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



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