As has probably already been covered originally, if the components in the group have a Gaussian distribution, then the improvement in tolerance is root-N. Taking the Self RIAA preamp example, five 1% capacitors in parallel will have a combined tolerance of 0.1 divided by root-5, which is where the 0.48% comes from. BTW, this was not a measured "result", as implied in #27 - if you read the write-up of the pre-amp, the maths is explained fully. Self discusses the same thing in many of his works. Agree that the quote cited in #28 is out of character - I wonder if that's been clarified in the second edition?
It's quite reasonable to expect component like resistors to come off the production line with a decent Gaussian distribution - this is well documented in many text books - and that's why I take issue with Maplin's comments, which were clearly written by someone who didn't know about this because they simply made a glib statement with no hint that they knew the reality might be a little bit different. Yes, of course you could argue that they are correct in the extreme case, but in the real world, that rarely happens. As I say, it's the lack of knowledge that's the problem.
The joy of this is the ability to end up with something better than you can measure. Suppose you can measure resistors with 0.5% accuracy - not unrealistic for an affordable DMM - then ten pre-selected 10k resistors in parallel can give you a 1k resistor with a 0.16% tolerance. You can pay a lot of money for resistors with that sort of tolerance
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Originally Posted by Julesomega
Following the "Statistical DVM Reference" webpage shows the latter sophistications progressively being added while the statistical basis is being dropped
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I'll be honest: I'm confused by this comment. The very first diagram shows the 5 references and selector switch, and everything builds on that - the only places where there's no selector switch shown on a diagram is where it is omitted for clarity. If there are places where that is not immediately obvious, please let me know and I'll amend the text accordingly. One can see from the final schematic that the core idea is present throughout.
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Originally Posted by Julesomega
and we end up with one reference device being used for the 2.5V o-p, 2 for 5V, and it is not til you select 12.5V that you benefit from the full 0.48% accuracy from the 1% devices
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Yes, of course it's only "statistical" when using anything other than 2.5V. But as I selected the voltage sources, that's not an issue. You wouldn't want to put this into mass-production, but as a project for a time-rich hobbyist, that's fine.
Quote:
Originally Posted by Julesomega
Would it perhaps be more comprehensive to derive all outputs from the 12.5V by using resistive dividers made of series or parallel combinations of equal values?
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First of all you've got to get a whole load of precision resistors. Or select them and hope their value doesn't change when you solder them.
(You'll note the trimmer for the divide-by-10 option. I really didn't want to include that at first, so spent ages pre-selecting fixed resistors to do that job. The results were disappointing because they did indeed change their value during soldering.)
Having done that, you've got to buffer the output because there's no way you'd get a sufficiently low source impedance while retaining reasonable battery life. So now we're into the murky world of op-amp specs, plus don't forget the current it draws. Not impossible, of course, but it takes away from the KISS principle of the project.
Another drawback: battery life. You'll note that I'm only supplying current to the number of references required because when there isn't enough battery voltage to cope with 12.5V plus the dropout voltage of the LM317, there's still plenty of life in the cells. If you go with 12.5V followed by a potential divider, then you'll be throwing away perfectly good batteries for no good reason.
However, if the idea appeals, I'd consider using 10V and a high quality 10 turn potentiometer with a dial. In fact, if you haven't already seen it, take a look at my Time Electronics 1030 Microcal write-up - you could get a lot of ideas from that. The LM10 is a handy little IC.
https://www.markhennessy.co.uk/time_...1030_microcal/
OK, that moves away from the "statistical" element of the project, but it's important to realise that the whole thing was just a bit of fun. The idea came to me, I did some initial experimentation, and decided it was worth putting together and doing a bit of a write-up that might inspire others. That's all. It has proved to be very handy, and it's one of my more frequently used bits of gear. For example, I use it to test LEDs, as it's a 2.5mA current source.
I hope that helps,
Mark