### Author Topic: Scope rising time  (Read 41442 times)

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#### Technojunk

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##### Scope rising time
« on: May 24, 2010, 09:54:57 pm »
Hi folks,

I was watching Dave's blog about the rigol 100MHz hack, chekking the rise time of the signal.
Now I was wondering, what kind of signal do I have to put in, to check if my scope is really 100MHz?

0.35 / Trise = bandwith, but if I put an signal in of 100Khz the bandwith will be different with a 20Mhz signal in!

Thanks allot.

#### alm

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##### Re: Scope rising time
« Reply #1 on: May 24, 2010, 10:21:53 pm »
The rise time should be much faster that the rise time of the scope, say a 1ns or less (for a 3.5ns scope) step of known shape. You can make do with a known risetime in the same range (if you feed it a 3.5ns signal, the measured 10-90 rise time should be about 5ns, since they add as the square root of the sum of squares). The rise time is independent of the frequency (although it will always be lower than half the period), you can have a 1kHz signal with a really fast rise time. Note that the rise time and aberrations of the probe (if you use it) are added to those of the signal and the scope, so you should really use a 50ohm BNC-BNC coax cable and a 50ohm feed-through terminator right on the scope BNC connector (assuming you use a 50ohm source).

#### chscholz

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##### Re: Scope rising time
« Reply #2 on: May 25, 2010, 02:27:46 am »
What Alm said...

You need to be a bit careful: the BW*t_r product of modern digital storage oscilloscope can significantly deviate from 0.35. As a general rule, the higher the bandwidth the higher the BW*t_r product tends to be.
It is always a good idea to check the manufacturer's spec sheet.

Chris
Don't trust me I work in marketing!

After a few years with LeCroy and R&S I work for HIOKI USA. If there is anything I can help with, please contact me.

#### saturation

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##### Re: Scope rising time
« Reply #3 on: May 25, 2010, 10:32:47 am »
The rise time of a system is a constant, practically, regardless of frequency. But you need a a square wave to do the test.  Any frequency will do and you simply stretch the time base to find the rise time of the step.  Since you can discern the 7th harmonic sine wave component of sq wave, to see the effect of 100MHz easily try ~ 100/7 = 12 MHz square will start to push 100MHz limits on the scope.

Chris is right, but these calculations are only estimates.

http://www.tek.com/Measurement/scopes/selection/performance/vertical_sys.html

Aside, be aware of the limitations of your frequency generator and your scope probes when making the measurements, what you see as its bandwidth maybe the limitations of these items.

Hi folks,

I was watching Dave's blog about the rigol 100MHz hack, chekking the rise time of the signal.
Now I was wondering, what kind of signal do I have to put in, to check if my scope is really 100MHz?

0.35 / Trise = bandwith, but if I put an signal in of 100Khz the bandwith will be different with a 20Mhz signal in!

Thanks allot.
« Last Edit: May 25, 2010, 10:35:27 am by saturation »
Best Wishes,

Saturation

#### alm

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##### Re: Scope rising time
« Reply #4 on: May 25, 2010, 05:42:34 pm »
It's true that any ideal square wave would do, but I'd be very careful to estimate the rise time purely based on repetition frequency. Depending on the quality of the generator, a square wave near the top of the frequency range may be almost a sine, so you'd be lucky to even find a third harmonic of any significance. Most generators will specify the rise time, which is indeed usually independent of the output frequency.

#### Technojunk

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##### Re: Scope rising time
« Reply #5 on: May 26, 2010, 10:23:24 am »
Well, Here a measurement with a signal of 10Vtt, @ 100Khz.

If i do the math: 0.35 / 3.5E-7 = 1 000 000 , so its says my scope is 1Mhz?

#### saturation

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##### Re: Scope rising time
« Reply #6 on: May 26, 2010, 11:53:18 am »
Hi, thanks for posting the image, it says a lot.

Math is right, but your measurement is off.  It looks like this scope can do this measurement with ease.
If those settings are right, it says its 50nS per division horizontal sweep and 2V p-p.

You do not have it zeroed.  Your waveform is 1.5 graticules below the zero mark.  Make sure the p-p reach from 0 to 100% on this scope.

Those vertical bars, seem to be movable.  The rise time is between the 10% and 90% marks; align one vertical bar at the 10 and 90% mark.

Your trace is either out of focus or its near the limits of its frequency response: its a bit fat or its jittering, thus it looks fat.

I eyeballed that waveform, and with your equation, the rise time gives a frequency response ~ 2 MHz.  The roll off near the top of the wave suggests its near the limits of its response.

Now, that is the rise time of the worst case element in your test set up, it could be the probes, the signal generator, or the scope.

Enjoy.

Well, Here a measurement with a signal of 10Vtt, @ 100Khz.

If i do the math: 0.35 / 3.5E-7 = 1 000 000 , so its says my scope is 1Mhz?
Best Wishes,

Saturation

#### tecman

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##### Re: Scope rising time
« Reply #7 on: May 26, 2010, 02:05:11 pm »
I still think your source is the issue.  Without a good pulse generator, into the correct impedance, you are likely to not have a good reference source.  Even HCT logic gates at 5 volts are in the 20 ns time range.  ECL logic offers the best rise/fall times (< 5 ns) but harder to find and apply.

Early pulse generators used a special mercury relay to generate pulses.  Other schemes use spark gaps.  You could estimate using a 100 mHz sine generator, if it has a leveled output, but I suspect that the source you are measuring is just a lot slower than your scope.

Paul

#### alm

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##### Re: Scope rising time
« Reply #8 on: May 26, 2010, 04:34:19 pm »
It's actually the rise time of your total system, sqrt(t_r(source)^2+t_r(probe)^2+t_r(scope)^2). In this case, it's likely dominated by the source. You don't mention the source, if it's a function generator, the rise time is usually specified. I wouldn't count on a <50MHz or so function generator to have a fast rise time, you might have better luck with a dedicated pulse generator, or you can built something yourself. The avalanche pulser from Jim Williams is a bit hard to use if you don't know the real output amplitude (hard to measure without a really fast scope), but I think there's a version of that design with a charge line which delivers a longer pulse. Something like 1ns might just be achievable with fast logic gates or something discrete. Even then, it's hard to verify a system with a signal generator of unknown specifications.

A leveled signal source with a bandwidth from 50kHz or so to >100MHz is also a good way, you use it to measure the -3dB point directly (increase the frequency until it's just 1/sqrt(2) times the amplitude at some low frequency like 50kHz).

#### Technojunk

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##### Re: Scope rising time
« Reply #9 on: May 26, 2010, 05:20:52 pm »
I'm using a home-build frequency generator, based on an XR2206 article here: www.technojunk.nl/files/84111NL.PDF [14MB!]
@saturation:
The fatness is becouse the delayed timebase, and may not focused right.

@alm:
Using a piece of coax with propper BNC connectors, so no probes.

EDIT:
With my probe on the CAL signal on the scope gives the same result: ~350nS risetime!
« Last Edit: May 26, 2010, 05:49:03 pm by Technojunk »

#### tecman

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##### Re: Scope rising time
« Reply #10 on: May 26, 2010, 07:21:14 pm »
Specs on the XR 2206 chip for a square wave output is 250 ns.  If you have the supporting circuity to support that sort of bandwidth, the best you will get is 250 ns.

As I mentioned before, the generator is your problem.

Paul

#### Technojunk

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##### Re: Scope rising time
« Reply #11 on: May 26, 2010, 07:26:20 pm »
Thanks Paul for the quik research!
What could I bult, to do a propper measure? something with a square signal, with 500pS ?

#### Matt

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##### Re: Scope rising time
« Reply #12 on: May 26, 2010, 07:36:46 pm »
Seen this referenced a couple places:  http://www.i9t.net/fast-pulse/fast-pulse.html

Haven't really looked at it, i just bookmarked it to look into it at a later date.

-Matt

#### Technojunk

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##### Re: Scope rising time
« Reply #13 on: May 26, 2010, 08:17:10 pm »
Thanks!
What is the best way to connect this generator to my scope?

BNC output from generator to scope, 50R resistor from signal to ground on both sides?
[not really in to terminators etc)

#### alm

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##### Re: Scope rising time
« Reply #14 on: May 26, 2010, 09:23:15 pm »
That was the Jim Williams design that I mentioned. The issue with that design is that if the rise/fall time is faster than the system rise time of your scope, you can't determine the actual amplitude, so you can't determine the 10%-90% points (rise times are usually specified between 10% of the amplitude and 90% of the amplitude). He did publish an improved version with a charge line, but this one is more complex. For both designs, you're flying blind without a sampling scope to tune it (which he did), especially for those 'adjust for best pulse shape' components.

The source should have a 50ohm output amplitude (I think the Jim Williams design does, and most commercial sources do too), and you should terminate it with 50ohm on the scope end. If the scope has a 50 ohm setting, that's the best option (probably not for a 100MHz scope), second best is a feed-through terminator (basically a BNC male-female coupler with a termination resistor in the middle), and third best is a BNC T-adapter with a standard terminator on one side. Make sure to use good quality BNC hardware, not the cheap crap designed for 10base2. The Jim Williams design has harmonics up to 1GHz or so, so you're dealing with pretty high frequency stuff. I don't think you'd get an acceptable performance with soldering a resistor to a coax cable.

#### tecman

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##### Re: Scope rising time
« Reply #15 on: May 26, 2010, 10:40:58 pm »
Thanks!
What is the best way to connect this generator to my scope?

BNC output from generator to scope, 50R resistor from signal to ground on both sides?
[not really in to terminators etc)

Source has the 50 ohm.  50 ohm coax cable to the scope with a 50 ohm terminator (it should be a BNC coaxial terminator).  The 50 ohms at the scope is critical.  If you don't use a proper terminator you may see ringing.

paul

#### Technojunk

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##### Re: Scope rising time
« Reply #16 on: June 18, 2010, 09:35:09 pm »
So, i build this: http://www.i9t.net/fast-pulse/fast-pulse.html
Only the down part, 2N2369 with 3 resistors and cap.

When i put 90V on the input (1M resistor) i'm seeing a kind of saw signal of 200mV?
Is this good, or do i have to build te upper part to?

#### saturation

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##### Re: Scope rising time
« Reply #17 on: June 18, 2010, 11:09:44 pm »
How are you generating the 90V?  From a PSU?  Chances are you are seeing the ripple, or its oscillating.  Send a pic if you can.
You'd best make the 'upper half' too, its AA battery powered for a reason, for cleanest power.

So, i build this: http://www.i9t.net/fast-pulse/fast-pulse.html
Only the down part, 2N2369 with 3 resistors and cap.

When i put 90V on the input (1M resistor) i'm seeing a kind of saw signal of 200mV?
Is this good, or do i have to build te upper part to?
« Last Edit: June 18, 2010, 11:11:15 pm by saturation »
Best Wishes,

Saturation

#### Technojunk

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##### Re: Scope rising time
« Reply #18 on: June 18, 2010, 11:17:11 pm »
2 bench power supplies in series.
I think its better to to bult the upper part, but where do i grab the LT1073 off?

#### saturation

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##### Re: Scope rising time
« Reply #19 on: June 18, 2010, 11:27:12 pm »
2 bench power supplies in series.
I think its better to to bult the upper part, but where do i grab the LT1073 off?

Digikey or if you are not in the USA, see findchips.com or octoparts.com

About $3-5, to make it worth your while in S&H buy all the parts from the same supplier. http://search.digikey.com/scripts/DkSearch/dksus.dll?Detail&name=LT1073CN8%23PBF-ND Best Wishes, Saturation #### Technojunk • Contributor • Posts: 15 ##### Re: Scope rising time « Reply #20 on: June 19, 2010, 12:53:32 pm » Here a pic of what I build: On my scope: #### alm • Guest ##### Re: Scope rising time « Reply #21 on: June 19, 2010, 02:32:09 pm » Looks like ringing, not surprising since you use a probe and long ground lead. I think it's designed for a 50 ohm load, so you should terminate it with 50 ohms. The best way would be to solder a 50 ohm BNC connector right to the transistor lead, use a 50 ohm cable, and terminate at the scope. Terminating at the source and use a probe with a really short ground lead (BNC connector + probe-tip-to-BNC adapter or ground spring) might also work. The 50-ohms resistors should have a low inductance (standard metal film might be too much), since there are frequency components up to 1GHz or so in this signal. As I mentioned before, you need to know the real amplitude to calculate the actual rise time. #### Technojunk • Contributor • Posts: 15 ##### Re: Scope rising time « Reply #22 on: June 19, 2010, 02:54:38 pm » Or the design is crap! I mean, why put 90V on a transistor that is made for MAX. 40V? Now, with terminators and 50R cable: #### tecman • Frequent Contributor • Posts: 444 • Country: ##### Re: Scope rising time « Reply #23 on: June 19, 2010, 05:21:34 pm » The circuit uses the transistor breakdown to generate the fast pulse. The high supply impedance keeps the transistor from being destroyed. It looks like you have grounding/termination issues by the amount of ringing you are showing. Paul #### alm • Guest ##### Re: Scope rising time « Reply #24 on: June 19, 2010, 05:49:33 pm » 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 ($$). The original appnote (I hate how people keep linking to the website from one guy who built it instead of the Jim Williams appnotes) might contain more details and pictures. #### Technojunk • Contributor • Posts: 15 ##### Re: Scope rising time « Reply #25 on: June 19, 2010, 07:12:03 pm » I just made everything on the connector, and this works I think! #### saturation • Super Contributor • Posts: 4787 • Country: • Doveryai, no proveryai ##### Re: Scope rising time « Reply #26 on: June 19, 2010, 07:38:49 pm » Yes, if folks read the app notes, its explains a lot of what we discussed here. Alas, its a pdf file, so linking it has no photos to see right away. http://www.linear.com/pc/downloadDocument.do?navId=H0,C1,C1154,C1009,C1028,P1219,D4138 Jim Williams is one of the great analog designers, we should put a face to the name: http://www.eetimes.com/special/special_issues/1998/timespeople98/williams.html Not sure what that is, it's really low level, a 167kHz radio station being picked up? Or from a switching power supply somewhere? Does not look like a signal from the avalanche transistor to me, or it's just not breaking down and this is the capacitor charging? I would just solder a female BNC connector to it, they're cheap. And keep wiring outside the coax as short as possible. That's probably why the i9t guy used a shielded Pomona box with integrated BNC connector ($$$). 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.
« Last Edit: June 19, 2010, 09:37:10 pm by saturation »
Best Wishes,

Saturation

#### alm

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##### Re: Scope rising time
« Reply #27 on: June 19, 2010, 07:42:56 pm »
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

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##### Re: Scope rising time
« Reply #28 on: June 19, 2010, 08:25:55 pm »
There is no /10 probe attached attached!
The only strange think, is that it's not a 3.5nS rise time! (100Mhz scope)

#### sigxcpu

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##### Re: Scope rising time
« Reply #29 on: June 19, 2010, 08:51:21 pm »
It is 1.5 subdivisions (wrong cursor position).
That is 5ns = 1 div = 5 subdiv => 1.5ns rise time. Very nice.

#### Technojunk

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##### Re: Scope rising time
« Reply #30 on: June 19, 2010, 09:11:05 pm »
Could you paint the right way to set the cursors?

#### marianoapp

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##### Re: Scope rising time
« Reply #31 on: June 19, 2010, 10:37:58 pm »
The only strange think, is that it's not a 3.5nS rise time! (100Mhz scope)

350ps = 0.35ns

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

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##### Re: Scope rising time
« Reply #32 on: June 19, 2010, 11:04:05 pm »
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

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##### Re: Scope rising time
« Reply #33 on: June 20, 2010, 12:22:13 am »
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

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##### Re: Scope rising time
« Reply #34 on: June 20, 2010, 08:12:11 am »
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
« Last Edit: June 20, 2010, 08:16:14 am by jahonen »

#### alm

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##### Re: Scope rising time
« Reply #35 on: June 20, 2010, 08:29:06 am »
@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

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##### Re: Scope rising time
« Reply #36 on: June 20, 2010, 12:37:31 pm »
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

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##### Re: Scope rising time
« Reply #37 on: June 20, 2010, 01:31:43 pm »
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
« Last Edit: July 13, 2010, 09:57:18 pm by jahonen »

#### alm

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##### Re: Scope rising time
« Reply #38 on: June 21, 2010, 03:58:45 am »
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 (t10%-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

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##### Re: Scope rising time
« Reply #39 on: June 21, 2010, 05:24:39 pm »
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
« Last Edit: June 21, 2010, 05:33:21 pm by jahonen »

#### alm

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##### Re: Scope rising time
« Reply #40 on: June 22, 2010, 04:09:05 am »
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

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##### Re: Scope rising time
« Reply #41 on: June 22, 2010, 04:45:25 pm »
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:

Quote
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
« Last Edit: June 22, 2010, 05:03:51 pm by jahonen »

#### alm

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##### Re: Scope rising time
« Reply #42 on: June 23, 2010, 06:50:16 am »
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

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##### Re: Scope rising time
« Reply #43 on: June 23, 2010, 03:20:23 pm »
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
« Last Edit: June 23, 2010, 03:23:51 pm by jahonen »

#### jahonen

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##### Re: Scope rising time
« Reply #44 on: July 13, 2010, 07:03:46 pm »
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

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##### Re: Scope rising time
« Reply #45 on: July 21, 2010, 06:33:41 pm »
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

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##### Re: Scope rising time
« Reply #46 on: July 21, 2010, 07:43:24 pm »
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

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##### Re: Scope rising time
« Reply #47 on: April 24, 2011, 05:48:30 pm »
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

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##### Re: Scope rising time
« Reply #48 on: April 25, 2011, 07:30:56 am »
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
« Last Edit: July 05, 2012, 07:03:07 am by jahonen »

#### tnt

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##### Re: Scope rising time
« Reply #49 on: April 25, 2011, 01:40:31 pm »
Can somone explain why the switcher as this weird "3 diodes" configuration ?

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##### Re: Scope rising time
« Reply #50 on: April 25, 2011, 02:38:59 pm »
Can somone explain why the switcher as this weird "3 diodes" configuration ?

actually voltage doubler/pump

http://en.wikipedia.org/wiki/Voltage_doubler
I don't want to be human! I want to see gamma rays, I want to hear X-rays, and I want to smell dark matter ...
I want to reach out with something other than these prehensile paws and feel the solar wind of a supernova flowing over me.

#### jahonen

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##### Re: Scope rising time
« Reply #51 on: April 26, 2011, 02:09:06 pm »
Ok, here are the results with a 6 GHz scope, with RG-174 charge line and without for comparison. Didn't test the ribbon cable, though. Slew rate of the signal is also shown (20 V/ns scale), so that it can be seen if volts/time unit figure is changed. It seems that attaching the RG-174 cable does not degrade the edge, although the rise time figure seems to be quite mediocre, maybe I should try a different transistor specimen.

And I almost forgot, thanks to Leo Bodnar pointing out this trick, otherwise I wouldn't have bothered to check this as charge line implementation in LTC AN-94 is slightly different. I have some Suhner sucotest cables which are spec'ed up to 18 GHz or so and would like to know how they would work as a charge line, but I am reluctant to butch those just for curiosity

Regards,
Janne
« Last Edit: April 26, 2011, 02:11:31 pm by jahonen »

#### vk6zgo

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##### Re: Scope rising time
« Reply #52 on: April 28, 2011, 04:10:04 am »
All of the above brings to mind the TU-5 Pulser,which was an accessory for the Tektronix 545B .

This device used a Tunnel diode to create the sharp risetime.

In use,it was driven from the 545B calibrator,which was set to 90v,if I remember
correctly.

The calibration signal caused the Tunnel diode to breakdown after a set voltage level,producing a fast  risetime for the part of the rise above that voltage.

In use, 10% to 90% of this section was used to measure rise time.

I had one,but it wasn't much use without the  high level calibration voltage,so I gave it away to a friend who was collecting 545s & their accessories.

VK6ZGO

#### tnt

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##### Re: Scope rising time
« Reply #53 on: May 03, 2011, 07:28:51 pm »
Interesting, with my 350MHz Agilent DSO-X 3000, I get 900 ps rise time just measuring a clock signal ...

Smf