What to use for an array of very high Q resonators?

[LM21]

Yes, it is possible to get all sorts of nice and interesting effects with plain coils and capacitors, without any Scifi.

[RoGeorge]

Characterization of Clocks and Oscillators - NIST
https://www.nist.gov/sites/default/files/documents/calibrations/tn1337.pdf

Parsing 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.pdf
https://nvlpubs.nist.gov/nistpubs/Legacy/TN/nbstechnicalnote1337.pdf

So far some categories emerged (from all the suggestions):
- Quartz crystals
- Re-entrant cavities
- Coaxial and Helical resonators

Then, there is generic topics like
- Waves, Resonators, etc. (e.g. Feynman's Lectures on Physics)
- Clocks and oscillators
- Filters
- Crystal filters

Then, 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.   

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.

I 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.   

That 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.

You can't reproduce superposition. There is no macroscopic 2 state system that can be in both of those states at once.

I 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.

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.

My 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 the Bell test and Bell'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:  Wikipedia https://en.wikipedia.org/wiki/Bell%27s_theorem

Well, 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.

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.

That's a billion Dollar statement right there.

Not sure I understand where you aiming there.  My disagreement was about how the Big O was 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

[TimFox]

A nice simulation of the experiment I described.
When I did the experiment, I kept k and Q constant, 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." 

[RoGeorge]

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 = X_L/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*X_L = {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)?

[TimFox]

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-independent Q, but constant Rs suffice for this demonstration.

[T3sl4co1l]

You might have some success playing with this,
https://www.seventransistorlabs.com/Calc/Filter1.html
disclaimer, 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

[Marsupilami]

I 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.)

Ok, 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.

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 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.




 

[RoGeorge]

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.

[RoGeorge]

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", meaning k x Q > 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.

Found recently a Qucs version called QucsStudio, which can add interactive sliders to a simulation.

Too fun not to add a live demo for that experiment about line splitting and peaks moving in coupled resonators.



 

[TimFox]

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.

I 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 applied E field and the induced polarization in the medium.  He then did the usual Fourier decomposition of the applied field into an integral over w of E(w) e^iwt dw to look at the dependence on the frequency w.  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!"

[T3sl4co1l]

Mathematicians complain about physicists' loose, hand-waving methods; but us engineers sometimes just need to get stuff done.

Tim

[coppercone2]

there is another cheap resonator that is not considered, maybe, that is a chemical resonator.


14 min 30 seconds to see it in action

[LM21]

I think it would be too easy if simulators would show something new. You should build your array of resonators and play with them.

[Warpspeed]

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.

[TheUnnamedNewbie]

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", meaning k x Q > 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.

Found recently a Qucs version called QucsStudio, which can add interactive sliders to a simulation.

Too fun not to add a live demo for that experiment about line splitting and peaks moving in coupled resonators.



 

didn'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.

[mawyatt]

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,