Author Topic: Generating a <3 pS rise time step  (Read 9553 times)

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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 rhbTopic starter

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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 rhbTopic starter

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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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Online 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 rhbTopic starter

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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 rhbTopic starter

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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.
 
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Offline rhbTopic starter

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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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