Tolerance and measurement uncertainty deserve separate budgets

Nominal is the center of a model

A nominal value is the number used for design arithmetic. Component tolerance defines a range around it, while instrument uncertainty defines what a measurement can establish. These are different from numerical simulator tolerance. An ideal SPICE resistor at 10 kΩ does not become a ±1% component unless you deliberately vary its value.

Consider the 10 kΩ, 100 nF low-pass, with R tolerance ±1% and C tolerance ±5%. Nominal corner is 159.154943 Hz. The lowest corner uses both largest values: $159.154943/(1.01\times1.05)=150.075382$ Hz. The highest uses both smallest values: $159.154943/(0.99\times0.95)=169.223757$ Hz. These are worst-case bounds under independent allowed ranges, not probability estimates.

A resistor ratio example

A noninverting stage with Rf = 100 kΩ and Rg = 10 kΩ has nominal gain 11. With both resistors ±1%, minimum gain is $1+100(0.99)/(10(1.01))=10.801980$, and maximum is $1+100(1.01)/(10(0.99))=11.202020$. The ratio is not automatically ±1% just because each resistor is. Matched networks may offer a separate ratio-tolerance specification.

Temperature drift can move values beyond a room-temperature tolerance calculation. For a 50 ppm/°C resistor over a 40°C change, the approximate additional fractional change is 0.2%, assuming a linear temperature coefficient. A capacitor's voltage dependence can be another major term; use its actual characterization for a physical design.

Plan a useful measurement

Write an acceptance interval based on the design requirement and known uncertainties. If an instrument reports 160 Hz with uncertainty ±2 Hz, it supports an interval rather than an exact 160.000 Hz claim. A result near a limit may require a better measurement, not an automatic pass.

Sweep worst-case component corners before a random Monte Carlo study. Random sampling may miss a legal extreme and requires a distribution assumption. Preserve the model, tested values, measurement settings, and acceptance rule so another learner can reproduce the decision rather than only the plot.