# What is the peak - peak voltage of 15mV rms white noise?

I've been experimenting with zener diode based noise sources. I have such a source for which I want to determine the peak to peak noise voltage. I've measured the noise with my trusty multimeter and it's approximately 15 mV which I believe is RMS. The noise from these things is white.

So how can I obtain the peak to peak voltage, as I don't have an oscilloscope? I think that it should be possible to calculate it from the RMS voltage and some statistics knowledge. My multimeter is a digital Maplin Precision Gold (M-5010EC) from 1989. The specification booklet says that it has a frequency range for AC measurements of 45 Hz – 500 Hz. This is calibrated for a sine wave of course and not a white waveform. Is that enough to obtain Vp-p?

• Infinite, but with infinitely low probability. See Andy's answer for a commonly used approach.
– user16324
Mar 22, 2016 at 10:26
• Unless you’re making the measurement with the device in a faraday cage I’m not sure you can confidently say that you are seeing just the intrinsic noise of the device .... is this an unbiased device or are you ac coupled to it. 15mv seems like an enormous number. 15uv? Apr 27, 2019 at 18:50
• Ah, this question was asked years ago when I was only a lad with only a wooden multimeter and stupidity. I now have lot more stupidity, but also a 'scope. I now get 300mV RMS by scope. It's surprising because I use 24V diodes with a 6V overhead, and the diodes are extremely noisy. If you op-amp buffer it (G=1), you can actually hear it on a 64 Ohm speaker! Apr 27, 2019 at 20:45
• I think that the Magnatecs must incorporate super dooper shrunken 1000uF capacitors in there somewhere. ~3Vp-p. Apr 27, 2019 at 21:01

Thermal noise (approximately white) has a gaussian distribution and we can use statistics to state what the probability is that a certain p-p level is exceeded: -

For instance in the diagram above a range of 6 sigma tells you that the probability of 1 V of noise remaining within the bounds of 6 Vp-p is 99.7% or put another way, 1 V RMS will remain below 6 Vp-p for 99.7% of the time.

It will also remain below 8 Vp-p 99.99% of the time.

Most engineers use 6.6 sigma - this produces a confidence level of 99.9% i.e. 1 V RMS remains within 6.6 Vp-p for 99.9 % of the time.

MT-048 page 5 from ADI is a useful reference for this: -

As for zener noise this article states that zener noise is "shot" noise and this article states it can be modeled as a Poisson process. This type of distribution can be very similar to a normal distribution: -

• "White noise has a gaussian distribution' is just flat-out wrong. The "color" of a noise signal refers to how the power is distributed in the frequency domain. White noise has the same power for a given bandwidth at all frequencies in a specified range. However, the probability of measuring a particular voltage (or current) is a completely orthogonal measure. It can be anything from a uniform distribution (equal probability of any given voltage within a range) to triangular to any number of statistical distributions such as Poisson or Gaussian. Mar 22, 2016 at 11:39
• @DaveTweed I meant to say thermal noise. Mar 22, 2016 at 12:33
• Um, OK, but Zener noise is technically not thermal noise, although in practice it is essentially indistinguishable. If you edit your post, I can remove the downvote. Mar 22, 2016 at 12:41
• It's edited with a few comments about the zener shot noise. Mar 22, 2016 at 12:48

No, it isn't. You also need to know the distribution of the noise.

Most natural sources closely approximate a Gaussian distribution, for which the peak-to-peak value is actually unbounded — although extreme values are very rare. Technically, Zener noise is shot noise, which has a Poisson distribution, but in practice, this is essentially indistinguishable from a Gaussian distribution.

That's why noise is most usefully measured as an RMS (power) value.

EDIT: Other noise sources can have different distributions. For example, consider the quantization noise that an ADC adds to a signal. This noise is also "white" (equal power at all frequencies) and has a well-defined RMS value that a meter can measure. But this kind of noise ALSO has a well-defined peak-to-peak value (which is equal to the step size of the ADC) and a uniform distribution within that range.

• There is no "premise" to accept. It's implicit in the physical processes that generate the noise and the math that we use to analyze it, as Andy explained. Yes, the power is real and a real meter can measure it -- as an averaged (RMS) value. But that doesn't mean that there a voltage that you can say that the signal NEVER exceeds, which is the definition of peak-to-peak. Mar 22, 2016 at 11:48
• I've made some zener noise sources. They are white, but not at all gaussian. (20 V zener at low currents 10-100uA). Random pulses as the zener breaks down, but the pulses are typically all about the same size. Other zener sources are more "gaussian" in their amplitude distribution. Mar 22, 2016 at 13:29
• @GeorgeHerold: You were operating in a region in which the difference between Poisson and Gaussian is significant. Mar 22, 2016 at 13:31
• @DaveTweed I don't see it was a poisson vs gausssian thing, but I guess that's one way to look at it. My pictures is more a physics thing. For these HV zeners (I think) when there is a break down the entire charge in the zener capacitance goes at one time.. and then you have to wait some time before another random pulse can happen... so you never get multiple pulses at the same time. (You'll sometimes see a smaller pulse right after a big one, when the zener lets go before it has fully re-charged. There are other examples of white noise that is not gaussian... random digital generators. Mar 22, 2016 at 13:41
• @PaulUszak, Well I get big pulses. 3-4 Volts peak to peak. (but I use two zeners one going each way... that's to try and make the noise a bit more symmetric wrt ground.) BW is only to ~1MHz or so. Put a buffer on the zener or you might load it down with too much capacitance. And if you have glass encapsulated zeners then make sure they are in the dark. (Light causes more breakdowns and less noise.) Mar 23, 2016 at 15:23

The measurement of peak to peak voltage on a noise source is poorly defined. In theory, the noise voltage does not have an upper bound, though big peaks become exponentially less likely to occur as they get bigger.

That's why we use rms, to indicate the power, which is much more consistent. However, rms is not an easy measurement to make without the correct equipment.

A measurement that was popular in the bad old days was 'tangential sensitivity' (google). This was measured with an oscilloscope, and a square wave generator. The amplitude of the square wave was adjusted, until a line could be drawn through the bottom of the noise on the +ve parts of the waveform, and the top of the noise on the -ve parts. Obviously this was subject to the characteristics of the 'scope, the chosen sweep rate, and the intuition of the operator.

Any attempt to measure the peak directly with a peak detector suffers the same problem that the response of the peak detector influences the measurement, fast peaks will not be caught by a slow detector.

A mathematically better measure is arrived at through the CCDF, though this also needs the correct equipment to make the measurement. This records the amount of time the signal spends above any given level. This is much used now that digital communication is the norm, as it's a good predictor of how many bits will be lost to noise. For instance, for guassian noise, IIRC, the noise signal spends in the ballpark of 1e-6 of its time above +11dB(rms), and 1% of its time above +5dB(rms) (don't use those figures without checking!)

• I realise that the rms measure is more appropriate. However, I'm trying to design an amplification circuit for the noise source, and need to know the ball park peak to peak voltage to avoid clipping it. I don't have one of those fancy oscilloscopes. I'd like my noise spikey, not flat topped. Mar 23, 2016 at 0:27
• With 15mV rms noise, there's plenty in hand, so we don't need to be too fussy. 15mV rms sine wave is less than 25mV peak, 50mV pp. Noise of the same power rarely exceeds 4x that (+12dB), or 200mV pp. If you allow another 5x headroom over that, so 1v peak to peak, you shouldn't see it clip within the age of the universe Mar 23, 2016 at 11:56