Author Topic: Generating a <3 pS rise time step  (Read 4403 times)

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