# Johnson–Nyquist Noise of Open Circuit

Johnson–Nyquist Noise increases with resistance - so does it become infinite for an open circuit? Specifically why is the input to an oscilloscope that is not connected to anything not completely saturated by Johnson–Nyquist Noise (assuming the resistance through air from oscilloscope input to GND is near infinite).

Johnson–Nyquist Noise Equation from Wikipedia:

• What is the bandwidth $\Delta f$of the oscilloscope input, assuming infinite source resistance and (say) 30pF capacitance to ground? – Spehro Pefhany Dec 20 '19 at 2:07
• Johnson-Nyquist noise is usually related to a concept of thermal vibrations of charge carriers in conductors. If you want to study similar (though more as quantum fluctuations in this case) effects through air, you could read Current Noise in Tunnel Junctions. It's really interesting and they do need to deal with it. – jonk Dec 20 '19 at 2:08
• Back to your topic. What do you think is the sensitivity of your oscilloscope to thermal charge motion in air? Or, put another way, suppose you divided these supposed voltage fluctuations by the resistance to get the referred-to-current noise and then apply that to the probe resistance and capacitance? – jonk Dec 20 '19 at 2:09
• By the way, this whole area is extremely interesting. I think Boltzmann's original paper is kind of hard to understand, when compared to Shannon's papers that use his concepts to develop information theory. (Shannon is who made me understand Boltzmann for the first time.) The equipartition theorem in thermodynamics places, on average, half the energy in potential energy and half of it in kinetic. So there is a direct relationship between Johnson-Nyquist noise and kT/C noise, because of this. I really recommend you spend some time here. It's really good stuff. – jonk Dec 20 '19 at 2:21
• Some papers to read are from an MIT class: Mathematical Theory of Claude Shannon and Information Theory. Please go though them. But I also recommend The Mathematical Theory of Communication, by Shannon and Weaver. Plus Shannon's original papers from around 1948. +1. It will be interesting to see an answer speaking broadly and not just answering an Oscilloscope question. – jonk Dec 20 '19 at 2:32

$$\dfrac{1}{2\pi RC}$$
Numerically this is 0.159 Hz and the equivalent noise bandwidth is that multiplied by $$\\pi/2\$$. This restricts noise voltage very significantly.