******************************************************************************** ** ** E 6 _ C o m b i n a t i o n s _ 2 _ B . t x t ** ******************************************************************************** ** ** FUNCTIONAL DESCRIPTION ** ** This text file contains a concise table of feasible combinations of the ** form 1/X = 1/x1 + 1/x2, where x1 and x2 are two values taken from the E6 ** series of preferred values and X is the resulting value of this combina- ** tion. The different E series of preferred values are specified in IEC ** Standard 60063. ** ** The E6 series consists of the following six base values: ** ** 100 150 220 330 470 680 ** ** The above type of combinations applies to parallel connections of two ** resistors, parallel connections of two inductors, or series connections of ** two capacitors, respectively. The latter two cases, however, are of minor ** practical importance. Single values are seamlessly included, in which case ** one of the x values is infinite. ** ** In order to limit the potentially infinite number of possible combinations ** to a reasonable amount, combinations where the ratio between the largest ** finite value and the smallest non-zero value would exceed an upper limit ** of 100 are excluded. Such an upper limit corresponds to nominal component ** tolerances in the order of 1% for the dominant values of a combination, ** should be sufficient for most cases of interest. Also, equivalent permu- ** tations are eliminated by ensuring that x1 <= x2. ** ** The table of feasible combinations below is sorted in ascending order of ** resulting values X, and these values are normalised such that they gener- ** ally fall into the base decade from 100 to 1000, thus 100 <= X < 1000. Of ** course, all table entries can be arbitrarily scaled up or down by factors ** of 10, 100, 1000, and so forth. ** ** This is best illustrated with resistors: ** ** ____ r1 ** +----|____|----+ ** o-----+ ____ r2 +-----o ** +----|____|----+ ** ** r1..r2 = resistance values of the used resistors ** R = total resistance of the resistor combination ** M = maximum allowed ratio of resistance values ** ** M = 100 ** 1/R = 1/r1 + 1/r2 ** 100 <= R < 1000 ** r1 <= r2 ** r2 may be infinite (one resistor) ** 1 <= r2/r1 <= M ; if r2 < inf ** ** All in all, the resulting table of feasible combinations contains a total ** of 84 entries, with 84 distinct values. The maximum relative difference ** between adjacent values is 10.0 percent. ** ** The normalised relative uncertainty (NRU) value, which is also given for ** each combination, is calculated via the common error propagation formula ** for independent variables and gives an estimate for the mean relative ** uncertainty of the resulting value X of this combination in relation to ** the mean relative uncertainties of its x values. This estimate is valid ** under the simplifying assumption that the x values are statistically inde- ** pendent and normally distributed about their nominal values and that they ** have identical relative uncertainties, in which case 0.707 <= NRU <= 1. ** ** This means that the relative dispersion of the resulting value X of a ** combination is somewhat reduced compared to the relative dispersions of ** its individual x values. The worst-case behaviour is not improved, though. ** Note, however, that the above independence assumption may already be vio- ** lated when a combination is made up of components from the same production ** batch, just to name one potential caveat. ** ** One last note on the file format: This is a Unix plain text file that uses ** single line-feed (LF) characters as line terminators and assumes a fixed ** tab spacing of eight characters. Thus, a monospaced font and proper tab ** settings are recommended for best readability; and on Windows, it may be ** necessary, too, to replace LF with CR LF. ** ******************************************************************************** ** ** VERSION HISTORY ** ** Author: Gert Willmann, Stuttgart, Germany ** ** Version: 1.0, 30-Jul-2017 (7792 bytes) ** ** Copyright: (C) 2017 Gert Willmann ** ** This file is free software; it can be redistributed and/or modified under ** the terms of the GNU Lesser General Public License (LGPL) as published by ** the Free Software Foundation, either Version 3 of the License or (at your ** option) any later version. ** ** This file is distributed in the hope that it will be useful, but without ** any warranty; without even the implied warranty of merchantability or fit- ** ness for a particular purpose. See the GNU Lesser General Public License ** for more details. ** ** A copy of the GNU Lesser General Public License should have come along ** with this file. If not, see . ** ******************************************************************************** Table of Combinations: ====================== -------------------------------------------------------- Line X x1 x2 NRU Series -------------------------------------------------------- 1 100 100 - 1 E3 2 103.125 150 330 0.755 E6 3 110 220 220 0.707 E3 4 113.70967742 150 470 0.796 E6 5 122.89156627 150 680 0.839 E6 6 130.43478261 150 1k 0.879 E6 7 132 220 330 0.721 E6 8 136.36363636 150 1.5k 0.914 E6 9 140.42553191 150 2.2k 0.938 E6 10 143.47826087 150 3.3k 0.958 E6 11 145.36082474 150 4.7k 0.97 E6 12 146.76258993 150 6.8k 0.979 E6 13 147.78325123 150 10k 0.985 E6 14 148.51485149 150 15k 0.99 E6 15 149.85507246 220 470 0.752 E3 16 150 150 - 1 E6 17 165 330 330 0.707 E6 18 166.22222222 220 680 0.794 E6 19 180.32786885 220 1k 0.839 E3 20 191.86046512 220 1.5k 0.881 E6 21 193.875 330 470 0.718 E6 22 200 220 2.2k 0.914 E3 23 206.25 220 3.3k 0.94 E6 24 210.16260163 220 4.7k 0.956 E3 25 213.10541311 220 6.8k 0.969 E6 26 215.26418787 220 10k 0.979 E3 27 216.81997372 220 15k 0.986 E6 28 217.82178218 220 22k 0.99 E3 29 220 220 - 1 E3 30 222.17821782 330 680 0.748 E6 31 235 470 470 0.707 E3 32 248.12030075 330 1k 0.792 E6 33 270.49180328 330 1.5k 0.839 E6 34 277.91304348 470 680 0.719 E6 35 286.95652174 330 2.2k 0.879 E6 36 300 330 3.3k 0.914 E6 37 308.3499006 330 4.7k 0.937 E6 38 314.72650771 330 6.8k 0.955 E6 39 319.45788964 330 10k 0.969 E6 40 319.72789116 470 1k 0.752 E3 41 322.8962818 330 15k 0.979 E6 42 325.12315271 330 22k 0.985 E6 43 326.73267327 330 33k 0.99 E6 44 330 330 - 1 E6 45 340 680 680 0.707 E6 46 357.8680203 470 1.5k 0.798 E6 47 387.2659176 470 2.2k 0.843 E3 48 404.76190476 680 1k 0.72 E6 49 411.40583554 470 3.3k 0.884 E6 50 427.27272727 470 4.7k 0.914 E3 51 439.61485557 470 6.8k 0.938 E6 52 448.90162369 470 10k 0.956 E3 53 455.72074984 470 15k 0.97 E6 54 460.16911437 470 22k 0.979 E3 55 463.40005976 470 33k 0.986 E6 56 465.34653465 470 47k 0.99 E3 57 467.88990826 680 1.5k 0.755 E6 58 470 470 - 1 E3 59 500 1k 1k 0.707 E3 60 519.44444444 680 2.2k 0.8 E6 61 563.81909548 680 3.3k 0.847 E6 62 594.05204461 680 4.7k 0.883 E6 63 600 1k 1.5k 0.721 E6 64 618.18181818 680 6.8k 0.914 E6 65 636.70411985 680 10k 0.938 E6 66 650.51020408 680 15k 0.958 E6 67 659.61199295 680 22k 0.97 E6 68 666.27078385 680 33k 0.98 E6 69 670.30201342 680 47k 0.986 E6 70 673.26732673 680 68k 0.99 E6 71 680 680 - 1 E6 72 687.5 1k 2.2k 0.755 E3 73 750 1.5k 1.5k 0.707 E6 74 767.44186047 1k 3.3k 0.802 E6 75 824.56140351 1k 4.7k 0.843 E3 76 871.79487179 1k 6.8k 0.881 E6 77 891.89189189 1.5k 2.2k 0.72 E6 78 909.09090909 1k 10k 0.914 E3 79 937.5 1k 15k 0.94 E6 80 956.52173913 1k 22k 0.958 E3 81 970.58823529 1k 33k 0.971 E6 82 979.16666667 1k 47k 0.979 E3 83 985.50724638 1k 68k 0.986 E6 84 990.0990099 1k 100k 0.99 E3 --------------------------------------------------------