Why Do Electronic Components Have Such Odd Values?

WBahn

Joined Mar 31, 2012
25,759
One thing I (and several others I know) have tried to track down is exactly how a few of the specific preferred values were chosen, because they aren't the rounded values that adhere most closely to the geometric progression. I've got lots of speculation about it, from bending to industry pressure to use a close value that was already extremely common, to trying to minimize possible confusion based on the color bands, to a handful of others. But who knows, since most standards-setting processes have a lot in common with sausage making, only bloodier. Unfortunately, I've never found anything that even discusses it, let alone references contemporary sources. I suspect that this is something that is simply lost to history.
 

crutschow

Joined Mar 14, 2008
24,959
I know that the E96 ( 1%) values are a geometric (log) progression because I wrote a simple program for my calculator that generated the closest 1% value to any value I input, and it used an exponential function (answer rounded to the closed 3rd digit) to calculate the 1% resistor value.
I suspect the other tolerance values follow a similar progression.

Basically the progression is such that each value's tolerance band is close to the tolerance band of the next value.
Thus for E96 1% it goes 1, 1.02. 1.05. 1.07, etc.
The tolerance band for these is (approximately) .99-1.01, 1.01-1.03, 1.04-1.06, 1.06-1.08, etc.
 
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crutschow

Joined Mar 14, 2008
24,959
Why is 21.5 in red?
That is not a mismatch as it's a standard 1% value.
Its also the value from the formula R = 10 * 10^i/96 (rounded to one decimal places).

What's the other supposed E96 mismatch you found?
 
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dl324

Joined Mar 30, 2015
10,737
Why is 21.5 in red?
That is not a mismatch as it's a standard 1% value.
It should be 21.6. To two decimal places, that cell is 21.54.

EDIT: Guess I have to take that back; 21.5 is the correct value. Don't know where I got 21.6. E96 and E48 are exact matches. The rest have discrepancies.
 
There is in fact an error in the E192 series. Using the formula 10^(185/192) we get an exact value of 9.19478686. This should become a 3 digit value of 9.19, but the value found in a table of commercially available E192 resistors is 9.20

Somebody made a slide rule error way back then.
 

shortbus

Joined Sep 30, 2009
7,683
There is in fact an error in the E192 series. Using the formula 10^(185/192) we get an exact value of 9.19478686. This should become a 3 digit value of 9.19, but the value found in a table of commercially available E192 resistors is 9.20

Somebody made a slide rule error way back then.
Not a EE but a die maker/machinist. But the way I was taught to round up machining dimensions, the 9.19478686 would be rounded up to 9.20. In machining dimensions you go back a few places, so 9.19478686 the ''78686" would cause the "4" to be a "5", and then the "5" would cause the "19" to become a "20". Guess I don't understand why it would be different in the EE world. :) Or maybe I was taught wrong? :(
 

shortbus

Joined Sep 30, 2009
7,683
It's an EE thing.

For E192, E96, and E48 we use 3 digits and a multiplier. For lower precision resistors, we use 2 digits and a multiplier.
I guess. This whole wide tolerance of values thing EE is still hard for me to get over. Metal isn't so forgiving, you can't force a 20% oversize part into most things, even with a big hammer. :D
 
Not a EE but a die maker/machinist. But the way I was taught to round up machining dimensions, the 9.19478686 would be rounded up to 9.20. In machining dimensions you go back a few places, so 9.19478686 the ''78686" would cause the "4" to be a "5", and then the "5" would cause the "19" to become a "20". Guess I don't understand why it would be different in the EE world. :) Or maybe I was taught wrong? :(

Have a look at the absolute value of the difference between the exact value and each of the two approximations:

Abs( 9.19478686 - 9.19) = .00478686

Abs( 9.19478686 - 9.20) = .00521314

The numerical "distance" from 9.19 to the true value is smaller.

One of the things to be learned in numerical analysis is that rounding in multiple steps can give a different result than doing it in one step.
 

WBahn

Joined Mar 31, 2012
25,759
Not a EE but a die maker/machinist. But the way I was taught to round up machining dimensions, the 9.19478686 would be rounded up to 9.20.
I would imagine that in mechanical assemblies it would be common to decide whether a given dimension should be rounded up or rounded down based on the particular goal and I would expect those considerations to require dimensions be rounded up most of the time. If you are designing a shear pin to have a safety factor of two and the needed diameter comes out to be 9.014 inches and your final part dimension is to be dimensioned to a tenth of an inch, then you would dimension it as 9.1 inches because 9.0 inches doesn't have the required safety factor. The same thing CAN happen in circuit design, but the natural tolerances of the parts generally swamps this so that, when needed, you use a larger margin and then round normally. It's also usually very application specific whether a value should be rounded up or rounded down to achieve a particular constraint, so having the component standards adopt one or the other makes little sense.

In machining dimensions you go back a few places, so 9.19478686 the ''78686" would cause the "4" to be a "5", and then the "5" would cause the "19" to become a "20". Guess I don't understand why it would be different in the EE world. :) Or maybe I was taught wrong? :(
That really doesn't make any sense. Which value is closer to 9.19478686, 9.19 or 9.20? If your intent is to choose the dimension that is closest to the ideal one, then you would choose 9.19.

According to your approach, you would round 9.19444445 upward.
 

shortbus

Joined Sep 30, 2009
7,683
According to your approach, you would round 9.19444445 upward.
No because the number of "4's" in that number don't approach the higher numbers in the original example. It's not a statisical thing at all. But you guy's also come from a different back round than I do.
 

WBahn

Joined Mar 31, 2012
25,759
No because the number of "4's" in that number don't approach the higher numbers in the original example. It's not a statisical thing at all. But you guy's also come from a different back round than I do.
Where's any statistics?

So when DO the number of 4's approach a high enough number to justify rounding 0.4xxx up to 1.0 ?
 

GopherT

Joined Nov 23, 2012
8,012
Not a EE but a die maker/machinist. But the way I was taught to round up machining dimensions, the 9.19478686 would be rounded up to 9.20. In machining dimensions you go back a few places, so 9.19478686 the ''78686" would cause the "4" to be a "5", and then the "5" would cause the "19" to become a "20". Guess I don't understand why it would be different in the EE world. :) Or maybe I was taught wrong? :(

@WBahn
The value 9.19478686 would not have existed in any reasonable engineers notebook back when resistor values were set. The log tables would usually have been 4 digits, or, 9.195 - especially if they were only looking for 1% accuracy.

Now, round that one = 9.20
 
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