Yes, I understand that electrons must tunnel thru the separation, I was a bit lazy and didn't explain very fully.
My point was that an "island" 100 nm thick was very unlikely to be separated by a trench only 1 nm wide to another "island".
I just can't see any realistic way such a structure could be formed when a film of that thickness is deposited.
Thank you for the reference. I will try to obtain it soon.
Best wishes and compliments of the season
David
My library lists it as freely available on-line but the link doesn't work.
Google books has most of it, looks educational.
Is there a full version in the public domain?
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They are parallel paths so electrons will, theoretically, take both, in accordance with old, classical "resistors in parallel" formula.
I just estimate that one path is so much lower resistance that the other path is totally irrelevant.
I recall that there are situations where one electron can take both, quantum mechanically.
But this requires such specialized experimental conditions that I really can't see how it could possibly be relevant.
If anyone wants to help my recall on this then it would be fun, in another thread, way too off topic for here.
Best wishes
David
Only for relatively low frequencies. Higher frequency current (even part of the audio band) seeks the path of least inductance,
which can be quite different.
Nice work,! Have you thought of making your efforts available for others to play around with - I would be interested in the model parameters changing with frequency thing ... always like looking into chewy things ...
I meant to say temperature, not frequency. Most models are accurate where frequency is concerned. My focus with the thermal simulation was to work out a cohesive system to make real-time temperature simulation intuitive. I also added some simple MTBF and lifetime calculations based on dynamic temperature.
True, but I thought this discussion was primarily for audio frequencies and generally low impedance circuits. Some people seem to think proportional and relative means absolute.
RF frequencies can certainly seem to defy logic, especially with antennas.
--Damon
Even in a copper ground plane, current will seek the lowest inductance path well within the audio frequency range.
Okay, let me say that again. Self-heating effects are frequency-dependent, so they will cause frequency-dependent distortions in the transistors in question. My model can only affect Vbe, not the model parameters. Still, it demonstrates harmonic variances due to self-heating effects at frequencies as high as 1KHz (from my memory, which may be bad).
True and well within audio frequencies.
Okay, now you're just messing with my head and sense of perspective. How can this be measured? (and does my dual trace 'scope operate in differential mode?)
--Damon
Think about the corner frequency between the mutual inductance and the resistance of the ground plane. Depending on the thickness of the copper it can be in or above the audio range.
When there is very little mutual inductance and total inductance is >> resistance, I would expect the current path to become thinner and straighter, although I may be totally wrong about that since I know there are things about currents sticking to edges and holes in the plane.
When there is very little mutual inductance and total inductance is >> resistance, I would expect the current path to become thinner and straighter, although I may be totally wrong about that since I know there are things about currents sticking to edges and holes in the plane.
True and well within audio frequencies.
THx-RNMarsh
Yes, we have a beautiful experimental demonstration of this in a professional development EMI course that we present at our university.
A long, L-shaped trace is on the top layer of a pcb, driven at one end, with the other end terminated to the ground plane, and the return current
in the ground plane is made visible.
Below about 1kHz, the ground plane return current goes directly from the terminated end of the L to the source ground diagonally, in the path of least resistance.
At higher frequencies, the current flows directly under the arms of the L, tracing out its shape faithfully, in the path of least inductance.
With copper traces and ground planes we also must keep in mind skin effect, even at upper audio frequencies. If I recall correctly, skin depth is about 1/3 inch at 60 Hz and gets smaller as the square root of frequency. I could be wrong here, and there are many here who know more I'm sure. All I'm saying is that we have to take into account the fact that the trace becomes effectively thinner at high frequencies, and this may increase the effective resistance. Maybe someone can do a swag on this and see if the numbers suggest an issue in terms of how much percentage the effective resistance of the copper trace increases at upper audio and low RF frequencies.
Cheers,
Bob
Cheers,
Bob
Skin depth for copper at 20kHz is about 0.5mm. The typical "1 oz" PCB copper is about 0.035mm.
As a rule of thumb, a typical signal PCB trace over a groundplane has an AC resistance 33% more than its DC resistance due to skin and proximity effect, at 1GHz. So at 20kHz the increase in resistance must be negligible.
Proximity effect can do some weird things, though. You could have two huge areas of copper, and all the current could end up flowing along one edge, even at 20kHz.
As a rule of thumb, a typical signal PCB trace over a groundplane has an AC resistance 33% more than its DC resistance due to skin and proximity effect, at 1GHz. So at 20kHz the increase in resistance must be negligible.
Proximity effect can do some weird things, though. You could have two huge areas of copper, and all the current could end up flowing along one edge, even at 20kHz.
Huh? Copper skin depth is 461um at 20KHz and even at 1MHz is x2 the regular PCB traces thickness.
Perhaps you are confusing with the proximity effect, which is a completely different kettle of fish, and may indeed have a slight impact at audio frequencies, if ground planes are used.
Even so, magnetic effects are by orders of magnitude larger are more evil to fight. I am having lots of fun watching so-called (that is, Spiced only, never measured) ultra low distortion designs that are integrating the output coil on the PCB, happily radiating in the input stage build (how else?) with through hole parts.
Yes, this is very similar to our EMI course demonstration, using a pcb trace over a ground plane, and with the same frequency behavior.
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