The central limit theorem rocks, (summing Zener noise)
in [Design]
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From: Jay Ts on 4 Jun 2010 14:50 On Fri, 04 Jun 2010 06:44:40 -0700, George Herold wrote: > 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? The sound card is flat to about 45 KHz. It's a 96 KHz card (M-Audio Audiophile 2496), and it drops off slightly before 48 KHz. I played around with the circuit some more, and I found that the spectrum became flatter as I reduced the R1,R2 zener resistors from 1k to about 300 ohms. (And the noise voltage dropped too, but not badly.) Now I'm seeing about a 2 dB drop from near DC to 40 KHz. And that's just 1 dB from 20 Hz - 20 KHz, so I think it's pretty good now. Also, I saw the asymmetry drop so much that I now wonder if the subractor circuit is necessary. After that, I tried 10k resistors to see what would happen, and got huge asymmetry. At that level, I could easily see that my 2 diodes are not acting the same, and one was about twice as asymmetric as the other! So now I understand the comment I read somewhere that it's important to get your zeners from the same batch. And maybe even try to match them (?). I think if I spend any more time on this, I will go nuts from watching noise waveforms and trying to make sense of them -- this is not my usual cup of tea. But, I now have some questions ... like, why is the noise voltage waveform more asymmetric at lower currents, why is it asymmetric at all, and why is it that there is more noise at low currents than at high currents? Trying understand these things is making me feel stupid. ;-) Are there any solid state physics geniuses around who would like to try explaining this? > Do you have a digital 'scope with FFT? Sorry, no. Just an old Tek DSO from the 1990s. The equipment I use here is all pretty basic, but are already overkill for the audio frequency circuits I work on. Someday, your model of scope will be $200 on eBay, and I will buy one! ;-) So thanks for the tip on getting better FFTs. I will try to remember it. I found the averaging function in Spectrum Lab's multitude of options, and now I'm getting much smoother traces from it. Jay Ts
From: John Larkin on 4 Jun 2010 14:50 On Fri, 04 Jun 2010 14:29:36 +1000, Grant <omg(a)grrr.id.au> wrote: >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? That would stuff power supply ripple directly into the signal path. As is, the zener impedances and CMRR of the diffamp mostly ignore the power supply. John
From: Jay Ts on 4 Jun 2010 15:20 On Fri, 04 Jun 2010 06:33:46 -0700, George Herold wrote: > On Jun 3, 11:52 pm, Jay Ts <bitbuc...(a)example.com> wrote: > >> 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). >> >> >> 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? Both are TI OPA2134. Slew rate is 20 V/us, and the gain-bandwidth product is 8 MHz. They should be able to handle a gain of 33 to well over 40 KHz, but since I never trust datasheets or theories (or myself), I may try adding more gain stages to make sure. The schematic makes it look like the opamps are separate chips because gschem didn't have a dual opamp symbol for the 2nd (using pins 5-7 instead of 1-3). Jay Ts
From: Grant on 4 Jun 2010 16:53 On Fri, 04 Jun 2010 11:50:44 -0700, John Larkin <jjlarkin(a)highNOTlandTHIStechnologyPART.com> wrote: >On Fri, 04 Jun 2010 14:29:36 +1000, Grant <omg(a)grrr.id.au> wrote: > >>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? > > >That would stuff power supply ripple directly into the signal path. As >is, the zener impedances and CMRR of the diffamp mostly ignore the >power supply. Hmm, okay, I was wondering what stopped PS noise getting into input through zeners and assumed PS was well-filtered. Grant. > >John -- http://bugs.id.au/
From: Tim Williams on 4 Jun 2010 21:21
"Jay Ts" <bitbucket(a)example.com> wrote in message news:WVbOn.11132$es1.10886(a)unlimited.newshosting.com... > After that, I tried 10k resistors to see what would happen, and got > huge asymmetry. At that level, I could easily see that my 2 > diodes are not acting the same, and one was about twice as > asymmetric as the other! So now I understand the comment > I read somewhere that it's important to get your zeners from > the same batch. And maybe even try to match them (?). So the knee currents are probably a bit different, so they act a little different at the same load. > But, I now have some questions ... like, why is the noise voltage > waveform more asymmetric at lower currents, why is it asymmetric > at all, and why is it that there is more noise at low currents > than at high currents? Trying understand these things is making > me feel stupid. ;-) Are there any solid state physics geniuses > around who would like to try explaining this? Well, you're operating it like a spark. The physics are all very similar: instead of electrons accelerated and smacking into gas molecules, releasing more electrons and ions, making it way more conductive; you have electrons and holes accelerated and smacking into crystal atoms, releasing more electrons and holes (EHP = electron hole pairs), making it way more conductive. The energy levels are ~10eV for atoms, and ~1eV for silicon (i.e., the bandgap). One thing that's different is, under most conditions, a gas glow/spark discharge has a remarkably constant voltage, maybe 20V. This can be despite a very high breakdown voltage, like 10kV. So the plasma is very conductive indeed, and exhibits negative resistance. In silicon, the breakdown is quite conductive, but not quite as dramatically so; a zener averages out quite nicely to a remarkably constant slope, with a generally positive (incremental) resistance. But, there are conditions where negative resistance is observed. One example is the 2N2369 or 2N3904, which can avalanche quite effectively in the same way a neon tube does. You can make a relaxation oscillator, with about 80V breakdown and 10V saturation. But unlike the neon tube, which requires several microseconds for ions to travel across the spark gap, a transistor needs only a fraction of a nanosecond for the EHPs to traverse the depletion region (a few um). Now, in a zener, you can imagine this avalanche behavior going on, and every so often an electron or hole pops into the depletion region (by thermal motion or diffusion), and it gets sucked rapidly to the side, so rapidly that it tears up electrons and holes along the way. These charges get sucked away as well, tearing up even more. So from just one electron or hole, a huge cascade of charge blasts its way to the electrodes. When this burp reaches the electrodes, the voltage falls suddenly, because dQ = C * dV, C = the capacitance of the junction. Once the voltage falls, the cascade stops, because there isn't enough electric field to cause EHP production (avalanche gain drops). So you can imagine, if the average current is small, it might be only one cascade, a very large one, that causes the voltage to fall very suddenly. Once the voltage is down, the cascade stops, but the total charge released keeps coming, so it undershoots, and voltage drops suddenly by a lot of milivolts. Gain drops to 1, so cascades stop and you get ordinary leakage, which is small, so the junction capacitance charges by the source current again. Hence, you get this random ramp sort of waveform. So when you turn up the current, all these little avalanches start overlapping, and maybe more regions are avalanching simultaneously. The electric field start bouncing up and down more regularly, holding the average close to breakdown. By the central limit theorem, Poissonian turns into Gaussian, and by averaging, the noise amplitude drops proportionally. Incidentially, I have a Gaussian Noise Generator from the 60s which uses a pair of 6D4 gas thyratrons (in magnetic field, for some reason). You can imagine that, as gas-filled tubes, they work on exactly the same principle explained above. AFAIK, they are arranged exactly as in your circuit, with a series of amplfiers after (6AU6s mostly.. the 2N3904s of their day). Supposedly, its output is good to 3-4 sigma. http://myweb.msoe.edu/williamstm/Images/Gaussian_Noise1.jpg (1-6) Tim -- Deep Friar: a very philosophical monk. Website: http://webpages.charter.net/dawill/tmoranwms |