Preferred values Information - preferred resistor values

Preferred values

When developing a product, designers must choose numerous lengths, distances, diameters, volumes, and other characteristic quantities. While all of these choices are constrained by considerations of functionality, usability, compatibility, safety or cost, there usually remains considerable leeway in the exact choice for many dimensions. Preferred numbers are standard guidelines for choosing exact product dimensions within such constraints.

They serve two purposes:

Using preferred numbers increases the probability that other designers will make exactly the same choice. This is particularly useful where the chosen dimension affects compatibility. For example, if the inner diameters of cooking pots or the distances between screws in wall fixtures are chosen from a series of preferred numbers, then it will be more likely that old pot lids and wall-plug holes can be reused when the original product is replaced.

Preferred numbers are chosen such that when a product is manufactured in many different sizes, these will end up roughly equally spaced on a logarithmic scale. They therefore help to minimize the number of different sizes that need to be manufactured or kept on stock.

Renard numbers

The French army engineer Col. Charles Renard proposed in the 1870s a set of preferred numbers for use with the metric system. His system was adopted in 1952 as international standard ISO 3. Renard's system of preferred numbers divides the interval from 1 to 10 into 5, 10, 20, or 40 steps. The factor between two consecutive numbers in a Renard series is constant (before rounding), namely the 5th, 10th, 20th, or 40th root of 10 (1.58, 1.26, 1.12, and 1.06, respectively), which leads to a geometric sequence. This way, the maximum relative error is minimized if an arbitrary number is replaced by the nearest Renard number multiplied by the appropriate power of 10.

The most basic R5 series consists of these five rounded numbers:
R5: 1.00 1.60 2.50 4.00 6.30

Example: If our design constraints tell us that the two screws in our gadget can be spaced anywhere between 32 mm and 55 mm apart, we make it 40 mm, because 4 is in the R5 series of preferred numbers.

Example: If you want to produce a set of nails with lengths between roughly 15 and 300 mm, then the application of the R5 series would lead to a product repertoire of 16 mm, 25 mm, 40 mm, 63 mm, 100 mm, 160 mm, and 250 mm long nails.

If a finer resolution is needed, another five numbers are added between the R5 numbers, and we end up with the R10 series:
R10: 1.00 1.25 1.60 2.00 2.50 3.15 4.00 5.00 6.30 8.00

Where an even finer grading is needed, the R20 and R40 series can be applied:
R20: 1.00 1.12 1.25 1.40 1.60 1.80 2.00 2.24 2.50 2.80
3.15 3.55 4.00 4.50 5.00 5.60 6.30 7.10 8.00 9.00

R40: 1.00 1.06 1.12 1.18 1.25 1.32 1.40 1.50 1.60 1.70
1.80 1.90 2.00 2.12 2.24 2.36 2.50 2.65 2.80 3.00
3.15 3.35 3.55 3.75 4.00 4.25 4.50 4.75 5.00 5.30
5.60 6.00 6.30 6.70 7.10 7.50 8.00 8.50 9.00 9.50

In some applications more rounded values are desirable, either because the numbers from the normal series would imply an unrealistically high accuracy, or because an integer value is needed (e.g., the number of teeth in a gear). For these needs, more rounded versions of the Renard series have been defined in ISO 3:
R5': 1 1.5 2.5 4 6

R10': 1 1.25 1.6 2 2.5 3.2 4 5 6.3 8

R10": 1 1.2 1.5 2 2.5 3 4 5 6 8

R20': 1 1.1 1.25 1.4 1.6 1.8 2 2.2 2.5 2.8
3.2 3.6 4 4.5 5 5.6 6.3 7.1 8 9

R20": 1 1.1 1.2 1.4 1.6 1.8 2 2.2 2.5 2.8
3 3.5 4 4.5 5 5.5 6 7 8 9

R40': 1 1.05 1.1 1.2 1.25 1.3 1.4 1.5 1.6 1.7
1.8 1.9 2 2.1 2.2 2.4 2.5 2.6 2.8 3
3.2 3.4 3.6 3.8 4 4.2 4.5 4.8 5 5.3
5.6 6 6.3 6.7 7.1 7.5 8 8.5 9 9.5

As the Renard numbers repeat after every 10-fold change of the scale, they are particularly well-suited for use with SI units. It makes no difference whether the Renard numbers are used with metres or kilometres. But one would end up with two incompatible sets of nicely spaced dimensions if they were applied, for instance, with both yards and miles.

Renard numbers are rounded results of the formula

,

where b is the selected series value (for example b = 40 for the R40 series), and i is the i-th element of this series (starting with i = 0).

Capacitors and resistors

International standard IEC 60063 defines another preferred number series that is commonly used for electronic components, especially resistors and capacitors. It works similar to the Renard series, except that it subdivides the interval from 1 to 10 into 6, 12, 24, etc. steps. These subdivisions ensure that when some random value is replaced with the nearest preferred number, the maximum error will be in the order of 20%, 10%, 5%, etc.

Use of the E series is mostly restricted to resistors and capacitors. Commonly produced dimensions for other types of electrical components are either chosen from the Renard series instead (for example fuses) or are defined in relevant product standards (for example wires).

The IEC 60063 numbers are:
E6 (20%): 10 15 22 33 47 68

E12 (10%): 10 12 15 18 22 27 33 39 47 56 68 82

E24 ( 5%): 10 11 12 13 15 16 18 20 22 24 27 30
33 36 39 43 47 51 56 62 68 75 82 91

E96 ( 1%): 100 102 105 107 110 113 115 118
121 124 127 130 133 137 140 143
147 150 154 158 162 165 169 174
178 182 187 191 196 200 205 210
215 221 226 232 237 243 249 255
261 267 274 280 287 294 301 309
316 324 332 340 348 357 365 374
383 392 402 412 422 432 442 453
464 475 487 499 511 523 536 549
562 576 590 604 619 634 649 665
681 698 715 732 750 768 787 806
825 845 866 887 909 931 953 976

There is also an E192 series (0.5%).

Buildings

In the construction industry, it was felt that typical dimensions must be easy to use in mental arithmetic. Therefore, rather than using elements of a geometric series, a different system of preferred dimensions has evolved in this area, known as "modular coordination".

Major dimensions (e.g., grid lines on plans, distances between wall centers or surfaces, widths of shelves and kitchen components) are multiples preferred resistor values of 100 mm. This size is called the "basic module" and represented by the letter M. Preference is given to the multiples of 3 M (= 300 mm) and 6 M (= 600 mm) of the basic module. For larger dimensions, preference is given to multiples of the modules 12 M (= 1.2 m), 15 M (= 1.5 m), 30 M (= 3 m), and 60 M (= 6 m). For smaller dimensions, the submodular increments 50 mm or 25 mm are used. (ISO 2848, BS 6750)

Dimensions chosen this way can easily be divided by a large number of factors without ending up with millimetre fractions. For example, a multiple of 600 mm (6 M) can always be divided into 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, etc. parts, each of which is again an integral number of millimetres.

Paper documents, envelopes, and drawing pens

Standard paper sizes use the square root of two and related numbers (√√√2, √√2, √2, 2, or 2√2) as factors between neighbor dimensions (Lichtenberg series, ISO 216). The √2 factor also appears between the standard pen thicknesses for technical drawings (0.13, 0.18, 0.25, 0.35, 0.50, 0.70, 1.00, 1.40, and 2.00 mm). This way, the right pen size is available to continue a drawing that has been magnified to a different standard paper size.

Computer engineering

When dimensioning computer components, the powers of two are frequently used as preferred numbers:
1 2 4 8 16 32 64 128 256 512 1024 ...

Where a finer grading is needed, additional preferred numbers are obtained by multiplying a power of two with a small odd integer:
3 6 12 24 48 96 192 384 768 1536 ...
5 10 20 40 80 160 320 640 1280 2560 ...
7 14 28 56 112 224 448 896 1792 3584 ...

These correspond to binary numbers that consist mostly of trailing zero bits, which are particularly easy to add and subtract in hardware.

Software developers should keep in mind, though, that using powers of 2 in software, especially with array sizes, may also have disadvantages, such as reduced CPU cache efficiency.

In computer graphics, widths and heights of raster images are preferred to be multiples of 16, as many compression algorithms (JPEG, MPEG) divide images into square blocks of that size.

Retail packaging

In some countries, consumer-protection laws restrict the number of different prepackaged sizes in which certain products can be sold, in order to make it easier for consumers to compare prices.

An example of such a regulation is the European Union directive on the volume of certain prepackaged liquids (75/106/EEC [1]). It restricts the list of allowed wine-bottle sizes to 0.1, 0.25, 0.375, 0.5, 0.75, 1, 1.5, 2, 3, and 5 litres. Similar lists exist for several other types of products. They vary and often deviate significantly from any geometric series in order to accommodate traditional sizes when feasible. Adjacent package sizes in these lists differ typically by factors 2/3 or 3/4, in some cases even 1/2, 4/5, or some other fraction of two small integers.

References

ISO 3, Preferred numbers — Series of preferred numbers. International Organization for Standardization, 1973.

ISO 17, Guide to the use of preferred numbers and of series of preferred numbers. 1973.

ISO 497, Guide to the choice of series of preferred numbers and of series containing more rounded values of preferred numbers. 1973.

ISO 2848, Building construction — Modular coordination — Principles and rules. 1984.

ISO/TR 8389, Building construction — Modular coordination — System of preferred numbers defining multimodular sizes. International Organization for Standardization, 1984.

IEC 60063, Preferred number series for resistors and capacitors. International Electrotechnical Commission, 1963

BS 2045, Preferred numbers. British Standards Institute, 1965.

BS 2488, Schedule of preferred numbers for the resistance of resistors and the capacitance of capacitors for telecommunication equipment. 1966.

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Provided by wikipedia.org

Electronics Topics

The field of electronics is the study and use of systems that operate by controlling the flow of electrons or other electrically charged particles in devices such as thermionic valves and semiconductors. The design and construction of electronic circuits to solve practical problems is part of the fields of electronic engineering, and the hardware design side of computer engineering. The study of new semiconductor devices and their technology is sometimes considered as a branch of physics.

# - A | B | Co - Cz | C - Cm | D

Em - F | E - El | G - H | I - K | L - Ma

Me - N | O - Ph | Pi - Ra| Rc - Rz

Sk - Sy | S - Si | T | U - Z

When developing a product, designers must choose numerous lengths, distances, diameters, volumes, and other characteristic quantities. While all of these choices are constrained by considerations of functionality, usability, compatibility, safety or cost, there usually remains considerable leeway in the exact choice for many dimensions. Preferred numbers are standard guidelines for choosing exact product dimensions within such constraints.

Renard numbers

The French army engineer Col. Charles Renard proposed in the 1870s a set of preferred numbers for use with the metric system. His system was adopted in 1952 as international standard ISO 3. Renard's system of preferred numbers divides the interval from 1 to 10 into 5, 10, 20, or 40 steps. The factor between two consecutive numbers in a Renard series is constant (before rounding), namely the 5th, 10th, 20th, or 40th root of 10 (1.58, 1.26, 1.12, and 1.06, respectively), which leads to a geometric sequence. This way, the maximum relative error is minimized if an arbitrary number is replaced by the nearest Renard number multiplied by the appropriate power of 10.

Example: If our design constraints tell us that the two screws in our gadget can be spaced anywhere between 32 mm and 55 mm apart, we make it 40 mm, because 4 is in the R5 series of preferred numbers.

Example: If you want to produce a set of nails with lengths between roughly 15 and 300 mm, then the application of the R5 series would lead to a product repertoire of 16 mm, 25 mm, 40 mm, 63 mm, 100 mm, 160 mm, and 250 mm long nails.

If a finer resolution is needed, another five numbers are added between the R5 numbers, and we end up with the R10 series:

In some applications more rounded values are desirable, either because the numbers from the normal series would imply an unrealistically high accuracy, or because an integer value is needed (e.g., the number of teeth in a gear). For these needs, more rounded versions of the Renard series have been defined in ISO 3:

As the Renard numbers repeat after every 10-fold change of the scale, they are particularly well-suited for use with SI units. It makes no difference whether the Renard numbers are used with metres or kilometres. But one would end up with two incompatible sets of nicely spaced dimensions if they were applied, for instance, with both yards and miles.

where b is the selected series value (for example b = 40 for the R40 series), and i is the i-th element of this series (starting with i = 0).

Capacitors and resistors

International standard IEC 60063 defines another preferred number series that is commonly used for electronic components, especially resistors and capacitors. It works similar to the Renard series, except that it subdivides the interval from 1 to 10 into 6, 12, 24, etc. steps. These subdivisions ensure that when some random value is replaced with the nearest preferred number, the maximum error will be in the order of 20%, 10%, 5%, etc.

Use of the E series is mostly restricted to resistors and capacitors. Commonly produced dimensions for other types of electrical components are either chosen from the Renard series instead (for example fuses) or are defined in relevant product standards (for example wires).

Buildings

In the construction industry, it was felt that typical dimensions must be easy to use in mental arithmetic. Therefore, rather than using elements of a geometric series, a different system of preferred dimensions has evolved in this area, known as "modular coordination".

Major dimensions (e.g., grid lines on plans, distances between wall centers or surfaces, widths of shelves and kitchen components) are multiples preferred resistor values of 100 mm. This size is called the "basic module" and represented by the letter M. Preference is given to the multiples of 3 M (= 300 mm) and 6 M (= 600 mm) of the basic module. For larger dimensions, preference is given to multiples of the modules 12 M (= 1.2 m), 15 M (= 1.5 m), 30 M (= 3 m), and 60 M (= 6 m). For smaller dimensions, the submodular increments 50 mm or 25 mm are used. (ISO 2848, BS 6750)

Dimensions chosen this way can easily be divided by a large number of factors without ending up with millimetre fractions. For example, a multiple of 600 mm (6 M) can always be divided into 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, etc. parts, each of which is again an integral number of millimetres.

Paper documents, envelopes, and drawing pens

Standard paper sizes use the square root of two and related numbers (√√√2, √√2, √2, 2, or 2√2) as factors between neighbor dimensions (Lichtenberg series, ISO 216). The √2 factor also appears between the standard pen thicknesses for technical drawings (0.13, 0.18, 0.25, 0.35, 0.50, 0.70, 1.00, 1.40, and 2.00 mm). This way, the right pen size is available to continue a drawing that has been magnified to a different standard paper size.

Computer engineering

When dimensioning computer components, the powers of two are frequently used as preferred numbers:

Where a finer grading is needed, additional preferred numbers are obtained by multiplying a power of two with a small odd integer:

These correspond to binary numbers that consist mostly of trailing zero bits, which are particularly easy to add and subtract in hardware.

Software developers should keep in mind, though, that using powers of 2 in software, especially with array sizes, may also have disadvantages, such as reduced CPU cache efficiency.

In computer graphics, widths and heights of raster images are preferred to be multiples of 16, as many compression algorithms (JPEG, MPEG) divide images into square blocks of that size.

Retail packaging

In some countries, consumer-protection laws restrict the number of different prepackaged sizes in which certain products can be sold, in order to make it easier for consumers to compare prices.

An example of such a regulation is the European Union directive on the volume of certain prepackaged liquids (75/106/EEC [1]). It restricts the list of allowed wine-bottle sizes to 0.1, 0.25, 0.375, 0.5, 0.75, 1, 1.5, 2, 3, and 5 litres. Similar lists exist for several other types of products. They vary and often deviate significantly from any geometric series in order to accommodate traditional sizes when feasible. Adjacent package sizes in these lists differ typically by factors 2/3 or 3/4, in some cases even 1/2, 4/5, or some other fraction of two small integers.

References

Back to the top of Preferred values.

Provided by wikipedia.org