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



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
--------------------------------------------------------
