Humorous mistake in Douglas Self Active Crossovers book - diyAudio
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Old 7th April 2012, 09:35 PM   #1
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Default Humorous mistake in Douglas Self Active Crossovers book

Found on page 344:
Quote:
You may object that putting four 1% resistors in series means that the worst-case errors can be four times as great. This is obviously true -- if all the components are 1% low, or 1% high, the total error will be 4%.
Oops! The total error will be, at most, 1%.

Suppose we want a 400 ohm resistance. If we put four (100 ohm, 1%) resistors in series, the maximum possible series resistance is (101+101+101+101) = 404 ohms. The error is ((404 - 400) / 400) = +0.01 = +1%. Likewise the minimum possible series resistance is (99+99+99+99) = 396 ohms, for an error of -1%. I am tempted to write "obviously!" but that would be unkind.
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Last edited by Mark Johnson; 7th April 2012 at 09:35 PM. Reason: typo in page number
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Old 7th April 2012, 09:50 PM   #2
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Old 7th April 2012, 10:05 PM   #3
Leon08 is offline Leon08  Germany
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But he mentioned that probability of this occurring is very, very small. This means that he himself does not believe that it can actually happen.
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Old 7th April 2012, 10:44 PM   #4
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Good one markj. I could have read right past that one and not picked it up.
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Old 8th April 2012, 09:10 AM   #5
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Originally Posted by Leon08 View Post
But he mentioned that probability of this occurring is very, very small. This means that he himself does not believe that it can actually happen.
Yes, the probability that all parts error in the same direction is very small. In fact you get a smaller error in percent for combined parts in most cases.
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Old 8th April 2012, 09:47 AM   #6
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Quote:
Originally Posted by gk7 View Post
Yes, the probability that all parts error in the same direction is very small. In fact you get a smaller error in percent for combined parts in most cases.
That is true if the value errors are truly uncorrelated from part to part, and uniformly distributed across the tolerance window. In some situations that's probably a good assumption.

But if all 4 parts come from the same production batch . . .
  • Produced at the same time under the same ambient temperature, humidity, atmospheric pressure, etc
  • From the same batch of raw materials, with the same level of impurities
  • On the same machine, with the same degree of wear, misalignment, calibration errors, etc
. . . then I would expect the 4 parts are likely to have correlated tolerance errors, and add all in the same direction. The 4 parts may, in fact, be much more closely matched in value (whether that value is high or low, positive or negative, in the tolerance window) than you would expect from selecting 4 parts "at random" from a group with variations uniformly distributed across the tolerance window.


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Old 8th April 2012, 11:01 AM   #7
AndrewT is online now AndrewT  Scotland
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Self discusses this issue of increasing accuracy with increased numbers of parts.

He also gives some space to selecting the multiple parts to give a guaranteed tolerance that is considerably better than the basic component tolerance.
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Old 8th April 2012, 10:50 PM   #8
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Quote:
Originally Posted by gk7 View Post
Yes, the probability that all parts error in the same direction is very small. In fact you get a smaller error in percent for combined parts in most cases.
Actually, it is more likely they are in the same direction if they were made at the same time under the same process. That is the holy grail of manufacturing, consistency. Still, pretty big slip. We do need to always give an author a bit of slack sometimes. These are not reviewed academic papers, but a ton of work.
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Old 8th April 2012, 10:51 PM   #9
tvrgeek is offline tvrgeek  United States
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I do wonder if worrying about tolerance of 1% resistors matters when we are dealing with transistors and caps.
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Old 8th April 2012, 11:30 PM   #10
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Quote:
Originally Posted by transistormarkj View Post
Oops!
1.014 ~1.04
Slipe of the Pipe.
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