Scope rising time

[Technojunk]

I just made everything on the connector, and this works I think!
   

[saturation]

Yes, if folks read the app notes, its explains a lot of what we discussed here.  Alas, its a pdf file, so linking it has no photos to see right away.

http://www.linear.com/pc/downloadDocument.do?navId=H0,C1,C1154,C1009,C1028,P1219,D4138

Jim Williams is one of the great analog designers, we should put a face to the name:



http://www.eetimes.com/special/special_issues/1998/timespeople98/williams.html

Not sure what that is, it's really low level, a 167kHz radio station being picked up? Or from a switching power supply somewhere? Does not look like a signal from the avalanche transistor to me, or it's just not breaking down and this is the capacitor charging? I would just solder a female BNC connector to it, they're cheap. And keep wiring outside the coax as short as possible. That's probably why the i9t guy used a shielded Pomona box with integrated BNC connector ($$$). The original appnote (I hate how people keep linking to the website from one guy who built it instead of the Jim Williams appnotes) might contain more details and pictures.

[alm]

That looks much better. The 1.2V amplitude seems a bit low (does it think there's a 10x probe attached?), but the scopes bandwidth might be a factor, plus the capacitor selection (I think says adjust for about 10V amplitude with a sampling scope). That attached scope probe might influence things, since it adds an extra 15pF or so of capacitance, which is quite a lot.

[Technojunk]

There is no /10 probe attached attached!
The only strange think, is that it's not a 3.5nS rise time! (100Mhz scope)

[sigxcpu]

It is 1.5 subdivisions (wrong cursor position).
That is 5ns = 1 div = 5 subdiv => 1.5ns rise time. Very nice.

[Technojunk]

I dont get your math..
Could you paint the right way to set the cursors?

[marianoapp]

The only strange think, is that it's not a 3.5nS rise time! (100Mhz scope)

350ps = 0.35ns

I dont get your math..
Could you paint the right way to set the cursors?

the rightmost cursor should be set at 90% of the rising edge to measure the rise time. In the current position you're measuring the pulse width.

[alm]

It should be set at 90% of the signal amplitude, not the amplitude of the signal measured by the scope. If the pulse is faster than the scope, its amplitude will appear smaller. That might be the reason why the rise time appears so fast, if the real amplitude something like 10V. This is one of the issues with using a pulse instead of a step, and why Jim Williams added a charge line to increase the pulse width in a later design.

[Technojunk]

I dont know what I did, but now the amplitude is much larger:


Is this good? I was thinking the rise time is a little too small, it have to be 3.5nS I think (100Mhz scope), but he, with 2 bench supplies in series! I will make a DC/DC converter. And built everything nice in a box.

@alm:
What does a ''charge'' line? and where can I find some schematics?

[jahonen]

For me, that result looks quite OK, if you adjust the signal amplitude using volt/div and vernier controls so that you can use the 10% and 90% lines on the scope graticule, i.e. zero volts adjusted to the next line below the 10% marker and top of the pulse adjusted to next line above the 90% line. I believe you will get something quite close to 3.5 ns when you adjust the markers so that they will coincide with crossings of 10% and 90% lines.

I don't think that knowing actual pulse amplitude is required here, since very idea of having the pulse generator of very fast pulse is just that it is much faster than the thing you are testing, so that results are not effected. When bandwidth drops, the amplitude will fall and rise time will increase in a such way that correct rise time is obtained. 1/?t figure is of no value here, just calculate the bandwidth from 0.35/?t, so 4 ns would be 87.5 MHz.

Here is a picture of the PCB I intend to eventually build this thing, with DCDC-converter integrated.



I'll see how this thing performs, I expect my Agilent MSO6034A to show something like 1 ns risetime, if everything works as expected.

Regards,
Janne

[alm]

@alm:
What does a ''charge'' line? and where can I find some schematics?

A charge line is an unterminated piece of high-frequency coax (i.e. not RG58, he recommends hard line), it's used to stretch the pulse. See AN-94 for details. This is basically an improved version of his AN-47 design.

I don't think that knowing actual pulse amplitude is required here, since very idea of having the pulse generator of very fast pulse is just that it is much faster than the thing you are testing, so that results are not effected. When bandwidth drops, the amplitude will fall and rise time will increase in a such way that correct rise time is obtained. 1/?t figure is of no value here, just calculate the bandwidth from 0.35/?t, so 4 ns would be 87.5 MHz.

You really need the original amplitude for calculating rise time. Otherwise, a resistive divider would improve the rise time (half the amplitude = half the rise time assuming the transition is linear). This is why every professionally designed pulse generator for transient response / bandwidth testing (eg. Tek PG506) will use a pulse width that's much larger than the rise time, and why Jim Williams released an updated version with charge line. The AN47 design can work, if you have some way to measure the real amplitude (eg. the sampling setup Jim Williams used).

[Technojunk]

Here you go:


The right cursor is a bit to far to the left, but he, lets say 1.9nS for a 100MHz scope!
I build everything in a metal case, so less radio and wifi shit on it.

What do you say?

[jahonen]

I don't think that resistive divider would change the transition time, as the final voltage is also changed, but it will affect the slew rate, which AN-94 deals with.

But, I have to admit that after experimenting with LTSPICE it seems after all that short pulse is not directly usable for rise time based bandwidth measurement.

However, it is also known that a very short pulse inputted to linear network produces the impulse response of the linear network and Fourier transform of the impulse response is the frequency response of the linear network. Thus it must be possible to calculate the bandwidth from the output pulse, even if the amplitude of the input pulse is not known. The relative width of the Gaussian pulse determines the bandwidth, thus the method of measuring the pulse width with some care of choosing the points is not so far fetched after all.

Regards,
Janne

[alm]

You're correct, I misspoke, it's slightly more complex. The issue that I remembered was from a Tektronix training video that I watched once. They had a generator with a 50 ohm output impedance and 20pF output capacitance. It had a rise time of 2.2 ns (t_10%-90%=2.2*RC). Then they added a lo-Z 500 ohm, 1pF probe. This decreased the amplitude by about 10% (50/500ohm voltage divider). The new output impedance of the system (including the probe) is 45 ohm (50 ohm in parallel with 500 ohm), the new output capacitance is 21pF. This gives a rise time of 2.2*45*21p = 2.08ns as the scope sees it.

In my opinion, measuring a system with an unknown signal is very hard, but I'd love to be proven wrong. In the AN47 appnote, Jim Williams mentions that about 82% of the 2N2369's switched in less than 650ps, and some may either switch faster than 350ps (the limit of the sampling system he used). So your device might switch faster than 350ps, or slower than 650ps if you're unlucky or have issues with the construction. In the latter case, it's only five times faster than a common 100MHz scope, not sure if that's enough to be considered 'very short' for Fourier analysis, I assume that your very short pulse refers to the delta function?

He chooses C1=2pF for a 10V amplitude, and experiment with lead lengths for pulse purity, this means that picofarads of parasitic capacitance of nanohenries of inductance might change the amplitude or shape, and might be why Technojunk had issues with building one. You also don't now the spectral composition (i.e. shape). The circuit depends on unspecified behavior and parasitics, plus fairly high frequencies. I don't think you've any chance of simulating or calculating this behavior. Both Jim and the i9t guy used a sampling system to determine the actual pulse shape and size, but some of us cheap hobbyists don't have one on our bench . Although one of those 20GHz Agilent real-time scopes might be good enough...

[jahonen]

Yes, I meant Dirac delta function indeed. The method of Gaussian approximation has its own limits, like scope may not have Gaussian behavior at all, so it might be very flawed in the first place. Even 5 cascaded 1st order low-pass filters do not exactly produce Gaussian response, but it seems that it still gives reasonable bandwidth estimates. If you want better, then it is better to check it with a RF generator.

What I tried on the LTspice, was 1 picosecond long pulse with 1 femtosecond edges (quite difficult to realize indeed) gives me bandwidth of about 124 MHz using FFT, and increasing the pulse width to 1 ns and rise/fall to 300 ps gives 115 MHz. Whereas AC simulation gives about 123 MHz.

Measuring outputted pulse width based on 1/e of the peak amplitude points (using 300 ps edges with 2 ns width), width of the peak is about 3 ns of width, which results 0.35/3 ns = 114 MHz. I don't know if the magic constant of 0.35 is appropriate here but it seems to produce acceptable results So that actually is in the ballpark compared to the FFT method. See attached image.

Edit: slowing edges to 500 ps, gives 104 MHz based on the pulse width using above formula.

Regards,
Janne

[alm]

Yes, I meant Dirac delta function indeed. The method of Gaussian approximation has its own limits, like scope may not have Gaussian behavior at all, so it might be very flawed in the first place. Even 5 cascaded 1st order low-pass filters do not exactly produce Gaussian response, but it seems that it still gives reasonable bandwidth estimates. If you want better, then it is better to check it with a RF generator.

Agreed. Although Gaussian response is a standard for scope response, so most high-quality scopes are likely to be a pretty good approximation. The exception is fast DSO's that oversample less than 10x, they often use a sharper roll-off to prevent aliasing. I recall something like .45/risetime, but there's an Agilent appnote describing that quite well.

What I tried on the LTspice, was 1 picosecond long pulse with 1 femtosecond edges (quite difficult to realize indeed) gives me bandwidth of about 124 MHz using FFT, and increasing the pulse width to 1 ns and rise/fall to 300 ps gives 115 MHz. Whereas AC simulation gives about 123 MHz.

Measuring outputted pulse width based on 1/e of the peak amplitude points (using 300 ps edges with 2 ns width), width of the peak is about 3 ns of width, which results 0.35/3 ns = 114 MHz. I don't know if the magic constant of 0.35 is appropriate here but it seems to produce acceptable results So that actually is in the ballpark compared to the FFT method. See attached image.

Thanks for doing the actual simulations. Does it also work for something resembling the AN-47 pulser, i.e. a single pulse with ~350ps rise/fall time and a width of maybe 200ps? Seems the 300ps/2ns pulse is quite usable for the FFT method, not sure if the data from the scope (if it's a digital scope) has enough resolution for this? The 8-bit might be an issue.

I wonder if the pulse width results are fundamentally correct, or if it's coincidence. The filter acts as a low-pass filter, so it's basically about spectral composition of the pulse multiplied by the Gaussian response, I can't see some fundamental relation there unless the pulse edge is perfectly Gaussian. Seems to me that the spectral composition is variable and depends on construction details, parasitics and how well your transistor avalanches (since Jim Williams talks about tuning for cleanest pulse shape). I can't find any really high resolution measurements of the avalanche pulser, even the sampling setup Jim Williams used was limiting the rise time.

Edit: slowing edges to 500 ps, gives 104 MHz based on the pulse width using above formula.

What about if your pulser was really slow? Jim Williams specifies better than 650ps for the 'good' transistors, so lets say 1ns for a bad one. What if the signal isn't a regular Gauss pulse, but with some aberrations like asymmetry, overshoot, ringing?

[jahonen]

It seems that slowing the edges to the 1 ns gives about same result, not much effect. It seems that this method errs on the low side anyway, when the pulse source is less than ideal. Of course, pulses from LTspice have a trapezoid form, not Gaussian. I found a technical brief by Tektronix that says:

The Gaussian response, however, is not always desirable in a real time digital oscilloscope intended to measure fast rise time digital signals. The reason for this can be seen in Figure 1. Notice, the Gaussian response in Figure 1 begins its gentle roll off already at low frequencies, exceeding 3% error at only 0.3 of the rated bandwidth. This gentle roll off continues above the –3dB bandwidth, leaving significant amplitude above the Nyquist frequency resulting in aliasing, leading to jitter and increased measurement uncertainty on single shot pulse edges.

There is an exact relation between Gaussian pulse width and bandwidth, but I have not yet figured out it exactly. As far as the resolution is concerned, 8 bits should be enough, you don't need very much dynamics to extract the relevant information.

We have a 6 GHz scope at work, I can check the generator with it when I build it, 6 GHz should be enough to reveal the waveform details. BNC connectors become a limiting factor at these frequencies, however. Williams himself used "only" a 1 GHz scope in AN-47. There is a mention at page 93 of AN-47 that the generator was also measured at HP with a 12 GHz scope and they measured rise and fall times of 216 and 232 ps. I guess that that generator was one of the better ones.

Another quite cheap fast edge source is the Altera Cyclone II FPGA output set to maximum current strength, produces something like 170 ps edges:



Regards,
Janne

[alm]

A slow pulse would indeed show a too low bandwidth. It still seems to me that the relation between pulse width and bandwidth is somewhat arbitrary, depending on other factors than just bandwidth and pulse rise time. Will have to do some more tests to be sure. Could you post your LTspice circuit so I don't have to build it from scratch?

If I can find the time, I might even try to do it in hardware. I don't have the equipment to generate adjustable <1ns pulses, but I could just slow everything down one or two orders of magnitude and build a low-pass filter for 1 or 10MHz, since it seems pretty obvious to me that actual frequency doesn't matter. The added advantage would be that I wouldn't have to pay attention to transmission line effects. But that seems quite a lot of work, so I'm not sure when I'll be able to do it.

There are indeed advantages to a sharper roll-off. This Agilent appnote (AN-1420) describes the advantages pretty well. It's not usually needed for scopes that oversample at least 10x, so I would expect any scope that does to have a Gaussian response. Rise time is usually specified as well as bandwidth, so it's easy to determine if it's the magic 0.35 or some other number. A flat response is probably hard to get without DSP, that might be the reason why it used to be Gaussian. Plus you can just add up (RMS) rise times of Gaussian systems, you can't easily calculate the total risetime when at least one system with a flat response is involved. Agilent says to rely on the scope vendors numbers, that's very useful when other parts than scopes and probes are involved.

There are various other places to get fast signals (I've used the memory bus from a PC mainboard in the past), but the trick is to know how fast it is, you need something that samples at 20GS/s or so to determine that . Of course, as long as it's a lot faster (170ps for a 100-200MHz scope), and the pulse is sufficiently long that even a slow scope will eventually rise to the full amplitude, you don't need to know the exact rise time, the result will basically be the scope rise time. One issue might be that it probably can't drive a 50 ohm load and the output amplitude isn't 50 ohms, so you have to use a probe, which increases the rise time.

[jahonen]

A slow pulse would indeed show a too low bandwidth. It still seems to me that the relation between pulse width and bandwidth is somewhat arbitrary, depending on other factors than just bandwidth and pulse rise time. Will have to do some more tests to be sure. Could you post your LTspice circuit so I don't have to build it from scratch?

Here is the LTspice schematic, feel free to experiment with it and see if you can find the culprit The ideal integrator at the right side of the schematic is just for converting the impulse to the step, to compare the results.

Experimenting with much slower edges should be a good thing to do, and it does not affect the principle. It is much easier to generate, say 1 µs pulse than 1 ns pulse. If it works there, it can be assumed that same thing applies if things go faster.

Regards,
Janne

[jahonen]

I finally assembled the avalanche pulser circuit and made some measurements. The final PCB is quite compact (20x40 mm), including also the step-up converter for converting the 1.5 volts to ~90 volts DC to avalanche the transistor. It has been designed RF in mind, using microstrip techniques whenever possible, and minimizing loop areas, also in 3D-fashion (I bet that even Jim Williams himself could not do much better ):



Here is the result from my Agilent MSO6034A, avalanche pulser connected directly to the scope using BNC gender changer, and scope set to 50? internal termination:



I did not quite get the results I expected from the pulse width-based measurement (measuring the time between the 1/e points of measured peak voltage), as the rise time of the MSO6034A is about 1 ns, and pulse width produced by the avalanche pulse generator is in same league. Above picture also shows integral of the measured signal, so the pulse is converted to a step and step rise time is then measured. That is quite correct (0.35/1.26 ns =~278 MHz), just a little lower than specified bandwidth. The difference is just probably because the pulse is too long. I would guesstimate that it would be certainly short enough for 100 MHz scope, which would have 3.5 ns rise time, which is ~3.5x the duration of the whole pulse.

I did also a quick check with a 6 GHz Agilent 54855A Infiniium oscilloscope at work. Unfortunately the maximum volts/div was only 1 V (54855 has only 50 ohm inputs) and I didn't have an attenuator around, so the entire pulse did not fit to screen at once. But nevertheless it can be seen that pulse width is less than 1 ns, and the rise time can be estimated to be around 200 ps (to confirm this I have to do another measurement with the attenuator), and peak voltage is around 9 volts. That is remarkably close what Williams mentioned, considering this circuit is operating based on completely undefined behavior of the transistor!




Regards,
Janne

[jahonen]

Finally got the 20 dB DC-8 GHz attenuator and performed the measurements of the pulse. It seems that falling edge is much slower than rising edge on this one, but rise time seems to be in line with Williams:



Used math function to calculate the slew rate (scale for slew rate is 20 GV/s, or 20 V/ns if you prefer):



Regards,
Janne

[alm]

Thanks for the data! I would have expected the falling edge to be cleaner, but this might be intrinsic in the avalanche behavior. I don't think Jim Williams published any high-bandwidth scope pictures of the pulse. The closest thing I found is this from i9t.net, but it's only a 1.5GHz/4GS/s scope. I would have liked to see that without interpolation, it looks like the pulse is severely undersampled to me. The fall time is slightly slower, but significantly lower than on your much faster scope. Either the avalanche transistor behaves different (not unlikely, I think Jim Williams selected both his transistor and capacitor for best rise time/aberrations), or there's some phase distortion in your test setup (eg. parasitic low-pass filter). Not sure how to verify this, though.

[Leo Bodnar]

I have used a standard 100ft (30m) reel of 8 way ribbon cable as an open ended delay line (wired as Gnd-Gnd-Signal-Gnd-Gnd-Signal-Gnd-Gnd  to the BJT's collector and open on the other end) without even taking it off the reel.

The rising front is still like a brick wall - it actually shows as 1.7ns on my 200MHz scope.  Falling edge is obviously dispersed after travelling 30m in both directions.

Cheers
Leo

[jahonen]

Finally, I got around to try out the coax "charge line", described by Jim Williams in LTC AN-94. The coax was relatively low-spec, RG-174. I simply put open-ended coax in parallel to capacitor at collector. Anyway, here are the results with my Agilent MSO6034A. I still have to measure that at work, with higher bandwidth scope to find out the true performance.

Regards,
Janne

[tnt]

Can somone explain why the switcher as this weird "3 diodes" configuration ?