[HomeBrew] Questions about passive components

[Ron Youvan]

   Richard VA3NDO R. Blackman wrote:

> ** Please do NOT cross-post messages when posting to HOMEBREW **
>
> Hello to group.
> Not much activity these days so I thought a discussion would be fun.
> Question:
>
> why do components have the 'standard' values that the have?
> for example:  resistors have 47 , 470, 4.7K 47K etc,  instead of perhaps
> 48 which is easier math  for 12 volts
> Why does a 1/4 watt resistor have the value 49.9 instead of 50 ohms? (
> just checked digikey)
> Capacitors:  seem to like the numbers 22, 33  or 68 for example.
>
> does this refer back to the old days of high voltage systems?
>
> Happy to hear any ideas

   It's not a matter of ideas.

Although there are several different systems for standardizing preferred 
resistor values, the most common system uses 12 different standard 
values.  the E12 values are:
First Two Colors
Brown – black   10
Brown – red     12
Brown – green   15
Brown – gray    18
Red – red       22
Red - Violet    27
Orange – Orange 33
Orange – white  39
Yellow – violet 47
Green – blue    56
Blue – gray     68
Gray – red      82

These values are standardized values that are designed to provide a
wide range of resistance values. Although not exact, each value is
approximately 1.2 times larger than the previous value.
The E12 standard uses all of the same values as E6, but with 6 more
values mixed in. These 6 additional values are roughly where the E6
values overlap, and now in order to cover the entire range our %-error
is reduced to 10%. Starting again at 10, we have 10, 12, 15, 18, 22,
27, 33, 39, 47, 56, 68, and 82. The math holds true here as well, with
the error values just slightly overlapping.

There are four more E-series as well, namely E24, E48, E96, and E192.
The image above lists all values included in the E6/E12/E24 standards.
With each doubling of values between consecutive powers of 10, there is
an associated halving of the %-error allowance as well. So E24 values
have a +/- %-error of 5%, E48 is set at 2%, and so on. The values
associated with E192 are also available with 0.25% and 0.1% tolerances,
and E24 and E96 are also available with 1% tolerances.

Below is a simple graphical view of how the E12 values relate to one
another. Along the bottom of the graph you will see the first 13 terms
of an ideal geometric sequence as well. (The sequence is given by
y=10^(i/b), where b is the value of the series (e.g. 12) and i is the
term desired (e.g. the 8th term would yield 10^(8/12)=4.64).) Notice
how closely the values are related.

   The tolerance of each value of series slightly overlaps the value 
above and below it.

   See: 
https://blog.digilentinc.com/index.php/why-do-electronic-components-have-such-odd-values/ 


While it is possible to have a 3.3kΩ resistor with 20% tolerance test
out between 2.64kΩ and 3.96kΩ, I would be hesitant to use it. I want
3.3kΩ, so I would tend to use resistors with a higher tolerance,
usually 5%, so I can just reach in my bin and know that I’m reasonably
close. Looking back at the table in the beginning, we see that there
are values of 68 and 75 listed. If I’m looking for a value of 70 (or
some multiple power of 10, like 700), what can I do to achieve it? I
can certainly start testing every 68 valued resistor I can find (75 is
just out of range of 5% tolerance), hoping to find one that is just
right, but just because it says 5%, doesn’t mean it is. That is a
maximum allowance, and my experience has been that the tolerances are
much tighter than that. I could go up to an E96 (681 0r 715) or even
E192 (698!), but resistors with that level of %-error tolerance are not
common and cost more. I just want something simple that I already have
in my bin! The answer is actually quite simple. Just add a 33 and a 47
and call it good. You get your 70 +/- whatever tolerance you want since
33 and 47 are preferred numbers in every E-series. The point is that
any value can be made for any circuit requirement simply by adding
components together. When you throw in the rules for calculating
components in series and parallel, the combinations are endless.
-- 
   Ron  KA4INM - Youvan's corollary:
                 Every action results in unwanted side effects.