
********************************************************************************
**
**  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 <http://www.gnu.org/licenses/>.
**
********************************************************************************



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
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