More accuracy from multiple resistors in series or parallel?
What happens to the overall accuracy of a resistor if I implement it as multiple resistors in series or parallel? For example, can I get better than 2 kΩ 5% by putting two 1 kΩ 5% resistors in series? Or are two 4 kΩ 5% resistors in parallel better?
Is there some way to use multiple resistors to get tighter tolerance than any of the individual resistors?
2 answers
The worst case won't get any better, whether series, parallel, or some other combination. The result of two 1 kΩ ±5% resistors in series is a 2 kΩ ±5% resistor.
The probability that the result is closer to the middle gets better with multiple resistors, but only if each resistor is random within its range, which includes that it is independent of the others. This is not the case if they are from the same reel, or possibly even from the same manufacturer within some time window.
The manufacturer's selection process may also make the error non-random. For example, if they make resistors with a wide variance, then pick the ones that fall within 1% and sell them as 1% parts, then sell the remaining ones as 5% parts, the 5% parts will have a double-hump distribution with no values being within 1%.
Because you can't know the error distribution within the worst case error window, and because even if you did, the worst case stays the same, doing what you are suggesting is not useful to electronic design.
That depends on whether you are just building something for yourself, say a prototype, or if you are designing a product for mass distribution. In the later case, you are subject to probability laws, and the answer of Olin is just fine.
In the former case, though, you may improve the performances by simply trying different resistor combinations (usually two or more equal resistors in series), and measuring the resistance with a Ohm meter. I did that several times in my lab to improve the accuracy of the resistance.
Doing so, it is usually better to try combination of resistors from different manufacturers, because resistors from the same manufacturer (or worse, from the same package) often possess the same bias.
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