A signal-to-noise ratio (SNR) lets us express the relationship between signal and noise powers, as well as between the root-mean-square (rms) values of signal and noise voltages:
SNR (dB) = 10log10(signal power/noise power).
SNR (dB) = 20log10(rms signal voltage/rms noise voltage).
In an analog-to-digital converter (ADC), noise -- or nonsignal power -- relates to the ±1/2 LSB quantization error introduced by digitizing a signal into discrete steps. The familiar equation below provides the SNR for an N-bit ADC based solely on quantization error for a pure sine wave over the Nyquist bandwidth; DC to fsample/2:
SNR (dB) = (6.02*N) + 1.76.
But this value tells only part of the story. ADC noise can arise from another source called effective input noise, created by the ADC's electronics. And jitter in the ADC clock signal also affects the ADC output. A poorly designed circuit board can let digital noise and other ambient signals couple to the clock signal and cause jitter.
Jitter in an ADC causes a large measurement error (∆V) in a signal with a high slew rate (A) when compared with the error caused at a lower slew rate (B), or frequency. Thus jitter can greatly influence
high-frequency-signal measurements.
You can find the complete root-sum-of-squares SNR equation that combines quantization noise, clock-jitter noise, and effective input noise in the document "Fundamentals of Samples Data Systems" by Walt Kester and James Bryant (page 2.72). The authors also show the theoretical basis for the third SNR equation.
You cannot overcome effective input noise except by choosing a different ADC that introduces less noise. Proper PCB layout, decoupling, and use of a stable low-noise clock signal can reduce jitter. The overall jitter time combines aperture jitter, which occurs in the ADC's sample-and-hold amplifier, with jitter in the ADC's sampling clock signal. The latter jitter usually predominates.
Clock jitter of a few picoseconds might seem to contribute little to an SNR value, but keep in mind that the effect of jitter increases with the frequency of an ADC input signal, as shown in the diagram.
The SNR value does not include power contributed by harmonics of the signal of interest, because you can -- and should -- eliminate harmonics with an anti-alias filter. If you include power from harmonics (but not DC), you get a signal-to-noise-and-distortion, or SINAD, ratio, also expressed in dB. Because a SINAD value includes all nonsignal energy, it can provide a good indication of actual ADC performance.
Having been in a couple of different industries, I often wonder why noise is specified in RMS. RMS makes sense, for example, in video, where the eye integrates and RMS gives you a direct measurement of how the image would look to the human eye. But what about other applications? If you are trying to determine uncertainty in a measurement, wouldn't specifying noise in RMS give you a very large discrepancy in numbers versus performance? Of course, comparing RMS to RMS of different systems will give you the relative performance comparison. Now take a step from comparing systems to Output. What does your output respond to? If it responds to every peak, then giving an RMS noise measurement is marketing not engineering.
What do you think?
I get in trouble with our sales department because I measure in P-P and at the point of greatest noise. This, to our customers, would give them the total uncertainty, rather than a number that tells them the total uncertainty can be 6 to 8 times higher.
Thanks for your comment. It is good to get a peak-to-peak value along with a root-mean-square (rms) value. The latter provides a statistical value that squares amplitudes and thus accounts for positive and negative noise. With a peak-to-peak value you don't know whether you observe that value all of the time, most of the time, or infrequently. So to me, a p-p value represents a worst case and rms represents an average value. Both have value. --Jon
(maybe off topic a bit, but...) As an ME using electronic gear for making vibration and dynamic stress measurements, the prevalence of RMS has always been a nuisance. We measure most things in P-P. Failures occur on the peak stress values and journal bearing damage can occur when rotors move more than the available distance within the bearing clearance. The early spectrum analyzers (like the HP 3582A or 5451c) would make RMS measurements apparently because they came from the EE world. We had to do odd things like use voltage dividers to obtain PP spectral values (or actually 0.1 PP).
Now, although any DAQ system can provide PP, many of the allowable specs were written for RMS and are still used.
It's simple, all signals that do not convey information are noise. A useful concept to keep in mind next time you listen to a speach or watch the news only to see a piece with puppies in it.
LOL walter, that made me laugh. OTOH, when it comes to humans, the signal is in the beholder, so to speak. For some people, those puppies are definitely a signal, just not the one other people may have been expecting when they tuned in. And a speech can certainly contain multiple types of signals meaningful to humans, but not all humans (even those that speak the language) will pick up the same signals from the same speech. This is, of course, assuming that we define "signal" as meaningful content, or information.
I think you've missed my point. The signal is the sound pressure wave, or whatever, that you receive. It contains information and noise. Thus a speach that does not contain information IS noise and a news article that does not contain information IS noise. It also means that signals containing stuff that is self evident are not information, i.e. they are nosie.
Off topic - I always get some sort of error message when I access these pages. Everything looks fine except for the text "Error on page." Is it just me or are others getting this as well?
I got your point. I just disagreed with the definitions of information and noise. My point was that when humans are involved, the definitions are highly variable. So the same speech may contain information for one person, but not for someone else. That's one of the problems with applying facts and processes from the physical sciences as metaphors for human behavior and experience.
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