1/f (pink noise) generator in the ELF band

[researcher]

Hello Guys,

I am a cancer researcher and for one of my research project I want to build a special device. The major component of the device is a 1/f noise generator. The problem is that I need extremely low frequency noise in the range from 0.001Hz - 100Hz having 1/f power spectral density.
Does anybody has any idea how this unique 1/f noise generator can be constructed? Any suggestions, recommendations or source are very appreciated!

(However I have biology background, I am very familiar in electronics, so I can easily build many devices according to the proper schematic. Unfortunately my expertise is not enough to design a circuit.)

Thanks

 

[AnalogKid]

That frequency range is so low that you probably could grow a noise pattern in software more reliably than with traditional noise techniques. After all, how do you measure/test random AM and FM or calculate an FFT at 1/1000 Hz? 1/2 cycle is over 8 minutes.

A six decade bandwidth means a 60 dB power range or 120 dB voltage range. Difficult, becaused opamps and things have heir own 1/f noise.

This is *not* a normal question.

ak

 

[researcher]

Thanks.

I know very well, this was not a normal question. If it would be, I could find the solution.

I need this extremely low frequency range, because the physiological processes in the living organisms also produce fluctuations in the same frequency range.
But I have no idea how can I generate it artificially.
My other problem that the fluctuations must have its own internal "structure", so filtering a white noise is not an option (Or just the last solution) For the same reason computer generated noise pattern is also excluded.
I need something "natural" pink noise source in very low frequency range. (for example oscillations in plasmas or chaotic oscillators in a very low frequency)

 

[OBW0549]

My approach to this problem would be to generate the noise using an opamp-- one with the crappiest noise performance you can find, including a high 1/f noise corner frequency. Three that could do the job are the TLC271 (http://www.ti.com/lit/ds/symlink/tlc271b.pdf) operated in low-bias mode, the LT1803 (http://cds.linear.com/docs/en/datasheet/180345f.pdf) and the OPA349 (http://www.ti.com/lit/ds/symlink/opa2349.pdf).

Configure the opamp as a DC amplifier (inverting or non-inverting, doesn't matter) with grounded input and gain of around 100 to 1000, add some means of nulling out the opamp's input offset voltage (the TLC271 has connections for an offset trimming pot, the others do not), and follow it with additional DC gain stages to obtain whatever output amplitude you need. You might have to house the circuit in some sort of constant temperature environment to eliminate the effects of offset voltage temperature shift.

 

[dr pepper]

There are some crystal ovens on ebay that would give you constant temp with enough space inside for a circuit, I have an ex mil one, the seller still lists them.

 

[researcher]

Thank you very much for this useful comments.

May I ask an approximate schematic about the proper configuration of the method you have suggested? I would really appreciate...
(As I wrote I am not an electrical engineer, I can just build circuits according to the schematic)

Thank you in advance!

 

[AnalogKid]

Or servo the noise amp's offset with a loooooooooooooog time constant integrator. And that's the problem - when the period of the lowest frequency of interest is over 16 minutes, you would need a servo integrator with a time constant of 27 minutes or more. OTOH, the 100 Hz bandwidth is so low that a chopper stabilized amp could do this easily. Hmmm... OK, so now the problem is pink-ifying the post #4 noise source.

What is this "internal structure" thingy?

ak

 

[researcher]

Well, this "internal structure" of the pink noise is the real point in the 1/f fluctuations. (at least for a biologist)

I think you know if you make a FFT analysis on a music (for example a Mozart sonata) you will get the perfect 1/f power spectral density. And you will got the same thing if you analyse in the same way a Chopin concerto, however the two music can be distinguish easily, because the internal structures are different but looks exactly the same after spectral analysis.
This internal structure of the pink noise is come from (...well nobody knows exactly from where...) the so called self organised criticality. The real pink noise has a fractal structure, has a strong correlation, has "memory". You can find a very good summary about it here: **broken link removed**
I would strongly recommend the references, too.
The most widely used pink noise generators are basically white noise sources which are filtered to look like a pink noise in a spectrum analyser, but lack of the unique feature of a real pink noise.
For biological experiments I need a real pink noise which is generated by a self organised process like a plasma discharge or chaotic oscillation (Chua's circuit).

 

[AnalogKid]

I respectfully disagree.

A spectrum analyzer is not a perfect instrument; it does not show you the true reality of the signal it is analyzing. It shows you a limited picture of a short-cut calculation of an opinion of an approximation of the real signal. More than for any other instrument used in circuit design and system analysis, spectrum analyzer results must be interpreted very carefully.

What you said about the power spectral densities of Mozart Vs, Chopin is not correct. The two spectra might look the same when displayed on a spectrum analyzer, but that is nothing near the reality of the two energy patterns. If they "look exactly the same after spectral analysis", then you need to buy a better spectrum analyzer. They do not sound the same because the spectra are not the same; no other reason. Yes, most orchestral music has similarly shaped spectra in a general sense over a long time frame like 10's of minutes. That's because they all use the same instruments, and those instruments have evolved to sound balanced to the human hearing system, and that system has a logarithmic response to energy vs. frequency.

Pure white noise is equal energy at each frequency within a specified bandwidth. Pure pink noise is equal energy within each octave or other sub-bandwidth within the overall bandwidth. Since each octave has twice as many frequencies as the one below it, it has half the energy. As the sub-bandwidths reduce to the limit of individual frequencies, the 1/f relationship emerges from the math. This is the internal structure of true pink noise. We do know where it came from and why, and why it is called "pink". Anything that is true white noise shaped to the 1/f characteristic is true pink noise.

What do you mean by a self-organized process? If you mean a native signal, as in one that is generated as pink noise from the start rather than one that starts out as white noise and is shaped, I think verifying that your signal source has a 1/f shaped spectrum to such low frequencies will be very difficult.

ak

 

[OBW0549]

May I ask an approximate schematic about the proper configuration of the method you have suggested? I would really appreciate... (As I wrote I am not an electrical engineer, I can just build circuits according to the schematic)

Something like this is what I had in mind:

 

[AnalogKid]

Other than maybe an offset trimmer for each stage, looks good to me. Still, how do you confirm its spectral shape at 0.001 Hz? I wonder what a linear feedback shift register (LFSR) wiz would say about spectral purity at 0.001 Hz. It might take a very long shifter, but chips is cheap if the math is tight.

ak

 

[OBW0549]

Still, how do you confirm its spectral shape at 0.001 Hz?

About the only practicable way to do that, I imagine, would be to use a high-resolution A/D converter to sample the output, then crunch the numbers to compute the noise voltage spectral density at different frequencies. Short of that, you'd be forced to take it on faith that the 1/f noise density curve of the opamp continues indefinitely upward with decreasing frequency without leveling off-- an assumption that might or might not be valid.

I wonder what a linear feedback shift register (LFSR) wiz would say about spectral purity at 0.001 Hz. It might take a very long shifter, but chips is cheap if the math is tight.

My own preferred approach to this would be to generate the noise with a long linear feedback shift register, filter the raw random number output in software with a multi-stage digital pinking filter, and output the result through a high-resolution DAC. But the TS indicated he doesn't like this approach...

 

[audioguru]

The reverse-biased emitter-base of a 2N3904 transistor was shown to produce lots of random noise. Look in Google for the Pink Noise Circuit and increase the value of the capacitors so it works at your very low frequencies.

 

[dr pepper]

That circuit in a stabilised ambient temp looks like a good starting point, simple circuits are often the best.
A dsp would give you best results as inferred, or even a microcontroller at such low freq's, if you dont want that route then you'll have to settle for something a little less pure o/p.
The supply for OBW's circuit can be assembled from a 6-0-6 transformer and a 7805 and 7905 voltage regulator, a stable supply is probably a good idea, you could put the reg's in the temp controlled oven with the rest of the cct.
Also I dont know what your connecting this to however you'll need to constantly trim the dc offset(use a 10 turn trimmer or panel pot), or use a very large dc decoupling cap, if the load impedance is high then a decoupling cap would be practical so long as its big enough uF wise not to affect the response, obviously an audio amp isnt going to be suitable to amplify the o/p you'll need a servo amp.
The crystal oven i mentioned unfortunately is no longer on ebay I think the seller has shifted them all, there are a few pages that show you how to build one, I built one back in spring for a frequency generator.

 

[AnalogKid]

At 0.001 Hz, a 10,000 uF capacitor has an impedance of 16 K. Not a show-stopper, but you've got to wonder how leakage current would affect the output. If that cap were coupling into a 10x impedance like 160 K for less than 10% signal loss, 6 uA of leakage current would equal 1 V or error. That's a lot. Temperature-induced changes in leakage current would look just like noise at the low end of the required bandwidth and upset the pinkishness. So I think the system has to be DC coupled.

ak

 

[dr pepper]

Agreed

 

[Tony Stewart]

A Pink noise filter is many half octave LPF's cascaded for each decade required (many)
A Brown noise filter is a single Octave 1st order LP filter or an Integrator, which has twice the slope of Pink noise and easy, but not what you want.

I prefer the digital approach of a maximal length pseudo random sequence generator for white noise.

Chaos is not always pink, although I have generated chaos in SMD SMPS buck to boost regulator coils by accident and the tiny SMD coil sounded like running water in the lab.

They used to make ML-PRSG chips but had a 2 second cycle for audio and you need a wider range spanning 5 decades ! or 50 dB in SNR of noise power as signal.

The 1/2 of the lowest frequency will be the length of the shift register (consecutive 1 or 0's) and clock rate or fmin=1/2* fc/N. for N series shift register. Harmonics of pulses are dependant on duty cycle , D and 1/N in the special case of 50% D with odd harmonics only.

So for extra margin and maximally flat spectrum per octave, let's choose a big sequence
These are special prime numbers for XOR feedback. There is only one illegal state either all 1's or 0's if using reset, so an inverted input if there is an even number of XOR inputs or no inverter if using an odd number of FB inputs.

let's use for n outputs from a 32 bit shift register n= 1 to 32, use 2,3,5,7,32 or if you prefer Q0-Q31, n=1,2,4,6,31 with the equivalent of a 5 input XOR gate to D input, thus after reset, D=1 and next Q0 goes from 0 to 1 and the random sequence begins with up to 32 consecutive 0's and 31 comsecutive 1's and a random spread in between. Output can be from the Q0 or any output.

Here is a 16 bit example, which only starts if preset to all 1's. you will need 4 XOR gates and reset to 0's. you can stop any time by gating the clock at random to get a random start, when enabled, or get a predictable sequence start with power on or manual reset.

**broken link removed** that duplicated my experience except only 4 decades with 4 stage filter, you may want a 5 stage filter.
Each filter is -3dB at breakpoint instead of -6dB thus called "half-order linear filter." For White to pink filtering.
The ML-PRSG 32 bit I described fits in box 32bit PRSG for pseudo random sequence generator.

The digital way is most stable in terms of spectral density over time, temperature.

The analog zener diode method is most linear but needs heat regulation for stable input and high gain.
Both need Pink noise filters. Your choice.
If you are wanting to discriminate controlled chaos with biological chaos, consider two as S & N and decide what is more important. High SNR? or smoothest slope on 3dB/decade of noise distribution or ease of controlling minimum frequency by clock rate.

You can also use this fourier web synthesizer to create any wave or random noise and see spectrum and hear it. Then shift the frequencies lower in software like Audacity, if you have a DC response amplifier.

 

[chemelec]

An MM5837N is a Motorola Pink Noise Generator IC.
I use one of these in a piece of equipment I built 20 Years ago.

I Noticed There are a few for sale on ebay.com.
Might Help you with your needs.

 

[Tony Stewart]

An MM5837N is a Motorola Pink Noise Generator IC.
I use one of these in a piece of equipment I built 20 Years ago.

I Noticed There are a few for sale on ebay.com.
Might Help you with your needs.

I used the same NSC chip in 1978, which previously noted is only good above ~1Hz.

If you wanted random impulse generation , you might be able to use amplified logical output to 10 bit counter to reduce frequency by 3 decades, followed by pink noise filters.


Anyway it is done must be calibrated on Spectr.Analyzer or FFT using Audacity free SW with recorded input on Aux on PC with some skill on settings.

 

[audioguru]

My audio pink noise generator also uses the MM5837 digital IC. Its white noise is converted to pink noise with a resistor in series with its output that feeds a few series RC filters to ground.
Its noise has a rhythm to it since the noise is pseudo-random and repeats every couple of seconds. The pattern is different each time it is powered up.