Path-Loss and Margin Numbers: Checked Calculations
Ada reproduces the chapter’s free-space, log-distance, and link-budget numbers from the units and the reviewed ledger
ADA · CALCULATION AUDIT
Path-Loss and Margin Numbers: Checked Calculations
The physics story is signal spreading; the mathematics is logarithmic bookkeeping. We can reproduce every headline number in this chapter from the units and the reviewed link ledger.
The chapter’s reviewed link ledger sends a sensor at +14 dBm through a 0 dBi antenna and 1 dB enclosure loss to a gateway with +3 dBi gain and 1 dB cable loss, landing at a receiver whose sensitivity is -126 dBm once 12 dB of fade and shadowing margin is reserved. The same free-space model gives reference losses of about 91.5 dB at 900 MHz, 100 dB at 2.4 GHz, and 107 dB at 5 GHz over 1 km. This audit asks the question that ledger invites: do these free-space reference points and the reviewed link budget actually close to the stated raw and available margin?
Companion to the chapter Path Loss and Link Budgets — every number here comes from that chapter.
Free-Space Reference Points
1. Free-space reference points. The chapter uses distance in kilometers and frequency in megahertz:
Each row below carries the logarithm result through the calculation before rounding the displayed teaching value.
| Reference | Calculation | Checked result |
| 900 MHz at 1 km | 32.45 + 20 log10(1) + 20 log10(900) = 32.45 + 0 + 59.08 | 91.53 dB, so about 91.5 dB |
| 2.4 GHz at 1 km | 32.45 + 0 + 20 log10(2400) = 32.45 + 67.60 | 100.05 dB, so about 100 dB |
| 5 GHz at 1 km | 32.45 + 0 + 20 log10(5000) = 32.45 + 73.98 | 106.43 dB, which rounds to the chapter's about 107 dB |
The Anchor Used by the Log-Distance Example
2. The 1 m anchor used by the log-distance example. A 2.4 GHz signal at 1 m is the same FSPL equation with 0.001 km for distance:
The Free-Space and Indoor Examples
3. The 30 m free-space and indoor examples. Starting from the chapter's rounded 40 dB 1 m reference, only the distance-growth term changes:
| Model | Calculation | Checked result |
| Free-space, n = 2.0 | 40.0 + 10(2.0) log10(30) = 40.0 + 29.54 | 69.54 dB, so about 69.5 dB |
| Indoor, n = 3.2 | 40.0 + 10(3.2) log10(30) = 40.0 + 47.27 | 87.27 dB, so about 87.3 dB |
The Reviewed Link Budget
4. The reviewed link budget. The example ledger is intentionally simple so the sign of each gain and loss is visible:
What the calculation buys you: the spreadsheet is not the proof, but it shows exactly what must be checked in the field. If the measured RSSI, SNR, retries, or packet delivery contradict the 9 dB remaining margin, the release record knows which assumption to retest.
Every number above is taken from the chapter’s own link ledger and re-derived step by step.