How do you make a closed signal loop?

Is this any different from a clocked synthesizer?

What you describe sounds an awful lot like an oscillator.

For instance, place two phones next to each other, dial one from the other obviously, and listen for the squeal (if there's an unusual amount of line between them, you may have trouble getting feedback.. cellphones especially). A signal, perhaps hiss on the line, is picked up by one and send through the line to the next, and so on. Same as microphone squeal, and any other powered, oscillating system (you can generalize it to, say, dragging your shoe across the floor so that your rubber sole grabs, bounces, falls and bounces again).

In an electrical circuit, you might have two tuned amplifier circuits. Each one amplifies most signals, but in particular they amplify signals around a given tuned frequency especially well (tuned gain and how fast gain drops away from the center frequency are determined by the tuned circuit's characteristics). Couple them together and, more than likely, you'll get a self-sustained oscillation. You have your requisite two inductors, and you have a circulating signal.

If you actually meant a particular waveform, then please, do tell.

Sure.

Tim

What do you mean by a 'signal carrier'? If you mean that you generate a changing signal once, and then want it to circulate in a wire forever, I don't think it would, because a changing magnetic field has to cause radiation that would gradually radiate away the signal energy, even if the wire is a superconductor. If you have something there to add energy and regenerate the signal, if it's not a digital signal, there would be some noise addition that would gradually smear the signal beyond recognition.

-- John

Yes, exactly. I am looking for a "universal" oscillator/amplifier. The problem I have with the basic oscillator/amplifier (as I understand it) is that it only sustains a fixed set of frequencies. If you put a random signal into the amplifier, it amplifies only part of the signal and loses the other information.

Is there another circuit design that will sustain a signal, so that I can modify it at will?

-Craig

Yes, exactly, but not forever. Just long enough to go through the loop/oscillation ~10^4 times.

Yes, it's an analog signal, and your criticism is exactly what I fear is insurmountable. How dramatic is the smearing/dissipation?

The theory is that instead of using the addition of sine waves to generate a signal (Fourier theory), successive additions of bump functions generate the signal. By "bump function" I mean exp(-x^2), the Gaussian. I believe this is roughly the signal generated by turning on and off an inductor adjacent to the signal carrier (wire). Doing this once generates the bump. How long you turn it on, with what current, and what size inductor, controls how big the bump is. (You cannot leave the inductor on long enough to let the magnetic field fully charge or else the bump will flatten out at the top).

So, new research gives an algorithm for generating any signal from a sequence of these bumps. This suggests that a long enough series of inductors will be able to generate any signal--independent of any particular frequency. Is there a more economical way to make a shorter series of inductors by looping the signal? I'm so out of my depth I'd be happy to know of a feasible design is for the dissipating loop you describe--just a timed gate onto a looped wire?

-Craig

Well there's a pretty basic wave function going on here.

Imagine you have a 1kHz signal, and you send it through a delay line so it comes back to the amplifier in 1ms. The period of 1kHz is 1ms, so it's the same signal you started with. If the loop gain is adjusted just right so it doesn't get stronger or weaker, then the 1kHz will always appear at the input and output of the amplifier and delay line just right.

If you instead excite this circuit with 2kHz (with a period of 0.5ms), there will be two cycles in the delay at any given time. At 3kHz, three, and so on. These are perfectly allowed states, and any combination of them is also allowed (indeed, Fourier proved that any waveform repeating indefinetly can be represented by a discrete number of harmonics (multiples) of the repeat frequency).

However, say you want to loop 1.5kHz, a period of about 0.67ms. Send that through the delay line and, at any given time, you have 1.5 cycles inside the delay: in other words, when the output is going up, the input (and thus the amplifier that feeds it) is going down. (If you can't see this, draw it.) But the amplifier connects output to input instantaneously, so this can not be. It is a disallowed state.

For sufficiently large values of n (perhaps more than 100), it starts looking continuous, because the 100th harmonic (100kHz) is only 1% away from the 101st (101kHz). But now, your delay is also very long: each cycle is a mere 10us, while the delay is 1000us. It takes a long time to input your complete signal into the line.

For audio frequencies, this delay is very much tangible -- it may take several seconds of continuous delay to cause a reasonable looping action. If you need to initialize the delay line with some signal pattern before playing a note based on it, you've already incurred an intolerable delay for playing that note!

Tim

Can't this be generated digitally?

I doubt anyone even uses Fourier synthesis anymore, if ever, for generating particular tones. Timbre controls are typically frequency response and nonlinear (i.e. distorting) amplifiers.

Makes sense, enough chained together is going to look a damn lot like a sine wave. Also, in the frequency domain, extremely narrow gaussians represent harmonics.

No, that creates -- depending on how exactly you're turning it on and off -- a decaying pulse, with frequency corresponding to 1/(2*pi*sqrt(L*C) and decay rate depending on Q.

Inductor current rises linearly with time, in proportion to voltage. When charging, you want current to rise, so voltage is positive. When discharged, current is falling, so voltage must be negative; how much so depends on the load. With no load, voltage goes infinitely low (negative), which in reality is obviously cought with a spark through the air (or worse, if you're using transistors). In either case, the voltage (actually EMF) induced in a nearby wire or coil depends on the geometry of the arrangement (size, turns, distance), and the EMF is in direct proportion to the applied voltage, having nothing to do with the instantaneous value of current or magnetic field strength. If you apply a square wave, you'll get a square "bump" induced.

Tim

I still find it hard to picture what you mean. When you say 'signal', do you mean a periodic function with harmonics, to get a particular waveshape (no matter how generated)? If you want a periodic irregular signal to circulate somehow, you have to have it in a path whose time length is greater than the period of the signal, so the ends don't overlap. That could be costly. If you are just wanting to generate a periodic signal by adding some sort of gaussian driblets, couldn't you do that to an array in computer memory, and then clock it out to an A/D, continuously, if you needed it in analog form? I'm probably not quite understanding what you mean.

-- John

I mean a single inductor, all by itself, adjacent to--but not connected to--the signal wire. No capacitor involved to get any type of periodicity or frequency. By "turning it on/off", I mean running current through the inductor for a short time--just enough for the magnetic field to start building, but not long enough for it to stabilize. The magnetic field strength will rise while current is running through the inductor and fall after the current is switched off. The rising and falling magnitude of the magnetic field will induce a current in the adjacent signal wire. Corresponding to the rising and falling magnetic field strength, I expect the induced signal will look like a Gaussian/Bell curve (I'm starting to realize I should not use the term "bump function" in this EE atmosphere since it is used in other, inequivalent contexts).

Yes, except there is a subtlety in the new theory that I didn't explain. The interesting thing about the new theory is that it claims if you are very tricky, you do not need to be able to control the width of the bump/Gaussian. I.e., if the Gaussian is given by a*exp(-x^2/s) you only need to be able to control the a-parameter, not the s-parameter (which controls the width or spread of the Gaussian). This means physically, that only one type of inductor is needed to generate any signal (instead of many different inductors which generate different width Gaussians).

Thanks for all the help, so far.

-Craig

Ooh. Thanks for the insight. That is exactly what I had in mind, and I hadn't considered that failing (not being of a practical orientation).

In theory, yes, but in practise, no. An analog signal will rapidly degrade from noise, dispersion, and frequency imperfections.

If you digitize a signal, then you can run it around any way you like, forever, without degradation. Someone once made a spectrum analyzer that did just this, Nicolet's "Ubiquitous Spectrum Analyzer" I think.

I've played with synthesizing an arbitrary waveform from a series of weighted Gaussian pulses (and have a product, a laser modulator, that does this) and Wavelet Synthesis is a generalism of this idea.

John

Sorry- remarkably hard to do in real life. Any two wires, heck any two points in space, have a certain capacitance between them, because an electric field exists in that space.

You might be able to run some simulations on paper or computer, where capacitance doesn't necessarily have to come into play, but in reality if you charge an inductor and release it quickly, the rate of voltage change depends on the current and capacitance present. The initial current provides the energy to excite the L-C resonance.

Current is directly proportional to magnetic field. I think you meant voltage?

Not a problem. Note that, ideally it won't, but series resistance causes a limit to current flow, which can be seen as stabilizing it for a given supply voltage, if you want to put it that way. (You can also drive the inductor through a constant-current amplifier, with the result that you have a certain current slewing rate limitation instead.)

Only if it's a short circuit (which is rare, outside of superconductors, and reasonably conductive metals depending on conditions). Open circuit, like a coil of wire, produces an EMF.

The problem is, your expectations are quite different from reality.

The fundamental equation of a perfect inductance is: V = L * dI/dt Where V is terminal voltage, L is the inductance between those terminals, and dI/dt is the rate of change of the current flowing through those terminals.

If you apply a constant voltage, current rises at a constant rate. If you break the circuit (that is, force current towards zero), dI/dt must be arbitrarily very negative, which forces V very negative. As I mentioned, the usual result from simply "pulling the plug" is a spike of voltage, causing a spark through the air.

Note that combining a capacitor (whose equation is strikingly similar, I = C

• dV/dt) with an inductor creates a differential equation whose solution is the sine function -- oscillation.

To obtain a gaussian function, you need a gaussian input, either of voltage or current, depending on just what you're doing with it.

Oh, and note also that voltage doesn't like to stay above zero. If it did, current would rise indefinetly. It's okay to have current statically at any arbitrary value, so long as the real inductor can handle the stresses -- but the voltage across the pure inductive component must average zero.

The integral of a "bump" is nonzero.

Overall I think you've come to the wrong component; gaussians are great for statistics and distributions, but they don't work very well with components govorned by differential equations.

"Bump" is fine with me.

Hmm, I think I can see that- if s is small, just make A bigger, so the overlapping "bumps" have a bigger effect.

Tim

None of this will work the way you want it to in a real world circuit, due to the significant differences between theoretical & real world components. By far the simplest way to model your idea would be with a software simulation. One of the circuit emulator packages like 'Spice' would be the obvious place to start, as you can turn off the "real world" tweaks & treat the components as being perfect.

Then, when you "turn on" the real world, everyting will f*ck up.

... Donkey

Sure, but if I understand him correctly, the OP's more interested in verifying a mathematical theory than building an actual working circuit. And even if he does end deciding to build the real thing, one, it'll be a lot easier to design if he's already verified that the theoretical side is solid.

If I try to be serious for a moment... I agree that in this case, since it's mainly a theoretical question, simulation is probably the way to go. In fact, after seeing so many references to Spice simulation lately, it's time I gave it a go myself. After all, I use a simulator for my micro-controller circuits and it helps enormously. ... Donkey

True enough, but we now know superconductors and cryogenic equipment can keep the noise way down.

Not quite true. You would still have to regenerate the signal due to the same items you bring up above. It is just that when a signal is digital it is easier to regenerate the signal while not the noise.