E series

An E series is a standardized sequence of property values of electrical components. The values of the E series result from the Renard series . Commercially available resistors , capacitors , coils or Zener diodes usually have nominal values from an E series. An E-series covers the range of values in such a way that the ratio of successive values is as equal as possible. In addition, the values are chosen so that the sequence of digits is repeated in every decade.

Seven E series are defined in the DIN IEC 60063 standard: E3, E6, E12, E24, E48, E96 and E192. The number after the E indicates how many values the series contains within a decade. The standard came into force in December 1985 under the title Preferred Series for the Nominal Values of Resistors and Capacitors . Its content corresponds to the international standard IEC 60063 from 1963. Cable cross-sections (according to IEC 60228 ) and fuse values (according to IEC 60269 ) are based on Renard series with a different number of values in a decade.

calculation

The E12 series over two decades

The number of an E series describes the number of nominal values within a decade. The first row with three values per decade is row E3. The next larger series has twice as many nominal values per decade. Other series are E6, E12, E24, E48, E96 and E192. In the E series, the values are not distributed linearly, but logarithmically within a decade . The individual values within an E series are described - according to the same principle as in the Renard series - by the following mathematical sequence : ${\ displaystyle k}$

{\ displaystyle k = {\ sqrt [{n}] {10 ^ {m}}} = \ left ({\ sqrt [{n}] {10}} \ right) ^ {m} {\ text {,} } m \ in [0; n-1] \ cap \ mathbb {Z}}

, for the E series .

{\ displaystyle n}

The terms of the sequence are rounded in such a way that there are two significant digits in the series E3 to E24 and three significant digits in the series E48 to E192 and also minimal differences between adjacent sequence elements. The next more precise series of resistances is obtained by doubling the number and halving the tolerance. The higher E series contains all values of the lower series within the scope of the rounding accuracy.

Since the series E3, E6, E12 and E24 were defined in 1948 and 1950 and thus before the standard DIN IEC 63 was created, the values in the E3 to E24 series correspond to 2.7 to 4.7 and 8.2 not the rounding rules, but this has not been changed due to the widespread use.

example

The resistor series E3 has three resistance values per decade. Therefore: n = 3.

Thus for the decade from : ${\ displaystyle m \ in \ lbrace 0,1,2 \ rbrace}$

The first resistance value	${\ displaystyle m = 0: R = {\ sqrt [{3}] {10 ^ {0}}} = \ left ({\ sqrt [{3}] {10}} \ right) ^ {0} = 1 {,} 000 \ dotso = 1 {,} 0}$
The second resistance value	${\ displaystyle m = 1: R = {\ sqrt [{3}] {10 ^ {1}}} = \ left ({\ sqrt [{3}] {10}} \ right) ^ {1} = 2 {,} 154 \ dotso \ approx 2 {,} 2}$
The third resistance value	${\ displaystyle m = 2: R = {\ sqrt [{3}] {10 ^ {2}}} = \ left ({\ sqrt [{3}] {10}} \ right) ^ {2} = 4 {,} 642 \ dotso \ approx 4 {,} 7}$

You can see that the value per step always increases (rounded) by the factor . Since the E3 series consists of only three values within a decade, the calculation is over; the next numerical values are 10, 22, 47 etc. ${\ displaystyle {\ sqrt [{3}] {10}}}$

values

The fixed values for the decade from m = 0 are listed below:

E3	E6	E12	E24	E48	E96	E192
1.0	1.0	1.00	1.00	1.00	1.00	1.00
					1.00	1.01
					1.02	1.02
					1.02	1.04
				1.05	1.05	1.05
					1.05	1.06
					1.07	1.07
					1.07	1.09
			1.10	1.10	1.10	1.10
					1.10	1.11
					1.13	1.13
					1.13	1.14
				1.15	1.15	1.15
					1.15	1.17
					1.18	1.18
					1.18	1.20
		1.20	1.20	1.21	1.21	1.21
					1.21	1.23
					1.24	1.24
					1.24	1.26
				1.27	1.27	1.27
					1.27	1.29
					1.30	1.30
					1.30	1.32
			1.30	1.33	1.33	1.33
					1.33	1.35
					1.37	1.37
					1.37	1.38
				1.40	1.40	1.40
					1.40	1.42
					1.43	1.43
					1.43	1.45
	1.5	1.50	1.50	1.47	1.47	1.47
					1.47	1.49
					1.50	1.50
					1.50	1.52
				1.54	1.54	1.54
					1.54	1.56
					1.58	1.58
					1.58	1.60
			1.60	1.62	1.62	1.62
					1.62	1.64
					1.65	1.65
					1.65	1.67
				1.69	1.69	1.69
					1.69	1.72
					1.74	1.74
					1.74	1.76
		1.80	1.80	1.78	1.78	1.78
					1.78	1.80
					1.82	1.82
					1.82	1.84
				1.87	1.87	1.87
					1.87	1.89
					1.91	1.91
					1.91	1.93
			2.00	1.96	1.96	1.96
					1.96	1.98
					2.00	2.00
					2.00	2.03
				2.05	2.05	2.05
					2.05	2.08
					2.10	2.10
					2.10	2.13

E3	E6	E12	E24	E48	E96	E192
2.2	2.2	2.20	2.20	2.15	2.15	2.15
					2.15	2.18
					2.21	2.21
					2.21	2.23
				2.26	2.26	2.26
					2.26	2.29
					2.32	2.32
					2.32	2.34
			2.40	2.37	2.37	2.37
					2.37	2.40
					2.43	2.43
					2.43	2.46
				2.49	2.49	2.49
					2.49	2.52
					2.55	2.55
					2.55	2.58
		2.70	2.70	2.61	2.61	2.61
					2.61	2.64
					2.67	2.67
					2.67	2.71
				2.74	2.74	2.74
					2.74	2.77
					2.80	2.80
					2.80	2.84
			3.00	2.87	2.87	2.87
					2.87	2.91
					2.94	2.94
					2.94	2.98
				3.01	3.01	3.01
					3.01	3.05
					3.09	3.09
					3.09	3.12
	3.3	3.30	3.30	3.16	3.16	3.16
					3.16	3.20
					3.24	3.24
					3.24	3.28
				3.32	3.32	3.32
					3.32	3.36
					3.40	3.40
					3.40	3.44
			3.60	3.48	3.48	3.48
					3.48	3.52
					3.57	3.57
					3.57	3.61
				3.65	3.65	3.65
					3.65	3.70
					3.74	3.74
					3.74	3.79
		3.90	3.90	3.83	3.83	3.83
					3.83	3.88
					3.92	3.92
					3.92	3.97
				4.02	4.02	4.02
					4.02	4.07
					4.12	4.12
					4.12	4.17
			4.30	4.22	4.22	4.22
					4.22	4.27
					4.32	4.32
					4.32	4.37
				4.42	4.42	4.42
					4.42	4.48
					4.53	4.53
					4.53	4.59

E3	E6	E12	E24	E48	E96	E192
4.7	4.7	4.70	4.70	4.64	4.64	4.64
					4.64	4.70
					4.75	4.75
					4.75	4.81
				4.87	4.87	4.87
					4.87	4.93
					4.99	4.99
					4.99	5.05
			5.10	5.11	5.11	5.11
					5.11	5.17
					5.23	5.23
					5.23	5.30
				5.36	5.36	5.36
					5.36	5.42
					5.49	5.49
					5.49	5.56
		5.60	5.60	5.62	5.62	5.62
					5.62	5.69
					5.76	5.76
					5.76	5.83
				5.90	5.90	5.90
					5.90	5.97
					6.04	6.04
					6.04	6.12
			6.20	6.19	6.19	6.19
					6.19	6.26
					6.34	6.34
					6.34	6.42
				6.49	6.49	6.49
					6.49	6.57
					6.65	6.65
					6.65	6.73
	6.8	6.80	6.80	6.81	6.81	6.81
					6.81	6.90
					6.98	6.98
					6.98	7.06
				7.15	7.15	7.15
					7.15	7.23
					7.32	7.32
					7.32	7.41
			7.50	7.50	7.50	7.50
					7.50	7.59
					7.68	7.68
					7.68	7.77
				7.87	7.87	7.87
					7.87	7.96
					8.06	8.06
					8.06	8.16
		8.20	8.20	8.25	8.25	8.25
					8.25	8.35
					8.45	8.45
					8.45	8.56
				8.66	8.66	8.66
					8.66	8.76
					8.87	8.87
					8.87	8.98
			9.10	9.09	9.09	9.09
					9.09	9.20
					9.31	9.31
					9.31	9.42
				9.53	9.53	9.53
					9.53	9.65
					9.76	9.76
					9.76	9.88

Tolerances

The larger the E series, the smaller the tolerances of the components have to be, as these could otherwise overlap neighboring values:

E3	E6	E12	E24	E48	E96	E192
> 20%	20%	10%	5%	2%	1 %	0.5%

However, the standard only specifies the tolerances for series E3 to E24 and the maximum permissible deviations. For the production of unmatched resistors, in particular, the mutually contacting tolerance ranges mean that any values of produced resistors can be assigned to a value and sold.

In fact, however, the values of the corresponding series are also available with narrower tolerances. For example, B. for resistors the series E12 with 5% tolerance and the series E24 with 2%.

Demarcation

Decadal voltage dividers cannot be implemented exactly with individual resistors from the E series. Therefore there are different series of resistances for this purpose, e.g. B. with the numerical values 1, 9, 99, 999. Such combinations of resistors are offered in particular with coordinated temperature and voltage coefficients in order to be able to realize voltage dividers whose division ratios are much more precisely defined than those of the individual resistors.

Web links

electronicsplanet.ch: Resistance series and their values with color code