******************************************************************************** ** ** E 6 _ C o m b i n a t i o n s _ 2 _ A . t x t ** ******************************************************************************** ** ** FUNCTIONAL DESCRIPTION ** ** This text file contains a concise table of feasible combinations of the ** form X = x1 + x2, where x1 and x2 are two values taken from the E6 series ** of preferred values and X is the resulting value of this combination. 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 series connections of two resis- ** tors, series connections of two inductors, or parallel connections of two ** capacitors, respectively. Single values are seamlessly included, in which ** case one of the x values is zero. ** ** 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, ** which should be sufficient for most cases of interest. Also, equivalent ** permutations 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 ____ r2 ** o-----|____|----|____|-----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 ** R = r1 + r2 ** 100 <= R < 1000 ** r1 >= r2 ** r2 may be zero (one resistor) ** 1 <= r1/r2 <= M ; if r2 > 0 ** ** All in all, the resulting table of feasible combinations contains a total ** of 84 entries. As some values can be realised in different ways, however, ** there are only 80 distinct values. The maximum relative difference between ** adjacent values is 9.0164 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 (7194 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 2 101 68 33 0.748 E6 3 101 100 1 0.99 E3 4 101.5 100 1.5 0.985 E6 5 102.2 100 2.2 0.979 E3 6 103.3 100 3.3 0.969 E6 7 104.7 100 4.7 0.956 E3 8 106.8 100 6.8 0.938 E6 9 110 100 10 0.914 E3 10 115 68 47 0.719 E6 11 115 100 15 0.879 E6 12 122 100 22 0.839 E3 13 133 100 33 0.792 E6 14 136 68 68 0.707 E6 15 147 100 47 0.752 E3 16 150 150 - 1 E6 17 151.5 150 1.5 0.99 E6 18 152.2 150 2.2 0.986 E6 19 153.3 150 3.3 0.979 E6 20 154.7 150 4.7 0.97 E6 21 156.8 150 6.8 0.958 E6 22 160 150 10 0.94 E6 23 165 150 15 0.914 E6 24 168 100 68 0.72 E6 25 172 150 22 0.881 E6 26 183 150 33 0.839 E6 27 197 150 47 0.798 E6 28 200 100 100 0.707 E3 29 218 150 68 0.755 E6 30 220 220 - 1 E3 31 222.2 220 2.2 0.99 E3 32 223.3 220 3.3 0.985 E6 33 224.7 220 4.7 0.979 E3 34 226.8 220 6.8 0.97 E6 35 230 220 10 0.958 E3 36 235 220 15 0.938 E6 37 242 220 22 0.914 E3 38 250 150 100 0.721 E6 39 253 220 33 0.879 E6 40 267 220 47 0.843 E3 41 288 220 68 0.8 E6 42 300 150 150 0.707 E6 43 320 220 100 0.755 E3 44 330 330 - 1 E6 45 333.3 330 3.3 0.99 E6 46 334.7 330 4.7 0.986 E6 47 336.8 330 6.8 0.98 E6 48 340 330 10 0.971 E6 49 345 330 15 0.958 E6 50 352 330 22 0.94 E6 51 363 330 33 0.914 E6 52 370 220 150 0.72 E6 53 377 330 47 0.884 E6 54 398 330 68 0.847 E6 55 430 330 100 0.802 E6 56 440 220 220 0.707 E3 57 470 470 - 1 E3 58 474.7 470 4.7 0.99 E3 59 476.8 470 6.8 0.986 E6 60 480 330 150 0.755 E6 61 480 470 10 0.979 E3 62 485 470 15 0.97 E6 63 492 470 22 0.956 E3 64 503 470 33 0.937 E6 65 517 470 47 0.914 E3 66 538 470 68 0.883 E6 67 550 330 220 0.721 E6 68 570 470 100 0.843 E3 69 620 470 150 0.796 E6 70 660 330 330 0.707 E6 71 680 680 - 1 E6 72 686.8 680 6.8 0.99 E6 73 690 470 220 0.752 E3 74 690 680 10 0.986 E6 75 695 680 15 0.979 E6 76 702 680 22 0.969 E6 77 713 680 33 0.955 E6 78 727 680 47 0.938 E6 79 748 680 68 0.914 E6 80 780 680 100 0.881 E6 81 800 470 330 0.718 E6 82 830 680 150 0.839 E6 83 900 680 220 0.794 E6 84 940 470 470 0.707 E3 --------------------------------------------------------