Cool visual patterns:
The waveforms decay, which must be some Spice setting. Ideal resonators wouldn't lose energy. Gear integration is much worse than trap.
-- John Larkin Highland Technology, Inc picosecond timing laser drivers and controllers jlarkin att highlandtechnology dott com http://www.highlandtechnology.com
LTspice has a default of a series R for each inductor. ...Jim Thompson
-- | James E.Thompson | mens | | Analog Innovations | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | San Tan Valley, AZ 85142 Skype: skypeanalog | | | Voice:(480)460-2350 Fax: Available upon request | Brass Rat | | E-mail Icon at
If you do an AC sweep, you'll see either a nice sharp peak, or two individual peaks. How much depends on the coupling between resonators and their individual Qs. The positioning of the peaks depends more on the coupling coefficient than the tuning of the individual resonators, but the balance between peaks does depend upon tuning.
With ideal SPICE components (whether you've checked that or not; LTSpice lies about its schematics) and no losses, you can expect every grouping of resonators to have two very sharp peaks. With no coupling from or to anything, it's not very practical, of course.
The necessary time-domain function arising from such a system is, of course, a complementary pair of sine-enveloped decaying exponentials, with the period of that envelope being the difference between peaks.
Tim
-- Seven Transistor Labs Electrical Engineering Consultation Website: http://seventransistorlabs.com "John Larkin" wrote in message news:5o4qcatachr67e1paofbck23f6jsrsej26@4ax.com... > > > Cool visual patterns: > > https://dl.dropboxusercontent.com/u/53724080/Circuits/Oscillators/Coupled_Resonators.jpg > > The waveforms decay, which must be some Spice setting. Ideal > resonators wouldn't lose energy. Gear integration is much worse than > trap. > > > -- > > John Larkin Highland Technology, Inc > picosecond timing laser drivers and controllers > > jlarkin att highlandtechnology dott com > http://www.highlandtechnology.com >
On a sunny day (Sat, 31 Jan 2015 12:07:23 -0600) it happened "Tim Williams" wrote in :
Right, we used to call that a bandfilter :-)
On a sunny day (Sat, 31 Jan 2015 19:07:30 GMT) it happened Jan Panteltje wrote in :
PS the Dutxh wikipedia shows it better than the English one, with a picture of the peaks versus coupling you describe:
If you want more peaks (and sharper skirts), add more resonators in the chain; or if you want notches, add resonators on the side (or couple between odd ones).
This is a good page,
Back in the day of course, analog TV had nice broad IF (usually around
45MHz, with a 6MHz span), often called "stagger tuned", but if they were at all smart, they were actually doing this (overcoupled resonators).There are some lovely examples of cavity and coaxial type resonators in cell tower equipment, say for FDM/multiplexing channels in the 900MHz range, and others. Any commercial radio equipment, really; anywhere the stuff up on the tower is more important (limited space for wideband antennas; limited access due to, well, yeah).
Tim
-- Seven Transistor Labs Electrical Engineering Consultation Website:
On a sunny day (Sat, 31 Jan 2015 13:40:30 -0600) it happened "Tim Williams" wrote in :
Got it working and display the TV IF curve.
I designed the whole thing in the sixties, VHF tuner, 38 MHz IF, and 5.5 MHz FM demodulator (audio was 5.5 MHz FM inter-carrier here). H and V deflection 90 degrees, I also wound the HV transformer. Transistor TV! Used staggered tuning. I spend days calculating that H output transformer, with all I had learned... until finally it hit me: the DY type HV rectifier tubes ran on about 1.4 V from a ONE turn loop on all TVs I came across. so the transformer HAD to be 1. something volt per turn. :-) The H deflection coil was 440 Vpp I think, that only left the choice of ferrite, everything else just fell into place. The ferrite was easy as there were plenty of old HV transformers around... Primary 12V DC, and factor 4.5 or so peak on transistor switch off, say 70 V (more would kill the output transistor anyways), I think I can still do it without any calculation. Using just turns ratio, Q for the IF coils.
I have some nice RF attenuators in that superconducting cellphone filter I have, need to get that out some time and use it for testing, adjust1 and adjust2:
The later analog TVs had SAW filters, made things a lot easier and cheaper. I once had to 'wobble' a TV IF to fix the curve, not so easy, takes a lot of time.
In classical physics, search "line splitting" of coupled oscillators. It' s the chassical version of QM's Pauli Exclusion principle, where two oscill ators aren't allowed to be in the same state (have the same freq.) Note t hat as oscillations "slosh" between the resonators, the sloshing period is the same as the separation between peaks in the frequency domain.
Make a big square array of resonators, and you've got a 2D crystal, and so much line-splitting that we end up with an "energy band" which is actually a large number of closely-spaced peaks. Hmmm, if we could plot the absolu te value amplitude of every oscillator as a raster, then slam single elemen ts (or groups) with transient spikes, what's that look like? For low coup ling, it's thermal vibrations in solids. With high coupling it's just a p atch of 2D waveguide with 2D waves bouncing around inside. Make a low-cou pling "wave tank" where the "liquid' only passes slowly-moving oscillations along, rather than propagating waves.
Wow, I never made that connection before. Thanks! Mark
That's not what the Pauli principle states, and it only applies to fermions anyway.
Splitting of coupled quantum oscillators is what gives rise to the band structure of solids. Photons and other bosons don't behave the same way. (That's why there are lasers, among other things.)
Besides IF transformers, two coupled classical modes make directional couplers possible. The math is simple and quite pretty.
Cheers
Phil Hobbs
OK, here are three resonators in-line.
The waveforms are sort of beautiful, and vary radically as the coupling caps are changed, especially if C3C6.
-- John Larkin Highland Technology, Inc picosecond timing laser drivers and controllers jlarkin att highlandtechnology dott com http://www.highlandtechnology.com
I've got some very similar waveforms at work from a 230 kV, 3 phase cable circuit which had a 45 MVAR shunt reactor hanging off it when the line was tripped. All three phases resonated at nearly equal frequencies and you had energy transfer via the inter-phase capacitance and mutual inductance of the overhead portion of the line.
t's the chassical version of QM's Pauli Exclusion principle, where two osci llators aren't allowed to be in the same state (have the same freq.) Note that as oscillations "slosh" between the resonators, the sloshing period i s the same as the separation between peaks in the frequency domain.
I would just call them (the oscillations) the normal modes of the system. If you can excite the system in one of it's normal modes, then it will stay in that mode and not have the energy sloshing back and forth.
George H.
o much line-splitting that we end up with an "energy band" which is actuall y a large number of closely-spaced peaks. Hmmm, if we could plot the abso lute value amplitude of every oscillator as a raster, then slam single elem ents (or groups) with transient spikes, what's that look like? For low co upling, it's thermal vibrations in solids. With high coupling it's just a patch of 2D waveguide with 2D waves bouncing around inside. Make a low-c oupling "wave tank" where the "liquid' only passes slowly-moving oscillatio ns along, rather than propagating waves.
Well, obviously it's a gross simplification. But I don't think unreasonable.
If you look at the characteristics of the phenomena, quanta are well defined, give or take externalities: the line width of an atomic transition is for all intents and purposes infinitessimal, minus splitting (fine structure, fields, etc.), doppler and such (properties of a gas, etc.). Whereas the classical peak is fully described by a continuous function of amplitude, with the "line" width determined by Q.
Likewise, where you have systems containing fermions, coming together, you get exclusion, and you get splitting of energy levels. Two isolated hydrogen atoms have identical spectra, but two hydrogen atoms in relative proximity experience a splitting and shift. The effect is not un-analogous, at least on a grossly descriptive level. When things like this happen, there's often some underlying theoretical truth to it, that it doesn't happen for mere coincidence.
No, photons and phonons and such don't behave the same way, but their interactions -- mediated by electronic transitions -- often are. So, we're talking about the fermionic structure that's probed by bosons, not the statistics of bosons themselves. Which would be boring -- like talking about only superposition in linear classical systems. :)
Tim
-- Seven Transistor Labs Electrical Engineering Consultation Website: http://seventransistorlabs.com
.
on
Hi Tim, Just a fine point of correction. Atomic transitions have a finite width that is set by the lifetime of the e xcited state. For a typical ~10 ns lifetime, it's about a 10 MHz width... (there's a factor of 2 * pi in there.) You can actually see this width wit h diode lasers.. and some tricks. (search for saturated absorption spectro scopy.)
George H.
u
us,
re
Atomic transitions have a finite width that is set by the lifetime of the excited state. For a typical ~10 ns lifetime, it's about a 10 MHz width... (there's a factor of 2 * pi in there.) You can actually see this width with diode lasers.. and some tricks. (search for saturated absorption spectroscopy.)
Ah yes, I should've remembered this. Uncertainty and all.
Better phrasing; for being atomic transitions, they can be surprisingly sharp, much sharper than you'd expect for a frequency in the 600THz range!
Tim
-- Seven Transistor Labs Electrical Engineering Consultation Website: http://seventransistorlabs.com
The Pauli principle has nothing to do with splitting, it has to do with wave function symmetry.
With indistinguishable particles, the wave function has to be symmetric or antisymmetric, under the operation of interchanging particle A and particle B.
The reason for this is that it has to be invariant under the operation of swapping them and then swapping them back.
If the particles are indistinguishable, though, swapping one way is indistinguishable from swapping back. That means that the eigenvalue of the transformation has to be +- 1. (It can't have a magnitude other than unity, because the normalization sets the number of particles.)
Bosons are particles for which the eigenvalue is +1, and fermions are those for which the eigenvalue is -1.
With two or more bosons in a single state, interchanging them doesn't change anything, so it's the more, the merrier.
With two fermions in a single state, interchanging them has to make the wave function invariant under a multiplication by -1. That is, its magnitude has to be 0--which means there's no such state.
_That's_ the Pauli principle.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 hobbs at electrooptical dot net http://electrooptical.net
Fun, thanks. I'd never heard the double swap gets you back to where you started, argument before. (though kinda obvious in retrospect.) So there can be two, and only two, types of indistinguishable particles.
George H.
ElectronDepot website is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.