# What is the noise level as read on my oscilloscope?

The above is what I'm seeing on my oscilloscope. It's zener diode noise. Scope's set for 0.5V/div vertically, and 1ms/div horizontally. The oscilloscope has a 20MHz bandwidth, but the noise doesn't really change much at higher speeds. You certainly can't see individual waves at 20MHz.

The trace is about 5 divisions high (this may be difficult to make out on my image). 5 divisions = 2.5V from top bit of green to bottom bit of green as judged by eye. The longer you watch it, the higher some of the peaks can be seen to go. That's the stochastic nature of white noise.

What does this 2.5V represent? It can't be RMS as it's only some bit of green that I can see. It's a kinda peak to peak but one that changes depending on how long you watch it. Is there a rule of thumb to determine a X volts/sqrt(hz) value? Datasheets give noise values for op amps. They must be able to measure it somehow.

## 4 Answers

There is a trick to estimate noise amplitude of your display if you have a two-channel oscilloscope. First, turn off any triggering mechanism.
Apply the same noise signal to both channels so that you see something like this:
[ Now slide one trace closer to the other. As they approach, the dark space between the two traces gets brighter, but you still see two "peaks" of brightness (one above, and one below). Sliding closer still, the dark space between the two traces increases in brightness. At some point, brightness between the two traces seems constant (please excuse the crude editing):
Now remove the noise from both channels and measure the offset of two channels. This is a crude estimate of RMS noise. It is probably a better estimate than "eyeballing" one trace.
Since the noise you see has a "brightness" that corresponds to a gaussian distribution, the brightness of one trace has a profile like this:

cumulative noise distribution related to RMS

As you say, peak is not well defined for noise. That's why an opamp, anything really that defines noise, measures it as RMS.

Look up Normal distribution, wikipedia for instance. When people want to know how noise peaks behave, they usually plot the Cummulative Distribution Function. It will give figures like (these from memory will be wrong in detail, but are correct in 'feel') noise is 6dB above RMS 1% of the time, and 11dB above RMS for 0.000001 of the time, for an underlying Gaussian distribution.

the peak-to-peak noise of a signal is 8 times that of the root-mean-square (RMS) value of the noise.

However judging by the enhanced brightness it is not Gaussian due to your measurement method.

4 div x 0.5V/div p-p or $2V_{pp}$ equates to $0.25 V_{rms}$ or $105dB\mu V$ per 20MHz or $56\mu V/\sqrt Hz$ or $35dB\mu V/\sqrt Hz$

More likely due to asymmetric peaks and matching of outer and inner envelopes, the random pp noise is just the white part about 70% of 4 divisions or down 3dB from above or $32dB\mu V/\sqrt Hz$ ... (final answer :)

• Rather than a non-gaussian noise shape, I think the step between intensity levels is more likely to be caused by the nonlinear response of the phosphor in the scope. – Tom Anderson Jan 17 '17 at 18:18
• possible quantum phosphor steps you think? I was thinking line noise – Sunnyskyguy EE75 Jan 17 '17 at 18:22
• Possibly just saturation. Phosphor was complicated. For example in good vintage gear, to get the phosphor to be more sensitive, a radioactive element added to get the phosphor just to the edge of glowing. That way it would take fewer electrons to get it glowing. My old scope still glows in the dark. I think some tubes were designed to have a more linear response, but they weren't the brightest. – Tom Anderson Jan 17 '17 at 18:36
• It's a Hameg 203-4. The advertising material for it states that it's got integrated circuits inside! Not sure of the age though... – Paul Uszak Jan 17 '17 at 21:27
• No, you're right. It's not Gaussian. If you look very closely, you'll see one side of the trace is brighter than the other. That is correct and not measurement artefacts. Proper avalanche noise is actually log normal so it might range -0.5V to +2V either side of the most frequent. Therefore the trace is asymmetric as confirmed by the literature regarding avalanche noise. This is not Zener noise as I'm at 24V. – Paul Uszak Jan 17 '17 at 21:42

Here is an approximate way to get a noise level on an analog oscilloscope:

Use dual trace mode, and put the same noise signal on the second trace with the same settings. Change the offset between the two noise signals so that the two bright bands barely touch, but there is no longer a visible darker gap between the bands of noise. Then disconnect the probes and observe the offset between the two channels. This offset is the 'noise level'. This technique is good for relative measurements but it is not calibrated.

The bandwidth of oscilloscope noise is the full bandwidth of the oscilloscope, such as about 20MHz in your scope. It is the sum of the noise added up across the whole frequency range of the scope. It is not a 'spot noise' measurement like the ones in opamp datasheets.

A high-end oscilloscope has a noise marker and can measure RMS and 'peak-to-peak' noise.

A spectrum analyzer can measure noise level at a spot frequency. You can adjust the receiver bandwidth in the analyzer. As the analyzer bandwidth decreases by a factor of 10, the noise floor drops by 10dB. The extrapolation of this measurement to 1dB is the 'per root Hertz' noise level. Getting the noise level from this measurement is a little tricky because of the various correction factors. Good spectrum analyzers have a 'noise marker' that provides an automatic noise reading at a spot frequency.

Keysight has far more than you ever wanted to know about noise measurement. Much of the information is about measuring very low noise levels. For the math of how a spectrum analyzer noise marker works, see the FAQ question How does the noise marker function work on my spectrum analyzer?

A good book that explains these measurements is Spectrum and Network Measurements.

• Sorry Tom (we've posed very similar answers). Just spent some time to try to illustrate the technique after vainly searching the web for illustrations...so did some image editing. It is a technique that is difficult to easily describe with words. – glen_geek Jan 17 '17 at 18:22
• No problem, I like your graphics, and I have more about spot-frequency noise measurements. – Tom Anderson Jan 17 '17 at 18:46