Author Topic: Generating a <3 pS rise time step  (Read 3777 times)

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Offline rhb

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Generating a <3 pS rise time step
« on: March 13, 2019, 10:47:35 pm »
I have a pair of Leo Bodnar's wonderful BNC pulsers, both the 40 pS step and a 100 pS impulse version.  However, I'm afraid that was a grave mistake as it led to my buying a Tek 11801 and a pair of SD-22 heads.

Rather obviously I cannot test 23 pS rise time heads with any of Leo's pulsers which use a laser diode driver with a 21 pS rise time.  So I am trying to design a faster step.  For a hobbyist a mercury wetted relay, good connectors and Rogers laminate seem the path of least difficulty.  The latter being entirely relative.

Pickering offers SMD mercury wetted reed relays specified with 4 pF between the closed contacts and the coil and were kind enough to send me a simulation which assumed slightly more capacitance across the relay and about the same from the output to ground.  That showed ~3 pS 20% - 80%.  Not as fast as I'd like for testing an SD-32 with 7 pS rise time, but not too bad for the SD-22s.

The minimum sampling rate for the 11801 is 200 Hz which is asking rather a lot of a relay.

Has anyone tried to do this?  Is there an alternate design I should consider?  How do modern laboratories produce sub pS steps?  Literature links especially appreciated.  I have not found google very helpful at exotic subjects like this.
 

Offline David Hess

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Re: Generating a <3 pS rise time step
« Reply #1 on: March 13, 2019, 11:32:14 pm »
Has anyone tried to do this?

Tektronix did it in their 108 and 109 pulse generators.  The relay operating life is limited and the repetition rate is a problem except for real time oscilloscopes.  A sampling oscilloscope will require a delay line which compromises the edge speed or random sampling like the 7T11.

Quote
Is there an alternate design I should consider?

Maybe a non-linear transmission line built inside of a transmission line structure would work?  I do not know if they can get below 10 picoseconds.

Tunnel diodes only got down to 10s of picoseconds as far as i know.
 

Offline rfeecs

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Re: Generating a <3 pS rise time step
« Reply #2 on: March 13, 2019, 11:55:02 pm »
Isn't 3pS about 100GHz bandwidth?

You could search for Nonlinear transmission line pulse generator, NLTL, Shock Line pulse generator.

If you amplify the output with a high slew rate amplifier, you can improve the rise/fall time.

Here is Keysight's "New world standard" sub 7pS pulse generator:
http://literature.cdn.keysight.com/litweb/pdf/5991-0311EN.pdf
« Last Edit: March 13, 2019, 11:57:14 pm by rfeecs »
 

Offline rhb

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Re: Generating a <3 pS rise time step
« Reply #3 on: March 14, 2019, 01:07:27 am »

Tektronix did it in their 108 and 109 pulse generators.  The relay operating life is limited and the repetition rate is a problem except for real time oscilloscopes.  A sampling oscilloscope will require a delay line which compromises the edge speed or random sampling like the 7T11.


Thanks.  Why the delay line?  That adds capacitance.  As I understand the problem, capacitance is the big issue.  Are you referring to the trigger delay?  That might be better handled by a clock chip with sub pS  jitter. I think those are fairly easy to find, at least relative to the raw physics of charging the transmission line capacitance.

Yes, this is insanely high BW.  Failure is the most likely outcome, but it seems worth taking a crack at it.  Learning to use a suitable  PCB design tool is far more trouble than the rest.

I'd never heard of "nonlinear shock line pulse generators" so I should have fun chasing that.
 

Online DaJMasta

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Re: Generating a <3 pS rise time step
« Reply #4 on: March 14, 2019, 04:14:55 am »
That bandwidth is going to be near impossible to achieve, the highest end Keysight UXR uses a pulser like what you're describing for its self calibration, and uses the many fast amplifiers on a hard edge approach.... and it's all custom silicon (and achieves sub 3.5ps rising and falling edges).  You may be able to get into the tens of GHz region with a self designed pulser, but you're going to need faster amplifier processes and smaller physical construction to get anywhere near 100GHz.  You're also going to need a faster rated connector, doing this on a regular 3.5mm is just not going to physically happen.

The UXR calibrator is this one: https://www.keysight.com/en/pd-2949589-pn-N2125A/infiniium-uxr-real-time-oscilloscope-calibration-module-100-mm-80-ghz-and-higher


FWIW, what I think LeCroy was using to demo very fast edges on its 100GHz scope was an optical signal into an extremely fast photodiode integrated into the connector that plugs into the 1mm channel input.
 

Offline Henrik_V

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Re: Generating a <3 pS rise time step
« Reply #5 on: March 14, 2019, 10:50:32 am »
There's a technique to use a photo conductive switch and femto-second laser pulses...
https://www.researchgate.net/publication/231119820_Optoelectronic_measurement_of_the_transfer_function_and_time_response_of_a_70_GHz_sampling_oscilloscope

migth have improved since then..
Greetings from Germany
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Offline rhb

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Re: Generating a <3 pS rise time step
« Reply #6 on: March 14, 2019, 02:08:01 pm »
Both the 108 and the 109 are much slower than Leo's unit.  However, they are a good reference for the design concept. I've got a description of the switch and transmission line concept somewhere, but don't recall what book it is in.

The SD-30/32 input is 2.4 mm.  So I have to live within the constraints of that connector. Ultimately, the capacitance of the mated connectors and the 50 ohm load determines the minimum rise time possible.

The photodiode and femto second laser pulse reminds me of how to make a small fortune on Wall Street. Start with a large fortune.

I just found Michael G. Case's 1993 UCSB dissertation on NLTLs.  That looks *very* promising.

Getting a researchgate account is proving rather irritating.  Big oil doesn't let contract scientists publish much.  It's  actually fairly painful to get permission on anything really interesting even for regular staff.
« Last Edit: March 14, 2019, 03:06:31 pm by rhb »
 

Offline David Hess

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Re: Generating a <3 pS rise time step
« Reply #7 on: March 15, 2019, 02:52:18 am »
Thanks.  Why the delay line?  That adds capacitance.  As I understand the problem, capacitance is the big issue.  Are you referring to the trigger delay?

The delay line is a transmission line and splitter.  The problem is that 50 nanoseconds of coaxial transmission line by itself limits bandwidth.

Sequential sampling oscilloscopes require a pretrigger which for the 11801 is 47.5 nanoseconds.  The Tektronix DL-11 delay line for the 11k series limits bandwidth to 5 GHz.  Some of the mainframes have the DL-11 built in.  Check out the Tektronix 113 for the old school way.

Quote
That might be better handled by a clock chip with sub pS  jitter. I think those are fairly easy to find, at least relative to the raw physics of charging the transmission line capacitance.

The main signal is the part which must be delayed.  If your clock chip provides a 5 picosecond edge on its output, then this whole discussion is irrelevant.

The problem with the mercury relay based pulse generator is that the delay must be generated after the pulse is generated.  Triggered pulse generators including tunnel diode, avalanche, and step-recovery can generate the pretrigger pulse before the pulse is produced.
 

Offline FriedLogic

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Re: Generating a <3 pS rise time step
« Reply #8 on: March 15, 2019, 10:50:30 pm »
Pickering offers SMD mercury wetted reed relays specified with 4 pF between the closed contacts and the coil and were kind enough to send me a simulation which assumed slightly more capacitance across the relay and about the same from the output to ground.  That showed ~3 pS 20% - 80%.
Is that the rise time across the relay, or just the time taken for the contact to be made?
 

Offline rhb

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Re: Generating a <3 pS rise time step
« Reply #9 on: March 15, 2019, 11:43:34 pm »
It's a SPICE simulation of the rise time.  The capacitances are a guesstimate.  I've attached the figure Pickering sent me

I found a 1993 dissertation at UC Santa Barbara by Michael Case on non-linear transmission lines which looks very interesting.

https://www.ece.ucsb.edu/Faculty/rodwell/publications_and_presentations/theses/theses.html

Bottom of page.

It's more applicable to ICs than discretes,  but a stripline on Rogers laminate and some diodes is cheap relative to a 2.4 mm connector.
 

Offline JohnG

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Re: Generating a <3 pS rise time step
« Reply #10 on: March 16, 2019, 03:38:21 am »
I highly suggest adding some inductance to the simulation and see what happens. I would suggest sticking adding some where yo think there might be interfaces, let's say 50 pH and 100 pH to start. This might the inductance of a solder bump for a die attach or similar.

John
 

Offline T3sl4co1l

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Re: Generating a <3 ps rise time step
« Reply #11 on: March 16, 2019, 04:31:39 am »
Note that 3ps requires a lumped equivalent of say 75pH and 60fF (for 50 ohms), and stub lengths much less than 1mm.

This rules out all but the tiniest diodes (single dice in a hybrid assembly?), and even rules out a lot of transmission lines, since the width and height of the TL are similarly limited, lest TE/TM modes take over and introduce weird dispersion.  Needless to say, as the cross section of the TL goes down, the losses go way up, and so the length must be that much smaller to maintain sharpness.

This requires monolithic construction.  There is actually nothing you can do with conventional materials (PCBs and SMT components) or a normally-equipped machine shop that will succeed here.

The next best thing seems to be bulk physics -- optics and lasers -- as has been mentioned.  Not really easier, but stands a chance of doing it with off the shelf components, materials and a machine shop.

Tim
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Online DaJMasta

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Re: Generating a <3 pS rise time step
« Reply #12 on: March 16, 2019, 04:36:14 am »
Yes, I would agree that some key parasitics are missing.  There is a reason this isn't an every day thing even in test equipment: that it's REALLY difficult to get this fast based on the parasitics of even very high frequency connectors.  As has been mentioned a few times now, <3ps rise time or fall time is not going to happen with hand assembly of discrete parts, the parasitics of bond wires can even be too far out of tolerance at this sort of level.


Going for fast is great and a worthy target, <3ps is not realistic.
 

Offline rhb

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Re: Generating a <3 pS rise time step
« Reply #13 on: March 16, 2019, 03:37:10 pm »
I verified last night that a mercury wetted relay is not viable for a sampling scope because of the length of the required delay line (~50 ft).

This is a best effort project.  If I can compress the 100 pS pulse from Leo's unit to even 10-20 pS it will be better than what I have now.  <3 pS is a goal, not an expectation.

I'd be much more interested in suggestions for diodes.  For example, might a microwave transistor have lower junction capacitance than readily available diodes?

I can get the required 50 ohm impedance by simply scaling the diameter of the wire to the height of  whatever device I use.  Spacing is more problematic, but it's also periodic.  I still don't know the mathematical details.

Unfortunately, my printer appears to be having trouble with some pages of the dissertation.  At least that's the most common problem, but it is fairly old.  So it may be that it is dying.
 

Online Marco

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Re: Generating a <3 pS rise time step
« Reply #14 on: March 16, 2019, 04:01:06 pm »
As I've said before in threads like this, the fastest edge I've seen on this forum is here. It's the falling edge though, not the rising one. I suspect the differentiator causes the relatively slow rising edge, so a step without the differentiator might retain the speed of the falling edge.

More information about the principle.
« Last Edit: March 16, 2019, 04:33:15 pm by Marco »
 

Offline rhb

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Re: Generating a <3 pS rise time step
« Reply #15 on: March 16, 2019, 04:29:06 pm »
I have two of Leo's units.  The square wave version has a measured rise time of 36 pS.  The impulse version has measured rise time of 48 pS and a duration of 100 pS.

That's significantly better than the other units.  Leo's units may well be the physical limit.  They are extremely good.  I'm likely to get a 3.5 or 2.4 mm unit when they become available again.

The logical next step is some basic calculations followed by a simulation using openCEM if the hand calculations don't kill the idea.

Ex cathedra pronouncements have no value at all.  Mathematical physics calculations are the only authority I  recognize.  And then only after I've reviewed them.
 

Online Marco

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Re: Generating a <3 pS rise time step
« Reply #16 on: March 16, 2019, 04:34:50 pm »
Oops, linked the wrong thread. This is the one.

Measurements trump math, he copy pasted a result from his  LeCroy WAVEMASTER 8620A ... it is objectively the fastest edge on this forum AFAICS. Substantially faster than 36 ps.
 

Offline rhb

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Re: Generating a <3 pS rise time step
« Reply #17 on: March 16, 2019, 05:31:45 pm »
I already read that thread.  I see no justification for saying that unit is faster.  The fall time might be, but the rise time is not and the pulse is wider.

I'm not aware of a thread that discusses an attempt to produce NLTL pulse compression using discrete parts.  I had never heard of NLTL when I started the thread, but I suspected someone on the forum would toss a stone in the right direction.  So this thread has morphed into attempting to build an effective  NLTL compressor for use with Leo's pulsers.  Once I have my 11801 working I'll be able to proceed.

Measurements trump math only if they are correctly made.  I've got measurements made by Leo for my units done with a CSA803  which, based on Leo's comments, were done using an SD-30 (40 GHz) head.

Leo is using a Maxim LED driver with a 21 pS rise time.  The main limitation on my units is the BNC connector.

I bought an 11801 because I thought Leo's measurements were so cool.  Now having acquired a system which outstrips my current verification capability I'm looking to improve that.  It's a vicious cycle.  There's a very long forum thread on that topic.
« Last Edit: March 16, 2019, 05:39:22 pm by rhb »
 

Online Marco

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Re: Generating a <3 pS rise time step
« Reply #18 on: March 16, 2019, 05:54:58 pm »
I already read that thread.  I see no justification for saying that unit is faster.  The fall time might be, but the rise time is not and the pulse is wider.
The topic asked for a step, not a pulse.
Quote
I'm not aware of a thread that discusses an attempt to produce NLTL pulse compression using discrete parts.
I haven't seen anyone DIY one for the hell of it, but here's an academic description of one (they call it hybrid, but they just use reflow soldered SMD components, so I don't see what's hybrid about it). They don't measure the rise time though.

PS. if you have a spare ~3K$ there's the Macom MLPNC-7103 :) This is a module for a modular microwave development system, but I doubt the Macom unit on its own is much cheaper.
« Last Edit: March 16, 2019, 06:06:46 pm by Marco »
 

Offline rhb

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Re: Generating a <3 pS rise time step
« Reply #19 on: March 16, 2019, 07:28:54 pm »
I'd have posted the step response, but I don't know where it is.  The thread you linked showed a spike and Case's dissertation is focuses on spike compression.  I used a step in the subject line because I'd never heard of NLTL pulse shaping.  I like spikes better as the math is easier, but I'll take whatever I can get.

Interesting paper.  Thanks for the link.  Looking at their figures it appears they were getting around 50-75 pS rise times.

Keysight sells a 3 pS rise time unit.  I haven't bothered to look at the price.  I can justify 100 diodes and a 2.4 mm connector.  The latter will take some searching to get for under $100.

Edit:  I've added the step response for my square wave unit.
« Last Edit: March 16, 2019, 08:52:36 pm by rhb »
 

Offline rs20

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Re: Generating a <3 pS rise time step
« Reply #20 on: March 16, 2019, 09:30:35 pm »
I know that in this thread it's obvious from context, but that's no excuse to use poor terminology. It's a bad habit. Capital S is Siemens (conductance), small s is seconds (time). You want a <3 ps rise time step, not <3 pS.
 
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Offline David Hess

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Re: Generating a <3 ps rise time step
« Reply #21 on: March 16, 2019, 10:53:45 pm »
This rules out all but the tiniest diodes (single dice in a hybrid assembly?), and even rules out a lot of transmission lines, since the width and height of the TL are similarly limited, lest TE/TM modes take over and introduce weird dispersion.  Needless to say, as the cross section of the TL goes down, the losses go way up, and so the length must be that much smaller to maintain sharpness.

This is what limited the performance of Tektronix's early sampling heads.  The size of the GR-874 connectors allowed other propagation modes but nobody had an instrument fast enough to measure or confirm it initially.

Quote
This requires monolithic construction.  There is actually nothing you can do with conventional materials (PCBs and SMT components) or a normally-equipped machine shop that will succeed here.

On a larger scale it requires transmission line construction for the entire switching assembly which suggests placing a mercury wetted reed relay inside a coaxial transmission line or coplanar waveguide such that the impedance is maintained through the entire structure.  But the reed relay's glass envelope alters the dielectric constant so that much be taken into account and as you point out, the physical size will allow other propagation modes limiting performance above a certain frequency.  I assume that is what limits performance of the Tektronix 284 pulse generator to 70 picoseconds even with the tunnel diode embedded in the coaxial transmission line.

The S-2 sampling head and Tektronix 284 with GR-874 sized transmission lines are both limited to 75 or 70 picoseconds respectively.  I suspect changing the connector on the S-2 would improve its performance to at least 8GHz.

Like you say, that rules out such a fast pulse generator using commonly available construction techniques unless you can build it into the rigid cable used with 3.5mm or smaller RF connectors.  The NLTL assemblies I have seen for sharpening an existing pulse used MMICs and hybrid construction.

This is a best effort project.  If I can compress the 100 pS pulse from Leo's unit to even 10-20 pS it will be better than what I have now.  <3 pS is a goal, not an expectation.

I'd be much more interested in suggestions for diodes.  For example, might a microwave transistor have lower junction capacitance than readily available diodes?

Look for a suitable varactor or step-recovery diode which are essentially the same thing intended and specified for different applications.  I have been told than some bipolar RF transistor junctions are also very good for this but I think you are going to have to qualify any part you want to use.

 

Offline David Hess

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Re: Generating a <3 pS rise time step
« Reply #22 on: March 16, 2019, 10:56:14 pm »
I know that in this thread it's obvious from context, but that's no excuse to use poor terminology. It's a bad habit. Capital S is Siemens (conductance), small s is seconds (time). You want a <3 ps rise time step, not <3 pS.

If only there had been a previous unit of conductance with the same dimensions which could not be confused with seconds or samples.
 

Offline rhb

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Re: Generating a <3 pS rise time step
« Reply #23 on: March 17, 2019, 12:07:45 am »
I think the point about pS vs ps perfectly valid even if there was no ambiguity.

The paper that Marco linked used a microwave varactor.  Hopefully one that is not too expensive.

For an initial test I'm going to use Leo's pulsers as the source and focus on constructing the NLTL dead bug style over a ground plane.  The varactors will be tombstoned and a wire of the proper dimension to produce 50 ohm impedance for the height of the varactors running between a pair of SMA connectors soldered to the tops of the varactors.  That is tractable with manual calculations and perhaps some manual wire drawing.

So assuming at least 1 channel on my two eBay SD-22s works, I should be able to see an effect.  If it does work, I'll switch to using the same LED driver that Leo is using to eliminate the ~15 ps reduction in the rise time introduced by the BNC and buy 3.5 and 2.4 mm connectors to replace the SMAs.

As David pointed out earlier, a mercury relay is not usable at these speeds.  I had not been aware of the length of the trigger delay required.

I finally manage to get Michael Case's dissertation printed, so I'll have a better grasp of the mathematics in a few days.  My chief concern at this point is the horizontal spacing of the diodes.

All of this is Leo's fault.  He sells these absolutely wonderful fast edge pulsers at prices one can justify for a hobby.  He even supplies plots for the particular unit you receive made on his sampling scope. 

I got sucked into wanting a sampling scope and now that I have one, I want a signal source capable of verifying its performance.  With the rise times of the SD-30 (9 ps) and the SD-32 (7 ps) I need something faster to quantify their performance.  The SD-22 and SD-24 are slower, so if I can't beat the SD-24 step I'll stop and not buy an SD-30 or SD-32.

I'd much rather have access to all the data at a supermajor oil company, but there's no way I can get that.  So I'm playing with electronics.
 
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Offline David Hess

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Re: Generating a <3 pS rise time step
« Reply #24 on: March 17, 2019, 12:19:30 am »
I think the point about pS vs ps perfectly valid even if there was no ambiguity.

Oh, I agree.  I just hate the SI unit for conductance because it replaced a better unit.

Quote
I got sucked into wanting a sampling scope and now that I have one, I want a signal source capable of verifying its performance.  With the rise times of the SD-30 (9 ps) and the SD-32 (7 ps) I need something faster to quantify their performance.  The SD-22 and SD-24 are slower, so if I can't beat the SD-24 step I'll stop and not buy an SD-30 or SD-32.

Tektronix made a calibration generator for these oscilloscopes which was built into some of the mainframes.  You might be able to find a junked one which has the calibration generator.
 
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Online Marco

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Re: Generating a <3 pS rise time step
« Reply #25 on: March 17, 2019, 12:38:44 am »
MACOM has some affordable flipchip varactors which should be superior to the SOD882 ones used in the paper.

BTW the reverse recovery pulser breaks my brain. The wrong edge is sharp, the leading edge should be sharp and the trailing edge should be slow because of the impedance mismatched stub ... it makes no sense.
« Last Edit: March 17, 2019, 12:46:43 am by Marco »
 

Offline rhb

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Re: Generating a <3 pS rise time step
« Reply #26 on: March 17, 2019, 02:42:57 am »
My brain is pretty broken, too.  I just finished a first pass through Case's dissertation.   Lots of the plots look backwards to me.  And I really wish people would stop inventing new jargon.

I think I'm going to take a look at what Brekhovskikh  has to say in "Waves in Layered Media" and look at the impulse response of various reflector spacings in a 1D layered medium. From reading Case it's clear that the diode spacing is a critical parameter.  Unfortunately, it also appears to significantly alter the impedance.  So it's looking as if I'll be writing some simulation software.

My 11801 has a calibration output.  And the SD-24s have a very good step output.  But Leo is not far behind if I get a 2.4 mm version.
 

Offline rhb

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Re: Generating a <3 pS rise time step
« Reply #27 on: March 17, 2019, 01:42:19 pm »
Given:

A low (<< 50 ohms) impedance symmetric pulse source

A linear lossless transmission line matched to the source with  steps in impedance terminating in 50 ohms

It follows that:

If the impedance steps are separated by ever smaller delays, the transmission response will be shaped such that the leading edge is steeper and the trailing edge has reduced slope.

Each step in the impedance creates a pole in the response which delays a particular frequency range.  The range being determined by the Q of the segment and the phase delay of that resonator is determined by its position in the series.

Comments:

This is the analog equivalent of an infinite impulse response filter.  The analysis and design are easily performed in the time domain as a lumped constant problem using the Z transform.

The technique is the basic introduction to signal processing problems in reflection seismology.  I've not done one of these in over 30 years, but in grad school working under a member of Norbert Wiener's  GAG group I submitted a solution to the most general case as a homework exercise.  About a month later another member of the GAG published the same solution to the same problem in the leading reflection seismology journal, Geophysics, published by the Society of Exploration Geophysicists though with completely different notation.

It will likely take a day or two for me to regain proficiency in the analysis.  Reducing infinite series to closed form is notationally difficult.  For this case I'll have to develop a notation that suits the particular problem at hand.  The time invariant linear lossless case is pretty straight forward, but making the reflection coefficients time dependent may well prove difficult.

At 1 mm spacing between capacitors the final segment will have a resonant frequency of 150 GHz which at 2.3 ps meets my original goal.

Case touches on the topic in his dissertation, but without fully grasping the degree to which his results apply to a linear system.
« Last Edit: March 17, 2019, 01:49:50 pm by rhb »
 

Offline David Hess

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Re: Generating a <3 pS rise time step
« Reply #28 on: March 17, 2019, 03:24:05 pm »
BTW the reverse recovery pulser breaks my brain. The wrong edge is sharp, the leading edge should be sharp and the trailing edge should be slow because of the impedance mismatched stub ... it makes no sense.

That is exactly how a step-recovery diode diode works; the fast edge is the recovery edge.  There are a couple of ways to work the circuit but if the output has a parallel termination, then only the termination matters after the diode "disconnects" except for the diode's capacitance and any stub length.

Any diode or forward biased PN junction can be used but step-recovery diodes are specifically constructed so that the minority carriers dissipate with a minimum of dispersion after the storage time has expired allowing very high edge rates.
 

Offline rfeecs

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Re: Generating a <3 pS rise time step
« Reply #29 on: March 17, 2019, 04:45:44 pm »
Given:

A low (<< 50 ohms) impedance symmetric pulse source

A linear lossless transmission line matched to the source with  steps in impedance terminating in 50 ohms

It follows that:

If the impedance steps are separated by ever smaller delays, the transmission response will be shaped such that the leading edge is steeper and the trailing edge has reduced slope. ...

It sounds like you are saying that a linear transmission line structure can give you increased frequency components.

A linear structure can only act as a filter.

With a step recovery diode or an NLTL, you can input a pure sine wave and output a step that is rich in higher harmonics.

You can't do that with a linear structure.
 

Offline 5065AGuru

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Re: Generating a <3 pS rise time step
« Reply #30 on: March 17, 2019, 05:51:33 pm »
Here is a link to a commercial NLDL.

Harmonics to 30Ghz so I'm not sure the rise time is short enough for you.

They don't spec the rise time.

https://cdn.macom.com/datasheets/MLPNC-7103.pdf

Cheers,

Corby
 

Online Marco

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Re: Generating a <3 pS rise time step
« Reply #31 on: March 17, 2019, 06:27:55 pm »
That is exactly how a step-recovery diode diode works; the fast edge is the recovery edge.

That's not the point, the point is how the stub differentiates it. Here's a simplified representation of how I think the circuit works (the transistor is the current source, which suddenly stops conducting current) and what kind of pulse a high impedance stub would create. Notice the rising flank is sharp and the falling flank is slow, exactly the opposite of his circuit ... how did that happen? If I slow down the cut off of the current source I get a more symmetrical pulse, but I don't see how you can get a nearly vertical falling flank. That would mean the differentiator is actually sharpening and a linear circuit can't do that.

PS. unless somehow the output diode, is sharpening that edge. It's not shown in my model because in theory it's only intended to remove the negative going bump from the transistor slowly turning on ... it's the only other nonlinear component though, so that would be the only explanation I can come up with (not much use including it, those kind of effects aren't going to show up in Spice).
« Last Edit: March 17, 2019, 06:59:21 pm by Marco »
 

Offline T3sl4co1l

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Re: Generating a <3 pS rise time step
« Reply #32 on: March 17, 2019, 10:29:46 pm »
It will likely take a day or two for me to regain proficiency in the analysis.  Reducing infinite series to closed form is notationally difficult.  For this case I'll have to develop a notation that suits the particular problem at hand.  The time invariant linear lossless case is pretty straight forward, but making the reflection coefficients time dependent may well prove difficult.

I was going to point out a contradiction earlier in this post, but it seems you left out time-invariant intentionally, so that's basically a 'gimme' to make any kind of filter you like (including those with gain; presumably this thing is active in some way). :-//

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Offline rhb

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Re: Generating a <3 pS rise time step
« Reply #33 on: March 17, 2019, 11:16:59 pm »
Given:

A low (<< 50 ohms) impedance symmetric pulse source

A linear lossless transmission line matched to the source with  steps in impedance terminating in 50 ohms

It follows that:

If the impedance steps are separated by ever smaller delays, the transmission response will be shaped such that the leading edge is steeper and the trailing edge has reduced slope. ...

It sounds like you are saying that a linear transmission line structure can give you increased frequency components.

A linear structure can only act as a filter.

With a step recovery diode or an NLTL, you can input a pure sine wave and output a step that is rich in higher harmonics.

You can't do that with a linear structure.

Each layer is a frequency selective time delay and 90 degree phase shift.  By delaying the lower frequencies first it has the effect of making the leading edge steeper.  You will get a similar effect merely by making a symmetric (zero phase)  waveform minimum phase.   Bode showed that physically realizable filters are minimum phase.  That only requires a 90 degree phase shift.  The layered structure provides additional delay beyond just applying a convolution with a Hilbert operator aka quadrature operator.

If the thinnest layer is first it will steepen the trailing edge.

Case describes this as Bragg spacing.  He then talks about the importance of tapering the NLTL spacing, but he's relying on simulation results rather than analysis.

 A significant portion of the incident pulse is reflected.  Even in a lossless medium, the energy of the transmitted wave will be significantly smaller than the incident wave.

Until I've derived the closed form Z transform I can't evaluate how much effect the non-linear diode response contributes to the results.

A linear lossless system is time invariant.  So no need to state that. The non-linear case is not time invariant.

An LC frequency multiplier is a linear time invariant system.  Lossless implies infinite Q. I deliberately restricted my statements to the linear lossless case because it's easier to understand the idea without being distracted by the additional complexity of the non-linear, time variant case.
 

Offline rfeecs

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Re: Generating a <3 pS rise time step
« Reply #34 on: March 17, 2019, 11:54:46 pm »
An LC frequency multiplier is a linear time invariant system. 

 :-//
 

Offline rhb

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Re: Generating a <3 pS rise time step
« Reply #35 on: March 18, 2019, 02:05:14 pm »

No one  has any authority beyond what they can prove by an articulate logical argument.

I'm afraid I'm mystified by your smiley.  I certainly would not describe your response as articulate.

I have not said that a passive system can generate harmonics.  What i have said is that a passive system can modify the phase of the frequency components of the input.  And by applying a larger phase delay to the the low frequencies can sharpen a leading edge and by applying a larger delay to the high frequencies can steepen the falling edge.

After careful thought, I believe those to be accurate assertions.  I have not yet derived a mathematical proof.  The Z transform of an infinite impulse response is rather untidy and a cascade still more untidy.  My previous work dealt with completely arbitrary layering.  So even if I could find it, it would not be much help as I moved rather quickly from a single layer to the arbitrary case. In this instance I need to solve for a particular set of layer impedances and thicknesses which is best able to produce the desired response.

Once I have that expression I can evaluate what I can do with readily available discrete capacitors.  At the conclusion of that experiment I shall construct a similar device using discrete diodes.

Case treats the linear case of a segment of  a transmission line in the 2nd chapter of his dissertation. I have attached two figures from his dissertation.  In the figures k is the imaginary part of the complex propagation constant and d is the physical length. The figures compare a lumped constant solution to a linear transmission line case with constant shunt capacitance.  As a consequence, it only shows the effect of considering the circuit as a transmission line rather than as a lumped constant filter.

On p. 16 he concludes that the dispersion is adequately modeled by the LC case and that non-linearity only affects the velocity term.

From there he starts discussing the problem in terms of solitons.  As I have no prior experience with solitons I must first acquaint myself with the mathematical niceties before I proceed further.

Case made 3 design iterations of an IC.  But does not compare a multi-segment linear TL  to a multi-segment non-linear TL.  I still do not know whether that is presented in any of the other work he references.

My sole reason for pursuing this is it is a fiendishly difficult problem with which I have little prior experience.  So whatever the outcome I shall learn a great deal.  It is research as a gentleman's amusement rather than an industrial product.
 

Offline David Hess

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Re: Generating a <3 pS rise time step
« Reply #36 on: March 18, 2019, 04:55:39 pm »
I have not said that a passive system can generate harmonics.  What i have said is that a passive system can modify the phase of the frequency components of the input.  And by applying a larger phase delay to the the low frequencies can sharpen a leading edge and by applying a larger delay to the high frequencies can steepen the falling edge.

...

On p. 16 he concludes that the dispersion is adequately modeled by the LC case and that non-linearity only affects the velocity term.

...

My sole reason for pursuing this is it is a fiendishly difficult problem with which I have little prior experience.  So whatever the outcome I shall learn a great deal.  It is research as a gentleman's amusement rather than an industrial product.

This seems suspiciously like the very old problem of "dribble-up" in transmission and delay lines.  Skin depth and therefor resistance per unit length varies with frequency and the dielectric constant also varies with frequency.  Under these conditions, a passive network which corrects for the phase distortion induced by the transmission line decreases the transition time.  This problem is also why high frequency systems often use 20% to 80% or 50% transition time measurements; 10% to 90% measurements are pessimistic or meaningless when dribble-up is significant.

Check out page 186 of Tektronix 062-1145-00 - Oscilloscope Vertical Amplifiers - December 1969 which discusses "dribble-up".  There is also considerable information about the compensation networks.

On a slightly different subject, what kind of edge performance should be feasible with common surface mount construction using SOT-23 sized devices?
 

Offline rfeecs

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Re: Generating a <3 pS rise time step
« Reply #37 on: March 18, 2019, 06:44:27 pm »

No one  has any authority beyond what they can prove by an articulate logical argument.

I'm afraid I'm mystified by your smiley.  I certainly would not describe your response as articulate.

The smiley means "confused", as I am totally confused by your statement "An LC frequency multiplier is a linear time invariant system."

This may be because I don't know what you mean by an LC frequency multiplier.  Can you provide an example?

In my mind, a linear time invariant system by definition cannot be a frequency multiplier.
 

Offline rhb

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Re: Generating a <3 pS rise time step
« Reply #38 on: March 18, 2019, 07:13:42 pm »

On a slightly different subject, what kind of edge performance should be feasible with common surface mount construction using SOT-23 sized devices?

LOL  Obviously you have me confused with someone who knows what they are doing.  I have no idea, but I hope to find out.

The dual oscillator-NLTL hybrid circuit  that Marco linked used some MW diodes that are available in a very small package.  Unfortunately, I can't easily vary the impedance of a conductor over ground as either the wire diameter or the height has to vary to change the impedance of the TL.  So my original construction concept is pretty much out the window.

The big issue I see with conventional microstrip is the stray inductance of the vias.

This is all uncharted territory for me.  The only thing I have going for me is I spent 4 years living on slave wages learning a lot of mathematics trying to get a PhD only to lose my financial support just as I was closing in on the solution of the problem.  I made the mistake of proving my supervisor wrong.  He was going blind from retinal detachments and did not react well.  In the end, except for not being able to get certain jobs it didn't matter.  But two PhDs who regularly came to me for Unix computer help got jobs with Thinking Machines. as customer support engineers for which I was considered ineligible for lack of the certificate.. As much as I would have liked to get the degree, starting over at Stanford would have been another 6 years of lost income.  At 36 that was simply too expensive to consider.

I had two reasons for using dead bug.  I don't know how to use any of the PCB design packages.  And the analysis of a conductor above a ground plane is much simpler than a microstrip line or a coplanar waveguide.

One experiment I plan is to construct a coplanar waveguide from copper sheet surrounded by an air dielectric with steps in the width and spacing going from the output impedance of the LED driver Leo is using to 50 ohms.  That has the advantage of avoiding a lot of parasitics. The device has a 21 ps rise time.  So if I can match it properly I should be able to reduce that quite a bit.  Obviously a factor of 7 is not likely.  Keysight would not be selling a 3 ps rise time pulser if they could consistently build something faster.  I suspect that changes in the dielectric constant of room air due to humidity quickly becomes a serious problem as you get below 10 ps for any discrete component construction.

One of the things I find fascinating (and very beneficial) is how often I see familiar problems in new clothes.  I usually takes a while to dig through the new jargon, but once I do there's a vast amount of prior knowledge and experience I can bring to bear.

When I started reading Case's dissertation I had no Idea I'd be looking at the equivalent of a 1D layered medium problem.  Or that I'd be revisiting something I did over 30 years ago.

@rfeecs  It was once very common practice to derive signals in master oscillator-power amplifier (MOPA) transmitters for 21 and 28 MHz by using a tank circuit tuned to a harmonic of the MO.  It's not actually *generating* harmonics.  It's just amplifying a selected harmonic produced by the inherent non-linearity of the MO. Strictly speaking it's not a multiplier.  But that is the traditional terminology.

This whole effort is wandering around territory where it is horribly easy to make a misstatement or to overlook the elephant in the room such as the trigger to sweep delay of the 11801 which David Hess pointed out.

Communication is inherently and unavoidably difficult in a forum where the oldest members are close to 90 and the youngest in their teens.  Word meanings shift as the mental context of the two parties shift.

I've spent almost 2 hours writing this.  I'm going to make some connector reflection examples.

Have Fun!
Reg
 

Offline rhb

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Re: Generating a <3 pS rise time step
« Reply #39 on: March 18, 2019, 09:36:37 pm »
The part that Leo Bodnar is using in his pulsers is a Maxim 3949 LED driver.  It is specified as 22 ps typical. 36 ps max rise and fall times. It will dump 85 mA into 5 ohms.

I've attached the AC test circuit from the datasheet.  Once I work out the Z transform of the transmission response of a stepped impedance delay line I'll model it in openCEM as coplanar waveguide.

If I can get it to work, I'll drive it with my GPSDO.
 

Offline David Hess

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Re: Generating a <3 pS rise time step
« Reply #40 on: March 19, 2019, 12:32:50 am »

On a slightly different subject, what kind of edge performance should be feasible with common surface mount construction using SOT-23 sized devices?

The dual oscillator-NLTL hybrid circuit  that Marco linked used some MW diodes that are available in a very small package.  Unfortunately, I can't easily vary the impedance of a conductor over ground as either the wire diameter or the height has to vary to change the impedance of the TL.  So my original construction concept is pretty much out the window.

The big issue I see with conventional microstrip is the stray inductance of the vias.

...

I had two reasons for using dead bug.  I don't know how to use any of the PCB design packages.  And the analysis of a conductor above a ground plane is much simpler than a microstrip line or a coplanar waveguide.

One experiment I plan is to construct a coplanar waveguide from copper sheet surrounded by an air dielectric with steps in the width and spacing going from the output impedance of the LED driver Leo is using to 50 ohms.  That has the advantage of avoiding a lot of parasitics. The device has a 21 ps rise time.  So if I can match it properly I should be able to reduce that quite a bit.  Obviously a factor of 7 is not likely.  Keysight would not be selling a 3 ps rise time pulser if they could consistently build something faster.  I suspect that changes in the dielectric constant of room air due to humidity quickly becomes a serious problem as you get below 10 ps for any discrete component construction.

There was a trick of physical construction that Tektronix used 30+ years ago to reduce various parasitic effects and especially inductance.  They were making and packaging their own ICs and hybrids so besides including internal terminations as described below, they took advantage of the opportunity to include dual metal traces, bond wires, and pins where needed so that the connection to the active device was located along the transmission line instead of at the end of the stub formed by the lead, leadframe, and bond wire as shown below.  Unfortunately parts packaged like this are basically unavailable but then again, so are RF PNP transistors now also.

The part below shows both of these.  The emitters terminate together inside the package but each base has two separate metal runs, wire bonds, and leads.

The part that Leo Bodnar is using in his pulsers is a Maxim 3949 LED driver.  It is specified as 22 ps typical. 36 ps max rise and fall times. It will dump 85 mA into 5 ohms.

The Maxim and similar parts rely on an internal termination so stub length between the the output device and termination is minimized.  If a transmission line environment is maintained through the package, then performance is only limited by the output device.
 

Offline rhb

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Re: Generating a <3 pS rise time step
« Reply #41 on: March 19, 2019, 02:48:57 am »
Can you provide a link to a more complete description of the theory of operation?

I *think* I sort of understand the input, but the output is a good bit harder.

But maybe it will make more sense in the morning.  It is bedtime for Bonzo.
 

Offline tomato

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Re: Generating a <3 pS rise time step
« Reply #42 on: March 19, 2019, 04:06:48 am »
... the analysis of a conductor above a ground plane is much simpler than a microstrip line ...

Micro strip is a conductor above a ground plane.

Quote from: rhb
I spent 4 years living on slave wages learning a lot of mathematics trying to get a PhD only to lose my financial support just as I was closing in on the solution of the problem.  I made the mistake of proving my supervisor wrong.  He was going blind from retinal detachments and did not react well.  In the end, except for not being able to get certain jobs it didn't matter.  But two PhDs who regularly came to me for Unix computer help got jobs with Thinking Machines. as customer support engineers for which I was considered ineligible for lack of the certificate.. As much as I would have liked to get the degree, starting over at Stanford would have been another 6 years of lost income.  At 36 that was simply too expensive to consider.

... I've spent almost 2 hours writing this.

Suggestion: You’ve included the above story in dozens of posts.  If you put it in your signature line, you could save considerable time in the future.
 

Offline T3sl4co1l

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Re: Generating a <3 pS rise time step
« Reply #43 on: March 19, 2019, 07:42:47 am »
LOL  Obviously you have me confused with someone who knows what they are doing.  I have no idea, but I hope to find out.

So why not calculate it?

What is the highest frequency such construction could possibly support?  What is the highest frequency, or fastest velocity or acceleration or etc., that a device on that scale could produce?  What impedances could it have at those frequencies?

The answers broadly cluster in the 10s of ps range, due to wirebonds, pin and trace lengths and widths, and various other catches related to the geometry scale.  Material properties (namely, dielectric loss and dispersion of bodies and laminates) apply, too. :)

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Offline rhb

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Re: Generating a <3 pS rise time step
« Reply #44 on: March 19, 2019, 02:30:24 pm »
... the analysis of a conductor above a ground plane is much simpler than a microstrip line ...

Micro strip is a conductor above a ground plane.


Except that the dielectric is different on the top and bottom.  That complicates the velocity calculation.
 

Offline rhb

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Re: Generating a <3 pS rise time step
« Reply #45 on: March 19, 2019, 02:56:07 pm »
LOL  Obviously you have me confused with someone who knows what they are doing.  I have no idea, but I hope to find out.

So why not calculate it?


I am engaged in calculating the dispersion of a series of impedance steps  for the purpose of steepening the rise time of a Maxim 3949 LED driver which is specified as 22 ps typical, 36 ps maximum.

I have no control over device construction, so calculating device characteristics  such as you describe is not useful.  The datasheet provides a good enough answer.  In the end, the only thing that matters is the experimental result.

Interestingly, this turns out to be the transmission function of a source embedded in a layer with a perfect reflector at one boundary.   Milo Backus's major paper was the suppression of the reflection coda in the analog domain using an adjustable head on a magnetic drum in the late 50's before digital data acquisition became possible.  It is also the problem of feeding an ultra wide band antenna using an unbalanced feedline and an off center feed.

If you'd like to get a proper understanding of what I'm doing, calculate the transfer function for a 1 mm and 1 cm long transmission line with 49 ohm impedance embedded in a 50 ohm line.  In particular, examine the phase delay of the energy at resonance.
 

Online Marco

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Re: Generating a <3 pS rise time step
« Reply #46 on: March 19, 2019, 03:22:10 pm »
The answers broadly cluster in the 10s of ps range, due to wirebonds

I doubt any of the Skyworks Schottky's and varactors are wirebonded and the Macom varactor I linked is flipchip. Of course the groundplane is way too far away from the diode to maintain 50 Ohm impedance on the connections to the active part, but it's better than wirebond.
 

Offline David Hess

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Re: Generating a <3 pS rise time step
« Reply #47 on: March 19, 2019, 04:24:41 pm »
Can you provide a link to a more complete description of the theory of operation?

I *think* I sort of understand the input, but the output is a good bit harder.

The outputs in this case just have a single lead although they did make some which used two lead outputs but I do not have any of those datasheets.  In lower frequency applications, the extra leads were not connected.
 

Offline TheUnnamedNewbie

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Re: Generating a <3 pS rise time step
« Reply #48 on: March 19, 2019, 05:39:14 pm »
In my line of work, 110 GHz is considered 'the low end of our spectrum'.

Each layer is a frequency selective time delay and 90 degree phase shift.  By delaying the lower frequencies first it has the effect of making the leading edge steeper.  You will get a similar effect merely by making a symmetric (zero phase)  waveform minimum phase.   Bode showed that physically realizable filters are minimum phase.  That only requires a 90 degree phase shift.  The layered structure provides additional delay beyond just applying a convolution with a Hilbert operator aka quadrature operator.

A dispersive material used to compress a pulse and increase sharpness can only increase the sharpness of the edge insofar there is enough signal bandwidth already available to do so. To my knowledge this is what they do with femtosecond pulse lasers - but in order to do so, they need to start out with a wide-band pulse that contains lost of frequencies already.

Lets look at it this way: From the frequency-time-domain duality, we know that a pulse in the time-domain is \$\sin(x)\cdot x^{-1}\$ in the frequency domain --- in other words, we need infinite bandwidth to have an infinitly sharp pulse. If we band-limit this pulse, we chop off some of that bandwidth, and we get a lower rise time. How low a rise-time we get in relation to what we get doesn't matter for what follows:

A linear system \$H\$ cannot generate new frequencies. Let us prove this:

A system \$G\$ is linear if, for a given inputs \$x(f)\$ and \$y(f)\$ and scalars \$\alpha\$ and \$\beta\$ (if this holds in the frequency domain this also holds in the time domain, as the Fourier-transform itself is a linear operation), the following is true:

\$\alpha G{x(f)} + \beta G{y(f)} = G{\alpha x(f) + \beta y(f)}\$.

So let us say that for a given \$f_a\$, \$x(f_a)\$ and \$y(f_a)\$ equal zero (IE, signals \$x\$ and \$y\$ have no frequency content at \$f_a\$). Then if \$G\$ generates frequency components that weren't already there, \$ G{\alpha x(f_a) + \beta y(f_a)} = G{0} = c \neq 0\$, with \$c\$ a constant. We can now plug in this result into the LHS of our definition, and say that:

\$\alpha G{0} + \beta G{0} = \alpha c + \beta c\$

But the left-hand side of our equation must also equal \$G{\alpha x(f_a) + \beta y(f_a)}\$, which we already said was equal to \$G(0)=c\$. In other words, \$\alpha c + \beta c = c\$ for all possible \$\alpha\$ and \$\beta\$, which cannot be valid if \$c \neq 0\$. This proves by contradiction that if the input does not have any content at \$f_a\$, the output too does not have any content at \$f_a\$: a linear system cannot add frequencies - it can only 'reshuffle' them.

The problem in your suggested approach using is that your pulse source, that laser diode driver, will likely not have any spectral content high enough to make the pulse much faster. And even if it had: to get a 3 ps pulse, you would need spectral content up at 100 GHz - there is no way you are going to get that more than a few millimeters on an FR4 PCB. On a rogers substrate, maybe - but you would still need a connector that behaves itself past 100 GHz (only connectors that do that are 1 mm and 0.8 mm connectors), and that present an impedance you can work with. I also suspect that most micro-strip lines will be too dispersive to keep your pulse sharp very long. The difference in loss between frequencies will also cause issues, as this will reduce sharpness further and must be compensated for short rise-times.

In short: I think this won't work very well. A better solution to me would seem some kind of RF MEMS switch that is rated for many GHz, and try working with that. Creating a square wave can also be easier, since then you just need to play around with a discrete spectrum of harmonics. But I think in the end it is impossible to generate anything like this with discretes. This is hard enough to do on chip, with fancy technologies like SiGe, GaAs, GaN or InP (forget CMOS, won't slew fast enough me thinks).
The best part about magic is when it stops being magic and becomes science instead
 

Offline T3sl4co1l

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Re: Generating a <3 pS rise time step
« Reply #49 on: March 19, 2019, 06:08:11 pm »
I am engaged in calculating the dispersion of a series of impedance steps  for the purpose of steepening the rise time of a Maxim 3949 LED driver which is specified as 22 ps typical, 36 ps maximum.

LED?  LEDs don't respond that fast...

Mind, I'm not sure how much to take literally here, versus simple mistakes (did you mean diode laser?), versus factual errors.  This has all been very confusing...


Quote
I have no control over device construction, so calculating device characteristics  such as you describe is not useful.

You say that, but:

I doubt any of the Skyworks Schottky's and varactors are wirebonded and the Macom varactor I linked is flipchip. Of course the groundplane is way too far away from the diode to maintain 50 Ohm impedance on the connections to the active part, but it's better than wirebond.

So you have your choice of SOT-23s or beam leads or flip chips or whatever you like!

Not freedom as in, here's a die, here's a pantry of resins and here's a 3D printer that does teflon and copper.  Not by any means.  But some freedom, and it would be foolish to ignore such an opportunity!

Or put another way: if you are restricting yourself to SOT-23s or whatever, then that's all the performance you can possibly get out of it, full stop.  A typical SOT-23 (wirebond) has some characteristic length, impedance spread, and therefore cutoff frequency, associated with it, whatever the die inside is.

Repeat the analysis for each packaging option, and you're basically done, here are your options, make the most of them. :)


Quote
Interestingly, this turns out to be the transmission function of a source embedded in a layer with a perfect reflector at one boundary.   Milo Backus's major paper was the suppression of the reflection coda in the analog domain using an adjustable head on a magnetic drum in the late 50's before digital data acquisition became possible.  It is also the problem of feeding an ultra wide band antenna using an unbalanced feedline and an off center feed.

If you'd like to get a proper understanding of what I'm doing, calculate the transfer function for a 1 mm and 1 cm long transmission line with 49 ohm impedance embedded in a 50 ohm line.  In particular, examine the phase delay of the energy at resonance.

???

I can't tell to what "this" is referring.  What is a "source in a ... layer"?  What is a "coda" in signals analysis?  (Guessing something geophysicists use and no one else?)

How, exactly, does one "embed" a transmission line, in another transmission line?

This is all very confusing...

Tim
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Bringing a project to life?  Send me a message!
 
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Online Marco

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Re: Generating a <3 pS rise time step
« Reply #50 on: March 19, 2019, 08:08:25 pm »
I wonder if with very fine pitched PCB and a coplanar waveguide you could improve the high frequency performance of a flip chip diode by extending the ground plane under it.
 

Offline rhb

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Re: Generating a <3 pS rise time step
« Reply #51 on: March 19, 2019, 10:03:51 pm »
I suggest reading the datasheet for the Maxim 3949.  It's used to modulate laser diodes which are LEDs. Leo referred to it as an LED driver, so I did the same. It's made for 11 Gbps fiber optic links.

Coda is a musical term.  The earthquake seismologists use it often.  It is far less common in the reflection community.  It's what follows the initial impulse, i.e. the reverberations.  But we do read each other's literature so most research level scientists recognize the meaning.

I have never said that a passive device can create harmonics.  However, a passive device can and will of necessity change the phase.

Physically realizable filters are minimum phase.  Hendrik Bode described this in the 1930's.  I'm fairly certain it is this paper, "A general theory of electric wave filters" published in 1935 in the Bell System Technical Journal.  IEEE has it behind their paywall so I have not read it.

A symmetric triangular waveform is "zero phase" in signal processing parlance.  If you make the waveform "minimum phase"  it will no longer be symmetric. The leading edge will be steeper than the trailing edge. Three things happen.  There is a 90 degree phase shift, the portion of the sine waves before T0 is set to zero and the amplitudes of the values after T0 are doubled.  The amplitude and power spectra do not change.  The only thing that changes is the phase.

All pass filters are commonly used in signal processing to alter the phase of a signal.  In reflection seismic processing it is standard practice to zero phase the source waveform using a recording of the minimum phase impulse response of the input amplifier and filter chain and the signature of the seismic source.  This is particularly true with marine data which use an array of air guns to generate as sharp a spike as possible in a downward direction.  Air guns release air at well over 2000 psi into the water.  The bubbles oscillate as they rise to the surface causing unwanted signals following the initial impulse.

If you insert a segment of transmission line, e.g. a couple of BNC tees, the response of that segment is embedded in the response of the system as a whole.  This is standard terminology in vector network analysis.  The use of SOL and SOLT "calibrations" is to determine the response of the system without the DUT.  It is also referred to as "de-embedding" the DUT.

Johnson & Graham discuss multiple reflection in transmission lines at some length. Multiple reflections in the water column are a first order problem in reflection work because it creates a very narrow band pass filter in areas with hard water bottoms.  This is why Wiener got funding for the GAG students.  Solving the problem was of huge monetary value to the oil exploration community.

I'll provide an example of a symmetric waveform with Tr & Tf of 22 ps and the minimum phase equivalent later.  Octave running on Win 7 in a VirtualBox VM did not behave well and when I attempted to invoke the task manager in Win 7 it took down the host Unix system.

A 22 ps rise and fall waveform has its first zero at 45 GHz.  Because the frequency spectrum is a sinc(f)**2 there are minimal side lobes above the first zero. 
 

Offline rhb

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Re: Generating a <3 pS rise time step
« Reply #52 on: March 20, 2019, 12:04:13 am »
The preceding post took me over 2 hours to compose.  I do not intend to repeat that at such a low level.

If I reference a device, read the datasheet.  If I reference a paper, read the paper.  And if you don't understand the physics of a cavity filter, well, you're on your own.

Any reference to my personal history is intended as a hint to the reader that I have significant skills and not to jump to conclusions without careful thought.  Nothing more.  My usual statement is, "And beware of anyone who advertises they didn't get their PhD."

I'm accustomed to conversing with scientists with doctorates from Stanford, Austin, A&M, Mines, Delft and similar top rank schools. I don't care at all about degrees.  Bob Widlar, Jim Williams and Bob Pease were far better scientists and engineers than most PhDs.  The only thing that cuts any ice with me is the ability of the speaker.  I spent several years getting paid for reviewing and critiquing the work of Stanford professors and their students at consortium meetings.  Though not a Stanford consortium, I very nearly cut the funding for one consortium.  In retrospect, I should have as the work they were doing was of very poor quality.

So if I don't reply to your posts to this thread, you have your explanation of why.  I will post results and examples for future readers.
 

Offline T3sl4co1l

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Re: Generating a <3 pS rise time step
« Reply #53 on: March 20, 2019, 03:37:29 am »
I guess I'm glad I'm not in seismology; it looks like a whole separate culture of jargon and object definitions.  Makes me wonder how its development may've been held back from the benefit of related developments in radio or DSP; and vice versa, how much is lost to signal analysis, buried in obscure geophysical journals, or just trade-specific knowledge. :(

The reference is here:
https://archive.org/details/bstj14-2-211/
All BSTJ is public and free; it used to be hosted on the former Bell site (which was, uh, Alcatel-Lucent I think?), then they dropped it, then archive.org picked it up (good guys that they are!).

That seems to be just a note or preface for the meat of the subject here,
https://archive.org/details/bstj14-2-215/
which is a little dated with regards to modern analysis and notation, but still just as foundational as ever. :)

The minimum phase condition seems to be violated trivially with a transmission line, or an all-pass filter like,
https://en.wikipedia.org/wiki/Bridged_T_delay_equaliser
so I'm not sure where you're going with that?  An all-pole filter is minimal-phase, but nothing prohibits RHP zeroes in a passive network.

It sounds like you're talking about triangle waves like this,



This is a square wave approximated with I think 15 harmonics, with the phase of all the harmonics (same phase for all harmonics in each frame) going around the circle in the animation.  The Hilbert transformed version (90°) looks roughly triangular, so I wonder if that's what you are referring to?  But it's clearly not a triangle wave, because a triangle wave has harmonics that go as 1/N^2, while the square goes as 1/N.  Obviously, the Hilbert Square (as it were) will be much more peaky, maybe closer to a tan(theta) segment rather than a triangular segment?  Or maybe it's actually triangular, with Gibbs phenomenon isolated to the peaks only (hm, infinitesimal nipples?...nevermind), but no, that wouldn't make sense, the peaks have to have nonzero power to keep the same harmonic amplitudes.

Unfortunately, no matter how experienced you are, if you aren't communicating clearly, your point will simply be missed: this is one cost of domain-specific jargon. :-//

I've never heard "zero phase" applied to a signal (a "symmetric triangular waveform") before, admittedly I'm not terribly deep into signal processing myself but from an electronics background it just sounds like... word soup?

I assume it means something on the geophysical side -- but to show that meaning, you'll have to provide your definitions as well (in turn defined in terms of other definitions, as far down as necessary to find definitions that agree).  Which inevitably means some definitions that are so natural in your field that they feel intuitively obvious.

It's, well, learning a new language, to a modest extent.  It's going to be frustrating, yes. :-\

Tim
Seven Transistor Labs, LLC
Electronic design, from concept to prototype.
Bringing a project to life?  Send me a message!
 
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Offline rfeecs

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Re: Generating a <3 pS rise time step
« Reply #54 on: March 20, 2019, 04:46:55 am »

Each layer is a frequency selective time delay and 90 degree phase shift.  By delaying the lower frequencies first it has the effect of making the leading edge steeper.  You will get a similar effect merely by making a symmetric (zero phase)  waveform minimum phase.   Bode showed that physically realizable filters are minimum phase.  That only requires a 90 degree phase shift.  The layered structure provides additional delay beyond just applying a convolution with a Hilbert operator aka quadrature operator.

If the thinnest layer is first it will steepen the trailing edge.

Case describes this as Bragg spacing.  He then talks about the importance of tapering the NLTL spacing, but he's relying on simulation results rather than analysis.

 A significant portion of the incident pulse is reflected.  Even in a lossless medium, the energy of the transmitted wave will be significantly smaller than the incident wave.

Until I've derived the closed form Z transform I can't evaluate how much effect the non-linear diode response contributes to the results.

A linear lossless system is time invariant.  So no need to state that. The non-linear case is not time invariant.

An LC frequency multiplier is a linear time invariant system.  Lossless implies infinite Q. I deliberately restricted my statements to the linear lossless case because it's easier to understand the idea without being distracted by the additional complexity of the non-linear, time variant case.

I think you are totally off the mark here.

The NLTL works completely and simply based on the nonlinear capacitance of the transmission line.  The capacitance of the diodes depend on the voltage across them.  They are biased so they always have a negative voltage across the junctions.  As the voltage across them goes more negative due to the forward voltage wave, the capacitance drops, and the voltage wave speeds up for this portion of the waveform.  The result is the falling edge of the wave sharpens.  This results in the improved fall time.

Attached is a simple LTSPICE simulation showing 15 stages of just a basic diode model with 2pF Cjo, driven with a 1GHz sine wave.  The input is a single frequency sine wave.  The output is something of a sawtooth wave, with a sharpened fall time of maybe 50pS.  The output spectrum has harmonics going out to 8GHz or more.

The only other elements are the inductances between the diodes which I just set at 2nH for this experiment.

There is absolutely no way you could turn a single frequency sine wave into a sawtooth wave with just some linear transmission lines.

This is all spelled out in infinite detail in the two theses you referenced, by Mark Rodwell and Michael Case.  You'll find some similar plots to this simulation, for example figure 2.9 of Rodwell's thesis, attached.

To summarize, the capacitance is a nonlinear function of voltage.  That is the entire basis for how the NLTL works.

« Last Edit: March 20, 2019, 04:49:58 am by rfeecs »
 
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Offline RoGeorge

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Re: Generating a <3 pS rise time step
« Reply #55 on: March 20, 2019, 09:58:01 am »
Thank you for the topic, rhb.  Subscribed.

Please allow to point that the "magic dust" here is the non-linearity of the device (or transfer function).  If it's a passive or an active device, it doesn't matter.

To make an edge steeper, we need to add extra high spectral components (the steeper an edge is, the richer the spectrum of that edge).  In order to produce extra spectral components, a non-linear device is required.  Once we have the extra spectrum, all we need is to carefully match the phase in order to build the desired steeper edge.

In the non-linear transmission lines linked here, the non-linear devices are the diodes, but in theory can be anything as long as it will have a non-linear transfer function

I have not said that a passive system can generate harmonics.  What i have said is that a passive system can modify the phase of the frequency components of the input.  And by applying a larger phase delay to the the low frequencies can sharpen a leading edge and by applying a larger delay to the high frequencies can steepen the falling edge.

I have never said that a passive device can create harmonics.  However, a passive device can and will of necessity change the phase.

It doesn't matter if a device is passive or not.  As long as a device is linear, it will not generate extra frequencies.  The condition to generate new frequencies is the non-linearity of the transfer function.

As an example, a transformer (which is considered a passive device) can generate harmonics (i.e. if it is driven too hard).  This will happen because the magnetic properties of the transformer's core are not linear, so the whole transformer will become a non-linear passive device.

Without any math, the intuitive explanation for why a non-linear device will alter the output spectrum is in the following image:



- When the red line is a straight line (like in the picture), then the output will have the same shape.  In frequency domain, same shape means the output spectral composition is unchanged.
- When the red line is not a straight line any more, the output will be distorted.  Any distortion of our output waveform means we will need extra spectral components in order to produce a distorted waveform shape.
« Last Edit: March 20, 2019, 10:12:23 am by RoGeorge »
 
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Offline rhb

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Re: Generating a <3 pS rise time step
« Reply #56 on: March 20, 2019, 04:44:25 pm »
At all levels, but especially at the research level, reflection seismology is populated by people with degrees in electrical and mechanical engineering, physics, mathematics and probably a discipline or two I can't think of  at the moment in addition to people who got degrees in geophysics.  I don't know if anyone has ever collected statistics, but I would not be the least surprised if geophysics degrees were well under 1/3 of the group.

As a consequence, one has to be very nimble switching among lexicons when chatting in the hallways at the annual professional society meetings. 

Moreover, every organization has its own signal processing jargon.  I've worked in 7 organizations.  A reasonable guesstimate is that it takes about 6 months to learn the local dialect.

The wave equation is the wave equation no matter whether it is electromagnetic, elastic or optical.  I've sought refuge in that many times.

Good lord willing, the creek don't rise and Octave doesn't crash I should have some figures later today.
 

Online Marco

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Re: Generating a <3 pS rise time step
« Reply #57 on: March 20, 2019, 08:18:12 pm »
Math is nice and all, but the only diode which is going to get you >>10GHz bandwidth is the MAVR-011020-1411 and the datasheet is crap, on top of needing to include layout and substrate effects to actually get a model for which rigorous optimization makes much sense.

I'd just make a hacky varactor spice model using the datasheet capacitance graph and assuming say 150 pH of inductance and then working back from Q to Rs, throw it in spice with some transmission lines and just experiment to get some idea how to layout your PCB and see how it goes.
 

Offline rhb

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Re: Generating a <3 pS rise time step
« Reply #58 on: March 20, 2019, 10:09:57 pm »
Not sure math is all that nice :-(

So far as I can tell there is no way to create the minimum phase waveform from an amplitude spectrum via the Hilbert transform.  The causality constraint requires that the imaginary part be a *convolution* of the amplitude spectrum with the Hilbert operator (-1/pi*f).   That operation completely changes the amplitude  spectrum.

Which goes a long way to explaining why none of us were able to do it grad school.  I'd always thought we'd just got it wrong because of a software glitch in the DSP package we were using and were in too much of a hurry to get our homework done to get it right.  But the Wiener inverse of the Wiener inverse may be the only way other than an L1 solution.

This is clearly going to require deep thought and probably a good bit of reading starting with Robinson and Treitel.

FWIW An autocorrelation is a good example of a zero phase signal.  But it's really a recorded time DSP feature that's not available in real time.  Very common in data analysis, but not in circuit design.
 

Online Marco

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Re: Generating a <3 pS rise time step
« Reply #59 on: March 20, 2019, 11:01:55 pm »
From what I remember you use the cepstrum to go from magnitude frequency response to minimum phase filter ... well that's how you did it for discrete time DSP any way.

I don't really see what's the point though, as I said the system is going to be behaving so far out of the realm of good modeling that it's more suited to just plain experimentation.
 

Offline rfeecs

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Re: Generating a <3 pS rise time step
« Reply #60 on: March 20, 2019, 11:24:28 pm »
From what I remember you use the cepstrum to go from magnitude frequency response to minimum phase filter ... well that's how you did it for discrete time DSP any way.

Wow.  I had to look up cepstrum.  Which led me to other terms quefrency, alanysis, liftering, and saphe.  They correspond to spectrum, frequency, analysis, filtering, and phase.

Bizarro terminology.
 

Offline rhb

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Re: Generating a <3 pS rise time step
« Reply #61 on: March 21, 2019, 02:36:53 am »
Shades of homomorphic deconvolution!

I punted for the evening and finished reading "History of Semiconductor Engineering" by Bo Lojek.  Fabulous content, but hopelessly bad writing and editing.  Though vastly better than Henry Ott's book "Electromagnetic Compatibility Engineering" which is simply unreadable.

After today's results I'm probably going to put this on the back burner for a while and see what comes to mind.  There is a point where the fastest way forward is to do something else.

 

Online Marco

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Re: Generating a <3 pS rise time step
« Reply #62 on: March 22, 2019, 04:21:15 am »
For a laugh I've tried to simulate a 10 stage NLTL with a very simple varactor model consisting of CJ0=0.2e-12, M=2, VJ=8, Rs=15, Lp=150p. Calculated using the datasheet, the formulas for Cj and Q and the parasitic inductance for Skyworks 0201 flipchip components. It doesn't seem capable of speeding up a 25ps edge, mostly because of the parasitic inductance, if I lower that to 50p it's able to speed up the rise time by a couple of ps. Still pretty disappointing for 10 stages.

I'm not optimistic for a discrete solution to be able to do much at these timescales.

PS. I didn't add compensating inductance in series with the transmission lines here, which are supposed to be there for the classical NLTL modeling ... but when I tried to add them and vary the values a bit from 50p-250p it didn't seem to matter much. Maybe a higher capacitance varactor compensated with some inductance would work better than the ultra low capacitance MAVR-011020-1411? Kinda doubt it.
« Last Edit: March 22, 2019, 07:46:34 am by Marco »
 


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