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Q&A More accuracy from multiple resistors in series or parallel?

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 ...

posted 3y ago by Olin Lathrop‭ · edited 3y ago by Olin Lathrop‭

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#2: Post edited by

Olin Lathrop‭ · 2020-10-21T21:20:20Z (over 3 years ago)

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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. If you~~
~~specify 5% resistors, then the design must work correctly with any~~
~~resistance within the ±5% range.~~

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.

#1: Initial revision by

Olin Lathrop‭ · 2020-10-21T21:16:44Z (over 3 years ago)

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<p>The worst case won't get any better, whether series, parallel, or some
other combination.  The result of two 1 k&Omega; &plusmn;5% resistors in
series is a 2 k&Omega; &plusmn;5% resistor.

<p>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.

<p>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%.

<p>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. If you
specify 5% resistors, then the design must work correctly with any
resistance within the &plusmn;5% range.

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