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Sci.Electronics.Basics -> How do you make a closed signal loop?
There are 17 messages in this thread.
You are currently looking at messages 1 to 17.
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Hi Everyone,
Is it possible (in theory) to capture a signal in a closed loop,
keeping the signal stable and periodically travelling around the loop?
I am a mathematician who is quite ignorant about the practical details
and technical terminology of electronic circuits (as must be apparent).
I only understand the basics of the physics involved, and am
interested only in a general/vague/abstract explanation. I am working
on generating signals using only a series of inductors with alternating
orientation near the signal carrier, which generate magnetic fields,
which in turn make a controllable "bump" in the signal. I have
recently discovered an algorithm for generating any signal from a
sequence of these "bumps". [This is similar to, but fundamentally
different from, Fourier analysis.] If it is possible to keep a signal
in a loop then (as I understand it) only 2 inductors, of opposite
orientation, would be needed to make a converter or synthesizer
circuit.
I've just moved to China for a year and do not have physical access to
experts at the moment (no electrical engineering department at my
school). I see this postboard has more expertise than any university.
Is this the correct location for such a post? (I'm a new user.)
Thanks,
Craig
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Author: Tim WilliamsDate: 00:44 09-09-06
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<calcat@fastmail.fm> wrote in message
news:1157776200.937656.314690@p79g2000cwp.googlegroups.com...
> I have
> recently discovered an algorithm for generating any signal from a
> sequence of these "bumps". [This is similar to, but fundamentally
> different from, Fourier analysis.] If it is possible to keep a signal
> in a loop then (as I understand it) only 2 inductors, of opposite
> orientation, would be needed to make a converter or synthesizer
> circuit.
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.
> I've just moved to China for a year and do not have physical access to
> experts at the moment (no electrical engineering department at my
> school). I see this postboard has more expertise than any university.
> Is this the correct location for such a post? (I'm a new user.)
Sure.
Tim
--
Deep Fryer: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms
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Author: John O'FlahertyDate: 09:52 09-09-06
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calcat@fastmail.fm wrote:
> Hi Everyone,
>
> Is it possible (in theory) to capture a signal in a closed loop,
> keeping the signal stable and periodically travelling around the loop?
>
> I am a mathematician who is quite ignorant about the practical details
> and technical terminology of electronic circuits (as must be apparent).
> I only understand the basics of the physics involved, and am
> interested only in a general/vague/abstract explanation. I am working
> on generating signals using only a series of inductors with alternating
> orientation near the signal carrier, which generate magnetic fields,
> which in turn make a controllable "bump" in the signal. I have
> recently discovered an algorithm for generating any signal from a
> sequence of these "bumps". [This is similar to, but fundamentally
> different from, Fourier analysis.] If it is possible to keep a signal
> in a loop then (as I understand it) only 2 inductors, of opposite
> orientation, would be needed to make a converter or synthesizer
> circuit.
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
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Author: craigDate: 18:49 09-09-06
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> What you describe sounds an awful lot like an oscillator.
>
> 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.
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
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Author: craigDate: 19:29 09-09-06
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> 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,
Yes, exactly, but not forever. Just long enough to go through the
loop/oscillation ~10^4 times.
> 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.
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
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Author: Tim WilliamsDate: 19:35 09-09-06
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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
--
Deep Fryer: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms
"craig" <calcat@fastmail.fm> wrote in message
news:1157842184.232160.220330@b28g2000cwb.googlegroups.com...
> 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
>
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Author: Tim WilliamsDate: 19:50 09-09-06
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"craig" <calcat@fastmail.fm> wrote in message
news:1157844565.701097.166840@d34g2000cwd.googlegroups.com...
> 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.
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.
> By "bump function" I mean exp(-x^2),
> the Gaussian.
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.
> 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.
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
--
Deep Fryer: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms
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Author: John O'FlahertyDate: 22:05 09-09-06
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craig wrote:
> > 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,
>
> Yes, exactly, but not forever. Just long enough to go through the
> loop/oscillation ~10^4 times.
>
> > 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.
>
> 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?
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
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Author: craigDate: 22:17 09-09-06
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> > 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.
>
> 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.
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).
>> By "bump function" I mean exp(-x^2),
>> the Gaussian.
>
>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.
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
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Author: craigDate: 22:23 09-09-06
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> 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.
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).
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Author: John LarkinDate: 22:40 09-09-06
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On 8 Sep 2006 21:30:01 -0700, calcat@fastmail.fm wrote:
>Hi Everyone,
>
>Is it possible (in theory) to capture a signal in a closed loop,
>keeping the signal stable and periodically travelling around the loop?
>
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 have
>recently discovered an algorithm for generating any signal from a
>sequence of these "bumps". [This is similar to, but fundamentally
>different from, Fourier analysis.] If it is possible to keep a signal
>in a loop then (as I understand it) only 2 inductors, of opposite
>orientation, would be needed to make a converter or synthesizer
>circuit.
>
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
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Author: Tim WilliamsDate: 23:39 09-09-06
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"craig" <calcat@fastmail.fm> wrote in message
news:1157854675.954679.193060@m73g2000cwd.googlegroups.com...
> 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.
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.
> 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
Current is directly proportional to magnetic field. I think you meant
voltage?
> but not long enough for it to stabilize.
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.)
> The rising and falling magnitude of the magnetic field will induce
> a current in the adjacent signal wire.
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.
> Corresponding to the rising and
> falling magnetic field strength, I expect the induced signal will look
> like a Gaussian/Bell curve
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.
> (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).
"Bump" is fine with me.
> 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).
Hmm, I think I can see that- if s is small, just make A bigger, so the
overlapping "bumps" have a bigger effect.
Tim
--
Deep Fryer: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms
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Author: LionelDate: 00:18 20-09-06
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On 9 Sep 2006 16:29:25 -0700, "craig" <calcat@fastmail.fm> opined:
>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?
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.
--
W
. | ,. w , "Some people are alive only because
\|/ \|/ it is illegal to kill them." Perna condita delenda est
---^----^---------------------------------------------------------------
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Author: Donkey D...Date: 00:42 20-09-06
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"Lionel" <usenet@imagenoir.com> wrote in message
news:msf1h2ppqotrvp3uv4dcoev8qjarr87q6t@4ax.com...
> On 9 Sep 2006 16:29:25 -0700, "craig" <calcat@fastmail.fm> opined:
>
> >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?
>
> 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.
> --
> W
> . | ,. w , "Some people are alive only because
> \|/ \|/ it is illegal to kill them." Perna condita delenda est
> ---^----^---------------------------------------------------------------
>
Then, when you "turn on" the real world, everyting will fuck up.
... Donkey
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Author: LionelDate: 03:09 20-09-06
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On Wed, 20 Sep 2006 14:42:37 +1000, "Donkey D..." <NoSpam@fForMe.com>
opined:
>
>"Lionel" <usenet@imagenoir.com> wrote in message
>news:msf1h2ppqotrvp3uv4dcoev8qjarr87q6t@4ax.com...
>> 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 fuck up.
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.
--
W
. | ,. w , "Some people are alive only because
\|/ \|/ it is illegal to kill them." Perna condita delenda est
---^----^---------------------------------------------------------------
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Author: Donkey D...Date: 06:22 20-09-06
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"Lionel" <usenet@imagenoir.com> wrote in message
news:u2q1h2t8j23gdon3fkmgit27ouucn5rm9k@4ax.com...
> On Wed, 20 Sep 2006 14:42:37 +1000, "Donkey D..."
<NoSpam@fForMe.com>
> opined:
>
> >
> >"Lionel" <usenet@imagenoir.com> wrote in message
> >news:msf1h2ppqotrvp3uv4dcoev8qjarr87q6t@4ax.com...
> >> 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 fuck up.
>
> 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.
> --
> W
> . | ,. w , "Some people are alive only because
> \|/ \|/ it is illegal to kill them." Perna condita delenda est
> ---^----^---------------------------------------------------------------
>
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
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Author: DanaDate: 11:36 22-09-06
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"John Larkin" <jjlarkin@highNOTlandTHIStechnologyPART.com> wrote in
message
news:jbu6g2ds860unnahq699vf20pfu8c4pqef@4ax.com...
> On 8 Sep 2006 21:30:01 -0700, calcat@fastmail.fm wrote:
>
> >Hi Everyone,
> >
> >Is it possible (in theory) to capture a signal in a closed loop,
> >keeping the signal stable and periodically travelling around the loop?
> >
>
> In theory, yes, but in practise, no. An analog signal will rapidly
> degrade from noise, dispersion, and frequency imperfections.
True enough, but we now know superconductors and cryogenic equipment can
keep the noise way down.
>
> If you digitize a signal, then you can run it around any way you like,
> forever, without degradation.
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.
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