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Oscilloscopes give a Vrms noise and have a noise floor, but if I average for a long time to infinity, am I at the standard quantum limit and does SNR keep improving with the sqrt(N averages) forever?

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Yes for random noise Vrms keeps reducing by N for sqrt N samples

  • the SNR is then limited by drift, periodic noise and measurement accuracy

other

  • However, if the measurement is a frequency which is nearly as stable ( high SNR) as the clock in the counter measuring it, then some phase noise must be added in order to obtain an accurate reading. Then the noise can be defined by std or pp deviation or Hz/rt(Hz)
    • This can also be done by adding some AC voltage with a fixed trigger threshold.
    • with sqrt(N) more samples you obtain N-times better resolution and stability on the result just as in DC.
    • This AC exception example is due to harmonically-related synchronous effects with no jitter.
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    \$\begingroup\$ @ Tony Excellent summary, given you specialize in rockets. \$\endgroup\$ – analogsystemsrf Dec 2 '18 at 1:47
  • \$\begingroup\$ Well I started life as an EE in rocket instrumentation design in the mid 70's and this was useful info then, but used again as a Test Engineer in many other industries. \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Dec 2 '18 at 9:36
  • \$\begingroup\$ Grateful for your summary- as for "periodic noise and measurement accuracy", in the case where I can do post processing of data offloaded from the oscilloscope, is there any intrinsic "periodic noise" from the oscilloscope that is widely known to limit the lower limit? From another answer I see that "resolution of the number format and the accuracy of the averaging algorithms" can cause a limit from the "measurement accuracy side" \$\endgroup\$ – user5579188 Dec 2 '18 at 23:20
  • \$\begingroup\$ Yes, so what is it you are trying to measure? Normally the best way to increase SNR is to use a filter matched to the spectrum with a low noise amp, not by averaging. So what are the details? requirements? \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Dec 3 '18 at 1:50
  • \$\begingroup\$ understood about the filter and BW. I'm trying to understand if I have say a 60 GHz RF signal sitting at say -80 dBm, and I have a oscilliscope with 0.5 mV rms noise floor (-66.9 dBm), how long do I have to average to get to SNR=1 for that -80dBm-- is a calculation by standard quantum limit of sqrt(N) SNR improvements enough with averaging enough? Assuming drifts controlled for, are there other parts of the oscilliscope that make it impossible to detect that signal? Just want to see if my conceptual thinking is correct before considering filtering or mixing with other types of signals. \$\endgroup\$ – user5579188 Dec 3 '18 at 6:12
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Remember that the averages are being computed by a digital processor using binary arithmetic. At some point the accuracy and resolution of the average will be limited by the resolution of the number format and the accuracy of the averaging algorithms. Algorithms that calculate the mean of a very large set of values run into numerical problems because the mean value may be very, very small compared to the sum of a few very large samples.

Your question suggests that you are averaging an extremely large set of values. I would be surprised if any commercial oscilloscope, performing these calculations in real time, would approach the accuracy of even a good desktop computer.

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There is a couple of barriers that you will hit on the way there that have considerably more practical implications.

  • 1/f noise. The oscilloscope amplifier bias points, oscillators, and ADC voltage reference assume DC conditions. You are basically doing an infinite integral of those DC values, 1/f noise is theoretically infinite at DC.
  • ADC quantization. Regardless of the precision of the math and the oscilloscope ADC, the sqrt(N) gain in RMS noise only applies to noise that is uncorrelated to the signal, once your sqrt(N) gain drops your noise to a level below a single ADC step, your signal and your noise becomes the same. These become more and more correlated as you progress.

Interestingly, the way to bypass this correlation issue is to add larger and larger magnitudes of random noise to the signal. So the fundamental limit will end up being the dynamic range of the ADC. Which is the compromise achieved by sigma delta converters, as these use a 1-bit ADC.

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