******************************************************************************** ** ** E 1 2 _ 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 E12 ** 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 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 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, ** 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 ** +----|____|----+ ** 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 312 entries. As some values can be realised in different ways, however, ** there are only 310 distinct values. The maximum relative difference be- ** tween adjacent values is 3.1977 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 (15724 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 2 102 120 680 0.863 E12 3 103.125 150 330 0.755 E6 4 104.68085106 120 820 0.882 E12 5 107.14285714 120 1k 0.899 E12 6 108 180 270 0.721 E12 7 108.33333333 150 390 0.774 E12 8 109.09090909 120 1.2k 0.914 E12 9 110 220 220 0.707 E3 10 111.11111111 120 1.5k 0.929 E12 11 112.5 120 1.8k 0.94 E12 12 113.70967742 150 470 0.796 E6 13 113.79310345 120 2.2k 0.95 E12 14 114.89361702 120 2.7k 0.958 E12 15 115.78947368 120 3.3k 0.966 E12 16 116.41791045 120 3.9k 0.971 E12 17 116.47058824 180 330 0.737 E12 18 117.01244813 120 4.7k 0.975 E12 19 117.48251748 120 5.6k 0.979 E12 20 117.91907514 120 6.8k 0.983 E12 21 118.26923077 120 8.2k 0.986 E12 22 118.30985915 150 560 0.817 E12 23 118.5770751 120 10k 0.988 E12 24 118.81188119 120 12k 0.99 E12 25 120 120 - 1 E12 26 121.2244898 220 270 0.711 E12 27 122.89156627 150 680 0.839 E6 28 123.15789474 180 390 0.754 E12 29 126.80412371 150 820 0.859 E12 30 130.15384615 180 470 0.774 E12 31 130.43478261 150 1k 0.879 E6 32 132 220 330 0.721 E6 33 133.33333333 150 1.2k 0.896 E12 34 135 270 270 0.707 E12 35 136.21621622 180 560 0.795 E12 36 136.36363636 150 1.5k 0.914 E6 37 138.46153846 150 1.8k 0.926 E12 38 140.42553191 150 2.2k 0.938 E6 39 140.6557377 220 390 0.734 E12 40 142.10526316 150 2.7k 0.949 E12 41 142.3255814 180 680 0.818 E12 42 143.47826087 150 3.3k 0.958 E6 43 144.44444444 150 3.9k 0.964 E12 44 145.36082474 150 4.7k 0.97 E6 45 146.08695652 150 5.6k 0.974 E12 46 146.76258993 150 6.8k 0.979 E6 47 147.30538922 150 8.2k 0.982 E12 48 147.6 180 820 0.84 E12 49 147.78325123 150 10k 0.985 E6 50 148.14814815 150 12k 0.988 E12 51 148.5 270 330 0.711 E12 52 148.51485149 150 15k 0.99 E6 53 149.85507246 220 470 0.752 E3 54 150 150 - 1 E6 55 152.54237288 180 1k 0.861 E12 56 156.52173913 180 1.2k 0.879 E12 57 157.94871795 220 560 0.771 E12 58 159.54545455 270 390 0.719 E12 59 160.71428571 180 1.5k 0.899 E12 60 163.63636364 180 1.8k 0.914 E12 61 165 330 330 0.707 E6 62 166.22222222 220 680 0.794 E6 63 166.38655462 180 2.2k 0.927 E12 64 168.75 180 2.7k 0.94 E12 65 170.68965517 180 3.3k 0.95 E12 66 171.48648649 270 470 0.732 E12 67 172.05882353 180 3.9k 0.957 E12 68 173.36065574 180 4.7k 0.964 E12 69 173.46153846 220 820 0.816 E12 70 174.39446367 180 5.6k 0.969 E12 71 175.35816619 180 6.8k 0.975 E12 72 176.13365155 180 8.2k 0.979 E12 73 176.8172888 180 10k 0.982 E12 74 177.33990148 180 12k 0.985 E12 75 177.86561265 180 15k 0.988 E12 76 178.21782178 180 18k 0.99 E12 77 178.75 330 390 0.71 E12 78 180 180 - 1 E12 79 180.32786885 220 1k 0.839 E3 80 182.1686747 270 560 0.749 E12 81 185.91549296 220 1.2k 0.859 E12 82 191.86046512 220 1.5k 0.881 E6 83 193.26315789 270 680 0.77 E12 84 193.875 330 470 0.718 E6 85 195 390 390 0.707 E12 86 196.03960396 220 1.8k 0.898 E12 87 200 220 2.2k 0.914 E3 88 203.11926606 270 820 0.792 E12 89 203.42465753 220 2.7k 0.928 E12 90 206.25 220 3.3k 0.94 E6 91 207.64044944 330 560 0.73 E12 92 208.25242718 220 3.9k 0.948 E12 93 210.16260163 220 4.7k 0.956 E3 94 211.6838488 220 5.6k 0.963 E12 95 212.5984252 270 1k 0.816 E12 96 213.10541311 220 6.8k 0.969 E6 97 213.13953488 390 470 0.71 E12 98 214.25178147 220 8.2k 0.974 E12 99 215.26418787 220 10k 0.979 E3 100 216.03927987 220 12k 0.982 E12 101 216.81997372 220 15k 0.986 E6 102 217.34357849 220 18k 0.988 E12 103 217.82178218 220 22k 0.99 E3 104 220 220 - 1 E3 105 220.40816327 270 1.2k 0.837 E12 106 222.17821782 330 680 0.748 E6 107 228.81355932 270 1.5k 0.861 E12 108 229.89473684 390 560 0.718 E12 109 234.7826087 270 1.8k 0.879 E12 110 235 470 470 0.707 E3 111 235.30434783 330 820 0.769 E12 112 240.48582996 270 2.2k 0.897 E12 113 245.45454545 270 2.7k 0.914 E12 114 247.85046729 390 680 0.733 E12 115 248.12030075 330 1k 0.792 E6 116 249.57983193 270 3.3k 0.927 E12 117 252.51798561 270 3.9k 0.937 E12 118 255.33199195 270 4.7k 0.947 E12 119 255.53398058 470 560 0.71 E12 120 257.58091993 270 5.6k 0.955 E12 121 258.82352941 330 1.2k 0.813 E12 122 259.68882603 270 6.8k 0.963 E12 123 261.3931523 270 8.2k 0.969 E12 124 262.90165531 270 10k 0.974 E12 125 264.05867971 270 12k 0.978 E12 126 264.29752066 390 820 0.75 E12 127 265.2259332 270 15k 0.982 E12 128 266.00985222 270 18k 0.985 E12 129 266.72653794 270 22k 0.988 E12 130 267.32673267 270 27k 0.99 E12 131 270 270 - 1 E12 132 270.49180328 330 1.5k 0.839 E6 133 277.91304348 470 680 0.719 E6 134 278.87323944 330 1.8k 0.859 E12 135 280 560 560 0.707 E12 136 280.57553957 390 1k 0.772 E12 137 286.95652174 330 2.2k 0.879 E6 138 294.05940594 330 2.7k 0.898 E12 139 294.33962264 390 1.2k 0.794 E12 140 298.75968992 470 820 0.733 E12 141 300 330 3.3k 0.914 E6 142 304.25531915 330 3.9k 0.925 E12 143 307.09677419 560 680 0.71 E12 144 308.3499006 330 4.7k 0.937 E6 145 309.52380952 390 1.5k 0.82 E12 146 311.63575042 330 5.6k 0.946 E12 147 314.72650771 330 6.8k 0.955 E6 148 317.23329426 330 8.2k 0.962 E12 149 319.45788964 330 10k 0.969 E6 150 319.72789116 470 1k 0.752 E3 151 320.54794521 390 1.8k 0.841 E12 152 321.16788321 330 12k 0.974 E12 153 322.8962818 330 15k 0.979 E6 154 324.0589198 330 18k 0.982 E12 155 325.12315271 330 22k 0.985 E6 156 326.01536773 330 27k 0.988 E12 157 326.73267327 330 33k 0.99 E6 158 330 330 - 1 E6 159 331.27413127 390 2.2k 0.863 E12 160 332.75362319 560 820 0.72 E12 161 337.7245509 470 1.2k 0.772 E12 162 340 680 680 0.707 E6 163 340.77669903 390 2.7k 0.883 E12 164 348.7804878 390 3.3k 0.901 E12 165 354.54545455 390 3.9k 0.914 E12 166 357.8680203 470 1.5k 0.798 E6 167 358.97435897 560 1k 0.735 E12 168 360.11787819 390 4.7k 0.927 E12 169 364.60767947 390 5.6k 0.937 E12 170 368.84561892 390 6.8k 0.947 E12 171 371.73333333 680 820 0.71 E12 172 372.29336438 390 8.2k 0.956 E12 173 372.68722467 470 1.8k 0.82 E12 174 375.36092397 390 10k 0.963 E12 175 377.72397094 390 12k 0.969 E12 176 380.11695906 390 15k 0.975 E12 177 381.72920065 390 18k 0.979 E12 178 381.81818182 560 1.2k 0.752 E12 179 383.20678874 390 22k 0.983 E12 180 384.44687842 390 27k 0.986 E12 181 385.44474394 390 33k 0.988 E12 182 386.13861386 390 39k 0.99 E12 183 387.2659176 470 2.2k 0.843 E3 184 390 390 - 1 E12 185 400.31545741 470 2.7k 0.865 E12 186 404.76190476 680 1k 0.72 E6 187 407.76699029 560 1.5k 0.777 E12 188 410 820 820 0.707 E12 189 411.40583554 470 3.3k 0.884 E6 190 419.45080092 470 3.9k 0.899 E12 191 427.11864407 560 1.8k 0.799 E12 192 427.27272727 470 4.7k 0.914 E3 193 433.60790774 470 5.6k 0.926 E12 194 434.04255319 680 1.2k 0.734 E12 195 439.61485557 470 6.8k 0.938 E6 196 444.52133795 470 8.2k 0.947 E12 197 446.37681159 560 2.2k 0.823 E12 198 448.90162369 470 10k 0.956 E3 199 450.54945055 820 1k 0.711 E12 200 452.28548516 470 12k 0.963 E12 201 455.72074984 470 15k 0.97 E6 202 458.04006497 470 18k 0.975 E12 203 460.16911437 470 22k 0.979 E3 204 461.95850018 470 27k 0.983 E12 205 463.40005976 470 33k 0.986 E6 206 463.80368098 560 2.7k 0.846 E12 207 464.40334431 470 39k 0.988 E12 208 465.34653465 470 47k 0.99 E3 209 467.88990826 680 1.5k 0.755 E6 210 470 470 - 1 E3 211 478.75647668 560 3.3k 0.867 E12 212 487.12871287 820 1.2k 0.72 E12 213 489.68609865 560 3.9k 0.883 E12 214 493.5483871 680 1.8k 0.776 E12 215 500 1k 1k 0.707 E3 216 500.38022814 560 4.7k 0.9 E12 217 509.09090909 560 5.6k 0.914 E12 218 517.39130435 560 6.8k 0.927 E12 219 519.44444444 680 2.2k 0.8 E6 220 524.20091324 560 8.2k 0.938 E12 221 530.17241379 820 1.5k 0.737 E12 222 530.3030303 560 10k 0.948 E12 223 535.03184713 560 12k 0.956 E12 224 539.84575835 560 15k 0.965 E12 225 543.10344828 560 18k 0.97 E12 226 543.19526627 680 2.7k 0.824 E12 227 545.45454545 1k 1.2k 0.71 E12 228 546.09929078 560 22k 0.975 E12 229 548.62119013 560 27k 0.98 E12 230 550.65554231 560 33k 0.983 E12 231 552.07280081 560 39k 0.986 E12 232 553.40622372 560 47k 0.988 E12 233 554.45544554 560 56k 0.99 E12 234 560 560 - 1 E12 235 563.35877863 820 1.8k 0.755 E12 236 563.81909548 680 3.3k 0.847 E6 237 579.03930131 680 3.9k 0.864 E12 238 594.05204461 680 4.7k 0.883 E6 239 597.35099338 820 2.2k 0.777 E12 240 600 1k 1.5k 0.721 E6 241 600 1.2k 1.2k 0.707 E12 242 606.36942675 680 5.6k 0.898 E12 243 618.18181818 680 6.8k 0.914 E6 244 627.92792793 680 8.2k 0.927 E12 245 628.97727273 820 2.7k 0.802 E12 246 636.70411985 680 10k 0.938 E6 247 642.85714286 1k 1.8k 0.735 E12 248 643.53312303 680 12k 0.948 E12 249 650.51020408 680 15k 0.958 E6 250 655.24625268 680 18k 0.964 E12 251 656.7961165 820 3.3k 0.825 E12 252 659.61199295 680 22k 0.97 E6 253 663.29479769 680 27k 0.976 E12 254 666.27078385 680 33k 0.98 E6 255 666.66666667 1.2k 1.5k 0.711 E12 256 668.34677419 680 39k 0.983 E12 257 670.30201342 680 47k 0.986 E6 258 671.84191955 680 56k 0.988 E12 259 673.26732673 680 68k 0.99 E6 260 677.54237288 820 3.9k 0.844 E12 261 680 680 - 1 E6 262 687.5 1k 2.2k 0.755 E3 263 698.1884058 820 4.7k 0.864 E12 264 715.26479751 820 5.6k 0.882 E12 265 720 1.2k 1.8k 0.721 E12 266 729.72972973 1k 2.7k 0.778 E12 267 731.75853018 820 6.8k 0.899 E12 268 745.45454545 820 8.2k 0.914 E12 269 750 1.5k 1.5k 0.707 E6 270 757.85582255 820 10k 0.927 E12 271 767.44186047 1k 3.3k 0.802 E6 272 767.55070203 820 12k 0.938 E12 273 776.47058824 1.2k 2.2k 0.737 E12 274 777.49683944 820 15k 0.95 E12 275 784.27205101 820 18k 0.957 E12 276 790.53461876 820 22k 0.965 E12 277 795.83033789 820 27k 0.971 E12 278 795.91836735 1k 3.9k 0.822 E12 279 800.11827321 820 33k 0.976 E12 280 803.11401306 820 39k 0.98 E12 281 805.93893768 820 47k 0.983 E12 282 808.16613868 820 56k 0.986 E12 283 810.22958442 820 68k 0.988 E12 284 811.88118812 820 82k 0.99 E12 285 818.18181818 1.5k 1.8k 0.71 E12 286 820 820 - 1 E12 287 824.56140351 1k 4.7k 0.843 E3 288 830.76923077 1.2k 2.7k 0.758 E12 289 848.48484848 1k 5.6k 0.862 E12 290 871.79487179 1k 6.8k 0.881 E6 291 880 1.2k 3.3k 0.78 E12 292 891.30434783 1k 8.2k 0.898 E12 293 891.89189189 1.5k 2.2k 0.72 E6 294 900 1.8k 1.8k 0.707 E12 295 909.09090909 1k 10k 0.914 E3 296 917.64705882 1.2k 3.9k 0.8 E12 297 923.07692308 1k 12k 0.926 E12 298 937.5 1k 15k 0.94 E6 299 947.36842105 1k 18k 0.949 E12 300 955.93220339 1.2k 4.7k 0.822 E12 301 956.52173913 1k 22k 0.958 E3 302 964.28571429 1k 27k 0.965 E12 303 964.28571429 1.5k 2.7k 0.735 E12 304 970.58823529 1k 33k 0.971 E6 305 975 1k 39k 0.975 E12 306 979.16666667 1k 47k 0.979 E3 307 982.45614035 1k 56k 0.983 E12 308 985.50724638 1k 68k 0.986 E6 309 987.95180723 1k 82k 0.988 E12 310 988.23529412 1.2k 5.6k 0.842 E12 311 990 1.8k 2.2k 0.711 E12 312 990.0990099 1k 100k 0.99 E3 --------------------------------------------------------