The central limit theorem rocks, (summing Zener noise)
in [Design]
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From: George Herold on 3 Jun 2010 19:07 On Jun 3, 5:41 pm, "langw...(a)fonz.dk" <langw...(a)fonz.dk> wrote: > On 3 Jun., 21:41, George Herold <gher...(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. > > try subtracting instead ;) > > gets rid of the non zero mean > > -Lasse- Hide quoted text - > > - Show quoted text - Ahh inverting and adding. Yeah that would work. This really isn't about reducing the asymmetry as much as showing (to myself) that the central limit theorem works. George H.
From: John Larkin on 3 Jun 2010 19:10 On Thu, 3 Jun 2010 16:04:15 -0700 (PDT), George Herold <gherold(a)teachspin.com> wrote: >On Jun 3, 4:40�pm, John Larkin ><jjlar...(a)highNOTlandTHIStechnologyPART.com> wrote: >> On Thu, 3 Jun 2010 12:41:34 -0700 (PDT), George Herold >> >> >> >> >> >> <gher...(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. >> >> What current are you running the zeners at? More current will improve >> the distribution at the cost of a bit of amplitude. >> >> John- Hide quoted text - >> >> - Show quoted text - > >This is an old design done years ago. At the time I was looking for >maximal noise and didn't really care about the asymmetry. These are >made with 20 volt zeners running off the +/- 15 volt rails with I >think a meg of resistance... 10uA of current. (I'd have to check the >schematic.) > >George H. Pardon me for shouting, but YIKES! SPIKES! John
From: George Herold on 3 Jun 2010 19:10 On Jun 3, 6:02 pm, John Larkin <jjlar...(a)highNOTlandTHIStechnologyPART.com> wrote: > On Thu, 3 Jun 2010 14:41:32 -0700 (PDT), "langw...(a)fonz.dk" > > > > > > <langw...(a)fonz.dk> wrote: > >On 3 Jun., 21:41, George Herold <gher...(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. > > >try subtracting instead ;) > > >gets rid of the non zero mean > > >-Lasse > > It should make the symmetry converge faster, too. > > Maybe the mean is zero, but the spikies are just lopsided. If so, the > first case, +0.80 and -0.33, is really bent! > > John- Hide quoted text - > > - Show quoted text - Yeah the mean is zero. There is AC coupling somewhere in the signal chain. And yes it's has terrible asymmetry! I must have the zeners biased right near the knee. George H.
From: George Herold on 3 Jun 2010 19:17 On Jun 3, 7:10 pm, John Larkin <jjlar...(a)highNOTlandTHIStechnologyPART.com> wrote: > On Thu, 3 Jun 2010 16:04:15 -0700 (PDT), George Herold > > > > > > <gher...(a)teachspin.com> wrote: > >On Jun 3, 4:40 pm, John Larkin > ><jjlar...(a)highNOTlandTHIStechnologyPART.com> wrote: > >> On Thu, 3 Jun 2010 12:41:34 -0700 (PDT), George Herold > > >> <gher...(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. > > >> What current are you running the zeners at? More current will improve > >> the distribution at the cost of a bit of amplitude. > > >> John- Hide quoted text - > > >> - Show quoted text - > > >This is an old design done years ago. At the time I was looking for > >maximal noise and didn't really care about the asymmetry. These are > >made with 20 volt zeners running off the +/- 15 volt rails with I > >think a meg of resistance... 10uA of current. (I'd have to check the > >schematic.) > > >George H. > > Pardon me for shouting, but > > YIKES! > > SPIKES! > > John- Hide quoted text - > > - Show quoted text - Hee HEE, I'm kinda embarrassed by the circuits I designed years ago, But, "Damn it Jim I'm a physicist not an engineer. George H.
From: Jay Ts on 3 Jun 2010 23:52
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. Jay Ts |