Many newcomers to circuit design might find themselves puzzled by resistor values: why aren't common standard resistors integer values? For example, you often see 4.7kΩ or 5.1kΩ instead of a straightforward 5kΩ.
This is because resistors are manufactured according to an exponential distribution, following the standards set by the International Electrotechnical Commission (IEC). The standard resistor value system includes various series like E3, E6, E12, E24, E48, E96, and E192.
For instance:
- The E6 series has a ratio of 10^(1/6) ≈ 1.5
- The E12 series has a ratio of 10^(1/12) ≈ 1.21
Here's a detailed table of standard resistance values:
Now, why do we manufacture resistors with an exponential distribution? The primary reasons are related to production methods and cost efficiency. For resistor manufacturers, increasing the variety of resistance values means more production lines, leading to higher labor costs and thus, higher costs per resistor.
In resistor manufacturing, precision is never absolute; there's always some tolerance. For example, a 100Ω resistor with a 1% tolerance can range anywhere from 99Ω to 101Ω. Consequently, in the last century, the American Electronics Association established a standard system for resistor values.
To understand this system, let's consider resistors with a 10% tolerance. If you've already produced a 100Ω resistor, there's no need to make a 105Ω one because the 100Ω resistor's tolerance range covers 90Ω to 110Ω. The next resistor to produce would be 120Ω, as its tolerance range would be 110Ω to 130Ω, and so forth. For resistors from 100Ω to 1000Ω, you'd only need to produce 100Ω, 120Ω, 150Ω, 180Ω, 220Ω, 270Ω, 330Ω, etc. — just 12 values instead of one for every possible ohm. This approach reduces the number of resistor types on the production line, thereby lowering manufacturing costs.
This exponential approach to resistor values is akin to other systems where values are chosen for convenience and efficiency. For example, consider U.S. currency denominations like $1, $2, $5, and $10, where you don't see $3 or $4 bills because combinations of $1, $2, and $5 can cover these values. Similarly, the thickness of mechanical pencil leads comes in sizes like 0.25mm, 0.35mm, 0.5mm, and 0.7mm.
Moreover, the exponential distribution of resistor values allows users to find a suitable resistor within a given tolerance range. When resistors adhere to this distribution, the percentage error remains consistent across a range of operations, whether adding, subtracting, multiplying, or dividing resistances.