I didn't claim to make all my systems from 1% parts; what gave you that idea? Besides, we calibrate and sometimes temperature compensate precision circuits.
We have several analog circuits that have been measured to numbers like tens of PPM accuracy per year. Frequency can be way better, PPBs.
Actually, we're bad at that. What sells is our product performance.
Sales keep increasing, and we have big science and semiconductor and aerospace outfits that keep coming back for more.
Analog circuits that are not chaotic are predictable, and precision just takes money.
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John Larkin Highland Technology, Inc
lunatic fringe electronics
That's a marshmallow answer: metastability is an issue when the data is asynchronous to the clock, and FPGAs are a walled garden where that cannot happen.
Weakly chaotic? Meaning... what, exactly? New buzzphrase alert!
but most aren't designed that way (it's added expense).
Odd that you'd hazard a guess about that. You haven't TESTED most oscillators. A well-filtered power supply doesn't have much harmonic content in the megahertz-and-up range of a crystal clock, it's the oscillator amplitude (and frequency stability) that depends on time-after-power. Phase-after-power is indeterminate.
It is not true that one needs ppm equipment to achieve ppm accuracy. And how could it be so? Somehow we went from not knowing that electricity even existed to the point where we can measure and achieve ppm precision and accuracy. I have a 6.5-digit DMM that does this (for $1200 if I recall).
So there must be methods that allow better precision and/or accuracy than the available tools, so better tools can be built, and the cycle repeated. (The same kind of thing happened in the machine tool world.)
Start with the Wheatstone Bridge, which allows one to make ppm comparisons of equality of lumped-resistor DC values. What is needed is resistor stability, which is far easier than precision.
The process: Make one resistor and declare it the standard. Make a second resistor of equal resistance, by trimming the second against the first while comparing them on the bridge. Put the resulting two equal resistors in series and make a third resistor of twice the value of the first resistor. Rinse and repeat to generate a full ladder of resistors with precise resistance ratios. A binary 1,2,4,8 sequence allows all 2^N values to be achieved, as does a
1,2,2,5 sequence. And so on.
One can also put the two equal resistors in parallel, and trim a third resistor to one half the value of the first resistor. And so on.
This can also be done with capacitors and inductors, and with AC bridges, one can balance inductors against capacitors. And so on. There are a few hundred types of 4-arm bridge in the literature.
A RF parallel is a quadrature bridge, where one has a source, a power divider, a delay line in one arm, a component under test in the other arm, a phase detector followed by a very sensitive galvanometer. One can detect femtosecond changes in delay with such a setup - I have done it.
An ordinary dual-slope integrating digital multimeter derives all accuracy from a single precision resistor, and the use a a very stable (and low hysteresis) integrating capacitor whose exact value is not important - one can use a 5% unit.
There are specs and equations that predict a flop's metastability probability vs resolution time, and the likelyhood of a flop being unsettled (states 0 and 1 are available) drops ultra-radically with time, and once it's settled nothing else happens. The state of the weather system diverges radically with time and it never settles.
The situations are entirely different: one system settles after disturbance, one gets progressively more disordered. Flipflops are not very complex; the atmosphere is.
In classical physics, the fundamental differences between 2-body and
3-body systems was recognized hundreds of years before anyone discussed "chaos theory."
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John Larkin Highland Technology, Inc
lunatic fringe electronics
FPGAs have input pins, and often have multiple, asynchronous clock domains. But their internal flops resolve in picoseconds. It's prudent to design metastable-hard, but in real life it's seldom necessary. System general MTBFs are a vastly bigger concern than most metastability hazards.
Meaning the chaos is limited and usually unimportant. Aluminum makes lots of microscopic crystals when it solidifies, not gross defects. The chaos of crystallization rarely matters.
Dump molten aluminum into a mold and don't degass: that chaos will matter.
Not to worry, we charge a lot.
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John Larkin Highland Technology, Inc
lunatic fringe electronics
We often have per-channel cal tables that use 3rd or 4th order polynomials. The parts have to be stable but not initially accurate.
Temperature sensing and compensation is the next step, but temperature cycling is not something that we like to do in production.
Some products can auto-cal a bunch of measurement channels based on one or two really good, expensive references.
I recently designed a 600 MHz triggered oscillator whose tempco was sufficiently predictable (or predictably bad) that all units could be temp compensated without individual temp cycling in production. I think the big tempco was the FR4 PCB dielectric constant, which is reasonably repeatable, ballpark +800 PPM/K.
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John Larkin Highland Technology, Inc
lunatic fringe electronics
Metastaility is well understood, as are the particular flops in question. One can make very good predictions based on this information, particularly when the flop resolves many orders of magnitude faster than the data. No matter what AlGore says, the atmosphere is most certainly *not* well understood.
Unless they're asynchronous. Do you really design this stuff?
That's exactly what the AGWers are doing. Selling hokum.
Krw is completely wrong here. It's the anthropogenic global warming deniers who are selling hokum. Krw and John Larkin can't do good enough critical thinking to realise that they are being misled.
You don't need to know much to pick the signs, but neither krw nor John Larkin is that knowledgeable.
Chaotic systems are not limited by math. Your simulation of chaotic system s may be limited in their accuracy or resolution. That is the fundamental definition of a chaotic system, one with large scale deviations from very s mall differences in initial state. Your oscillators are the same way. You say they are ps accurate, but they aren't really, not over the long term. Then there are spurious modes of oscillation which can be suppressed to an y given low rate of occurrence you wish, but never eliminated... much like metastability.
For someone who works in chaotic systems, you seem to understand them poorl y.
I see you have a very limited understanding of both chaos and metastability . You say a FF never diverges once it has settled. But settling is define d to be an output that meets the conditions of your statement. If the outp ut appears to settle, then burst into oscillations for some time did it set tle and then upset again or was it never settled? That happens. I've seen images of this.
A system with many metastable FFs can be as arbitrarily complex as you make it. No one controls the weather. It is constantly stirred by heat input. FFs are constantly stimulated into metastability in a similar manner. Bu t what does that have to do with anything?
I used to believe that. At one point it was shown by some excellent Xilinx engineers that the resolution of metastability in a FF was very fast for t hat generation and expected to improve for the next generation. But more r ecently I was posting that info and someone showed this is no longer true a nd the metastability resolution numbers have been getting worse. They are still great, but if you are running fast transitions and fast clocks you sh ould not skip the calculations for your specific device.
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So "weakly" chaotic doesn't say anything about the chaos, it only speaks to whether you expect it to be important to your work. More of your personal ly referenced definitions.
Because your beliefs tend to be self-contradictory, or at least poorly expr essed, we do try to tease out what you actually think, and why you appear t hink that.
Never heard of Hadley Cells?
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That's largely because the continents move around, rather than the climate.
The current arrangement of continents is unusual - it permits ice ages, whi ch are rare (on the geological time scale.
Understanding how the current earth can flip between ice ages and interglac ials was part of the process of working out why anthropogenic global warmin g is real and why we should try to slow it down.
Atmospheric CO2 levels are about 180 ppm during ice ages and 270 ppm during normal interglacials. High albedo ice sheets across the more northern - an d higher - parts of the northern hemisphere are most of the rest of the exp lanation of of the difference between ice ages and interglacials.
The denialist web sites on which you rely for all your information on the s ubject don't reflect current scientific insights, for obvious reasons.
But more recently I was posting that info and someone showed this is no longer true and the metastability resolution numbers have been getting worse. They are still great, but if you are running fast transitions and fast clocks you should not skip the calculations for your specific device.
Dangerous blindness there: a flipflop that registers the MSD of an election, can steal the election. While it may comfort you to think that the flipflop 'settles after disturbance', that just means that the election was stolen, and then the evidence destroyed. This is NOT comforting.
The flipflop that settles after a microsecond, has damaged the electorate for the next two to six years...
Don't I hear a 'very complex' buzzphrase now? You're up to five of those so far, all capable of hiding bits of reality. Atmospheric makeup requires a big spreadsheet, all right, but it works on cause and effect just like the 'medium complex' and 'not complex' systems.
Peter was a cool guy. I had my head inside a box of books at the Foothill Flea Market and then there was another head inside: Peter's.
He was friendly and talkative and said to not worry about metastability in Xilinx chips. But just to be safe, we still do.
In some cases, metastability just reinforces the fact that the input transitioned too close to the clock, and in that case it doesn't matter if it resolves to 1 or 0.
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John Larkin Highland Technology, Inc
lunatic fringe electronics
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