You know that resistors and capacitors have values like 22 and 51 instead of nice numbers like 20 and 50. This is determined in consideration of manufacturing tolerances of parts.

For example, a 100 Ω resistor has a 5% error. The range of this resistance is 100 × (±0.05) = 95 to 105. If the resistance one level higher is 110 Ω, then 110 × (±0.05) = 104.5 to 116, which can be covered almost continuously. 100 is followed by 110, so the value increment is 10%.

However, if you increase by 10%, the 24th time will be 985, the 25th time will be 1083, not 1000. We want the 100 Ω digit and the 1 kΩ digit to be the same value, so if we make the increment slightly larger than the 10 % increment, it will be exactly 1000 at the 24th time. The formula is 10^(1/24) = 1.100694 which is 10.0694%.

In other words, 24 divisions of one digit on the logarithmic scale. This number is called the E24 series. Its half, E12, and its half, E6, are also defined. Conversely, there are also more detailed E48 and E96 series. The E24 series and below have 2 digits displayed, that is, 1.0 is followed by 1.1, but the E48 series and above have 3 digits. 1.00, 1.05, and so on. Table 1 shows these values.

* Red letters are 10

different from

Tolerances are generally specified as ±10% for E12, ±5% for E24, and ±1% for E96, but there are products with other tolerances.

For example, if the E24 series resistors range from 10 to 1 MΩ (mega ohms), there are 5 digits, so 24 × 5 + 1 = 121 types of parts must be prepared. We have prepared this many types of mounters for mounting components on printed wiring boards before manufacturing. Since there are 481 types in the E96 series, you will have to select and prepare only the amount that you will actually use, which incurs man-hours (expenses) for replacing parts. It's called "setup cost". As manufacturing automation progresses, it may be desirable to design with as few types of parts as possible, connecting in series or in parallel.

For example, you need 73 ohms, but the E24 series only offers 68 ohms and 75 ohms. Instead of using the E96 series 73.2 Ω, it can also be achieved with the E24 series by using two resistors, 51 Ω and 22 Ω in series. A parallel connection of 75 Ω and 2.7 kΩ is also possible. There is a trade-off between increasing the number of resistors and lower manufacturing costs. Design should be considered up to this point.

By the way, some of you may have tried calculating 10^(n/24). I've always been curious, so when I see articles like this, I want to do the math. In practice, for example, 10^(10/24) = 2.6, which is different from 2.7 in Table 1. There are some other cases where 10^(n/24) does not match. They are shown in blue in Table 1. 2.6 instead of 2.7 is more consistent with the E48 and E96 series. I'm not sure why there is such a difference. There is no such difference in the E48 or E96 series.