Re: Prefered resistor range

From: Larry Brasfield (donotspam_larry_brasfield_at_hotmail.com)
Date: 03/15/05 

Date: Tue, 15 Mar 2005 10:32:43 -0800

"John Woodgate" <jmw@jmwa.demon.contraspam.yuk> wrote in
 message news:uYUewiBywqNCFw+L@jmwa.demon.co.uk...
>I read in sci.electronics.design that Larry Brasfield <donotspam_larry_b
> rasfield@hotmail.com> wrote (in <G7xZd.64$oD6.990@news.uswest.net>)
> about 'Prefered resistor range', on Tue, 15 Mar 2005:
>
>>Can you reconsider that assertion? I cannot make sense of it, being
>>stuck in the following thought pattern: If there are 96 distinct values
>>per decade, then for each 96 value steps, a whole power of ten is
>>traversed. Expressed mathematically, (and ignoring the rounding
>>necessary to get standard values), the E96 set can be obtained as 10^(N
>>* log10(10) / 96) == 10^(N/96) for the 96 integer values of N from 0 to
>>95. This corresponds to a multiplicative interval equal to the 96th
>>root of 10, not the 97 root.
>
> My understanding is that the values in these series don't include the
> first value of the next decade. So the E6 series has 7 values (which
> actually don't quite match the calculated values for reasons lost in the
> mists of time) : 1, 1.5, 2.2, 3.3, 4.7, 6.8 and 8.2, involving 6
> multiplications by the *7th* root of ten; the 7th multiplication would
> give 10, which is the first value in the next decade.
>
> However, I don't have the 'preferred numbers' standard, so I won't
> assert that I am correct.

I should maybe leave this at that point, but I am responding also
to some points you make elsewhere in this thread.

>>In addition to the problem outlined above, what you say is contrary to
>>the algorithm that I successfully applied to devise the program I posted
>>earlier on this thread. I tested that quite a bit, so I am quite sure
>>that the decade should be split logarithmically into 96 equal steps
>>(sans rounding). In my testing, I compared results with the table
>>published by several resistor manufacturers.
>
> Well, it depends on how your algorithm works, and I can't read PERL.

You don't need to study my code to understand my point,
which is that by splitting the decade logarithmically into 96
intervals, the correct 96 values are obtained. I conveyed
this experience to underscore the idea that the reasoning I
laid out should be examined carefully, as it is likely correct.

> The
> 96th root is 1.024275221... To four significant figures, the two roots
> are 1.024... So if you preserve only those four figures and calculate
> the values by successive multiplications, you will get the same answers
> whether you use the 96th root or the 97th root.

When I evaluate 1.024^96, I get 9.7453 on my HP32S. (And
this agrees with another calculator I checked.) For the E96 series
starting with 1, the 96th and last member is 9.76. So your method
requires one more step (times 1.024) to reach the next decade. It
produces 97 values per decade, (assuming we round off to 3 digits
at each closest approach to whole powers of 10), whereas all the
tables I've seen have only 96 values per decade.

Maybe there is some trick rule for rounding, dropping accumulated
"erroneous" residue at special places, or other machinations, that
will convert what would otherwise be 97 intervals into the 96 that
are required to duplicate the standard values. I do not doubt your
ability to devise such a rule. But I would hope you could see, if
not acknowledge, the preferable simplicity of this rule:
      for (N = 0 to 95)
            standard_value[n] = round_to_3_digits( 10 ^ (N/96) )

Answering Mr. Phoull's request for "the formula that calculates the
1% 'preferred' range of resitors", absent any authoritive statement
about how somebody long ago derived those tables, we have a
choice: Use the above formula because it is easy and works; or
complete the task of devising or elucidating your formula, which
will be more complicated, amenable to no closed form solution,
and unintuitive; or await or discover some other formula in the
hope that it will be better. I should think it is an easy choice. 

-- 
--Larry Brasfield
email: donotspam_larry_brasfield@hotmail.com
Above views may belong only to me.

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