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Summary. While investigating loudspeakers non-linearity, I found non-linear effects in the 0.1 Ohm resistors I used as current sensors. It turns out that self-made copper wire and metal film resistors have acceptable distortion figures, but carbon film and cement resistors are not.

Method. I used the following instrumentation connected as show in the schematics below:

  • Focusrite 2i2 3rd gen,
  • Douk Audio TPA3255 PFFB amplifier,
  • a sensing network with R5 as the DUT Device Under Test)

enter image description here

The input signal was an exponentially swept sine wave, while I used MATLAB as signal processing tool for the measured output data.

Results. The following plot shows the processed data measured for several different kind of resistors. Distortions are dominated by the 3rd harmonics, see below. The amplifiers output voltage distortions are negligible and thus omitted for simplicity's sake. enter image description here

  1. d1 - carbon film 0R1 1W resistor;
  2. d2 - cement 5W 0R1;
  3. d3 - self-made ~1.5m copper wire, bent in halves, 0R1;
  4. d4 - 5 metal film 0R5 0.125W resistors in ||;
  5. 6w50 - 6R0 50W, wirewound;
  6. 5w5 - 5 of 3W 1R0 wirewound fuse, in series;
  7. 80 - 1.17V RMS.

Question. Do you have any scientific explanation for these results?

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  • \$\begingroup\$ Cement resistors? Do you mean cermet? \$\endgroup\$ Commented Nov 16 at 6:23
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    \$\begingroup\$ @hearth ‘cement’ resistors are usually wirewound in a ceramic case filled with ‘cement’. Google knows what they are. As for a ‘scientific’ explanation, I’d suggest certain resistors might have enough inductance to create the issues observed. \$\endgroup\$ Commented Nov 16 at 6:59
  • \$\begingroup\$ d1-d4 for R5, xwy for R4&R8? \$\endgroup\$ Commented Nov 16 at 7:02
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    \$\begingroup\$ Can you edit the question to link to the datasheets for metal film, carbon film and cement resistors you used? The datasheets might list the inductance. \$\endgroup\$ Commented Nov 16 at 7:08
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    \$\begingroup\$ If the test power is significant, then this may be simply a distortion induced by the self heating of the resistor. \$\endgroup\$ Commented Nov 16 at 15:37

4 Answers 4

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Resistors do indeed have non-linearity, specifically voltage dependent non-linearity, where resistance does not remain constant across the entire range of operating voltage. This is so well-known that it has a name: "Voltage Coefficient of Resistance", or "volt-co" for short, similar to "temp-co".

This non-linearity is completely independent of power dissipation (temperature), although the these two effects may become difficult to separate at higher applied voltages since that usually causes also higher power dissipation.

This is a well-known problem for high-voltage resistors used in voltage dividers for measurement purposes, eg: reducing a voltage in the range 0 to 1000V to, say, 0 to 5V, for feeding into a data acquisition system.

And it is not a problem that can be easily solved by applying a constant correction term: the voltage dependence varies with applied voltage.

Many resistor datasheets simply don't mention "voltage coefficient" - in which case you can assume it's pretty bad: > +/-1000ppm per volt (note the polarity can be positive or negative, and may even flip, for any given resistor sample when measured across a given voltage range).

So yes, it is entirely possible that the effects you are seeing are due to resistor "volt-co" & possibly also "temp-co".

More info here:

https://passive-components.eu/voltage-coefficient-of-resistance-explained/

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  • \$\begingroup\$ It's a good note... although on the opposite side of the same problem's spectrum. afaik, volt-co is more related to high voltages and huge ohm values, and frequency independent. \$\endgroup\$ Commented Nov 20 at 18:51
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I do not believe that any commercial resistor is discernibly nonlinear apart from possible heating-induced behavior. I would first suspect any other possible source of nonlinearity in the entire measurement train, especially active devices. After all, all active devices that we use are inherently nonlinear and much of analog design is directed at making them behave approximately linearly.

By the way, ANY combination of (linear) inductors, capacitors, and resistors is also linear in the sense that it cannot generate distortion, i.e. harmonics. Frequency-dependent, yes, non-linear, no.

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    \$\begingroup\$ Dear user67527, I also believed so, but the test showed otherwise. I measure Voltage in the same way, on the same active device, and distortions are below <-90dB. While measuring distortions, I simply replace the device-under-test in the measurement harness, not touching anything else. If the test setup were wrong, there would be the same errors for all resistors - but that is not what has been observed. I am a Sr. Scientist, and I am well familiar with how easy it is to make mistakes in experimental physics. I would not post the question if I were not sure. \$\endgroup\$ Commented Nov 17 at 19:05
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As well as simple unwanted inductance there can be eddy current effects that affect precision measurements of AC current. This is a major issue in some kinds of equipment (eg. medical).

See, for example, this paper "AC characteristics of low-ohmic foil shunts influenced by eddy currents in the mounting body.

I would definitely not use random resistors from unreliable sources as AC current shunts, particularly if I didn't have the time and/or equipment to properly characterize them.

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  • \$\begingroup\$ This is exactly what I was looking for \$\endgroup\$ Commented Nov 20 at 17:16
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There's a phenomena in RF circuitry called "Passive IM" developed in connectors. In connectors, you have different metal surfaces touching, and they can develop corrosion and start behaving like diodes. This will generate IM products, admittedly at very low signal levels, but enough to slightly desense receivers if the frequency plan allows.

You're swapping out different resistors in a circuit, are all the metal leads the same metal? Are you cleaning each terminal each time? Could this be relates to the sequence of measurements?

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  • \$\begingroup\$ No, they are not the same metal. Yes, I am cleaning terminals. No, it is not related to the sequence of measurements. \$\endgroup\$ Commented Nov 20 at 18:43
  • \$\begingroup\$ So it's tracking with the leads? I'd look at cutting leads and swapping them, and soldering them so there's no diodes being formed. \$\endgroup\$ Commented Nov 21 at 0:43
  • \$\begingroup\$ I agree about the "Passive IM" effect, but it will cause --roughly-- the same errors for all resistors. The problem I am concentrating on is that different resistors, all with the same nominal value, exhibit different behavior. One step at a time. \$\endgroup\$ Commented Nov 22 at 2:53
  • \$\begingroup\$ How do you know that will cause roughly the same errors for all resistors? \$\endgroup\$ Commented 2 days ago

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