I know that resistors exhibit resistance variations with temperature (temperature coefficient), and with voltage across them (voltage coefficient). These change with signal levels, causing the resistor to change value with instantaneous signal level, giving rise to signal distortion. All well documented and quantified.
But are these the only sources of resistor non-linearity? (I consider noise as a separate phenomenon so exclude it here).
Jan
But are these the only sources of resistor non-linearity? (I consider noise as a separate phenomenon so exclude it here).
Jan
Jan,
There was an article in Linear Audio that showed actual measurements. Did you see anything in those that showed another distortion mechanism of significance?
BTY some samples only showed thermal issues. I don't like the term voltage distortion as it is the catch all for every other form of distortion. So effectively it includes everything else.
Of course there are thermo-electric effects from non-uniform heating.
There was an article in Linear Audio that showed actual measurements. Did you see anything in those that showed another distortion mechanism of significance?
BTY some samples only showed thermal issues. I don't like the term voltage distortion as it is the catch all for every other form of distortion. So effectively it includes everything else.
Of course there are thermo-electric effects from non-uniform heating.
Voltage coefficient is a symptom of distortion, not the mechanism.
In carbon composition you have powdered carbon material in a binder, in other words particles in contact at the edges in haphazard ways. The resistance is in part due to the nature of conduction across these points of contact, and quantum effects (ie tunneling) will be relevant around such points of contact. So I'd be unsurprized if that's a major part of non-linearity in powdered composition resistors such as carbon compostion, ruthenium-oxide thick-film or carbon film (all are basically solidified pastes of semiconductor in an insulating matrix).
The GMR (giant magneto-resistive) effect is another quantum phenomenon displaying resistance thats non-linear and in this case dependent on magnetic field as electron-spin is important to the conduction mechanism. Tunneling itself is electric-field dependent.
And of course the most interesting situations where resistance and quantum effects come together is in superconductivity and quantum Hall effect, where resistances are quantized exactly (zero for superconductivity, integer fractions of 25.8128074593 k ohms for quantum Hall). - yes, that's how accurate it is, no spurious accuracy(!)
I should add that in metallic conductors resistance is effectively constant with electric field (this is the real meaning of Ohm's law BTW), certainly highly linear at normal current densities. At extreme current densities (where real metals vaporize in microseconds or faster), there is a depedence of resistance on voltage, as the drift velocity is then no longer a minute fraction of electron velocity.
In normal copper wire electron drift velocities are measured in fractions of a mm per second (much faster and you have a fuse!). The typical thermal/Fermi motion velocities in a metal are measured in 1000's of km per second. Ohm's law holds because 0.001m/s is vastly less than 1000000 m/s.
In carbon composition you have powdered carbon material in a binder, in other words particles in contact at the edges in haphazard ways. The resistance is in part due to the nature of conduction across these points of contact, and quantum effects (ie tunneling) will be relevant around such points of contact. So I'd be unsurprized if that's a major part of non-linearity in powdered composition resistors such as carbon compostion, ruthenium-oxide thick-film or carbon film (all are basically solidified pastes of semiconductor in an insulating matrix).
The GMR (giant magneto-resistive) effect is another quantum phenomenon displaying resistance thats non-linear and in this case dependent on magnetic field as electron-spin is important to the conduction mechanism. Tunneling itself is electric-field dependent.
And of course the most interesting situations where resistance and quantum effects come together is in superconductivity and quantum Hall effect, where resistances are quantized exactly (zero for superconductivity, integer fractions of 25.8128074593 k ohms for quantum Hall). - yes, that's how accurate it is, no spurious accuracy(!)
I should add that in metallic conductors resistance is effectively constant with electric field (this is the real meaning of Ohm's law BTW), certainly highly linear at normal current densities. At extreme current densities (where real metals vaporize in microseconds or faster), there is a depedence of resistance on voltage, as the drift velocity is then no longer a minute fraction of electron velocity.
In normal copper wire electron drift velocities are measured in fractions of a mm per second (much faster and you have a fuse!). The typical thermal/Fermi motion velocities in a metal are measured in 1000's of km per second. Ohm's law holds because 0.001m/s is vastly less than 1000000 m/s.
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Ed I've spelled that article several times in the past. In my understanding, resistor distortion is caused by resistor value changing with instantaneous signal level across it. The mechanism to cause that is heating/cooling with instantaneous level, and change due to voltage coefficient of resistance.
The reason I started this thread is a reference I found that smaller-value resistors were more nonlinear because of their low resistance value. That was new to me.
BTW There's a very nice paper by Vishay discussing, among other things, 'harmonic index'. It is a measure of the distribution of harmonics for a distorting resistor, which depends on the curvature of the tempco and voltco variation curves. Attached.
Anyway. Are you aware of anything that confirms change in linearity with resistor value, all things being equal of course?
Jan
Speaking of carbon composition resistors, some types are hygroscopic, and will over time absorb environmental moisture, causing their values to drift.
On the other hand, the heat generated by putting power through them will drive out some of the accumulated moisture, again causing their values to drift.
On the other hand, the heat generated by putting power through them will drive out some of the accumulated moisture, again causing their values to drift.
Yes I read that, but those issues seemed a bit extreme and not very relevant for 'normal' use. Strong magnetic fields, cryogenic temperatures, and who would still use carbon comp resistors if linearity is important?
And my question is really whether resistor linearity depends on resistor value, all things being equal.
No offense meant Mark.
Jan
And my question is really whether resistor linearity depends on resistor value, all things being equal.
No offense meant Mark.
Jan
He also mentioned carbon film and ruthenium-oxide thick-film resistors, as well as metallic conductors (at normal temperatures).
What types of resistor and what distortion levels are you interested in?
What types of resistor and what distortion levels are you interested in?
Yes, it does, very much so: high-ohm resistors tend to be severely non-linear, and it is a headache for people having to build physical standards for example.
Very thin films (metal, metal oxide or carbon) become non-linear because of the extreme current densities exacerbating exotic effects, like the non-adherence to the strict ohm law.
Wirewound resistors have a much lower current density, but they have problems of their own, like self-inductance, self-capacitance and bulk: imagine a 100Meg WW, even made from the thinnest wire and highest resistivity alloy
I saw that paper long ago. The harmonic structure quickly tells you if the issue is tempco, as heating and cooling occur at different rates. In good resistors, the tempco is almost unmeasurable and the other mechanisms just don't show up.
I have noticed a dependence based on value. It is hard to measure accurately. But it seemed small. I suspect this is because the film formula has to change to fit the resistance material in the space available. I can't image the material for a 1,000 ohm resistor would work for a 10,000,000 ohm one no mater how fine the laser cut spiral or trimming. It is interesting to note resistors have gotten better since the article.
Small value wirewound resistors frequently have distortion issues arising from the terminations.
Looking at how modern resistors are manufactured, contaminants from many different groups could cause non-linearity. I would imagine high purity ultra low-distortion resistors are verrry expensive to build.
The statement I found was that linearity increases when resistance gets lower, not higher.
Jan
Marcel, I'm looking for the very lowest levels possible. Currently working with Vishay Zfoil resistors. I want the circuit that uses these resistors to be linear down to minimum -180dB.
You know the Groner/Polak opamp, HD at 1kHz better than -200dB, better than -180dB at 10kHz, all 3V in 1k.
Using such building blocks requires exceptional linear passive parts.
Jan
Yes that's exactly what I said, I didn't mean that linearity was proportional to value
At such levels, Mark's remark that Ohm's law in metallic conductors only holds when drift velocity is negligible compared to thermal velocity just might become relevant; 1 mm/s is only 180 dB below 1000 km/s, if you may take 20 dB * log10(ratio).
Does anyone know if, besides Seebeck (thermocouple) effect, anything exotic happens at the end connections? Are the contacts between the resistor body and the terminals purely ohmic?
Hi Jan
You probably know that Bruce Hofer did a presentation on ultra low distortion passives as required for his Audio Precision company.
IIRC his comment on the Zfoil resistors was that they were excellent but not as low distortion as the nominal (quasi-static) temperature coefficient would lead one to expect.
Apparently there are some different mechanisms that balance to produce the ultra low tempco.
But the time constants are not the same so the dynamic cancellation is less perfect.
180 dB is beyond even AP so you may be on your own.
Best wishes
David
What reference is this?
Looks contradictory, typo?
There's probably a sweet spot for any specific process, where non linearity starts to increase at both extremes.
I understand for typical metal film process that lower values are more linear.
That is consistent with the Vishay document you posted, the lower values are more stable - probably some correlation
Best wishes
David
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