# technical noise measurement question

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#### cuibono

Hello all -

I asked this in Digital, and got no reply, so maybe I'll get lucky here if I rephrase it:

I'm measuring the noise floor of an USB ADC (the zoom H2) with Visual Analyzer, which is a software oscilloscope, with a built in spectrum analyzer.

The spectrum analyzer (broadband, 20-20kHz) shows noise down at -120dB all the way across. The scope gives a single number readout of the signal, saying it is about -75dB. How do they get between the two numbers? I'm assuming you have to do some sort of power integration, the math of which is beyond me, but I hope someone could give me a simple explanation of why the numbers are different.

But more so, can someone tell me if my noise floor is at -120dB or -75dB?

Thanks

#### SY

You have it. The total noise is an RMS summation of the noise energy contained within the specified bandwidth. It's usually calculated by separating the bandwidth into a number of bins of roughly constant noise density, then RMS summing the noise density in each bin times the bin's bandwidth.

The other issue is "dB with respect to what." -120dB is probably the noise with respect to full scale of the ADC. -75dB is probably the noise with respect to some signal that the scope is locked into or perhaps with respect to some standard level. I'm just speculating on that, but you do have to be careful to use the same reference in the dB calculations.

#### cuibono

Thanks!

The software seems well designed, but I can't figure its units out - the spectrum analyzer is labeled 'dBpp', and the scope just 'dB'. It seems like dBFS would be the appropriate unit. Also, I clipped the signal at 0dB on the analyzer, suggesting it is showing dBFS, and the scope was showing +/-1, which is either V or %, neither of which quite make sense...

#### cuibono

Interestingly, the spectrum analyzer noise floor drops when I change the number of samples for the FFT. Maybe that shouldn't be surprising though.

My only real concern is if the device under test is too noisy. My standard soundcard shows a noise level of -87dB, and I have had no problems with noise. Now the Zoom H2 (which is incredibly well designed overall) has a noise floor of -75dB, and initial listenings with headphone show an unacceptable level of noise. Where the noise is coming from, I haven't yet determined.

By the way, if the noise turns out to not be a problem, I would recommend the H2 highly. It is extremely well thought out, and makes recording very easy. Assuming it all works out, I plan on making my own test recordings - there is no better way to compare the reproduction if you know the original....

#### Corax

Hi cuibono,

I wouldn't worry about the different noise levels you mentioned (-75dB, -87dB, ...). Trust your ears and you'll be more than satisfied.

I have done a lot, doing right now some and will possibly doing in the future some more FFTs (programming and applications using it) and it's most of the time a question of the used window type (before you calculate the FFT itself) the used "processing unit" (i.e. an 8 bit micro controller, a fixed point DSP or, meanwhile, a floating-point DSP) and further methods (like time averaging of the FFT bins and so on).

Since you mentioned the Zoom H2 (where I'm not familiar with) as the recording source, capable of recording with 24 bit at 96kHz (that's all I could figure out in a hurry about this little thingy), I assume the issue will not be the ADC. It's more likely the algorithm/method of deriving the FFT from the input data (this points directly to the window application). There are certain types of windows used prior to run the FFT. For instance Blackman-, Hamming-, von Hann- (aka Hanning), Kaiser-Bessel-, etc., just to name a few of them. These windows determine, beside other things, the hight of the sidelobes - or the noise floor. Whatever your special interest is about the signal you want to put your magnifying glass on, this determines the proper selection of your window type.

As long as you don't have the choice to select the window type, or to get an info about what window type is used in a particular window application, I would be very carefully when interpreting such results.

If you're still interested / keen on it in reading more about FFTs and why windowing of the input data is necessary just 'google' and look for "FFT" and "windowing". You should come up with a couple a pages explaining it for you.

After all, my final rule would be: Never trust what you haven't cheated or manipulated yourself

#### Iain McNeill

As SY says, the -75dB(FS) is the sum of all the noise from the lowest frequency bin of the FFT (=sample rate / fft size) up to nyquist (=sample rate / 2)

As you divide this noise energy into more and more bins you get less and less in each bin. So if you divide the -75dB into 2 bins you'll get -78dB in each (we're talking power so only a 3dB drop), 4 bins -81dB in each etc etc etc.

That's why a noise figure only has meaning if you know the bandwidth.

#### jackinnj

to get an idea of the noise which is relevant to listening you should download the ITU CCIR ARM-486 paper -- the CCIR curve corresponds most acurately to the annoying aspects of noise (at least according to Dolby) -- and as I have stated on previous occasions, there is a very high R^2 to the pitch used by a screaming wife.

#### Corax

I definately agree with the statement from Iain.
FFTs are quite complexe for people who don't know what's really going on there. It just didn't come to my mind that the FFT size might be an issue with the H2 visual analyzer.
Therefore a question rises in my mind: is the FFT running on your PC (as a visualization application) or is it done on the Zoom H2?
If it's running on the H2 I do understand why the results might be worst than with other software running on a PC. An FFT is a big number crunching algorithm, in particular for a large number of points. It's basically a matter of CPU performance how fast an FFT will be calculated on a specific hardware. Even nowadays a PC is in most cases faster in doing an FFT than the specialized DSPs you'll might find.

Figure out how many points are taken by that software (or any other - if you're going to compare results) to calculate the FFT. For good analyzers I recommend at least 32k (32768) and more of analog samples for the FFT. This would give a satisfactory FFT bin 'width' of round about 1.5 Hz at a sample rate of 44.1 kHz. A 1k (1024) point FFT would result in approx. 43 Hz for each bin - what a difference!

Another point I wanna mention is the following:
Besides the correct way/method/size in calculating the FFT the theoretical limits are also important. For instance a 16 bit ADC wouldn't be capable of exceeding a signal to noise floor (aka SNR - signal to noise ratio) of about 96dB (20*LOG(2^16)) because of their resolution. For a 120dB in turn, an ADC of at least 20 bit of resolution would be required. Most (professional) audio equipment are currently featuring 24 bit ADCs, which could result in an amazing value of 144.5dB (imagine: with an input signal of 1V the smallest voltage level would be just 60nV(!) - in words: sixty nanovolt. Till today I have never seen an analog counterpart reaching that region. In particular phono/microphone preamps need to be extremely noiseless (and therefore extremely expensive) to come even close to that value. Any frontend is still analog and every ADC performance rises and falls (in most cases) with it.

At this point we're coming to the region where thermal noise (besides other noise types like shot/flicker/... and noise sources) in passive and active components starts to play a major role. That's for instance one reason why equipment dealing with voltages in the range of micro-/nanovolts has quite low impedances, for instance microphones or pick-up coils in MM systems (moving magnet) at turntables (besides any other mechanical issues) to keep up as much as possible the SNR.
In the corresponding formula (on calculating the thermal noise - just google for it) the frequency range plays an important role as the noise density in a given octave rises if the frequency your looking at rises (in the octave from 20 to 40 Hz the span would be just 20 Hz, but in the octave from 40 to 80 Hz the span would now 40 Hz). Since the noise is made up of 'all' frequencies evenly spaced you can imagine that the noise energy in the second octave would be twice as much as in the first mentioned octave.

Now I guess everything is said (from my point of view).

#### EC8010

It's as well to remember that the only certain thing about a 24 bit ADC is that it produces 24 bits. On most of them, at least the four least significant bits are rubbish.

#### jackinnj

EC8010 said:
It's as well to remember that the only certain thing about a 24 bit ADC is that it produces 24 bits. On most of them, at least the four least significant bits are rubbish.

bit 24 is 59.6nV, bit 23 is 119.2nV -- that's a pretty big gulp of water.

#### Speedskater

Digital bits don't have a voltage value until you run them through an D to A converter.

#### jackinnj

Kevin Graf said:
Digital bits don't have a voltage value until you run them through an D to A converter.

Read the prospectus carefully before you invest.

#### poobah

You're almost correct about bits and voltgage values. Amp-ohms are the proper unit in this situation.

#### EC8010

jackinnj said:
Bit 24 is 59.6nV, bit 23 is 119.2nV -- that's a pretty big gulp of water.

OK, I worked backwards, and you're referring to 2V. If I've done my calculations correctly, 59.6nV is the self-noise produced (over 20kHz) by a perfect 10 Ohm resistor. I stand by my original observation that on most 24 bit ADCs, the four least significant bits are almost certainly rubbish.

#### poobah

You did mean 59.6 nanoAmp-Ohms... right?

#### jackinnj

Wasn't that the point I was making as well ? there is no resolving power down in the nano's, and it's inadequate until you get over a microvolt or so.

#### EC8010

jackinnj said:
Wasn't that the point I was making as well ?

Ah, well I wasn't sure if I had understood your colloquialism correctly.

As for the nanoamp-Ohms, there are applications where the noise is given in numbers of electrons.

#### jackinnj

EC8010 said:

a perfect 10 Ohm resistor.

One of the things encouraged me early on with the HP 3581 and noise measurement -- it will run off batteries and with its 3Hz crystal filter bandwidth you can compare the theoretical noise and get a good idea of whether your nanos are really nanos.

To acurately measure noise with a DVM you need a darned good outboard RMS detector as well. The venerable AD536 is so-so for this purpose. Fortunately, the push for energy efficiency and power measurement has resulted in a windfall for us DIYr's --

#### EC8010

We demand rigorously defined areas of doubt and uncertainty!

jackinnj said:
To accurately measure noise with a DVM you need a darned good outboard RMS detector as well.

I've never really liked noise measurements presented on a DVM, whether it's an external bodgebox to your Fluke or the internal bits on an Audio Precision. Give me an analogue meter with properly designed ballistics (a PPM) so that I can watch to see if the meter twitches randomly or rhythmically...

#### jackinnj

Certainly when you are nulling an LC circuit the old d'Arsonval is the way to go -- with noise you should be integrating the RMS value over a period of time -- if you have a scope which allows you to see an envelope it would be as helpful.

I should make an animated GIF of the meter on the HP3581 -- it gives me a headache.

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