Humorous mistake in Douglas Self Active Crossovers book - diyAudio
 Humorous mistake in Douglas Self Active Crossovers book
 User Name Stay logged in? Password
 Home Forums Rules Articles diyAudio Store Gallery Wiki Blogs Register Donations FAQ Calendar Search Today's Posts Mark Forums Read Search

 Analog Line Level Preamplifiers , Passive Pre-amps, Crossovers, etc.

 Please consider donating to help us continue to serve you. Ads on/off / Custom Title / More PMs / More album space / Advanced printing & mass image saving
diyAudio Member

Join Date: May 2011
Location: Silicon Valley
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.
Attached Images
 dself_doac_p344.jpg (69.6 KB, 413 views)

Last edited by Mark Johnson; 7th April 2012 at 10:35 PM. Reason: typo in page number

 7th April 2012, 10:50 PM #2 diyAudio Member     Join Date: May 2002 Location: The great city of Turnhout, BE Blog Entries: 7 I learned something today! Thank you! jan didden __________________ Music is dither to the brain; lets me think below the usual chaos - me Linear Audio Vol 12 is out! Check out my Autoranger and SilentSwitcher on Kickstarter!
 7th April 2012, 11:05 PM #3 Banned   Join Date: Sep 2010 Location: at Home 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.
 7th April 2012, 11:44 PM #4 Speakerholic diyAudio Moderator     Join Date: Jan 2004 Location: Near Vancouver Good one markj. I could have read right past that one and not picked it up. Thanks. __________________ Next stop: Margaritaville Some of Cal's stuff | Cal Weldon Consulting
Account disabled at member's request

Join Date: Oct 2007
Quote:
 Originally Posted by Leon08 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.

diyAudio Member

Join Date: Mar 2011
Location: St Louis, Mo
Quote:
 Originally Posted by gk7 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.

Dale

 8th April 2012, 12:01 PM #7 diyAudio Member   Join Date: Jul 2004 Location: Scottish Borders 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. __________________ regards Andrew T. Sent from my desktop computer using a keyboard
diyAudio Member

Join Date: Dec 2009
Location: Md
Quote:
 Originally Posted by gk7 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.

 8th April 2012, 11:51 PM #9 diyAudio Member   Join Date: Dec 2009 Location: Md I do wonder if worrying about tolerance of 1% resistors matters when we are dealing with transistors and caps.
diyAudio Member

Join Date: Oct 2004
Location: At the sea front, Rotterdam or Curaçao
Quote:
 Originally Posted by transistormarkj Oops!
1.014 ~1.04
Slipe of the Pipe.
__________________
President Dwayne Camacho says you should drink Brawndo : It's got electrolytes

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are Off Pingbacks are Off Refbacks are Off Forum Rules

 Similar Threads Thread Thread Starter Forum Replies Last Post DouglasSelf Analog Line Level 293 21st May 2016 12:33 AM forr Analog Line Level 8 31st December 2010 06:20 PM blmn Solid State 7 22nd July 2009 07:00 PM jackinnj Everything Else 1 13th June 2005 05:19 AM mikee12345 Solid State 8 16th November 2003 02:16 AM

 New To Site? Need Help?

All times are GMT. The time now is 02:15 PM.

vBulletin Optimisation provided by vB Optimise (Pro) - vBulletin Mods & Addons Copyright © 2016 DragonByte Technologies Ltd.