Hi Edmond.
The slowness of the drift velocity has no relevance, and there's no real wave speed either.
The velocity that matters is the "Fermi Velocity", it varies a bit from metal to metal but in excess of 10^6 m/s, for copper, say, it's about 1500 km/sec, or 1/2% of c.
But it's like a transmission line with an enormous capacitor and 100k resistor at the end. Doesn't matter how fast the transmission line is, the RC time constant dominates.
This is why I made the comparison, it seems to me that in typical audio circuits that the base resistance * input capacitance of the FET will dominate and the "equivalent ft" won't matter.
But, as I already commented, I am not experienced in FETs so perhaps it will become clearer.
And I'm not an expert in condensed matter physics either so the explanation is only my recall of university lectures.
Best wishes
David
On a side note. I hope you read the thread before the moderator action.
Waly actually wrote that I was correct! It's like an authenticated photo of the Loch Ness monster, and now it's deleted
Hi David,
Do you mean WRT heat propagation? (that's what I meant)
Cheers, E.
Do you mean WRT heat propagation? (that's what I meant)
Regrettably, I've missed it.
Of course you were correct.
I love to see it, please, send it to me by PM.It's like an authenticated photo of the Loch Ness monster, and now it's deleted
Cheers, E.
Yes, specifically WRT heat conduction in metals.
D.Self speculated that heat travels at the speed of sound and I pointed out that this is not true in metals, which is what mostly concerns us with heat-sinks and heat spreaders in transistors.
He never thanked me for the information, for some reason
And Waly's post is now vanished, like the snows of yesteryear.
Best wishes
David
The same question occurred to me too, that this is not so obvious as is usually assumed, like most of physics once you think about the basics.
Obviously in transmission lines it is close to c, transmitted as an EM wave.
But I have never seen an analysis for wires, from first principles. it's just assumed it's "fast". Can I think about this some more?
Best wishes
David
>travels at the speed of sound
I didn't know that heat makes noise.
Well, heat in solids is lattice vibrations so his idea was not unreasonable.
There is even an unusual mode of heat "wave" that does travel like a sound wave, called "second sound" in fact.
But not relevant to metals because their dominant thermal conductivity is mediated by electrons.
Sorry to Bob it's bit off-topic, just came to mind in comparison to FETs.
Best wishes
David
The same question occurred to me too, that this is not so obvious as is usually assumed, like most of physics once you think about the basics.
Obviously in transmission lines it is close to c, transmitted as an EM wave.
But I have never seen an analysis for wires, from first principles. it's just assumed it's "fast". Can I think about this some more?
Best wishes
David
Maybe this helps: https://en.wikipedia.org/wiki/Single-wire_transmission_line
Cheers, E.
heat propagation.
So why has "the slowness of the drift velocity has no relevance" ? Forgive me if this is a dumb question.
Cheers, E.
edit: obviously, I'm no expert on thermodynamics.
So why has "the slowness of the drift velocity has no relevance" ? Forgive me if this is a dumb question.
Cheers, E.
edit: obviously, I'm no expert on thermodynamics.
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It's a bit like the transmission of sound which occurs at say, 333 m/s even if there is no breeze (=drift velocity). The drift velocity is how fast the mean position of individual units (atoms or electrons) move. So they can move quite quickly and transmit the sound (or heat) but if they bounce around a lot then they still have a low drift velocity.
That's the basic idea but electron behaviour needs a quantum mechanical treatment to be even approximately correct, the effective velocity of the electrons is the Fermi Velocity, because electrons are subject to the exclusion principle and subject to Fermi-Dirac statistics.
Happy to explain more, it's fun to revisit this stuff, but maybe move it from Bob's thread.
Best wishes
David
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The same question occurred to me too, that this is not so obvious as is usually assumed, like most of physics once you think about the basics.
Obviously in transmission lines it is close to c, transmitted as an EM wave.
But I have never seen an analysis for wires, from first principles. it's just assumed it's "fast". Can I think about this some more?
Best wishes
David
The signal propagation speed in a transmission line is denoted by Vf, which is the percentage of the speed of light. A typical Vf for a coaxial cable might be on the order 0.7 (70%). Vf is numerically equal to the reciprocal of the square-root of the dielectric constant of the insulator.
I usually use the approximation that the speed of light is 1 nanosecond per foot. For a cable I approximate it as 1.5 nanosecond per foot.
Cheers,
Bob
I would have thought that the propagation speed through an electrical circuit would have to be very well studied so that the concept of feedback in an audio amplifier could be well defined? Is this not so, is all of this just approximations and the Nyquist functions if that is the right term are just conceptual or has this been studied at a much higher level? I'm no mathematician so I don't need a specific reference to read but the last bit of back and forth had me ask this question. I surely don't want to fall into the camp that questions whether feedback circuits are fast enough not to change the signal, I just wondered why all the questioning here about circuit speed and even heat propagation through a metallic structure.
One last comment. I think when we look at many so called solids such as metals that on a molecular basis they aren't exactly a monolithic structure with no boundaries but are more like a foamed material in a sense. Aluminum comes to mind in its normal cast state, even forged aluminum has a grain structure to it. This would make me question the speed of heat transfer through any of these so called solid metal structures.
One last comment. I think when we look at many so called solids such as metals that on a molecular basis they aren't exactly a monolithic structure with no boundaries but are more like a foamed material in a sense. Aluminum comes to mind in its normal cast state, even forged aluminum has a grain structure to it. This would make me question the speed of heat transfer through any of these so called solid metal structures.
It takes signal about 3.33nS to traverse 1 meter of conductor. So for amplifiers it's on the order of pS.
Even an amplifier with a high ULGF at 15MHz is about at least 200 times slower than the speed of signal around the PCB.
I suppose it's possible this might have a very slight affect on the step response of the very fastest audio circuits?
Even an amplifier with a high ULGF at 15MHz is about at least 200 times slower than the speed of signal around the PCB.
I suppose it's possible this might have a very slight affect on the step response of the very fastest audio circuits?
No, please don't start that...
It has indeed been very well studied and, as many have pointed out, issues of delay are not relevant in typical audio power amplifiers.
I didn't mean to re-open that morass.
I just commented that while I had seen derivations of the wave speed in a co-axial cable or transmission line, I have not seen it done from first principles in a simple wire.
My initial intuition is that it should be much slower, but this is very likely incorrect.
Most intuitions on this stuff are simplistic and incorrect, hence the endless objections to feedback, the myths about A to D, D to A conversion and so on.
So it interests me where my intuitive model fails, how it really works.
This is another one where the intuitive model doesn't work.
Thermal and electrical behaviour in metals are closely related and there were similar views to claim subtle effects in cables.
But you can't take a classical, intuitive picture then add some complications and claim that your competitors ideas are simplistic.
Any classical model is simplistic to the point of useless.
In some areas of physics there are useful, semi-classical approximations but conduction in metals doesn't seem to have one.
It needs the whole catastrophe of quantum mechanics.
Best wishes
David
I am commenting only on the speed of the electronic signal vs electron drift velocity here.
The speed of signal travel through the transmission line ( include wires and pcb traces etc.) has NOTHING to do with velocity of electrons. The better the conductor, the slower the electron velocity.
Signal travels as EM wave, not at all as electrons that people think. The current and voltage is ONLY the consequence of the boundary condition in electromagnetic. This is very involve to proof. Bottom line, if you look at the velocity of the signal in a transmission medium, the Permittivity of the medium comes into the picture. The velocity U=1/sqrt{permittivity X permeability}. For example, the Relative permittivity of FR4 pcb is about 4, air is 1. Relative permeability of both FR4 and air is 1. So the speed of signal through a wire hanging in air is double the trace on the FR4 pcb.
The speed of signal travel through the transmission line ( include wires and pcb traces etc.) has NOTHING to do with velocity of electrons. The better the conductor, the slower the electron velocity.
Signal travels as EM wave, not at all as electrons that people think. The current and voltage is ONLY the consequence of the boundary condition in electromagnetic. This is very involve to proof. Bottom line, if you look at the velocity of the signal in a transmission medium, the Permittivity of the medium comes into the picture. The velocity U=1/sqrt{permittivity X permeability}. For example, the Relative permittivity of FR4 pcb is about 4, air is 1. Relative permeability of both FR4 and air is 1. So the speed of signal through a wire hanging in air is double the trace on the FR4 pcb.
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Because of the way energy propagates. It's not about exciting an individual electron and then waiting for THAT individual electron to come out the other end, rather you are doing that in a medium full of electrons, so one koncks out another and gets in it's place, that another knocks out still another etc - the disturbance propagates far faster than the single electron is able to move.
(VERY simplistic explanation).
Think of it as having a tube to pass rubber balls through. If the tube is full of balls, pushing one into one end will compress the last one right at the entrance, and this one will compress the next one etc until the compression 'wave' pops out the one right at the end and it falls out. The compression wave moves far faster than each individual ball, while it travels the whole length of the tube, the actual balls have only moved by one diameter of a ball, and this is the drift velocity - This is a very simple analogy of how it works
Don't we see this sum of delays as a low pass filter, I would think cob of devices plays a much bigger role in the limitations of the feed back, if signal transmission had unlimited speed we'd have to make frequency limiting compensation. The open loop bandwidth must equal the transmission time of the circuit
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That's incredible
I've always assumed 1 millisecond per foot for sound. I knew there was something fishy about this Metrication lark
In my previous life, when I pretended to work on Room Acoustics Simulation with Patrick Macy of PAFEC & Julian Wright of Celestion, we had PAFEC air and the Wright air, each with slightly different properties but this essentially held
There is one situation pertaining to heatsinks etc where heat travels at nearly the speed of sound. It's in heat pipes.
You test this by handing your friend an innocuous shiny metal rod to stir his hot coffee