Johnson noise is the same, it just depends on the resistance. Ditto excess noise, it only depends on the applied voltage which is the same for any parallel combination.
And, of course, it's pretty much meaningless at these voltage levels. If one wants to reduce it to zero, a wirewound resistor is the best choice.
Good review: https://dcc.ligo.org/public/0002/T0900200/001/current_noise.pdf
And, of course, it's pretty much meaningless at these voltage levels. If one wants to reduce it to zero, a wirewound resistor is the best choice.
Good review: https://dcc.ligo.org/public/0002/T0900200/001/current_noise.pdf
In short: carbon comp aside, there is damn little you can argue against modern resistors. That anything obeys Ohm's Rule (it should hardly be called a law, most things don't obey it!) at all is quite remarkable, and that resistors do, so well, so precisely and over so many orders of magnitude in voltage, current and frequency, is probably unmatched in electrical engineering, and perhaps in all other engineering disciplines as well. (Well, okay, perhaps astrophysics has us beat with something like the mass of a planet in orbit -- that could be a pretty pure gravitational tone in the nanohertz, and just imagine how little Johnson noise a 10^24 kg "capacitor" will have, even at that frequency! But then, I specified _engineering_, and I don't see no astronomers pulling planets into new orbits, do you? 
)
Tim
)Tim
Oh, a pair of resistors ... to do the work of "one" ... has a lot of utility! It is certainly the cheapest way to get higher-wattage dissipation tolerance, if space and layout is of little concern. Series-connected resistors are also quite a bit more tolerant to over-voltages (which for most amplifiers isn't really a concern). Did I mention "cheaper"? Its usually true: a pair of 1/2W resistors is usually less expensive than a 1W. Oh yes ... there's also increase-in-precision: the variance from stamped-on value tends to average by the number of resistors placed in parallel (or series). The increase in precision beats specially-vetted high-precision resistors any day (at least when manufacturing the things). Its also possible to use DIFFERENT resistors - with different temperature coefficients, to cancel each other's drift. Did that all the time up at LBL. Hmm... and cheaper.
Of course, the most-usual reason of all for using a pair or trio of resistors is to obtain a harder-to-find resistance value with off-the-shelf-in-your-lab candidates. That too saves money. And time. And frustration when the wrong part arrives.
GoatGuy
Of course, the most-usual reason of all for using a pair or trio of resistors is to obtain a harder-to-find resistance value with off-the-shelf-in-your-lab candidates. That too saves money. And time. And frustration when the wrong part arrives.
GoatGuy
Ah, but it can be very important for consistency rather than accuracy of stated value, for instance in push/pull or balanced circuits. That's why the Jensen discrete op amp uses an integrated circuit with massively paralleled transistors...the resulting characteristics are statistically averaged and achieves precision consistency so any two production items are perfectly matched. In theory...
Just been doing a bit of maths, combining normal distributions with the paralleling resistor formula.
I make it two 1% sd paralleled resistors of equal value become a 1.6% sd resistor, so paralleling is bad, not good. The error gets smaller, but not by as much as the resistance gets smaller, so comparatively the error is bigger.
However, combining series resistors does improve things. Two 1% resistors become a 0.7% resistor.
Of course I could have royally messed up here.
I make it two 1% sd paralleled resistors of equal value become a 1.6% sd resistor, so paralleling is bad, not good. The error gets smaller, but not by as much as the resistance gets smaller, so comparatively the error is bigger.
However, combining series resistors does improve things. Two 1% resistors become a 0.7% resistor.
Of course I could have royally messed up here.
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Massively parallel transistors are almost always for low noise, not consistency. BJTs are very consistent in following the Ebers-Moll exponential model.
Paralleling resistors should have the same effect on error as putting them in series, as you are just adding the conductances instead of the resistances.
Paralleling resistors should have the same effect on error as putting them in series, as you are just adding the conductances instead of the resistances.
errors in conductance don't have a linear relationship with errors in resistance. for example a +/- 10% tolerance in resistance becomes (roughly) a +11%/-9% error in conductance
for adding, multiplying and dividing standard deviations see.
http://www.cartage.org.lb/en/themes...s/AdditionSubtraction/AdditionSubtraction.htm
Multiplication and Division of Values with Standard Deviation
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10% was just an example.
CLT is for the arithmetic mean of many samples, and so works for their sum too, which is why it works for series resistors, hence the 1/sqrt(2) in my first post on this, sd will reduced by a factor of 1/sqrt
for n similar resistors.Paralleling resistors is related to the harmonic mean. I am not convinced it gives a similar result to the CLT. Though I confess I did the numbers when I was very tired.
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