Why do electronic components have such odd values? (2021)
Electronics engineers explain why resistors and other components come in seemingly odd standard values like 4.7 kΩ or 68 Ω: they follow logarithmic “E-series” of preferred numbers, chosen so that each value’s tolerance band overlaps neatly with its neighbors. Much of the debate centers on how manufacturing tolerances, temperature effects, and statistical variation interact when combining components in series or parallel, and why worst‑case tolerance, not optimistic averaging, is what real designs must withstand. Commenters also touch on modern availability of cheap 1% parts, the economics of binning components by precision, and when high‑accuracy resistors are truly necessary versus when simpler, more robust design choices suffice.
Clarifying the 70 Ω example
- Several commenters note the article’s last example seems numerically wrong: 33 Ω + 47 Ω = 80 Ω, not 70 Ω.
- Common view: it’s likely a typo and should be 22 Ω + 47 Ω ≈ 69 Ω.
- Others joke that 80 Ω is within common loose tolerances anyway, as are 68 Ω and 75 Ω.
Tolerance, statistics, and design practice
- Formal derivation: when adding resistors with the same percentage tolerance in series, the resulting percentage tolerance stays the same; absolute error adds, denominator (nominal resistance) also grows.
- Parallel combinations with identical percentage errors also retain that percentage; mixed high/low errors can partially cancel.
- Strong debate over “tolerance vs statistics”:
- One side stresses tolerance is a worst‑case contractual bound; good engineering designs to that, not to probability.
- Others note that random errors statistically average out (central limit theorem), so large series/parallel networks can have smaller expected relative error, though real distributions may be skewed or bimodal.
- Distinction drawn between tolerance (spec) and measurement uncertainty (instrument error).
Manufacturing, binning, and resistor technologies
- Discussion of resistor types: carbon film, metal film, wirewound, thin‑film, foil; choice affects accuracy, tempco, inductance, and cost.
- Some recall the idea that “5% parts are 1% parts that failed binning”; others argue this is usually uneconomic for very cheap parts and often a myth today.
- For tight tolerances and low tempco, manufacturers use different materials, geometries, and laser trimming; very high‑precision parts become extremely expensive.
E‑series preferred numbers and Renard numbers
- Commenters restate that E‑series values form geometric/logarithmic sequences rounded to two digits.
- The key idea praised: “tolerance overlap” — adjacent preferred values’ ±tolerance bands just touch, ensuring any target value is within a fixed relative error of some series value.
- Some point out the article blurs “usage tolerance” (acceptable design error) with fabrication tolerance of real parts.
- The Renard cable story is recognized as the same geometric / overlap principle applied to mechanical sizes.
Practical usage and power ratings
- Many say E12 (or even E6) plus 1% resistors is enough for most work, especially digital; analog and metrology may need finer series and matched networks.
- Trimmers and digital calibration are common where precision beyond basic resistors is needed.
- Power rating is usually inferred from package size; designers often standardize on the highest rating they expect to need in a footprint.