If thermal voltage is the average voltage of any given electron relative to the voltage at ground state, and this presumably fluctuates, how can you make any measurement on a circuit more accurate than 26mV?
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\$\begingroup\$ Everything is at the same temperature, noise should average out? Each lead would be subject to the same normal noise I believe... \$\endgroup\$– MadHatterCommented Aug 15, 2020 at 0:00
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\$\begingroup\$ i thought about this, but some measurement tools can get down to nanovolts or even smaller. It seems like fluctuations over a 26mV range would cause this to be impossible. \$\endgroup\$– TaakoCommented Aug 15, 2020 at 0:03
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\$\begingroup\$ That’s what amplifiers are for down to sub microvolt levels \$\endgroup\$– Tony Stewart EE75Commented Aug 15, 2020 at 1:36
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1\$\begingroup\$ I think this is a fairly deep question, maybe better suited to the physics SE. Probably relating the number of electrons, statistical effect of having many electrons and the degrees of freedom of one electron. But in practice we can measure voltages fairly easily down into the hundreds of nV at room temperature if the source impedance is reasonably low. \$\endgroup\$– Spehro PefhanyCommented Aug 15, 2020 at 2:27
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\$\begingroup\$ For high precision measurement a first stage shape or amplify the signal. Then an ADC can convert the signal. For instance sigma delta ADCs push low frequency noise to higher frequencies (noise shapping) such that the noise can be filtered with a low pass filter. At the end, the noise in the bandwidth of interest is lower. \$\endgroup\$– Ludwig CRONCommented Aug 15, 2020 at 7:55
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Thermal voltage noise has a magnitude of ~1nV/sqrt(Hz) at room temp. for a 60 ohms resistor.
Where did you get that 26mV from? 26mV is a lot (26 Million) higher than thermal noise. So there’s no measurement problem at 26mV if you got a good measurement device.
answered Aug 15, 2020 at 9:17
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1\$\begingroup\$ Where he got it from is obviously kT/e. The question is, why is that not a fundamental measurement limit? As Spehro says, a fairly deep question. My take is that it's the noise contribution from a single electron - a single coin flip if you like. Measuring at any reasonable current averages trillions of coin flips; but as you reduce the current you see shot noise increasing. \$\endgroup\$– user16324Commented Aug 15, 2020 at 9:35