Q: RLC Decade Formula?

[Mark Jones]

In electronics, the values of resistors/capacitors/inductors are generally grouped into logarithmic decade values. Since it is impractical to produce components of exact values (and values change with temperature), a range or "band" is used, usually of 20%, 10%, 5%, 1%, or 0.5% tolerance. This concept is illustrated in the following link:

http://www.logwell.com/tech/components/resistor_values.html

Here, the "E6" column shows the six standard logarithmic values for 20% precision across one decade. For increasing precision, the number of subdivisions simply doubles, resulting in 10%, 5%, 2%, 1%, and 0.5% values (E12/24/48/96/192.)

My question is this: Are the "standard" values calculatable? It would make much more sense to calculate these values at program start-up or on-demand, rather than statically include hundreds of values as REAL4s or packed DWs or similar.

The following link shows a formula for calculating the decade values, however its output does not match the "standard" decade values exactly!

http://www.rfcafe.com/references/electrical/resistor-values.htm

In fact, if you look closely enough, the red line on that graph is not entirely straight. I created an Excel spreadsheet to test this formula against the standard 20% decade values (x100 multiplier), and arrived at this:

Formula: R = d * 10^i/N
Where d = 100, i = index, and N = 12

Index 0-12...	Standard Decade Value...	Calculated Value...	% Error...
0	100	100.000	0.00%
1	120	121.153	0.96%
2	150	146.780	-2.15%
3	180	177.828	-1.21%
4	220	215.443	-2.07%
5	270	261.016	-3.33%
6	330	316.228	-4.17%
7	390	383.119	-1.76%
8	470	464.159	-1.24%
9	560	562.341	0.42%
10	680	681.292	0.19%
11	820	825.404	0.66%
12	1000	1000.000	0.00%

Here, it can be seen that using this formula will not produce the desired values, no matter how it is rounded. Am I stuck entering all these values by hand?

[dedndave]

well - for 10, and 20 percent value tables, there are 12 values to make a decade
notice that they all have only 2 signifigant digits
the step for a decade is
10 ^ (1/12)

0   1.0000  1.0
1   1.2115  1.2
2   1.4678  1.5
3   1.7783  1.8
4   2.1544  2.2
5   2.6101  2.6  adjust  2.7
6   3.1622  3.2  adjust  3.3
7   3.8311  3.8  adjust  3.9
8   4.6415  4.6  adjust  4.7
9   5.6234  5.6
10  6.8129  6.8
11  8.2540  8.3  adjust  8.2
12  10.000  10

now, don't ask me why the 5 values don't jive - lol
but, this is what it is (apparently loosely) based on
these values go back to the stone ages, as far as electronics is concerned (pre WW2)
(probably as near as they could calculate with a slide-rule or abacus - lol)
if you think this is bad, have a look at 1% values

[dedndave]

hi Mark
i have been giving this some thought
i am guessing they chose these values so that they could provide certain voltage ratios
like, a 1K ohm resistor in series with a 330 ohm resistor would give you a 4:1 ratio (1330:330)
it probably has something to do with biasing vacuum tubes with certain resistance ratios
also, old radio sets used batteries to provide "A" (filament), "B" (plate) and sometimes "C" (grid) voltages
the resistor standards may have something to do with the radio working as the batteries run down
if you can understand their thinking, it may help you develop a simplified polynomial
i can find simple polynomials to straighten out the inner values, but the 82 value just gets worse when i do
i also tried breaking the decade into 2, 3, or 4 "sub-decades" - again, the 82 throws it out of whack

it might help to start with the 20% table values
these were, for a long time, the values used for everything
if you can get a polynomial that works with that set, it may be expanded upon to acquire the higher resolution tables
that way, your algorithm logic can follow the history of the component standards, if you get my drift

if you have to use a table, use one decade of the 1% values
that should reduce and round into the other sets nicely
and you can use the same table for everything