What to use for an array of very high Q resonators? - Page 1
Forum section: electronics / rf-microwave

author: RoGeorge
author_rank: Super Contributor
timestamp: July 05, 2021, 11:20:25 pm
content: I need an array of resonators (10...100 of them) with quality factor (Q) as big as possible, for a physics experiment.Roughly, the experiment is about poking some energy at some of those high Q resonators, then observing what's happening and how the resonators exchange energy. The math alone or a numerical simulation probably won't cut it, because I expect to see something new. The resonant circuits have to be analogue by their nature, not digital.By high Q I am thinking very low losses of energy, so I can study the vibrations and how the energy travels. Assuming a single isolated resonator, once poked with some energy it should vibrate for as long as possible. Preferably the resonator has to be a passive circuit. A helping amplifier to increase Q might be allowed, but only as a last resort, and only if it doesn't turn the resonator into an oscillator.The resonant frequency is not important, but I would prefer to keep it less than 100 MHz so I can easily measure or generate that with the instruments I already have.To sum up the requirements:- any technology of resonators goes, mechanical/electrical/ultrasound/etc.- Q as high as possible- 10 to 100 resonators, all the same (preferably possible to fine tune them individually)- the exact frequency doesn't matter as long as all the resonators are tuned the same- the resonance is preferably to be at a single frequency, if it happens at more than a single frequency, then the many frequencies must be far away enough, so to be possible to distinguish between multiple resonant frequencies- helping circuits to increase Q are allowed, but only if they are analogue by their nature and do not self-oscillate- it's a hobby project made at home, budget in the range of $100So far I could only think of the 32768 Hz resonators used in real time clocks and wrist watches.Q1. Any recommendation for a particular model to use?Q2. Any other technology or idea to buy or to DIY very high Q resonators?Q3. Any schematics or control techniques or tricks I should use to achieve very high Q?Any other ideas welcomed, regarding how to study or how to experiment with an array of resonators.

author: Marsupilami
author_rank: Frequent Contributor
timestamp: July 05, 2021, 11:58:55 pm
content: Feel free to ignore my ignorance, but what is it that you expect not to be able to simulate about a general network of resonators?I hope you're not extracting vacuum energy, because if you do then don't.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: July 06, 2021, 04:07:54 am
content: Can you explain what you expect to find, that linear network theory doesn't establish?It doesn't sound like you're going to find anything new in terms of known physics or analysis; but it's definitely not obvious to one not experienced in the subject, and in that respect, you stand to find quite a lot of new-to-you behavior!The critical factor is the coupling. What kinds of signals/fields are you coupling from/to, and how do you propose to adjust that coupling?Very high Q resonators aren't very important, to the extent that Q factor is greater than system Q. There are multiple ways to measure Q:If we consider a component (substantially L or C) by itself, we can consider its terminal/port Q factor as the ratio of reactance to resistance, or vice versa depending on whether we're using series or parallel equivalent impedance.If we measure the Q of a resonator, we get high values at most frequencies, but (port) Q drops to 0 at resonance -- that is to say, at resonance, reactance goes to zero, and resistance is finite. We should use a different measure of Q, for example coupling very lightly (k < 1/Q) to the resonator and measuring its spectral width. The maximum bandwidth is obtained with minimal coupling (which still needs to be nonzero, lest we have nothing to measure at all). So when we say "resonator Q", we typically mean the combined Q factor of the L and C equivalent making up that resonator, rather than the Q of its measured terminal impedance.If we place a component into a network, now its resistance and reactance add to the impedance it's embedded in. For example, consider an inductor of 15.9uH with Q = 10 at 1MHz (X_L = 100R, ESR = 10R). If we embed it in series between a 50R source and load (terminator), total loop resistance is 110R and reactance is 100R, for a system Q of slightly less than 1. We get a first order low-pass filter with this being the cutoff frequency. The minimum insertion loss is 10% (assuming ESR = DCR).So there are different ways to express Q, and we must be careful which one we're talking about. The sharpness of a filter is determined by system Q, while system Q and insertion loss are determined (and limited) by component or resonator Q.Some resonators can't be coupled tighter than a certain amount, due to quirks of their design. It's not possible to pull a quartz crystal more than a few kHz, or equivalently, get more than about the same bandwidth, because of the ratio of effective resonator impedance to holder reactance; it's a series-parallel transformation which limits the coupling factor.When you're constructing resonators yourself, you have pretty broad control over Q. A cavity, coaxial or helical resonator, you simply connect the coupling link higher up on the structure, or enclose more area in the cavity. In this way, it's reasonable to get fairly low system Q's, maybe 3-5. At higher Q, mere proximity between resonators suffices (a small (magnetic) coupling factor), or a window in the shield between them, etc.At very low system Q, coupled-resonator approximations break down, and you're largely better off with a conventional ladder network. Which, on a related note: if you've ever had much of a play around with bandpass filter calculators, you've probably found some pretty grotesque -- obviously intractable -- values pop up, particularly at high Zo and low bandwidth (high Q). The reason is, each shunt and series branch is coupled to the next, by virtue of its impedance* as a ratio to Zo: the series tanks being Q times above, the parallel tanks being Q times below. You can very easily get fF capacitors this way, which obviously won't work out; the reciprocally massive inductors they're paired with, obviously will have much more self-capacitance, or to ground or other things nearby, and so the network will be fundamentally different than what is shown (namely, there's a capacitor divider in the middle of it, effecting an impedance match, which the calculator doesn't know about so the response goes all wrong).*Resonator impedance Zr = sqrt(L/C).For an array of resonators, the most general description is to have a matrix of coupling factors between them. This will be a symmetrical matrix (k_nm = k_mn) because the system is reciprocal. For practical filters, it will also be a very diagonal matrix: coupling along the main diagonal gives poles, while coupling on the off-diagonals give zeroes.A flat matrix (~equal coupling between all nodes) gives something of an EBG (electromagnetic band-gap) structure, for the same reason a crystal of atoms (closely coupled wave functions) gives an energy bandgap (or if you prefer, it's still frequency response, but what's being filtered is electron waves, because matter is waves, after all).With a small network, we can observe line splitting directly: two resonators over-coupled, effectively resonate against each other in parallel and series modes, thus exhibiting two resonant frequencies with some amount of notch between them, the spread being k12 / kp1 (p = port) or something like that. That is, the resonators are coupled more closely to each other than to the system. If we add more and more resonators to the network, each one contributes a new resonance, and the splitting continues; eventually we find there's a seemingly prohibited span of frequencies in the middle (Fo +/- bandgap/2), with forests of resonances (or overlapping as whole passbands) above and below the gap. (In the case of condensed matter, there are ~10^23 possible modes, so dense that we really can't tell, and don't care, about them individually; instead we integrate, assuming they form a continuum, and from there, derive various electronic and statistical-mechanical properties of the material.)And if, rather than coupling resonators to zero-dimensional ports, they are distributed through space; then we need to take account of 3D fields and polarization, and we can construct all sorts of cool things like metamaterials, but calculating/simulating/constructing them is another matter... If you intend to do experiments like arrays of antennas, understand that coupling drops off quickly (1/r^3 or faster in the near field, to 1/r^2 far) so you aren't likely to get much interesting behavior (i.e. pole splitting) at more than a modest distance. So you for example, get modest bandwidth on a Yagi (stack of ~closely coupled dipoles), but a bunch of antennas loose in a field is just that, a bunch of antennas that can be treated as independent absorbers/reflectors (as the case may be).Heh so... not that a statistical mechanical analog is likely all that helpful. Stat mech is NOTORIOUSLY hard, much harder than network theory (which doesn't even require integrals)... So, if that doesn't mean much to you, I understand. In that case, now at least you know that a complex and deep property of matter, arises in the same way that behaviors of your immediate-future experiments do.Tim

author: RoGeorge
author_rank: Super Contributor
timestamp: July 06, 2021, 04:38:00 am
content: Quote from: Marsupilami on July 05, 2021, 11:58:55 pmNot gonna do that, but not gonna do it only because I don't know how.In fact, it looks like the empty space is full of virtual particles that pop in and out of existence for a very short time (the so called vacuum fluctuations confirmed experimentally by the Casimir effect). It is supposed that those fluctuations can create permanent particles (therefore energy) if the fluctuations happens exactly at the event horizon of a black hole (because one of the virtual particle falls into the blackhole so the other one doesn't have its pair matching virtual particle to annihilate with, so the particle outside of the event horizon remains to live in our Universe as a real particle - or at least that's how I understood it).Anyways, I'm not looking to extract energy.I'm looking to verify some hypothesis about randomness and resonance. I'm afraid I'm not ready to disclose the details, but I can tell it's not about making a random numbers generator.It's hard for me to make a mathematical model because I don't have yet a very clear model in my head. Then, I don't think I have the skills (can hardly deal even with the undegrad level math used in EE). For a numerical simulation would be good to have the analytical model first, but even so I expect to have numerical artifacts, and to become too time consuming to simulate the interaction between the noise and the resonant objects.Then, where's the fun if I were to do that?Simulated physics, simulated fun.evb149thanks for the links, didn't read them yet but curios to browse them in the next days.The Q factor has to be big at a single frequency. Ideally will be to have very good LC tanks, but I don't know how much is this doable in practice, that's why I've asked in the ham section. I don't know how hard would be to make many LC with very high Q, probably much harder than to use quartz crystals or tuning forks.The pipes idea as resonant cavities seems interesting. The only mechanical installation I've considered so far was to use an array of weights suspended by very elastic metal springs, but measuring the springs in such an installation would have been too difficult. With pipes and microphones it will be much easier.T3sl4co1lyour message appeared while I was typing this reply. Had to run right now. Will reply later and try to answer what you asked. It might be that I am looking for something that is well known but I missed. Have to read all more careful one more time, thank you.

author: Bud
author_rank: Super Contributor
timestamp: July 06, 2021, 04:43:40 am
content: High Q means very narrow bandwidth. It will be difficult to couple and tune an array of high Q resonators. Guess your best bet may be a crystal ladder filter, design of which is well understood and there are software tools for it. But you'd need to measure the individual resonators. Also not sure how you intend to observe exchange of energy. As soon as you introduce a probe it will shunt the resonator being measured and lower its Q and/or detune the structure.

author: Berni
author_rank: Super Contributor
timestamp: July 06, 2021, 06:09:04 am
content: I think using quartz crystals is the best way to go because they are both high Q and are very precisely manufactured to have exactly the same frequency. High Q will always be very narrow in bandwidth so you will never get good energy transfer if the two narrow peaks don't line up and overlap.You can even fine tune the frequency of a quartz crystal by wrapping a heating coil around it.LC circuits can be made incredibly high Q if the inductor is air core and a good low loss capacitor is used, but getting the frequencies lined up might be rather difficult. There are RF antenna designs that use resonance to achieve a very high output power at long wavelengths out of a small antenna. Example of it:http://www.hi-q-webs.com/LoopAntPres/Intro.htmlThe trick used is the loose coupling between primary and secondary that lets the LC circuit reach massive current amplitudes, making it rise to such a high level that even a loop that is way too small for the wavelength still radiates a great deal of RF. They need a high Q to do this.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: July 06, 2021, 07:31:43 am
content: Yeah, capacitors aren't much of an issue. Good polypropylene film caps have a Q over 1000, as do average everyday C0G ceramic chips. Vacuum caps will push over 10k easily.Inductors are the hard part. Solid wire or powdered iron gets you up to a few hundred Q -- not bad by any means. Over 1000, at low RF (~1MHz) is achievable with fine stranded Litz cable and a loose winding (modest spacing between turns, as in a solenoid with pitch ~ 2 * (wire dia), or a spider coil, etc.).At VHF, helical resonators are comparable, and at UHF/MW, metal cavity resonators.Litz runs out in the 10s MHz range, I'm not sure exactly what fills the gap here. Maybe the construction needs to be different, space out the strands themselves. The problem is strand-to-strand capacitance, which starts to dominate as the conduction mechanism, making the cable look solid again. So if you can imagine something like a spider coil, where the cable itself is kind of spidered out... yeah.Resonators go much further, with special designs; layered dielectrics can produce supermirrors at up to optical frequencies, with extremely low losses -- Q in the millions. Downside is supermirrors take a lot of layers -- the reflection from each individual layer is modest (extremely high indices of refraction don't exist) so it takes many layers indeed to get such high reflectance (and precise thickness to get the interference perfect).Or if you have a cryocooler and Dewar handy, superconducting (typically spun and electropolished niobium) resonators get into the millions as well. These actually have practical industrial application in linear accelerators -- the particle beam is understandably quite weak, coupling very little with the accelerating field. The solution is to simply make the field monstrously huge, i.e. using very high Q resonators to get good coupling from the power source (typically a large klystron) to the beam.Tim

author: xmo
author_rank: Regular Contributor
timestamp: July 06, 2021, 04:36:42 pm
content: Perhaps not useful to you but interesting nonetheless - the accelerator people have many references such as:Introduction to RF Cavities for Accelerators, G Burt (Lancaster University Engineering)andChapter 12 Resonant Cavities and Waveguides (MIT class handout)

author: TimFox
author_rank: Super Contributor
timestamp: July 06, 2021, 09:38:29 pm
content: An interesting demonstration of coupling between resonators that I did at around 10 MHz, using two similar geometrically-large coils, each with a tuning capacitor, that were "overcoupled", meaningkxQ> 1.Let C2 on the right coil L2 be a fixed value that gives a free resonance of, say, 10 MHz without L1 coupled to it, while C1 is an air-variable capacitor whose maximum is roughly double C2. Connect a generator (loosely coupled to keep the Q high) to L1-C1, and a spectrum analyzer to L2-C2 (again, loosely coupled).With C1 at maximum capacitance, L1-C1 resonates at a frequency well below L2-C2, and the response shows a "double hump" at approximately the free-resonant frequencies of the two circuits.Now, slowly decrease C1 (slow compared to the scan update of the SA), so that the lower-frequency peak moves to higher frequency. As that frequency approaches the higher-frequency peak, the high-frequency peak moves to even higher frequency so that the two peaks never coincide, and the lower-frequency peak "stalls" at about the (fixed) free-resonant frequency of L2-C2. In atomic scattering theory, where you look at the valence electron energies as the nuclei approach each other, an analogous phenomenon is called "avoided crossing" of the energy levels of the electrons in the field of the two nuclei.

author: Marsupilami
author_rank: Frequent Contributor
timestamp: July 06, 2021, 11:26:16 pm
content: Quote from: RoGeorge on July 06, 2021, 04:38:00 amI'm not debating the existence of vacuum energy, I'm only wary of statements implying there's a gradient to it that allows us to extract useful work. Especially with homebrew methods, double especially without simulating it first.On the topic of simulated fun, I beg to differ. I do a good variety of both and I find simulation can be a wonderfully enlightening experience. You got to see and understand things that are not observable directly or at all and that often can lead to beautifully solid understanding how our world works. That doesn't mean that your experimental approach is necessarily bad, especially if you have fun along the way. However based on your description any potential emergent phenomena should be possible to be simulated to arbitrary precision relatively easily while building and tuning the system in real life sounds like major pain even considering you exactly know where you're going with it.I'm sure if you asked the question right here you'd be swamped with SPICE models of perfect resonator chains or alike.But, you do you. Good luck.

author: coppercone2
author_rank: Super Contributor
timestamp: July 07, 2021, 01:07:13 am
content: this is what you can do with an array of crystal resonatorshttps://spectrum.ieee.org/tech-talk/semiconductors/optoelectronics/mits-3d-microwave-camera-can-see-through-wallsdon't know where the picture is, but it looks like a push cart (the one you see in a factory) loaded with about 20 crappy metal duct horns connected to crystal filtersthere it ishttps://news.mit.edu/2011/ll-seeing-through-walls-1018

author: RoGeorge
author_rank: Super Contributor
timestamp: July 08, 2021, 02:23:15 pm
content: @bd139Thanks for pointing out the difference for the re-entrant cavities. Didn't know about re-entrant cavities before, was in a hurry and didn't google the term at the first reading, so I imagined them as something like organ pipe tubes-like. Had a good laugh at myself later that evening, when I start learning about re-entrant cavities.By briefly browsing random papers about re-entrant cavities, it looks like they need precise metalworking, for example this one has some photos:https://arxiv.org/pdf/1308.2755.pdf(I don't have access to any machining, just usual hand tools to be found in an electronics lab - by profession I am an electronist).More achievable in my lab would be the other suggestion, with pieces of coax.QuoteThat's what I'm after. I suspect it should be possible to build a functionally equivalent of aBloch sphere, but with macroscopic objects and no cooling to near 0K. That's an old pet-theory of mine from some years ago, idea that happen to surface again two days ago only by pure serendipity. Not trying to simulate that with a digital computer, but to use macroscopic objects about the same a photon or an ion is used in the existing (cryogenic) quantum computers.Just to be clear, I'm not a physicist by profession.Even if the macroscopic qubits will work, that won't change anything. It won't be scalable, the same as proper quantum computing is not scalable and it can never work as hoped. I think the whole field of quantum computing is based on a mistaken foundation. (I'm no expert about it, my most study about quantum computing was by watching a couple of uni classes and practicing a little on theonline and free IBM quantum computer).Briefly speaking, the key differences between big and quantum objects are the properties of superposition and entanglement.Superposition can be achieved macroscopic for example by putting together many spectral components in a signal, and entanglement can be achieved by synchronous oscillations and phase noise (the entanglement part is what I was planning to study with these high Q resonators I was asking about).I am aware how this sounds: Random dude saying mainstream physics is wrong, yet his pet-theory is correct.This is exactly why I would like to experiment. I've tried to take some online classes, but even something as basic as 101 classes about Schrodinger's equation at some point simply pulled a step in the demonstration out of thin air, render the whole previous lessons futile. I assumed there it must be some trivial math that the teacher didn't explained and I couldn't see it myself. Could be, the math was way over my head, but it didn't looked like that step was coming from math. It looked like an arbitrary physics decision made to match the theory.And even so, the current classes all start from the same experimental observation and the same mainstream premises, which premises (some of them) seems wrong to me. I don't know any physicists that would hand-walk me in understanding why it can not be like I think it is.So yeah, don't know how to settle this other than experimentally trying to disprove my own pet-theories.@Berni, @BudIndeed, there's not much energy in a Quartz, would be hard to measure. I was hoping to look at the voltage (amplitude) using high impedance FET op-amp, which should be easy at the 32kHz of clock quartz. This way I was hoping to trace the flow of energy between the resonators.@T3sl4co1lThe meaning of high quality, or big Q, was the one described in the OP, being I was looking for something that can oscillate for a long time before the oscillations decay (assuming the resonator remains isolated, no extra energy added or pulled out other than the "natural" losses that will happen without a source/load attached). The longer it takes the oscillations to decay, the better.QuoteFilter theory may apply, but I'm not trying to get any particular type of filter (though any resonance unintendedly implies filtering, too). In the beginning it will only be a pair of resonators, planning to add more resonators to the network only if the first two resonators won't prove my pet-theory to be wrong.QuoteWow, thanks, never thought about it that way. I need to google more about that.@TimFoxQuoteWow, I must try that! I already have a DDS and an oscilloscope instead of an SA, but no air capacitor for now, only a sugar cube size one, from a former AM radio. Between its moving fins it has a dielectric that looks like plastic foils, I hope that to be polypropylene.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: July 08, 2021, 04:24:26 pm
content: Bit of a long shot but it may well be fruitful to ask --Quote from: RoGeorge on July 08, 2021, 02:23:15 pmThis bothers me a bit as well; engineering is especially rife with assumptions, given apart from any reasoning or proof. I'm at least clever enough to see through those, or at least imagine what and why, if not exactly to write up rigorous proofs of them. Heh, or I was once upon a time, it has been a while since I learned these things after all.Physicists at least are more inclined to give proofs, but still have much in their toolkit that's simply taken as given.I think part of the reason can be given thus: a huge amount of work was done in the early history of modern physics as we know it. People far cleverer than us, came up with the tools (or found them in extant mathematics) to do work in the earliest, still very poorly understood, field of quantum mechanics. Who knows how many things they tried, or what thought process or intuitive leap led them to apply those things that were ultimately successful.Some illumination might be gained by reading the original sources -- actual papers and books by Schrodinger, Dirac, Pauli, etc.Or perhaps not, as they're likely quite dense documents, too. Well, one certainly does not gain understanding without putting in some effort.Alas, one cannot get far without a deep understanding of what mathematical tools were available; and I feel this myself, much of the higher level or cutting-edge stuff invented in the 19th century feels rather perplexing (but also, it seems, not especially useful in my work, so I also have noneedto pursue it), let alone since then.So, instead of following a convoluted, and ultimately not very useful, detailed history of the derivation and application of the methods -- I think physicists prefer to simply cut to the chase, and take the useful results as given.Does that sound like your sort of issue?I'd be glad to discuss it in detail, to the extent that I remember it anyway (and, having a classical physics education, I'm afraid I don't have the details of exactly that early work). Probably, others here even better versed in these subjects (I'm pretty sure at least one is, actually, though whether they're at liberty to discuss, for reason of free time or others, I don't know), so it may prove worthwhile after all.Oh, and that can be in a separate thread if you prefer.QuoteHmm, interesting. So, how will that be modeled? Without a given differential equation, we can at least make some assumptions/assertions:- The coherence time will be more or less equivalent to the time constant of the system. (I take it this is the reason you're particularly interested in high Q.)- We can represent complex numbers as AC signals (phase/amplitude or I/Q), and vectors as collections thereof.- What role would coupling (if any) play? We inevitably must couple signals into and out of this system, so it must ultimately be equivalent to a filter network. Whatever it is we're modeling, it must be an LTI system. (Note that in general, Schrodinger's equation is neither of these things; for that, the Hamiltonian must meet certain restrictions.)- What parameters will the model be equivalent to? (Position, momentum, energy, wave function, etc.? Those are particle-specific of course; for the Bloch sphere, it would seem two general variables would suffice.) Will the model evolve over time or frequency, or something less direct (more abstract)?Now, the thing about Q, given everything else, is this: to the extent that you wish to see any particular aspect of behavior of this system, you can always do it at some lower Q factor, if the couplings are adjusted, and rescaling the time/frequency appropriately. For example, two very-high-Q resonators coupled together, will have a double-peaked frequency response; if their individual Qs are low (Q*k < 1), the damping will dominate and only one peak will be observed; but we can just as well adjust parameters to create the same condition, scaled appropriately (increase k, driving the peaks proportionally further apart).The special part about quantum computing, is not just the creation of for example very high Q (superconducting) resonators, with specific coupling factors between them; but to do soand to extract energy from an auxiliary term, driving the output state to a desirable transformation of the input state. (Or, this is one possible realization; alas I know very little about modern techniques used for this.)Note that, since the computation must be lossless, there is no pure "AND" or "OR" gate, but we can construct gates with such a transfer functionplus auxiliary outputswhich preserve the "discarded" information that a lossy gate would otherwise incur. The gates are also reciprocal, so that we can remove energy from an "entropy" port, forcing the system into its desired final state.And all this must be done, while avoiding perturbations from the outside world; the thing about entanglement is, not that it's special, but actually thatvery low entangled statesare special. What we call "collapse of the wavefunction" or "classical physics" is just the collective effect of myriad particles entangled into a relationships so complex that they cannot be untangled, and the statistics of the system reduce to the classical case. It's an information entropy thing. So, that's why it must be impossibly cold, and well shielded and all that; the more error that seeps into the system, the more its state gets corrupted from the intended pure state, and the less likely it is that we will find the desired result after letting the computation settle.Which of course is why you say it's... difficult, at least, to scale up. I only take issue with this: I wouldn't go so far as to say impossible. It is certainly challenging. One option for example is to add error correction logic; the system becomes significantly larger (which helps even less with scaling), but the effective redundancy allows internal state to be preserved longer, basically allowing external interference to be bled off as excess heat, in the same way that the excess entropy (beyond the final desired state) is extracted.In the limiting case, computation -- of any sort, quantum or classical -- is still possible as long as the bit error rate is below 50%. The amount of error correction required goes to infinity as BER goes to 50%, but it is finite below that.Nondeterministic computation is something we have done very little practical work with, so far. Modern computers definitely do need to take account of errors -- with typical BER in the ppb range, we can afford to employ very modest error correction methods: parity check, CRC, hash, etc.; ECC RAM, detecting errors and simply repeating calculations; and in demanding cases, duplicating (or even tripling) direct effort (lockstep or redundant voting CPUs). It's all very inefficient, but it's easy to do, and the errors are sufficiently rare that it works out very well on the whole.Presumably, soon in the future, we'll need to face this tradeoff, and develop even still more complex logic to deal with transistors (or other kinds of logic) that are slower and even less reliable than what we have today. With those tools better understood, perhaps it will be relatively easy to apply them to quantum computing, and greatly improve the scalability as a result?Anyway, I digress. Back to the resonators -- it seems pretty obvious/intuitive, that some piecemeal LTI analog computer can't possibly have more computing power than even a classical nonlinear system (such as a digital computer, or any differential equation in general*) -- the challenge I take it, is showing how it must fail, while also showing how quantum computing can succeed -- would you agree?*Differential equations are Turing-complete, of course. As a semi-famous example, when Feynman was working on the Connection Machine late in his career, he drew up a diff eq encapsulating what that computer was best suited for. That's a... very physicist way to look at it, and probably not very useful to computer scientists, but is certainly a technically adequate description.QuoteUnintended, perhaps, but absolutely and inseparably equivalent! Perhaps the equivalence isn't all that helpful (which is to say, if you aren't real hot on network analysis to begin with?), in which case that might be a secondary goal, just as well.QuoteAlso -- he gave a simpler version of my bandgap example. They're the two extremes of the same problem, of course. An isolated atom has some spectral response; a diatomic molecule has split levels; polyatomic, further splits still; and so on, up to the trans-finite case where the levels are so dense that they seem continuous, except for a conspicuous gap splitting the bands in half. There are many practical upshots of this: quantum nanodots for example, that have characteristic fluorescence or etc. tunable by particle size.So, depending on how big of an array you wish to construct, and how you couple them together -- you can demonstrate this yourself.Resonators are not quantum of course, you'll get continuous amplitudes rather than discrete photons, and bandwidths rather than sharp lines. Which, on that note -- atomic lines are nearly ideal, by themselves; they are almost entirely spread out due to extrinsic physical processes, for example Doppler effect in the hot plasma of a glow discharge. Lines may also be split due to atomic physics (fine/hyperfine structure), which may thus become overlapped into apparent continuua. Splitting also depends on ambient fields (Stark and Zeeman effects) which may be subject to random processes (e.g. electrical noise in the glow discharge?). So there are lots of conditions that act to apparently broaden atomic transitions, but they're really quite ideal on a per-atom basis.This is probably most exaggerated with nuclear modes. NMR is extremely sharp, to the extent that the influence of local molecular fields is sensible (contributing consistent ~ppm shifts in resonant frequency, including -- you guessed it -- splitting due to nearby nuclei coupling to each other!). It even works all the way up with gamma rays (~EHz?), for extremely small (~Hz?) frequency shifts (Mössbauer effect).Maybe a bit beside the point, but an important and interesting difference.QuoteDouble tuned resonators are easily tested with, much of any network of the sort, really -- you can take two LCs of equal value, and couple them with a small capacitor for example. Give this a play-around:https://www.jrmagnetics.com/rf/doubtune/doubccl_c.phpOne of those AM radio varicaps should be fine, I'd guess (hope) the Q factor is well over 100, the main downside is probably just that you have only the one. Well, paired with a fixed resonator, you can see how the relative amplitude of the peaks shifts with mismatched Fo's -- one of the interesting behaviors of this system, you're not so much tuning the peaks in this way but the amplitude balance between them. The coupling factor determines splitting, and the geometric average of Fo's determines the center frequency (I think?).Tim

author: coppercone2
author_rank: Super Contributor
timestamp: July 08, 2021, 04:37:58 pm
content: a college curriculum of the lab classes would be helpful to show you what experiments to perform, not the book, but the lab instructions that might be on chegg or somethingyour 100$ budget = peizo if you already have AC equipment so you can characterize them, rf cavities to get high Q need a good machine shop most likely, inductors are more simple but I assume you have at least a work shop, you won't be making too much for 100$, a 1/4 of that will go on magnet wire already for 100 coils even if you get a good dealanything optics for 100$ is going to be a wash unless you are already heavily into optics, most cheap optics projects = optical modulation for communication, or optics sensors for controlling machineryI think 100 matrix of anything for 100$ is wishful thinking, you need money, try a matrix of 9 or 16I don't think you will increase the Q of a crystal with any electronics. it is 10,000+ Q

author: JohnG
author_rank: Frequent Contributor
timestamp: July 08, 2021, 09:18:58 pm
content: I always wanted to do something with helical resonators... need to find a copy of Zverev's Handbook of Filter Synthesis, which has a good chapter on them, IIRC.Cheers,John

author: TimFox
author_rank: Super Contributor
timestamp: July 08, 2021, 10:08:02 pm
content: A spectrum analyzer is ideal for my demonstration, since it shows the response changing in real time as you slowly change the tuning manually.If your generator can do frequency sweep, you can synchronize the oscilloscope horizontal to the frequency sweep by adjusting the time bases, and run the vertical input from a simple diode detector. You lose the narrow measurement bandwidth (SNR improvement) of the SA, but if your signal is strong enough it should work.

author: coppercone2
author_rank: Super Contributor
timestamp: July 08, 2021, 10:11:44 pm
content: the two resonators that timfox mentioned is a experiment you might find in a 2nd year physics course lab, I believe they sell those coils to do just that ready made, the only difference is that you won't get a spectrum analyzer and they will have you make the plots on paper with a cheap setup

author: TimFox
author_rank: Super Contributor
timestamp: July 09, 2021, 12:12:33 am
content: It’s a much more dramatic demonstration with the SA, watching the two peaks avoiding each other.

author: coppercone2
author_rank: Super Contributor
timestamp: July 09, 2021, 12:45:09 am
content: the undergraduate labs are usually really bad, the spectrum analyzer is probobly behind 3 keys held be separate professors, modified with custom made non compatible coaxial plug and cable that another professor wears as a necklaceteachers assistant pre lab demo assignment: move T141 chassis from the deans shed to physics lab

author: TimFox
author_rank: Super Contributor
timestamp: July 09, 2021, 02:49:45 am
content: When I was a teaching assistant, our first assignment was to manhandle eight Tektronix 541 scopes up three flights to the lab in the only physics building without an elevator.

author: RoGeorge
author_rank: Super Contributor
timestamp: July 10, 2021, 05:24:08 pm
content: Quote from: T3sl4co1lI would be curious to know more about Schrodinger Equation, but for now that's not what I disagree with regarding quantum computing (QC).Quote from: T3sl4co1lSee? Seems plausible to build that without quantum particles. I still don't get it, why superposition and entanglement are needed to do QC anyway? The more I learn about QC the more I fail to understand why doing all that. I'm tempted to say "The Emperor has no clothes", but then I think an army of students and professors and scientists and researchers can not be all blind. Therefore, I must be missing something very big here but what is that that I'm missing?About the LTI (Linear Time Invariant) aspect, it can be at most Piecewise LTI, meaning it is LTI but not for long, because the qubits in the currently existing QC are operated (as in reconfigured) from outside in order to form various types of quantum gates. Will detail later.Quote from: T3sl4co1lThat's mentioned everywhere, but why itmustbe lossless? What would be the benefit? I see no reason why I would ever want to run my own computation in reverse. Running my own computation in reverse will only return me my own input data which I already have, so why do I need the computation to be lossless?Quote from: T3sl4co1lI don't say it's "difficult", I say it can not scale up, and saying that for very different reasons than the ones you assumed. Will detail later, but that will take more than a paragraph. Roughly speaking, the reasons I'm saying it won't scale are about the same as the reasons for why the analog computing didn't scale up well, so in the end analog computing failed to compete with digital computing: limited resolution, and noise.Quote from: T3sl4co1lSince you mentioned that, it could be that all the QC field is just a dead end, and the fact that QC is now so hyped is only because Feynman considered QC as a "maybe possible" tool for computations in (some of his) physics, and as a side effect he lend a part of his big fame to the field of QC. (Having in mind stories like this onehttps://longnow.org/essays/richard-feynman-connection-machine/where if we read between lines we notice that it was also a startup, so any extra hype would have helped, which they did, but the hype persisted too many decades seeding a chimera research field, Quantum Computing, which seems to me like a dead end, saying this without any physics, only by looking at the bottom line - armies of researchers but not much progress in QC, zero if we compare it with the first decades of digital computing).Quote from: T3sl4co1lYep, noticed that they are the same, but only after reading what TimFox wrote. I knew before about the spectral splitting observed in molecules, because I did once some NMR attempts at home, failed, then took some chemistry classes about spectrometry and how chemists can deduce molecular structures by looking at Hydrogen lines, etc - just that I failed to identify that as afundamental property of two coupled resonators. Only after I read what you and TimFox highlighted for me I got the big aha! moment. Thanks a lot for that. Might be common knowledge for others, but I'm still hyped about it!Didn't experimented yet (still want to do that and watch how it splits while I'm putting the resonators closer and closer), but couldn't wait to finish cleaning the workbench and "cheated" by giving it a quick peek in LTspice. Yep, it splits!The two coupled L1C1 and L2C2 are identical, all fixed values and the same with the L3C3, which remains uncoupled with the other two, as a reference. Each color in the plots corresponds to a different coupling coefficient, here named K1 (for K1 = 0.00, 0.25, 0.50, 0.75, 1.00). Note how the green peak is missing from the LC2 (no signal out when they are not coupled at all), and how the magenta peak has no split (for K=1, when the two LC are "in parallel"), and how the resonance frequency for K=1 goes at sqrt(2) to the left relative to the reference frequency of LC3, and how for the other K in between 0 and 1 the two peaks are around the reference resonance of LC3.Quote from: coppercone2 on July 08, 2021, 04:37:58 pmThat would be interested to see. I suspect that would be very different from one place to another, so I don't know what to look for. Do you happen to have any good links for that, please?"Quote from: JohnG on July 08, 2021, 09:18:58 pmDunckxfound it online, and was kind enough to post the link in EEVblog, here:https://www.eevblog.com/forum/projects/analog-filters-a-compilation-of-standard-transfer-functions/msg3534588/#msg3534588Quote from: T3sl4co1l on July 08, 2021, 04:24:26 pmAny help would be great, especially in showing how or why it must fail.Though, I'm not sure about being LTI, but let's look at it anyway:Quantum Computing in two paragraphsMy understanding so far about QC, as it is now (independent of the technology that implements the QC physically):- a qubit is a Bloch sphere (BS)- the vector inside a BS is the spin (the quantum particle's spin from physics)- quantum algorithms (QA) are implemented with quantum gates (QG)- quantum gates are operations of rotating and/or mirroring the vector (the spin) inside the BS (qubit)https://en.wikipedia.org/wiki/Quantum_logic_gate- all qubits are processed in parallel, "driving" them step by step through various QG- to "run" a QA, first all the qubits must start from a reset state, meaning aligned all to have the same spin and phase- then, the whole word of qubits are passed through the first "layer" of QG- and so on steps by step until the result is read out- the result reading is always the last step, because it is said that the reading operation collapses the quantum state of the qubits, turning them from a BS to a simple 0 or 1 (spin up/spin down)- the spin collapse is probabilistic, therefor the QA must be repeated many, many times starting hundreds and thousands of times from the reset state to spin collapse, again and again, and each collapsed result is memorized and averaged by a normal digital computerNote that all in a QA is HARDCODED, there are no variables, no loops, no jumps, no execution branching.It is not like the usual computer programs, but rather like an FPGA.Quantum algorithms are an entirely new can of worms by themselves. Aside from the fact that everything in a QA is hardcoded, quantum algorithms are NOT "programs", they are "schematic diagrams" made out of quantum gates, same as for an FPGA one does not "write" a program, but rather ones "draws" a schematic diagram made out of logic gates.Example of a Quantum Teleportation circuit (algorithm):https://mareknarozniak.com/2020/03/22/simulating-quantum-teleportation/Source:https://mareknarozniak.com/2020/03/22/simulating-quantum-teleportation/A quantum algorithm looks very much like a musical score, where at the beginning there is a qubit on each line of the score, and all the qubits keeps advance step by step through QG already existing on that score, and a qubit stays on its own line on the musical score, always advancing from left to right, all the qubits passing each through their own gate at each step, but all at once, walking synchronous to the right end of the musical score.Quirkis an online quantum computer simulated by a digital computer with the "musical score" and everything, the qubits and the quantum gates, in a nice drag&drop interface, with live animations. Has an offline version , too, FOSS, etc.:https://algassert.com/quirkThat being said about quantum computing, I don't see why, or where exactly, a quantum particle or quantum behavior is mandatory. It should work with macroscopic objects just fine, and this is what I want to try.Apart from that, another thing I disagree about is how a quantum computer is considered advantageous over a digital one for certain algorithms, and where from this advantage is supposed to be coming from. I think it is calculated all wrong, but that's a different story.

author: coppercone2
author_rank: Super Contributor
timestamp: July 10, 2021, 05:47:57 pm
content: no, you would need to troll syllabus for physics lab from different universities, a dragnet searchfind top 20 engineering schools in your language and look through the physics and electrical department for general and relevant physics lab and electronics lab classes to see what comes up with resonators if you want to go for this route. Anything above physics I might start to have relevant things in the USA. in the USA I would look for stuff that has relations with physics laboratories or the navy. they are really cheap with students so you might find something budget friendly

author: Marsupilami
author_rank: Frequent Contributor
timestamp: July 12, 2021, 07:58:36 pm
content: Quote from: RoGeorge on July 10, 2021, 05:24:08 pmYou can't reproduce superposition. There is no macroscopic 2 state system that can be in both of those states at once. You can simulate it by using more than 2 states. That's what all the traditional computers do while simulating a qbit, with more then a single traditional bit. However that takes (exponentially) more resources and/or time to do which invalidates the whole point of quantum computing.Your FPGA analogy is good, except imagine that (assuming synchronous operation) your circuit, in one cycle, produces output to every possible input combination not just one particular input combination at a time. The magic and the fundamental difference to macroscopic systems is that you can do tricks to select results from this combination of all possible results in a somewhat deterministic way.I like Minute Physics' videos on Shor's Algorithm. The first 10-12 minutes is something that can be done totally conventionally, after that he gets to the point how do you measure an entangled part of the results to get a random periodic subset still in superposition then perform a quantum Fourier transform to find the periodicity in that subset via destructive interference of the superposed states, giving a deterministic final answer.https://youtu.be/lvTqbM5Dq4Qhttps://youtu.be/FRZQ-efABeQQuote from: RoGeorge on July 10, 2021, 05:24:08 pmThat's a billion Dollar statement right there.

author: LM21
author_rank: Regular Contributor
timestamp: July 13, 2021, 10:01:25 pm
content: No comments about Scifi part, but crystals have highest Q, I know and are easy to buy. Helical resonators and coaxial resonators have high Qs and are more like familiar L and C circuits. You can Google for them for building instructions. And they also can be stacked. If you are good at building things, you can get a nice looking system. NanoVna can tell you how it works.Edit: I deleted my joke about free energy, someone might take it seriously. Long antennas may well catch a lightning strike and burn you or your house.

author: TimFox
author_rank: Super Contributor
timestamp: July 13, 2021, 10:03:45 pm
content: For a demonstration, I would stick with lumped L and C in an appropriate frequency range, since variable Cs are easy to find and connect. Crystals have very high Q, but have a narrower tuning range. In the demonstration example I discussed above, it was useful to tune the free-resonant frequency of one L-C pair over a relatively wide frequency range.

author: LM21
author_rank: Regular Contributor
timestamp: July 13, 2021, 10:21:00 pm
content: Yes, it is possible to get all sorts of nice and interesting effects with plain coils and capacitors, without any Scifi.

author: RoGeorge
author_rank: Super Contributor
timestamp: July 14, 2021, 02:32:33 pm
content: Quote from: evb149 on July 06, 2021, 02:51:24 amParsing some of the materials. Just for the docs, found that in full (in the quoted link is the ToC):https://tf.nist.gov/general/pdf/868.pdfhttps://nvlpubs.nist.gov/nistpubs/Legacy/TN/nbstechnicalnote1337.pdfSo far some categories emerged (from all the suggestions):- Quartz crystals- Re-entrant cavities- Coaxial and Helical resonatorsThen, there is generic topics like- Waves, Resonators, etc. (e.g. Feynman's Lectures on Physics)- Clocks and oscillators- Filters- Crystal filtersThen, there is simulation vs. hands-on experiments. Well, at least here I have some progress, though it is not experimental as I would have wanted, but a simulation instead.Quote from: TimFox on July 13, 2021, 10:03:45 pmI made a tool that takes the data file produced by an LTspice simulation, and turns the ".step" directives from the schematic into a live slider that I can drag with the mouse.For each position of the slider, a new .step dataset of results is taken from the LTspice simulation results and slapped on the chart. Since the datasets were pre-calculated by LTspice, the dataset change on the plotted charts is very fast, like it would be if it were to change the capacitor or the coupling in an experimental setup while watching live the response of the circuit on a spectrum analyzer.As a result, there is a slider for "Cvar" and there is a slider for "Coupling factor". I found it very educative to see live, by dragging a slider, how the frequency peaks slide from left-right when changing C, or move apart while changing K. Looks crude if not lame, but that slider plot was just enough for me to get a grasp of the phenomena. Some 3D plots might make sense, too, for a better visualization.I'm not a software developer, but that would be a very useful thing, IMO, to polish the .step to slider tool, and make it a standalone visualization tool that can plot interactive parametric simulations from LTspice.Quote from: Marsupilami on July 12, 2021, 07:58:36 pmI would be curious to know what made you say so? Is this because this is what you were told it is, or is it some conclusion you draw for yourself? And how did you arrived at adopting your current position? (These question are not an attempt to intimidate you, or to have a flame, I'm asking because I am genuinely interested in what makes people in general, and you in particular, to agree with something or not. Again, not curious about you, but about the process of accepting an explanation or not, please try to answer those questions, only if you don't mind, of course, or maybe in a PM if you don't want to make that public.)Back to the the superposition, I'll say I can have that. For example, when I speak my voice produces many frequency at once, a full spectrum of it. That's a superposition of many tones. In fact, I'll dare to say that most of the macroscopic systems are rather in many states at once.Quote from: Marsupilami on July 12, 2021, 07:58:36 pmMy problem is that I fail to see any magic when I look under the hood, but rather misinterpretation and/or poetic/philosophical wording of well known physics, the physics of waves.Then, there is the misinterpretation of imaginary numbers from math. They are used a lot when it comes to waves and oscillations, but there's nothing imaginary there, the physics forces (e.g. in a mechanical oscillator), or voltages (in an electric oscillation) or whatever, those physical measures are real. In the real world there's no such thing like the imaginary part of a force, or the imaginary part of an electric current, like it is the imaginary part of a complex number, where imag(X=a + bi) is "b".I've tried to dig in the historic aspect of all the bamboozling related with QM. Letting aside the Copenhagen interpretation vs. Bohm's guiding wave (some are saying Copenhagen interpretation won only because the Bohm's political orientation did not aligned well with those times - but I won't go there), so letting aside that, the final debate that "settled" the dispute about quantum mechanics was if the entanglement was really "spooky action at a distance", or just "a predefined pair of gloves" so nothing acts at a distance and the entanglement is nothing but a prearranged pair of something that was predetermined from the very beginning.Well, there were many experiments trying to settle that, some quite complicated with bamboozling terms like time erasing and so on. At some point there was an experiment called now theBell testandBell's Theorem. Bottom line, it says if you measure straight lines, then entanglement is a "predetermined pair of gloves", if you see a curved shaped, like a bell (sic), then entanglement is "spooky action at a distance".Source: Wikipediahttps://en.wikipedia.org/wiki/Bell%27s_theoremWell, they measured the curved blue line, so it was "settled" the quantum weirdness is "for real". Well, not everybody was happy with that reasoning. Some showed how that blue curve can arise as well if you mix some noise in the clasical "pair of gloves", so the entanglement spooky action at a distance is not necessary at all to explain that blue curve that was measured experimentally.So yeah, right now I'm inclined to believe superposition is as common as the superposition of a head/tail coin while in the air, and the entanglement is nothing but synchronous oscillations with some phase noise.Quote from: Marsupilami on July 12, 2021, 07:58:36 pmNot sure I understand where you aiming there. My disagreement was about how theBig Owas applied to quantum computing in order to compare various algorithm run on a QC with an equivalent algorithm run on a digital computer.The analog nature of the numbers representation in a quantum computer was ignored, same it was ignored its parallelism. Then, it was compared with a run on a digital computer, which is essentially a binary and serial machine. That seems an unfair comparison, making the digital computers to appear much worst that they really are. If it were to have analog bits instead of binary digits, and if it were to make all the operations at once instead of making them in a serial manner, then the quantum computing won't be that advantageous after all.The thing is, vintage analog computers were doing just that: they were operating with real numbers instead of bits and serial arithmetic, but that doesn't scales well because of the limited resolution and the noise present in analog processing. That's why we all use digital computers now, though the analog computers were invented first.Later edit: a few typos fixes

author: TimFox
author_rank: Super Contributor
timestamp: July 14, 2021, 03:42:57 pm
content: A nice simulation of the experiment I described.When I did the experiment, I keptkandQconstant, but varied the tuning on one of the two resonant circuits.Can you modify your simulation to work that way?WRT analog computers: when they were popular, the statement was made that they took a long time to set up, but solved the problem immediately.Just as integrated operational amplifiers got good and cheap and small, history proceeded to obsolete the analog computer. I remember when Shure Bros. improved their phono cartridges in the early 1960s, they bragged about computer design, which meant that they ran simulations on a good analog computer to optimize the response.At the end of the previous millenium, I visited a Boeing facility, which received a monthly corporate newsletter with (among other things) nice historical photographs of aircraft. One issue had a photograph (ca. 1950) of an engineer solving a problem, while wearing white shirt and tie. To his left was a 6-foot high 19-inch rack full of analog computer, and to his right was a conventional chalkboard that summarized the relationship between the variables and the knob settings on the computer. The writer (much younger than I) stated something like "The computer ran so hot that 400 vacuum tubes were required to remove the heat."

author: RoGeorge
author_rank: Super Contributor
timestamp: July 14, 2021, 05:25:22 pm
content: I absolutely love such first hand stories, thank you.Right now the schematic was this one posted earlier, where C1=C2=10nF, L, C, Rs and Rp are constant, and variable coupling K1 between L1 and L2, like this:L3 is there just as a reference LC of 10nF||10uH, just like the other two LC resonators, But L3 is not coupled with any of L1 or L2. The plots on the left side are the ones made from inside LTspice, where each K is another color (5 colors total).The ".step param coupling 0 1 0.25" means the parameter called {coupling} will take five distinct values between 0 and 1 with an increment of 0.25. So for each K = 0, 0.25, 0.5, 0.75 and finally 1, the simulator will do a full frequency swipe between the requested frequency range, here between 300...1200kHz. All the results will be saved as complex values of amplitude and phase for each frequency and for each .step K coupling factor.To make my tool with a slider for K to feel like a continuous variation, I "abused" a little the settings, and make the .step directive to run the same simulation 101 times, once for each K between 0.00, 0.01, 0.02 ... 1.00. So for each of the 101 distinct values of K, the LTspice simulator computed 10 000 points/octave (20 kpoints total between 300kHz to 1200kHz, logarithmic distributed), and for each of these 100 steps of 20 000 frequency points each, all the currents and voltages from the given circuit were saved in a big file of amplitude/phase pairs (as complex numbers). As a roughly estimation, IIRC they were 17 different voltages/currents in that circuit, so a total of: 101 runs x 20 000 frequency points x 17 amplitude/phase pairs were saved in the final results file.34 million complex numbers. When the slider changes in the final visualization I was playing with, a different set of those 101 runs is selected, and all the 20 000 points are replaced in the plotted line according to the position of the slider, and it looks like this, but live, it changes accordingly when I drag the slider (!!! note that the plot in this capture was taken while debugging the software, it is not the final version, so the plotted line might not correspond to the slider value K = 0.59, but to some other dataset, it's just to show the idea of having some live sliders !!!):Might look like a lot of computation, and it is a lot, indeed, but it took only seconds to compute and save all those 34 million of complex numbers, and the 20 000 points on the final plot changes faster than the refresh rate. It's amazing how good are the nowadays computers at crunching numbers.While dragging such a slider, some very interesting properties are observed. For example, when I drag the variable C1 slider, both peaks moves left right, but the trough between them stays at a fixed frequency!Not sure if what I'm trying to say makes sense, I will add some video after polishing the software (right know the sliders range and number of steps were hardcoded manually, this can be made to adjust themselves, same for some new features, I want to make it add automatically a new slider for each .step directive - can be many, for example I can sweep K and C and some other parameter, etc., want to add a 3rd axis for a 3D view, etc. - that's why I say "simulated physics simulated fun" - because it all turns from having fun with hands on experiments into a programming chore).To answer the constant Q question, yes, it can be done that way. But that will be to change the value for R with the frequency, so that the Q = XL/R will stay fixed, isn't it?The current schematic used a fixed R in the RLC, but it can be any schematic, and the values of the components can be a parameter, and the steps for any parameter can be an arbitrary set of values, or a swiped range of values, or a formula, etc.I could make R as a formula, variable with f so to keep Q constant, as R = Q*XL= {Q*2*pi*f*L}, where f is the swiping frequency.Is the Q=ct. request as a verification against the known experimental results, or is it something that will change in a major way the results from the current setup (current setup being with Q variable with f)?

author: TimFox
author_rank: Super Contributor
timestamp: July 14, 2021, 06:00:39 pm
content: Dragging the C1 slider is equivalent to my experimental demonstration. I was intrigued by the same effect you found, where the distance between peaks remained approximately constant while the first one stopped and the second one moved away. Spice has no way to handle a frequency-independentQ, but constantRs suffice for this demonstration.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: July 14, 2021, 06:30:07 pm
content: You might have some success playing with this,https://www.seventransistorlabs.com/Calc/Filter1.htmldisclaimer, very much still in alpha stage, and the coupled inductors don't quite work yet (only M is used; N k LL are ignored). But you can do the same with the cap-coupled resonator architecture, minding the loading effect of the coupling caps (so, keep k low, and Q even higher, so that the parallel LC tanks dominate in setting frequency; the splitting range will be narrow, which is fine as the plot is basically unlimited resolution).Tim

author: Marsupilami
author_rank: Frequent Contributor
timestamp: July 15, 2021, 05:26:07 am
content: Quote from: RoGeorge on July 14, 2021, 02:32:33 pmOk, I'm game.This is an interesting conversation to have. I don't think it's flame or intimidation. I don't think you're right either, but you're making reasonable points and willing to discuss the topic which is how we all get smarter.To answer your second question I would say that I've been told, but I've been also told that the Earth is round and that the gravitational acceleration on Earth is give or take 9.8m/s^2. I'm not a physicist. I'm an engineer so I use my education and the experience in my field to extrapolate that to other fields. I have a reasonably good understanding of how Academia works and generally how science is made. This doesn't mean that I know and understand everything, nor that there can't be glitches in the system or even systemic biases but I think I have a good general feel of how much bs pseudoscience a person or even a whole scientific area could get away with to be still considered wildly accepted in appropriate circles.Probably the closest I ever got to quantum mechanics at work is with evanescent wave coupling which is basically quantum tunneling and, while this is not directly related to the topic we're discussing, knowing how the science behind that is made and used practically bolsters my confidence in neighboring fields. I learn new things everyday though, so I can be surprised.It's getting late here and I had a long day, I might get back to some of your point later but let me quickly address your comment on complex numbers.Quote from: RoGeorge on July 14, 2021, 02:32:33 pmI think you're missing a layer of abstraction here, as well as how do you define "real", but let's not get into the latter one.It's a difficult concept and I had been using complex numbers for years without understanding where do they arise from and why it is important in understanding of "real" physics.Let's take a sine wave, that is representing an oscillation of whatever, doesn't matter. To represent the state of that system at a point in time you need 2 real numbers: it's amplitude and it's phase. Even though a specific property of the system (whether that is position or potential energy or voltage or anything) is a single real value at a given point in time to describe the state of the system you need 2. You can actually select those two numbers in different ways but at the end you need a number pair or a 2 element (2D) vector that is a vector in an abstract space of states.If you happen to choose amplitude and phase of your oscillation you can easily represent all possible states (state space) in a polar coordinate system using those two exact numbers as your polar coordinates. If you move to a cartesian coordinate system one of your axes might line up with an observable quantity, e.g. voltage of the output of your resonator circuit. In other systems both axis have easily observable quantities associated with them e.g. in case of a pendulum or spring the displacement and the speed. So I argue that the imaginary part in complex representation of these physical systems is not "imaginary" at all. You do need both numbers of the number pair to describe the state of your system. Now yes, the naming might not be the most logical, but we're stick with that for historical reasons.So far this was only about number pairs, one might ask that ok what's up with the i = sqrt(-1) stuff.When working with your system states you might want to perform certain operations on them. E.g. you might want to add two together (superposition). Or multiply one with a scalar.If you go back to our 2D state space these operations can be really easily calculated and visualized using vector algebra. This is still only using a pair of ordinary numbers that can be visualized on a 2D graph, the 2 axis don't have too much to do with each other, they exist independently.The interesting stuff comes when you face the need to do multiplication between vectors in the state space. (In a plain old 2D Euclidean vector space multiplication between vectors in not defined.) Mathematicians realized that when they observe the resulting states of physical systems after multiplication it looks like that two numbers or two values corresponding to the two axis are not independent but seem to sort of interact with each other. Moreover they realized that they look a lot alike the real and imaginary parts of a complex number, which had been for other mathematical reasons already invented. This relationship that components of vectors in Euclidian spaces don't have is that multiplication resolves into a rotation. (If you multiply two complex numbers you multiply the amplitudes and add the phases to get the result.) There is nothing imaginary or made up about this. This describes real, existing properties of systems that might not be obvious that they have at first glance but they do.Ultimately complex representation of oscillations doesn't reveal any new underlying quantities in macroscopic systems however there is a whole bunch of emergent phenomena that it helped to describe. In terms of quantum mechanics it's not that obvious though because we don't have the means to look under the hood and separate "real" quantities that can be described by real numbers. The only thing we have is our predictive models in which system states seem to exhibit the same sort of rotating behavior.(Also let me point out that when you're describing a "real" quantity with a sine wave, that sine function have been defined as the 1D projection of a rotating 2D vector.)+1 Interesting fact I like is that they struggled a lot with coming up a higher dimension representation of something similar and it turned out to be impossible in 3D, however using 4 dimensions the same sort of rotating behavior can be described and that gave rise to the wide use of quaternions.

author: RoGeorge
author_rank: Super Contributor
timestamp: July 15, 2021, 10:50:05 am
content: Thanks for taking the time to answer.My bad about not giving some examples of what exactly bothered me with the imaginary numbers. I was not upset about using them in classical mechanics/oscillators.I'm OK with using complex numbers for waves or any other places where they fit, and fully agree with what you wrote. I was rambling about the interpretation of i when there's no pair of physical parameters like i.e. amplitude/phase, but it's all just probabilities like in quantum mechanics. It would be a long detour to explain what I was upset about.Sorry for my half baked phrase and unfinished thought that make it all look like I would try to dismiss the complex numbers. Not my intention to do that.

author: RoGeorge
author_rank: Super Contributor
timestamp: October 27, 2021, 08:04:07 pm
content: Quote from: TimFox on July 06, 2021, 09:38:29 pmFound recently a Qucs version called QucsStudio, which can add interactive slidersto a simulation.Too fun not to add a live demo for that experiment about line splitting and peaks moving in coupled resonators.

author: TimFox
author_rank: Super Contributor
timestamp: October 27, 2021, 08:25:40 pm
content: Quote from: RoGeorge on July 15, 2021, 10:50:05 amI have posted this anecdote elsewhere, but it is a fond remembrance of one of my professors at the University of Chicago.The late Prof. Ugo Fano had an interest in using quantum mechanics to calculate macroscopic phenomena. He was giving a lecture where he approached the question of dielectric polarization to calculate the dielectric constant. He started the quantum perturbation calculation by writing the Hamiltonion for the interaction between the appliedEfield and the induced polarization in the medium. He then did the usual Fourier decomposition of the applied field into an integral overwofE(w)eiwtdwto look at the dependence on the frequencyw. One of the theory-types in the front row objected: "Prof. Fano: that Hamiltonion is not Hermitian!", meaning that the energy was not real-valued due to the complex exponential. Dr. Fano proceeded to erase "i" and replace it by "j", stating that "Now it is Hermitian!"

author: T3sl4co1l
author_rank: Super Contributor
timestamp: October 27, 2021, 10:24:57 pm
content: Mathematicians complain about physicists' loose, hand-waving methods; but us engineers sometimes just need to get stuff done.Tim

author: coppercone2
author_rank: Super Contributor
timestamp: September 07, 2022, 12:33:32 am
content: there is another cheap resonator that is not considered, maybe, that is a chemical resonator.14 min 30 seconds to see it in action

author: LM21
author_rank: Regular Contributor
timestamp: September 08, 2022, 10:07:25 pm
content: I think it would be too easy if simulators would show something new. You should build your array of resonators and play with them.

author: Warpspeed
author_rank: Contributor
timestamp: September 09, 2022, 01:04:22 am
content: Coming back down to Earth....Passive resonator, less than 100 Mhz, as high a Q as possible.Watch crystals on 32.768Khz use a piezoceramic tuning fork type mechanism to get down that low in frequency without being excessively large.While they are reasonably accurate and temperature stable, not sure the Q is particularly high. It does not need to be for an oscillator.Any crappy old thing can be made to oscillate.A really sharp filter is a very different thing.What will definitely have a high Q, is a vacuum mounted quartz crystal, typically at 100 Khz, or some frequency not too far away from there.Right now I am building a two channel tracking filter using these 100Khz vacuum mounted crystals. The series impedance at resonance is about 320 ohms and the -3db bandwidth measures out at around 3Hz for a single crystal. It takes over a second for amplitude to stabilize.Parallel resonance probably has an unloaded Q of several tens of thousands, and I don't think you will do any better than that using any type of other plain hardware. Of course you can convert any incoming frequency up or down to exactly 100 Khz using a linear modulator such as an analog multiplier to do some frequency conversion.That is how I am doing it with my own two channel tracking filter.The same technique was used in older style spectrum analysers to get bandwidths down to 1Hz using several cascaded crystals.Today is all done with fancy Fourier software magic.A purely mathematical approach may be best of all, but its not without its own issues which may skew your results.It would be more difficult to go too far wrong with a purely hardware approach.

author: TheUnnamedNewbie
author_rank: Super Contributor
timestamp: September 09, 2022, 11:06:43 am
content: Quote from: RoGeorge on October 27, 2021, 08:04:07 pmdidn't read the entire post but that plot in your spice simulator seems like general two-resonance-peaks of transformers, used all the time on-chip at millimeter-wave frequencies to get wide bandwidth matching networks. See On the Design of Wideband Transformer-Based Fourth Order Matching Networks for E-Band Receivers in 28-nm CMOS by Marco Vigillante.

author: mawyatt
author_rank: Super Contributor
timestamp: September 09, 2022, 01:08:31 pm
content: Another technique for creating very high "Q" tunable filters were called Commutating Filters. They are based upon commutating a set of "N" simple RC Low Pass Filters with switches that cycle thru the "N" RC LPFs at a clock rate Ck. This produces a net resultant narrow bandpass filter at frequency Ck/N, with a 3dB bandwidth of 2*LPF/N, and can produce exceptionally high filter "Qs". We utilized this technique way back in ~1980 to find and isolate specific "tones" at MW frequencies.Best,