[hardware] origin of standard resistance value

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1. Standard resistance value

For large-scale production of resistors , International Electrotechnical Commission （ IEC：International Electrotechnical Commission ） stay 1952 In, it was decided to formulate a specification for the resistance value of resistance , And publish them in IEC 60063:1963 In the standard . These standard values are not only applicable to resistors , The same applies to capacitors , Inductance and other devices , Although these standard values are 1952 Issued in , however French military engineer Charles Renard As early as 19 century 70 The concept of geometric progression has been put forward since the s .

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2. The key factor determining the standard resistance of resistance

The key factor determining the standard resistance of resistance —— Resistance accuracy （ error ）

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3. The resistance value is taken linearly

Let's give you an example , For example, we want to produce a batch of resistors , The resistance value is defined by linear growth , The error is 20%：

We take 1Ω,2Ω,3Ω,4Ω… These resistors , At the same time, calculate its deviation range , Then arrange it linearly ：

You will find that the higher the resistance is , The bigger the deviation is , There will be overlapping parts between resistors with different resistance values due to errors , As shown in the figure above 3Ω Resistance and 4Ω How should we divide the resistance of the overlapping part ？

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4. The resistance value is taken in logarithm

If the resistance value is specified according to the linear standard , It will bring trouble in production and use . In order to make the resistors with different resistance values do not overlap due to error , Can we adopt the following ideal resistance definition method according to the error ？

We directly 20% Error from 1Ω Start to calculate the resistance of each resistor , Make them happen within the allowable error range “ No overlap ”, The calculation results are as follows ：

This is the ideal resistance , If the resistance value of the standard resistance is defined according to this set of Standards , Now the standard resistance table you see may look like this ：

Express these resistances in the form of curves ：

Obviously , This is an exponential function , And the general formula for calculating the resistance value by this method is easy to write ：

In the general formula above 1.5 According to the accuracy of resistance （ error ）20% Calculated ,1 Is the initial resistance .

In order to make the resistance value of the standard resistance distributed more evenly , More convenient for memory and use , The clever engineer thought of using 10 Base the index N The value taking method of equal division .

Or with precision （ error ） by 20% As an example , How to divide it equally to get closest to the ideal situation above ？

Suppose to proceed N Equal division , It can be calculated directly N：

So , If we want to make sure 1Ω To 10Ω Standard resistance of , It can be calculated directly by the following formula ：

1. d Is the initial resistance value ,d=1,10,100,1k,10k…
2. N Divide the quantity by index , Calculate according to the accuracy ,N=6(20%),N=12(10%),N=24(5%),N=48(2%),N=96(1%),N=192(0.5%)…
3. i=0,1,…,N-1

Suppose we want to make sure that the resistance value is 1Ω To 10Ω The resistance of , Suppose the error is 20%, The resistance value calculated by the above formula is ：

Then arrange them on the same scale ：

Calculate the resistance value and standard resistance value by comparison , We can find that they are basically the same .

Look at another group 10Ω To 100Ω The resistance distribution between the standard resistance values （20%）, Their resistance basically covers the whole area .

Seeing this, I believe you have a clear and intuitive understanding of the definition of the standard resistance of resistance , The higher the accuracy , The more exponentially divided , And this formula also applies to capacitance , Inductors and other devices .

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5. Standard resistance meter with different accuracy

Some of the pictures are quoted from B standing UP Lord 《 Maker SMIC 》
Reference material ：https://eepower.com/resistor-guide/resistor-standards-and-codes/resistor-values/#
Standard resistance meter ：https://www.smpspowersupply.com/Standard_Decade_Value_Table.pdf