Measurement of Pink Noise

[jez_145]

I'd be interested to hear any views on the "ideal" way (if there is such a thing) of measuring the level of a pink noise signal.

I'm working on a little audio test generator project at the moment which, amongst other things, requires a pink noise output set at 600mV RMS but I'm not sure how to best measure a signal that a) contains the full range of audio frequencies and b) randomly varies in amplitude ?

I have limited test gear available.

- An oscilloscope with built in automated measurements including Vrms
- A "true RMS" multimeter with a claimed 100kHz bandwidth
- A homemade audio millivoltmeter *

* This is the Arduino based "Digital Audio Millivoltmeter" project that appeared in Silicon Chip/Practical Electronics magazine (Oct 2020) and features the Analog Devices AD8307 logarithmic amplifier/detector used in conjunction with a LTC400, 24-bit A to D converter.

I attempted to measure the noise output from a commercially made unit, similar to what I'm attempting to build, which also has a stated 600mV output, results were as follows:-

Oscilloscope = 662 mVrms (though varied a little according to selected timebase).
"True RMS" multimeter = 647 mVrms
Homemade millivoltmeter = 436 mVrms

In each case, I attempted to derive an "average RMS" value by recording continuous RMS readings over a period of five minutes or so before calculating the average. Clearly, the scope and the multimeter aren't a million miles apart and my homemade millivoltmeter is a fair bit off, in this case, but all three are close when measuring a fixed frequency regular waveform input such as a sine wave.

It strikes me that, in general, whilst results can differ between the instruments, none of them are necessarily "wrong" as they each have their own method of measurement. Thinking about it (as a mere hobbyist), I can now appreciate that noise measurement is not a trivial task, given the random nature of the signal. I guess RMS measurement is preferable to just averaging peaks but I guess a lot depends on the frequency and quality of the samples taken in order to calculate the RMS value and this can vary depending on the approach taken by the apparatus used. Presumably, when quoting noise measurements, it would be desirable to qualify the results by stating the equipment used - as in the good old days when AVOs and other 20,000 ohm per volt meters were specified in, for example, military and radio servicing documentation?

Any thoughts/suggestions would be much appreciated.

Many thanks.

Jerry

[Radio Wrangler]

For measuring any form of random/pseudo random noise you need a true RMS measurement. Peak reading voltmeters with correction factors for sinewaves are pretty much useless.

Noise doesn't have a simple level as such. How much power you get depends on how much bandwidth you are looking at. So you can state a level, but only if you also state the equivalent noise bandwidth.

Pink noise gets more complicated because of its slope. You don't just need to know the bandwidth, but the level also depends on just where the bandwidth is located.

The easy way out would be to just digitise it with a wideband, flat digitiser and then chuck some DSP at it.

Averaging peaks or measuring peaks is very dodgy because true random noise of ANY level has INFINITE peaks so all you are measuring is whatever happens to be clipping.

Noise is weird. Manageable once you know the foibles. I dug into it on the 'know thine enemy' principle and years later had to design the HP/Agilent/Keysight noise figure analyser and its 'smart' noise sources.

Oh, the Analog devices log detectors are arrays of many diode detectors spread across cascaded amplifiers and they fall into the infinite peak trap.

David

[G0HZU_JMR]

I think it's also worth looking at the spectrum of the pink noise to see if it falls at 10dB/decade. This can be done with a PC soundcard.

See below for a quick measurement I made of a pink noise generator spanning 20 Hz to 20 kHz. You can see it has the correct slope for pink noise.

I've got various meters and analysers here that could measure the Vrms of this generator but some care is needed to make sure that out of band signals don't leak into the system as this can introduce errors if they are large enough. A scope will have maybe 100 MHz bandwidth and some Vrms meters could have 20 MHz bandwidth. So it would be worth it to make sure the signal is properly band limited before trying to measure it with some meters or analysers.

I'll have a go at measuring the pink noise generator tomorrow using several measurement devices.

[dave cox]

If you digitize with a PC soundcard you can persuade the free software "Audacity" to do an 'inverse pink filter' on the sample spectra. This makes level measurement easy. Of course, you still need to figure out a suitable calibration factor !!

Doing the inverse filter can be quite revealing on how good a pink noise source is. Several of the digital audio pink noise samples I found were rather poor, with large amounts of ripple due to them using a small number of terms in the synthesis ...

dc

[jez_145]

Thanks for the replies David, Jeremy and Dave C.

You've confirmed my suspicions.

Funnily enough, I've experimented with a variety of noise sources over the years, with various synthesizer projects etc, but it's only recently that I've needed to actually measure the output. That's made me realise that there's more to this than meets the eye.

The thing with noise is that it's easy to see on a scope, listen to through an amplifier and, subjectively, get a "feel" for the signal level BUT, attempting to measure and put some meaningful numbers against it is quite daunting - to me at least.

"Calibration factor" - ah well, that's just it Dave. That's the get out clause! Your PC sound card/Audacity idea sounds like it's on the same lines as David was suggesting when he mentioned digitising the noise and throwing some DSP at it, though I suspect David is more of an Audio Precision man - (I wish!). I do have a decent sound card and software but, those items in themselves require some sort of external calibration when it comes to using them for measurements.

The unit I'm trying to replicate (and improve on) is a "CAT 85C Pink Noise Generator" that was designed and manufactured by Dolby Laboratories in the 1980s. This was issued to service engineers responsible for maintaining cinema sound systems and took the form of a card that slotted into the "Cinema Processor" unit. This allowed the noise to be switched between the various sound channels when the auditorium was being calibrated for level and equalisation. Clearly, for this application, a consistent output is required. In their documentation, Dolby only specify a noise output of 600 mVrms (automatically switched down to 360 mV in certain processor units) but they do not qualify this against a frequency bandwidth or state how this was measured other than mentioning use of a "millivoltmeter". Who knows what they used? Something like an HP 3400 perhaps - which were popular at the time? Looking at the circuit diagram for the CAT 85C, a couple of resistors responsible for setting the output levels are marked as "Adjust On Test" so at least it seems that they put some effort into getting the calibration right according to their test gear at least. Perhaps my best bet is to regard the Dolby unit as my standard reference and adjust my own circuit to match it.

At the end of the day, all this is non-critical. I'm designing my unit purely for the fun of it and my own use, but I'm learning a lot on the way. I'm always interested in measurement and hearing about professional techniques used in industry so any further comments/ideas welcomed.

Thanks again,

Jerry

[Radio Wrangler]

Should be able to calibrate with a sine. Then measure noise, if the DSP is OK.

Audio Precision? No they were the enemy, or rather the enemy was within. HP made some rather good instruments and then left them alone for too long (EG 8566B) letting other firms get into pole position. HP let the 8903 lie on its laurels and Audio Precision got into the business and took the lead. Only belatedly did (then)Agilent decide to do a modern DSP instrument. Duncan B, a friend and colleague, got draughted into this to sort out the initial design and get it manufacturable. Rohde & Schwarz got ahead in spectrum analysers. The firm used to innovate and push progress just because it could. Once management processes had been defined and cast in concrete a new project could only be authorised if there was so much demand that it could be proved that it was too late to start. As they say, like watching a train wreck in slow motion.

David

[G0HZU_JMR]

I had a go at measuring the pink noise generator this evening with various bits of test gear and got the following results:

Analog Discovery 2 (scope Vrms measurement) 293mV averaged
Keithley 2000 DVM Vrms 297mV rms MovAv using 90 readings
HP Infiniium scope 296mV rms averaged
Racal 9300 Vrms meter probably 298mV rms.

I had to take a visual average using the old Racal meter as it was fluctuating +/- 8mV. I fed the DVM recorder output of the Racal 9300 to a Fluke 45 DVM to get a better reading.

I think it's important to keep in mind the low frequency cutoff of the pink noise generator and also the low frequency limits of the various measurement meters. I had a look on a LF spectrum analyser and the pink noise generator was cutting off at about 10Hz. This is within the range of all my meters.

Pretty much all my noise experience is with band limited white noise so pink noise is fairly new to me. However, I had a go at breaking up the pink noise (AF) spectrum into octaves as in the excel chart below. I hope I've understood pink noise correctly here in this chart as I assume the energy in each band will be the same. If I assume that band 1 is the top octave of the AF band covering 10kHz to 20kHz then it looks like my pink noise generator works up to band 11 which starts at 10Hz.

However, if the generator worked up to higher band numbers (lower frequencies) then I'd expect to see differences between my meters as I think the Racal meter is only spec'd down to 5Hz and the Keithley DVM is only spec'd down to 3Hz. Presumably the AD2 and the Infiniium scope are OK to much lower frequencies for a Vrms measurement.

[G0HZU_JMR]

I wrote a quick program to remotely read my Fluke 45 meter and used it to average 100 readings from the Racal 9300 via the DVM recorder output. The result was a bit different to my visual estimation before and the averaged reading typically showed 302mV rms for the Racal 9300.

I also tried measuring directly with the Fluke 45 set to Vrms and it consistently measured 297mV when averaged. This agreed very closely with the Keithley meter and the Infiniium scope. I'd expect the Keithley 2000 DVM to be top dog in this shootout in terms of measurement uncertainty.

The AD2 measurement was a bit low at 292mV but I'm not sure if I've formally calibrated the AD2 for stuff like this. I think it has a user calibration menu but I'm not sure it's worth messing with for such a small offset.
I just retried it for DC coupled Vrms and it measured 295mV rms. So I think this is a good result.

I also cleaned up the octave table such that it shows easier to read values at the band edges. See below for a nicer version.

[jez_145]

Firstly, thank you very much Jeremy for putting the time and effort into your investigation. I think you got some remarkably consistent results there (close enough for government work!), with a decent variety of test equipment too, which is very encouraging. I hope you enjoyed your experiment.

As I previously mentioned, my application involves building a pink noise source for audio calibration purposes - specifically cinema sound systems. I have experimented with various approaches starting with the (white) noise source. Firstly, I started with a transistor in reverse bias mode followed by a couple of stages of amplification then the pink noise filter etc. This worked fine but, of course, the noise level can vary considerably between different transistors when they are used(abused ?) in this way. I get the impression that commercial pink noise circuits tend to avoid transistors (in favour of shift registers) for this reason. Also, I worry a little about long term reliability of prolonged Vbe abuse but, in theory, you can get away with it provided the current is limited. Next, I tried a trio of 4094 shift registers with an xor gate tapped in the appropriate places. This worked fine to, although it was a bit of a "chip heavy" solution. My latest approach is using a PIC micro as a pseudo tapped shift register. This works much the same and has the advantage of minimal parts count (but needs to be programmed of course).

The white noise generation is followed by a 3dB/octave pink noise filter, due to Doug Self, which he claims to be accurate to within 0.1dB (of the required 3dB/octave). Initial tests support this. Finally, the pink output goes through a band pass filter; the first high pass stage is at 12dB/octave with a -3dB cutoff at 22 Hz and the second stage a 18dB/octave low pass at 19.6kHz. So, we're eliminating, or at least severely reducing the unwanted "equipment damaging" frequencies which would also affect the measurement instruments - as you suggest.

In contrast, the commercial Dolby CAT 85C noise generator, I'm loosely basing my design on, just spits out the noise after the pink filtering stage with no further band limiting. Thinking about it, this is something I'll need to take account of when comparing my circuit's output with their's.

Regards,

Jerry

[kevinaston1]

Is this any help?

A 31 band RTA from about 40 years ago by Dod/Digitech in Salt lake, sadly the company is long since gone.

[Radio Wrangler]

Originally Posted by jez_145

Who knows what they used? Something like an HP 3400 perhaps - which were popular at the time?

Interestingly the HP3400A did definitive true RMS. The input was subjected to impedance buffering ans switched amplification/attenuation then unceremoniously stuffed into a resistive termination. A matched, second termination was fed with DC. Each termination was provided with a thermocouple stack to measure its temperature and the DC to the second termination was adjusted by a bridging amplifier to make the thermocouple voltages balance. Thus the DC level had the same heating power as the incoming signal. Averaging was by thermal mass and loop BW. The whole thermopile assembly was in an evacuated metal can.

A later generation thermopile was done by Loveland division for their 3335/3336 levelled sig gens. This was in a tall TO-5 sized can and used diodes as the temperature sensors. Part number was 1SB1-0021. Odd what sticks in memory. We used it in the 3708A carrier/noise tester.

David

[jez_145]

Thanks David,

Re: the HP3400A/B you might find the following interesting if you haven't seen them already.


https://www.hpl.hp.com/hpjournal/pdf...Fs/1964-01.pdf

https://www.youtube.com/watch?v=NfxY74W7rNY



Jerry

[jez_145]

Originally Posted by kevinaston1

Is this any help?

Kevin, Thanks for the info.

Short answer No! Well, not in this case, concerning the low level measurement of pink noise.

BUT, the info you provided on Real Time Analysers is still interesting to me in that these devices were used a little further down the line by cinema sound technicians when making equalisation adjustments in the auditorium - using the amplified output from the pink noise generator we are discussing here. The RTA unit was typically connected to one or more measurement microphone(s), placed in strategic positions, and it displayed the overall spectrum response due to the cinema speakers, room characteristics and so on. The technician would then adjust the EQ controls (a form of graphic equaliser) within the cinema processor unit in an attempt to obtain as flat a response as possible - displayed on the RTA's screen.

Pink noise is a mixture of all frequencies (audio range in this case) at the same level for each frequency, which allows this measurement. It's not perfect but it does go some way into achieving a reasonable consistency of sound reproduction between different cinemas. They would also use a sound level meter, alongside the RTA to even out the overall volume of each sound channel e.g. the three main screen speakers (Left Centre and Right), the Left and Right surround channels and sub woofer (for typical 5.1 systems). Of course, these days, there can be way more channels (up to 64) and options when it comes to cinema sound. Also, the dedicated RTA hardware unit has typically been replaced by a laptop computer and appropriate measurement software.

Dolby never manufactured RTAs as far as I know, but they did recommend a few from other manufacturers such as Abacus, Altec, Crown et al. I think the DOD/Digitech device you provided info on came a bit later. As far as I can see, the DOD/Digitech name still lives on (just) in the guitar effect world after being swallowed up by Harmon.

Some info here

https://en.wikipedia.org/wiki/DOD_Electronics


Thanks again

Jerry

[G0HZU_JMR]

Yes, I think it's worth exploring the low frequency performance of any meter and also any generator.

I have a couple of Agilent sig gens here that have a DSP based function generator built in. This can output lots of waveform types with good performance. I tried exploring the low frequency range of the Keithley 2000, the Fluke 45 and the Racal 9300 meter using a 1V rms sine wave.

All of them lose performance very rapidly below about 5Hz to the point they become quite deaf. I wouldn't trust any of them below 5Hz because of this steep decline at 5Hz. By contrast the Infiniium scope and the AD2 worked fine down to 0.2 Hz and agreed within a tiny fraction of 1%. Below 0.2 Hz I got bored waiting for the scope timebase so that's as far as I looked.

I also compared all the meters with a 1 kHz sinewave at 1V rms and the performance was quite good in all cases.

I also compared against another Keithley meter the 2015THD.

K2015THD 1.00035V rms
K2000 1.00028V rms
Fluke45 1.0004V rms
Infiniium 0.9991V rms
AD2 1.0015 Vrms
R9300 1.0066V rms

It looks like my Racal 9300 could do with a cal tweak although it is still within spec. I tried measuring the pink noise source again with it on the 300mV range as it can cope with a crest factor of 7 at FSD. It measured 300mV when averaged with the Fluke 45. This is about +1% compared to the Keithley meters.

Looking at the specs a brand new Keithley meter can achieve 0.05% +0.03% of range on the 1V AC range in this frequency band. I'm not sure how accurate my meters are. The 2000 UKAS cal expired in 2016 just before I bought it. However, the Fluke 45 and the K2000 and the K2015 seem to agree very closely whenever I compare them.

The little Racal 9300 true rms meter is a really nice meter. I mainly use it for making relative measurements for signals and noise and the performance is superb when used with the Fluke 45 connected to the DVM output at the rear of the 9300. The Fluke 45 has an easy to use dB and dB relative function which makes this setup really easy to use. The accuracy of the 9300 scaling and attenuation is remarkable when making relative measurements.

[Radio Wrangler]

One of the first home-grown HP UK products was the 3721A correlator with the accompanying 3722A noise generator (a PRBS machine) and the 3720A spectrum display.

This was 1960s technology and together made up a real time analyser.

I knew the people who had originated and designed them, and worked amongst these folks for some time. They taught me quite a lot. Small amounts of noise could be injected into the control system of the sort of thing you wouldn't want to hit with transients or sweeps, and you could get the impulse response and frequency response without explosions, metted-down reactors, aircraft crashes and all that sort of stuff.

David

[Audiophile_AU]

Hi all,
a word from Down Under
A few years ago there was a project about the calibration of commercial cinemas by the Audio Eng. Soc. (AES) and the Sound & Motion Picture Televisin Engineers (SMPTE). As a spin off it was discovered that the various suppliers of cinema processors had different versions of pink noise.
As a spin off from that major project SMPTE developed a digital version as the Standard for pink noise and offers it for purchase. I have been told it is an algorithm which generates a .wav file, sampling rate either 48kHz or 96kHz. Bandwidth limits and slopes are also defined by the algorithm, as is crest factor amplitude distribution and the like.
Previous posts outlined the problems of creating and measuring pink noise. These are some of the reasons for the 'new' SMPTE ST 2095-1:2015 Calibration Reference Wideband Digital Pink Noise Signal USD 170 ka ching thank you very much!
It seems consumer pink noise would have to be converted from the 48kHz, although I believe there have been several requests for a 44.1kHz version.
Good luck with the analogue versions....
best regards
David

[Radio Wrangler]

You can build a lot of analogue for $170.

Unfortunately the slope does not relate to a finite integer number of poles, so a curve fit compromise is forced.

A single pole goes asymptotic to 20dB/decade and you want 10dB/octave. So you want half a pole!

Poles are roots of a transfer function equation, so you need an equation with 0.5 roots

The solution lies in the reduced slope near a pole, so you can use a constellation with alternating poles and zeroes. The spacing between poles and zeroes along with the number per octave sets the slope and the frequency range it covers. You don't really get 10dB/octave unless you can throw an infinite number of pole-zero pairs at the problem, instead you get yor wanted slope with an error ripple superimposed.

So pink noise sources (even digital ones) are compromises.

Human speech and orchestral music tend to have pink power distribution. This is why tweeters have lower power handling than woofers, and why we often use pink noise testing comms radios, and weighting filters for measurements.

Note that some individual instruments like synthesisers and electric guitars are not pink in power distribution, which is why attempts to use hifi speakers can end in smoke.

David

[G0HZU_JMR]

I had a play with a noise generator program and I think it has generated pink noise in a wav file format for 1 minute.

There's a 44.1kHz, 48kHz and 96kHz sample rate version below. I'm not sure what level to set the output level at so I've set it quite low.

All three files are in the web folder here:

https://www.qsl.net/g/g0hzu//RF%20Tr...%20data/SINAD/

The quality of the pink noise might not be up to studio standard (whatever that means) but each wav file looks OK on a spectrum analyser to me when averaged over time.

[Cruisin Marine]

You need a pink noise genny, recording software like Cool Edit etc. will produce that easily.
To show freq. response you, I guess you will need an inverse filtered record/monitor input sloping at 10dB/decade from memory (easy to design in CE).
See this https://en.wikipedia.org/wiki/Pink_n...e_spectrum.svg
Then you will need a calibrated microphone or correction filter to account for any bumps in the mic response, if looking at the response of a room or theatre. A sound card for the "record" side will suffice.

Taken from Cool Edit help
"Pink Noise
Pink noise has a spectral frequency of 1/f and is found mostly in nature. It’s the most natural sounding of the noises. By equalizing pink noise, you can simulate rainfall, waterfalls, wind, a rushing river, and other natural sounds. Pink noise falls exactly between brown and white noise (which is why some people used to call it tan noise, but pink was more appealing). Pink noise has a fractal-like nature when viewed. When zoomed in, the pattern looks identical to the way it appears when zoomed out, except at a lower amplitude."


Of course free software like Audacity will probably do the job too.