindled.

My LeCroy DDA-125 has a claimed 1.5 GHz BW and has the measured rise time for the 0.35/BW to match that.  It also has 20% overshoot on a fast step.  My DDA-120 has a 350 ps rise time on a stated 1 GHz BW and 17% overshoot.  It's worth noting that Nyquist for the DDA-125 is 1 GHz in 4 channel mode. Can you say "aliasing"?

The EE "ideal low pass filter" is only ideal if you don't care about the time domain behavior.  If you care about the time domain behavior you must apply a long taper to the BW.  If you make the corner 50% of Nyquist, the time domain step response is a minimum phase sinc(t)**2 which suppresses the sidelobes very well.  One can do better with a Gaussian or sech(f) taper which produce no ringing, but at the cost of slower rise times.

With regard to Tektronix I've been waiting since late April for a step response from the 3 series scopes.  I stated I didn't want to bother with a demo unless it had less than 3% overshoot on a <40 ps step.

Have Fun!
Reg

[StillTrying]

should be able to measure the DSO timebase jitter.

On my trigger diagram I was thinking maybe the trigger's low Y position was an even a bigger problem than the X position.
If the trigger position was going to do some clever sub 1ns position timing it wouldn't have any slope to work with if every ADC sample at that trigger low Y position was 00, - other than wait until the input V and ADC values start counting up from 00 - at some random time.
IF it does work like that I can imagine(why not!) up to 1ns of jitter creating some nice stairs somewhere.

On your latest capture, a 1 Vpp ? arriving at the scope on 10mV/div. shouldn't overload or out of range anything, - even the trigger!
- in theory.
DS1202Z-E  1 mV/div to 499 mV/div: Offset Range ±2V

While I'm there:
Trigger Level Range  Internal ±5 div from center of the screen

But even with the trigger's X and Y within the screen area you've beaten your record near infinite rise times with some slightly negative ones.
Whatever it's doing I don't think a scope showing any negative rise times on relatively simple waveforms is much use, I hope you've still got its box!

[Labrat101]

The failure of a DSO to produce analog scope trace quality is a design failure.  It is not inherent in the scope being digit

Try using  a good analog scope and then all those filters are not needed.
You see what is really there and not a computation Of the signal .
Adding the wrong filter in  the wrong place does not solve a problem. 
Tipex would also work . Unless you have a high end DSO the signal is being processed by  simulation. So if you play enough with filters etc you can get what looks good.
But is it correct . ?

[rhb]

Is a Tektronix 1 GHz 7104 "good enough"?  There is implicitly a BW filter on every analog scope.  The step response tells you what that filter shape is.

Is a 1.5 GHz LeCroy DSO "high end"?  The LeCroy has all the jitter analysis tools enabled, but I've not tried them out yet.  Not really much point until I have a GPSDO clock input set up to feed it.

I spent 30+ years in the oil industry writing and fixing seismic DSP codes.   That is far more exotic DSP than anything the EE community does.  Always has been.  In the 60's when ADCs barely existed we could live with 4 ms sample rates and had the money to pay for them and the computers to process the data.  A common seismic imaging operation today  takes 10,000 to 20,000 core clusters 7 to 10 days to complete.  The input is 10-15 TB.  Each output sample takes several gigaflops to compute.  What's more, this is not a one shot.  It's iterative.  You run the job, look at the results, update the velocity model and repeat.

Texas Instruments was a wholly owned subsidiary of Geophysical Services Inc created specifically to build seismic recording equipment.

The trigger point is shown on the last plot I posted. The signal is about 900 mVpp.  It's adjustable, but I have to run a program on the PC to do that and I don't have a Windows machine I can boot easily at the moment.

I'm afraid I don't grok "negative rise times".  Where is that from? I think the persistence for that plot was 1 second.

As best I can tell what's happening is the scope is triggering and the steps are slightly less than 200 ps.  So the vertical segment is samples at various points on a slope which then gets displayed at the same time.  As I remarked before, the 11801 will tell the truth about what the front end looks like.  If the steps are ringing in the front end they will show up as reflection events on the 11801 & SD-24.

Have Fun!
Reg

[StillTrying]

I'm afraid I don't grok "negative rise times".  Where is that from? I think the persistence for that plot was 1 second.

Well it's not going back in time by a massive amount.

The first part of the trace in the bottom left very near the trigger point looks about right and sharp, but the thin spike rising from there has no fall time, - at least not in the forward time direction.
Perhaps 1sec of persistence wasn't enough to catch any of the fall time, but there's nowhere else where a full division or even part of the trace is missing.

At 2ns/div I'd expect the next rising edge in the middle to look like it's always sloping slightly forward in time even if the slope is only around 5 degrees, at least to me it looks like it's curving back in time but only by about 2 or maybe 3 pixels, I make it 1 pixel width = 25ps.

Perhaps it is doing quite a bit of 25ps to 100ps dithering to capture every bit of the waveform, but they're forgetting to correct the dot sample positions by 1 to 4 pixel widths.

Could it be some interaction between the charging steps and sample rate both being 1ns wide.

Perhaps it's all fine and only some of us are seeing the verticals as unrealistic!

[rhb]

I think that is just jitter.

What caught my eye is the change from linear interpolation of pixels on the DS1102E to what looks like clock dithering on the DS120Z-E.

Leo's pulser has a few ps of jitter.  Not specified, but he's tried to minimize it. He's also working to a pretty brutal price point.  But I have other reference sources with less than 1 ps of jitter.  So just give me time.

More in the "Scope Wars" thread.

Have fun!
Reg