What is the proper procedure to measure RMS noise with an oscilloscope?
I have 2 standard resistors, 1k and 100k and a 1.5GHz BW, 5GSa/s Keysight DSO. I have a probe which offers 1:1 (1MOhm//100pF) and 10:1 (10MOhm//15pF) ratios.
I use AC coupling, 1:1 probe and "AC RMS – Full Scale" measurement – which 1mV/div and 100ms/div.
I measure 340uVrms for 1k and 940uVrms for 100k (just clipping the resistor between the probe).
However, I cannot reproduce this result using equations. Three attempts:
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The resistor is in parallel with the probe which is 1MOhm and 100pF for 1x. Hence the bandwidth will be 1MOhm//R//1pF ~ 1/(2*pi*RC). Since the total integrated noise is given by 4kTRB = 4kTR/(2*piRC) = 2kT/(piC) = 2/pi kT/C the result should be independent of the resistor 5.1363uVrms. This is far off from the numbers above but even worse – the numbers above are different
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I assume the bandwidth limitation comes from the probe itself which is 6MHz for 1x. The result would be sqrt(4*kT*100e3*6e6)=100uVrms for 100k and 10uVrms for 1k. Again, both far off.
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I assume the bandwidth is limited by the bandwidth spec of the scope which is 1.5 GHz. This gives 157.68uVrms for 1k and 1.5768mVrms for 100k.
Again, not consistent.
How do I measure noise with an oscilloscope?
Best Answer
A system with a single node: some R and some C, will have the total integrated noise defined EXACTLY by sqrt (K*T/C).
Thus a 10pF cap, at 290 degree K, produces exactly 20 microVolts RMS, regardlss of the value of the resistor.
Also, a 100pF cap would produce 1/sqrt(10) less noise, or about 6 microVolts RMS, regardless of the value of resistor.
To measure 6uV RMS in 10GHz bandwidth, the system noise density must be lower than 6uS/sqrt(10GHZ) = 6uV/sqrt(10^10) = 6uV/100,000 = 0.06 nanoVolts per rootHertz.
Given a 60 ohm resistor produces 1nanoVolt/rtHz noise density, and we need 0.06nV, or 16X smaller than 1nV, the total front end Rnoise my be 60/(16*16) 60/256 or 0.25 ohms.
Achieving Rnoise of 0.25 ohms will not happen.
Typical Rnoise (the rbb') of bipolars is 10 ohms or 100 ohms.
I cannot speak for typical rbb' for silicon-germanium bipolars.