Deriving the Chapter’s FSPL Numbers
Ada reproduces the chapter’s free-space path-loss figures from one formula, across both unit conventions
ADA · CALCULATION AUDIT
Deriving the Chapter's FSPL Numbers
The physics story is spherical spreading; the mathematics is a logarithmic unit check. The chapter’s distance, frequency, and comparison numbers should all reproduce from one formula — 100 m at 915 MHz costs about 71.7 dB, the same span at 2.4 GHz costs about 80 dB, and doubling distance always adds a fixed 6.02 dB. This audit rebuilds each figure from one equation across both unit conventions.
Companion to the chapter Free-Space Path Loss — every number here comes from that chapter.
Convert the Distance Once
1. Convert the distance once. The chapter uses the km/MHz form of FSPL, so the 100 m comparison becomes 0.1 km before any logarithms are taken:
| Chapter value | Calculation | Checked result |
| 100 m at 915 MHz | 20 log10(0.1) + 20 log10(915) + 32.45 = -20.00 + 59.23 + 32.45 | 71.68 dB, so about 71.7 dB |
| 100 m at 2.4 GHz | 20 log10(0.1) + 20 log10(2400) + 32.45 = -20.00 + 67.60 + 32.45 | 80.05 dB, so about 80 dB |
| Extra 2.4 GHz loss | 80.05 - 71.68, or 20 log10(2400 / 915) | 8.37 dB, so about 8.4 dB less headroom |
Verify the Same Answer With the Meters/Hz Convention
2. Verify the same answer with the meters/Hz convention. The alternate constant is useful only if the units change too:
Check the Distance-Doubling Rule From the Physics
3. Check the distance-doubling rule from the physics. Free-space power thins with distance squared, so the decibel penalty for doubling distance is independent of the starting range:
What the calculation buys you: these numbers are not range promises. They prove the open-air baseline before the review adds walls, antenna mismatch, Fresnel blockage, fade margin, receiver mode, and field evidence.
Every number above is taken from the chapter’s own FSPL example and re-derived step by step.