The central limit theorem rocks, (summing Zener noise)
in [Design]
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From: Grant on 4 Jun 2010 00:29 On 04 Jun 2010 03:52:24 GMT, Jay Ts <bitbucket(a)example.com> wrote: >langwadt(a)fonz.dk wrote: >> George Herold wrote: >>> So the following is the result of a previous thread where John Larkin >>> suggested that one way to get rid of the voltage asymmetry in a Zener >>> noise source was to sum a whole bunch together. I was initially >>> doubtful, but thought I should do the experiment. I had a whole bunch >>> (five) of lockins to test today. They have a build in Zener noise >>> source with terrible asymmetry. So I summed them with an opamp, fed >>> the signal to a digital 'scope and had it measure the min and max >>> voltage. (There is lots of noise in the measurements so the number are >>> not that accurate.. but the result is clear. The central limit theorem >>> rocks! >>> >>> Number Vmax Vmin. of >>> zeners >>> >>> 1 0.80 -0.33 2 1.20 -0.53 3 >>> 1.50 -0.75 4 1.60 -0.95 >>> >>> Thanks John, >>> >>> George H. >> >> try subtracting instead ;) >> >> gets rid of the non zero mean > >Here is a schematic of a little circuit I created >yesterday after following the original thread on >this topic: > >http://jayts.com/images/WhiteNoiseGen-Med.png > >I just put some ideas together from the discussion >here, along with other things I found from some >quick Internet searches. > >I used two opamps to bring the output up to >about +4 dBu (commonly used in pro audio). > >The circuit is not optimized, and it's certainly >not a great example of schematic capture. I was >just trying out gschem on my Linux system to see >how well (or _if_) it worked. Obviously, it's >better to pay money for schematic capture software. > >I put the output of the circuit into a PC >24/96 audio card, and on a spectrum analyzer app, >it showed about a 6 dB drop in amplitude from >near DC (0 dB) to 40 KHz (-6 dB). I did not >think this was really bad, but if anyone knows >how to make this flatter, short of an esoteric >and expensive "noise diode", please comment. > >On my Tek oscilloscope, I used the averaging mode >of the display, and the trace averaged out to >a bumpy line at 0 volts. It's quite symmetric >as far as I can tell. You might balance it a bit more swapping R2 and its zener? Grant. -- http://bugs.id.au/
From: Jay Ts on 4 Jun 2010 01:35 Grant wrote: > Jay Ts wrote: > >>> try subtracting instead ;) >>> >>> gets rid of the non zero mean >> >>Here is a schematic of a little circuit I created yesterday after >>following the original thread on this topic: >> >>http://jayts.com/images/WhiteNoiseGen-Med.png >> >>I put the output of the circuit into a PC 24/96 audio card, and on a >>spectrum analyzer app, it showed about a 6 dB drop in amplitude from >>near DC (0 dB) to 40 KHz (-6 dB). I did not think this was really bad, >>but if anyone knows how to make this flatter, short of an esoteric and >>expensive "noise diode", please comment. >> >>On my Tek oscilloscope, I used the averaging mode of the display, and >>the trace averaged out to a bumpy line at 0 volts. It's quite symmetric >>as far as I can tell. > > You might balance it a bit more swapping R2 and its zener? I don't understand what you mean by "balance it a bit more". I used the configuration for the zener and resistor that I found here: http://www.maxim-ic.com/app-notes/index.mvp/id/3469 I'm used to using them the other way around, but as far as I can tell, the circuit seems to work the same either way, or with one of the pairs reversed. Is there a reason it should be different? Here is a screen capture from Spectrum Lab for the exact circuit I posted earlier: http://jayts.com/images/WhiteNoiseGen-Spectrum.png Jay Ts
From: George Herold on 4 Jun 2010 09:33 On Jun 3, 11:52 pm, Jay Ts <bitbuc...(a)example.com> wrote: > langw...(a)fonz.dk wrote: > > George Herold wrote: > >> So the following is the result of a previous thread where John Larkin > >> suggested that one way to get rid of the voltage asymmetry in a Zener > >> noise source was to sum a whole bunch together. I was initially > >> doubtful, but thought I should do the experiment. I had a whole bunch > >> (five) of lockins to test today. They have a build in Zener noise > >> source with terrible asymmetry. So I summed them with an opamp, fed > >> the signal to a digital scope and had it measure the min and max > >> voltage. (There is lots of noise in the measurements so the number are > >> not that accurate.. but the result is clear. The central limit theorem > >> rocks! > > >> Number Vmax Vmin. of > >> zeners > > >> 1 0.80 -0.33 2 1.20 -0.53 3 > >> 1.50 -0.75 4 1.60 -0.95 > > >> Thanks John, > > >> George H. > > > try subtracting instead ;) > > > gets rid of the non zero mean > > Here is a schematic of a little circuit I created > yesterday after following the original thread on > this topic: > > http://jayts.com/images/WhiteNoiseGen-Med.png > > I just put some ideas together from the discussion > here, along with other things I found from some > quick Internet searches. > > I used two opamps to bring the output up to > about +4 dBu (commonly used in pro audio). > > The circuit is not optimized, and it's certainly > not a great example of schematic capture. I was > just trying out gschem on my Linux system to see > how well (or _if_) it worked. Obviously, it's > better to pay money for schematic capture software. > > I put the output of the circuit into a PC > 24/96 audio card, and on a spectrum analyzer app, > it showed about a 6 dB drop in amplitude from > near DC (0 dB) to 40 KHz (-6 dB). I did not > think this was really bad, but if anyone knows > how to make this flatter, short of an esoteric > and expensive "noise diode", please comment. What opamp(s) are you using? You've got gains of ~33 in both the differential and second stage. Perhaps they are limiting your bandwidth. Check the slew rate of the final opamp too. You could try distributing the gain over more opamps if you want a higher band width. (3 times ten stages would give you the same over all gain with maybe 3 times the bandwidth.) I like inverting gain stages but that's not that important. George H. > > On my Tek oscilloscope, I used the averaging mode > of the display, and the trace averaged out to > a bumpy line at 0 volts. It's quite symmetric > as far as I can tell. > > Jay Ts- Hide quoted text - > > - Show quoted text -
From: George Herold on 4 Jun 2010 09:44 On Jun 4, 1:35 am, Jay Ts <bitbuc...(a)example.com> wrote: > Grant wrote: > > Jay Ts wrote: > > >>> try subtracting instead ;) > > >>> gets rid of the non zero mean > > >>Here is a schematic of a little circuit I created yesterday after > >>following the original thread on this topic: > > >>http://jayts.com/images/WhiteNoiseGen-Med.png > > >>I put the output of the circuit into a PC 24/96 audio card, and on a > >>spectrum analyzer app, it showed about a 6 dB drop in amplitude from > >>near DC (0 dB) to 40 KHz (-6 dB). I did not think this was really bad, > >>but if anyone knows how to make this flatter, short of an esoteric and > >>expensive "noise diode", please comment. > > >>On my Tek oscilloscope, I used the averaging mode of the display, and > >>the trace averaged out to a bumpy line at 0 volts. It's quite symmetric > >>as far as I can tell. > > > You might balance it a bit more swapping R2 and its zener? > > I don't understand what you mean by "balance it a bit more". > > I used the configuration for the zener and resistor > that I found here: > > http://www.maxim-ic.com/app-notes/index.mvp/id/3469 > > I'm used to using them the other way around, but > as far as I can tell, the circuit seems to work > the same either way, or with one of the pairs reversed. > Is there a reason it should be different? > > Here is a screen capture from Spectrum Lab for > the exact circuit I posted earlier: > > http://jayts.com/images/WhiteNoiseGen-Spectrum.png That looks OK. Do you know the bandwidth of the sound card? How flat is it? Do you have a digital 'scope with FFT? Here's a trick for getting a better FFT from your scope. Trigger right up at the top of your noise peaks, with the scope set to normal triggering. Now average as many traces as your scope allows. You should get this ~delta function bump in the center of your screen. Now take the FFT of that. You'll have to play with the time base to get it to look OK. George H. > > Jay Ts- Hide quoted text - > > - Show quoted text -
From: John Larkin on 4 Jun 2010 11:18
On Thu, 3 Jun 2010 12:41:34 -0700 (PDT), George Herold <gherold(a)teachspin.com> wrote: >So the following is the result of a previous thread where John Larkin >suggested that one way to get rid of the voltage asymmetry in a Zener >noise source was to sum a whole bunch together. I was initially >doubtful, but thought I should do the experiment. I had a whole bunch >(five) of lockins to test today. They have a build in Zener noise >source with terrible asymmetry. So I summed them with an opamp, fed >the signal to a digital �scope and had it measure the min and max >voltage. (There is lots of noise in the measurements so the number >are not that accurate.. but the result is clear. The central limit >theorem rocks! > >Number Vmax Vmin. >of >zeners > >1 0.80 -0.33 >2 1.20 -0.53 >3 1.50 -0.75 >4 1.60 -0.95 > >Thanks John, > >George H. The kind of random noise generator that uses a pseudo-random shift register and a lowpass filter is the ultimate Central Limit machine. The filter gets an input with a PDF like | | | | | | | | | | | | -------------------------------- 0v +5v and outputs a Gaussian distribution centered on 2.5 volts. John |