******************************************************************************** ** ** E 1 2 _ 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 E12 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 E12 series consists of the following 12 base values: ** ** 100 120 150 180 220 270 330 390 470 560 680 820 ** ** 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 312 entries. As some values can be realised in different ways, however, ** there are only 269 distinct values. The maximum relative difference be- ** tween adjacent values is 3.5211 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 (13283 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 82 18 0.84 E12 2 100 100 - 1 E3 3 101 68 33 0.748 E6 4 101 100 1 0.99 E3 5 101.2 100 1.2 0.988 E12 6 101.5 100 1.5 0.985 E6 7 101.8 100 1.8 0.982 E12 8 102.2 100 2.2 0.979 E3 9 102.7 100 2.7 0.974 E12 10 103 56 47 0.71 E12 11 103.3 100 3.3 0.969 E6 12 103.9 100 3.9 0.963 E12 13 104 82 22 0.816 E12 14 104.7 100 4.7 0.956 E3 15 105.6 100 5.6 0.948 E12 16 106.8 100 6.8 0.938 E6 17 107 68 39 0.733 E12 18 108.2 100 8.2 0.927 E12 19 109 82 27 0.792 E12 20 110 100 10 0.914 E3 21 112 56 56 0.707 E12 22 112 100 12 0.899 E12 23 115 68 47 0.719 E6 24 115 82 33 0.769 E12 25 115 100 15 0.879 E6 26 118 100 18 0.861 E12 27 120 120 - 1 E12 28 121 82 39 0.75 E12 29 121.2 120 1.2 0.99 E12 30 121.5 120 1.5 0.988 E12 31 121.8 120 1.8 0.985 E12 32 122 100 22 0.839 E3 33 122.2 120 2.2 0.982 E12 34 122.7 120 2.7 0.978 E12 35 123.3 120 3.3 0.974 E12 36 123.9 120 3.9 0.969 E12 37 124 68 56 0.71 E12 38 124.7 120 4.7 0.963 E12 39 125.6 120 5.6 0.956 E12 40 126.8 120 6.8 0.948 E12 41 127 100 27 0.816 E12 42 128.2 120 8.2 0.938 E12 43 129 82 47 0.733 E12 44 130 120 10 0.926 E12 45 132 120 12 0.914 E12 46 133 100 33 0.792 E6 47 135 120 15 0.896 E12 48 136 68 68 0.707 E6 49 138 82 56 0.72 E12 50 138 120 18 0.879 E12 51 139 100 39 0.772 E12 52 142 120 22 0.859 E12 53 147 100 47 0.752 E3 54 147 120 27 0.837 E12 55 150 82 68 0.71 E12 56 150 150 - 1 E6 57 151.5 150 1.5 0.99 E6 58 151.8 150 1.8 0.988 E12 59 152.2 150 2.2 0.986 E6 60 152.7 150 2.7 0.982 E12 61 153 120 33 0.813 E12 62 153.3 150 3.3 0.979 E6 63 153.9 150 3.9 0.975 E12 64 154.7 150 4.7 0.97 E6 65 155.6 150 5.6 0.965 E12 66 156 100 56 0.735 E12 67 156.8 150 6.8 0.958 E6 68 158.2 150 8.2 0.95 E12 69 159 120 39 0.794 E12 70 160 150 10 0.94 E6 71 162 150 12 0.929 E12 72 164 82 82 0.707 E12 73 165 150 15 0.914 E6 74 167 120 47 0.772 E12 75 168 100 68 0.72 E6 76 168 150 18 0.899 E12 77 172 150 22 0.881 E6 78 176 120 56 0.752 E12 79 177 150 27 0.861 E12 80 180 180 - 1 E12 81 181.8 180 1.8 0.99 E12 82 182 100 82 0.711 E12 83 182.2 180 2.2 0.988 E12 84 182.7 180 2.7 0.985 E12 85 183 150 33 0.839 E6 86 183.3 180 3.3 0.982 E12 87 183.9 180 3.9 0.979 E12 88 184.7 180 4.7 0.975 E12 89 185.6 180 5.6 0.97 E12 90 186.8 180 6.8 0.964 E12 91 188 120 68 0.734 E12 92 188.2 180 8.2 0.957 E12 93 189 150 39 0.82 E12 94 190 180 10 0.949 E12 95 192 180 12 0.94 E12 96 195 180 15 0.926 E12 97 197 150 47 0.798 E6 98 198 180 18 0.914 E12 99 200 100 100 0.707 E3 100 202 120 82 0.72 E12 101 202 180 22 0.898 E12 102 206 150 56 0.777 E12 103 207 180 27 0.879 E12 104 213 180 33 0.859 E12 105 218 150 68 0.755 E6 106 219 180 39 0.841 E12 107 220 120 100 0.71 E12 108 220 220 - 1 E3 109 222.2 220 2.2 0.99 E3 110 222.7 220 2.7 0.988 E12 111 223.3 220 3.3 0.985 E6 112 223.9 220 3.9 0.983 E12 113 224.7 220 4.7 0.979 E3 114 225.6 220 5.6 0.975 E12 115 226.8 220 6.8 0.97 E6 116 227 180 47 0.82 E12 117 228.2 220 8.2 0.965 E12 118 230 220 10 0.958 E3 119 232 150 82 0.737 E12 120 232 220 12 0.95 E12 121 235 220 15 0.938 E6 122 236 180 56 0.799 E12 123 238 220 18 0.927 E12 124 240 120 120 0.707 E12 125 242 220 22 0.914 E3 126 247 220 27 0.897 E12 127 248 180 68 0.776 E12 128 250 150 100 0.721 E6 129 253 220 33 0.879 E6 130 259 220 39 0.863 E12 131 262 180 82 0.755 E12 132 267 220 47 0.843 E3 133 270 150 120 0.711 E12 134 270 270 - 1 E12 135 272.7 270 2.7 0.99 E12 136 273.3 270 3.3 0.988 E12 137 273.9 270 3.9 0.986 E12 138 274.7 270 4.7 0.983 E12 139 275.6 270 5.6 0.98 E12 140 276 220 56 0.823 E12 141 276.8 270 6.8 0.976 E12 142 278.2 270 8.2 0.971 E12 143 280 180 100 0.735 E12 144 280 270 10 0.965 E12 145 282 270 12 0.958 E12 146 285 270 15 0.949 E12 147 288 220 68 0.8 E6 148 288 270 18 0.94 E12 149 292 270 22 0.928 E12 150 297 270 27 0.914 E12 151 300 150 150 0.707 E6 152 300 180 120 0.721 E12 153 302 220 82 0.777 E12 154 303 270 33 0.898 E12 155 309 270 39 0.883 E12 156 317 270 47 0.865 E12 157 320 220 100 0.755 E3 158 326 270 56 0.846 E12 159 330 180 150 0.71 E12 160 330 330 - 1 E6 161 333.3 330 3.3 0.99 E6 162 333.9 330 3.9 0.988 E12 163 334.7 330 4.7 0.986 E6 164 335.6 330 5.6 0.983 E12 165 336.8 330 6.8 0.98 E6 166 338 270 68 0.824 E12 167 338.2 330 8.2 0.976 E12 168 340 220 120 0.737 E12 169 340 330 10 0.971 E6 170 342 330 12 0.966 E12 171 345 330 15 0.958 E6 172 348 330 18 0.95 E12 173 352 270 82 0.802 E12 174 352 330 22 0.94 E6 175 357 330 27 0.927 E12 176 360 180 180 0.707 E12 177 363 330 33 0.914 E6 178 369 330 39 0.901 E12 179 370 220 150 0.72 E6 180 370 270 100 0.778 E12 181 377 330 47 0.884 E6 182 386 330 56 0.867 E12 183 390 270 120 0.758 E12 184 390 390 - 1 E12 185 393.9 390 3.9 0.99 E12 186 394.7 390 4.7 0.988 E12 187 395.6 390 5.6 0.986 E12 188 396.8 390 6.8 0.983 E12 189 398 330 68 0.847 E6 190 398.2 390 8.2 0.98 E12 191 400 220 180 0.711 E12 192 400 390 10 0.975 E12 193 402 390 12 0.971 E12 194 405 390 15 0.964 E12 195 408 390 18 0.957 E12 196 412 330 82 0.825 E12 197 412 390 22 0.948 E12 198 417 390 27 0.937 E12 199 420 270 150 0.735 E12 200 423 390 33 0.925 E12 201 429 390 39 0.914 E12 202 430 330 100 0.802 E6 203 437 390 47 0.899 E12 204 440 220 220 0.707 E3 205 446 390 56 0.883 E12 206 450 270 180 0.721 E12 207 450 330 120 0.78 E12 208 458 390 68 0.864 E12 209 470 470 - 1 E3 210 472 390 82 0.844 E12 211 474.7 470 4.7 0.99 E3 212 475.6 470 5.6 0.988 E12 213 476.8 470 6.8 0.986 E6 214 478.2 470 8.2 0.983 E12 215 480 330 150 0.755 E6 216 480 470 10 0.979 E3 217 482 470 12 0.975 E12 218 485 470 15 0.97 E6 219 488 470 18 0.964 E12 220 490 270 220 0.711 E12 221 490 390 100 0.822 E12 222 492 470 22 0.956 E3 223 497 470 27 0.947 E12 224 503 470 33 0.937 E6 225 509 470 39 0.927 E12 226 510 330 180 0.737 E12 227 510 390 120 0.8 E12 228 517 470 47 0.914 E3 229 526 470 56 0.9 E12 230 538 470 68 0.883 E6 231 540 270 270 0.707 E12 232 540 390 150 0.774 E12 233 550 330 220 0.721 E6 234 552 470 82 0.864 E12 235 560 560 - 1 E12 236 565.6 560 5.6 0.99 E12 237 566.8 560 6.8 0.988 E12 238 568.2 560 8.2 0.986 E12 239 570 390 180 0.754 E12 240 570 470 100 0.843 E3 241 570 560 10 0.983 E12 242 572 560 12 0.979 E12 243 575 560 15 0.974 E12 244 578 560 18 0.969 E12 245 582 560 22 0.963 E12 246 587 560 27 0.955 E12 247 590 470 120 0.822 E12 248 593 560 33 0.946 E12 249 599 560 39 0.937 E12 250 600 330 270 0.711 E12 251 607 560 47 0.926 E12 252 610 390 220 0.734 E12 253 616 560 56 0.914 E12 254 620 470 150 0.796 E6 255 628 560 68 0.898 E12 256 642 560 82 0.882 E12 257 650 470 180 0.774 E12 258 660 330 330 0.707 E6 259 660 390 270 0.719 E12 260 660 560 100 0.862 E12 261 680 560 120 0.842 E12 262 680 680 - 1 E6 263 686.8 680 6.8 0.99 E6 264 688.2 680 8.2 0.988 E12 265 690 470 220 0.752 E3 266 690 680 10 0.986 E6 267 692 680 12 0.983 E12 268 695 680 15 0.979 E6 269 698 680 18 0.975 E12 270 702 680 22 0.969 E6 271 707 680 27 0.963 E12 272 710 560 150 0.817 E12 273 713 680 33 0.955 E6 274 719 680 39 0.947 E12 275 720 390 330 0.71 E12 276 727 680 47 0.938 E6 277 736 680 56 0.927 E12 278 740 470 270 0.732 E12 279 740 560 180 0.795 E12 280 748 680 68 0.914 E6 281 762 680 82 0.899 E12 282 780 390 390 0.707 E12 283 780 560 220 0.771 E12 284 780 680 100 0.881 E6 285 800 470 330 0.718 E6 286 800 680 120 0.863 E12 287 820 820 - 1 E12 288 828.2 820 8.2 0.99 E12 289 830 560 270 0.749 E12 290 830 680 150 0.839 E6 291 830 820 10 0.988 E12 292 832 820 12 0.986 E12 293 835 820 15 0.982 E12 294 838 820 18 0.979 E12 295 842 820 22 0.974 E12 296 847 820 27 0.969 E12 297 853 820 33 0.962 E12 298 859 820 39 0.956 E12 299 860 470 390 0.71 E12 300 860 680 180 0.818 E12 301 867 820 47 0.947 E12 302 876 820 56 0.938 E12 303 888 820 68 0.927 E12 304 890 560 330 0.73 E12 305 900 680 220 0.794 E6 306 902 820 82 0.914 E12 307 920 820 100 0.898 E12 308 940 470 470 0.707 E3 309 940 820 120 0.882 E12 310 950 560 390 0.718 E12 311 950 680 270 0.77 E12 312 970 820 150 0.859 E12 --------------------------------------------------------