Lab 11.6 — Measurement uncertainty budget and reporting

Goal

Standardize engineering reporting for measured metrics using:

• Type A and Type B uncertainty contributions;
• root-sum-square combined standard uncertainty;
• expanded uncertainty with coverage factor k=2.

Why this lab matters

A single EVM number such as "3.8 %" hides how much it could be off. The instrument has a stated accuracy, the cable drifts, the reference clock is not perfect, and the temperature changed while you measured. If you do not account for these, two engineers cannot tell whether "3.8 %" and "4.1 %" are different or the same. An uncertainty budget makes every contribution explicit and combines them by a standard rule, so the result is reported as a defensible interval and you can see which contribution to attack first.

Engineering question

How do we report a metric (for example EVM) with a defensible uncertainty interval instead of a single raw number?

Executable file

File	Purpose
blocks/block_11_integrated_sdr_project/python/lab_11_6_measurement_uncertainty_budget.py	uncertainty contribution example and report artifacts

Run from the repository root:

python blocks/block_11_integrated_sdr_project/python/lab_11_6_measurement_uncertainty_budget.py

Generated artifacts

docs/assets/lab116_uncertainty_budget_contributions.png
docs/assets/lab116_uncertainty_budget_table.md
docs/assets/lab116_uncertainty_budget_metrics.json

Core formulas

u_c = sqrt(sum(u_i^2))
U = k * u_c, with k = 2 for approximately 95% coverage
reported result = nominal +/- U

What to expect

The example budget (nominal EVM 3.8 %) prints and stores:

Source	Distribution	Input	Divisor	Standard contribution
repeatability (Type A)	normal	0.0222	1	0.0222
instrument amplitude accuracy	rectangular	0.2000	1.7321	0.1155
reference clock tolerance	rectangular	0.0800	1.7321	0.0462
cable + connector drift	rectangular	0.1200	1.7321	0.0693
temperature effect	normal	0.1000	1	0.1000

Combined standard uncertainty: 0.1754% EVM
Expanded uncertainty (k=2): 0.3508% EVM
Report interval: [3.449, 4.151]%

How to read it:

• A rectangular limit of half-width a becomes a standard uncertainty a / sqrt(3) (that is the divisor column: 0.2 / 1.7321 = 0.1155); normal contributions are used as given.
• The result is dominated by the instrument accuracy (0.1155) and temperature (0.1000), both Type B. The measured repeatability (Type A, 0.0222) is the smallest term, so repeating the measurement 100 more times would barely change the interval; a better instrument or a temperature-controlled setup would.
• The answer is a statement, not a number: EVM = 3.800 % +/- 0.351 % (k = 2). Two results are only distinguishable if their intervals do not overlap.

Report checklist

• Separate Type A and Type B sources.
• Show each standard contribution after distribution divisor.
• Provide u_c, U(k=2), and final interval.
• State assumptions and limits of the uncertainty model.