Electronic – Johnson–Nyquist Noise of Open Circuit

johnsonnyquistnoise

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:

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Best Answer

The big factor that you didn't consider is that "free space" has capacitance and therefore, an open circuit of (say) 1 G ohms shunted with (say) 1 pF (for example) has a bandwidth of: -

$$\dfrac{1}{2\pi RC}$$

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

Johnson–Nyquist Noise increases with resistance - so does it become infinite for an open circuit?

No it doesn't because of the effect of capacitance.

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