Yes, thank you.
'Balanced' is better used to define the interface (as in equal impedance on + and - lines).
'Balanced' is better used to define the interface (as in equal impedance on + and - lines).
John, here is another trick: imagine divider 1:10 - 3R (three resistors in series) and R/3 (three paralleled resistors). The precision of divider is greater than precision of individual resistors 😉 - sorry couldn't find source
As long as the distribution of the resistor values is normal. With binning, that may not be the case.
If the series R are all 1% low, and the parallel R are all 1% high, the attenuation is equal to
about 0.102 (2% off), which is the same worst case you'd expect from just two 1% parts.
Statistically it may be better.
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I think that series resistors, in this case, would be best, because we are concerned with the voltage sensitivity of the resistor.
You are thinking of the Hamon divider, in that case all R's are trimmed to measure an equal resistance.
Interesting. Our own Conrad Hoffman discusses it here: How to Build a Hamon Resistor Divider Network
Yes, this is a well known technique - Self also discusses parallel/series of passive storytelling improve accuracy.
Most resistors today are extremely good and the spreads aren't half bad as well - the result of decades of driving yield improvements and applying statistical methods in production.
Separately, I am also seeing very tight spreads on NPO chip resistors - pretty impressive devices.
However, this is not necessarily true under load; therefore, for minimum distortion this is not optimum. For that, you need 11 resistors in a 1:10 divider, so that all error terms under load equal out.
Only in the typical case; the worst case remains the same.
As another poster has remarked, if all terms in the numerator are off by +1% and all terms in the denominator are off by -1% then the ratio will be off by a wee tad bit more than 2%.
Once upon a time I saw the output of a programming exercise. It was a Monte Carlo simulation of a voltage divider, where each leg was composed of N resistors in series. Each resistor had a tolerance of ±1%. The program simulated 1E6 different voltage dividers, each of the resistors was drawn from a probability density function corresponding to ±1% tolerance.
Plot 1 was four histograms of voltage divider outputs, plotted on the same graph, for N=1,2,3,4 resistors in series. Resistors were drawn from a uniform probability density function.
Plot 2 was another four histograms of voltage divider output, plotted on the same graph, for N=1,2,3,4. This time the resistors were drawn from a Gaussian (normal) probability density function
Plot 3 was the same thing except the resistors were drawn from a triangular probability density function
Plot 4 used a truncated Gaussian pdf: Gaussian with mean=0 and St.dev = 1%, truncated at ±1%.
The four sets of histograms were not identical, which means: you need to know your resistor manufacturer's probability density function in order to predict the benefits of putting N resistors-with-tolerance in series.
Last time I bought 1-3% caps with 1% resistors for an RIAA the result was +-.1dB out of the box no sorting.
Considering the mix of R's and C's and that a couple of the caps were 3% tolerance I figured this means the manufacturing processes are better than the specs these days.
Bruce Hofer's presentation on super low distortion points to tempco variation superceding voltage coefficients, so power sharing, one way or the other, is to be prioritized.
I certainly haven't, nor expect anyone to have done this at the hobby level, but has anyone actually measured a distribution of 1% resistors? Especially if there are 0.5% and 0.1% series of that resistor as well. I do expect the distribution to be quite tight with some flattening of the distribution peak from binning out the higher precision bins.
In any case, I prefer soldering to measuring resistors, so series/parallel for achieving precision works for me.
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Exactly the opposite for me. Especially when used in a match-required application (current mirror degeneration resistors, folded cascode collector load resistors, etc), I prefer to buy 20 pieces of 1% resistors and hunt down the best matched pair. Part of the fun of DIY for me. I use a Keithley benchtop DMM with 6.5 digits.
The hobby craft ritual is very important. I prefer to mull (grind) and mix my own paints by hand.
I've filed resistors, probably not a good idea....
I don't mean I've filed them away...........well, yes, in a way
I don't mean I've filed them away...........well, yes, in a way
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