Antenna Scale, Airtime, and EIRP Limits
Ada re-derives this chapter’s own numbers step by step, at full precision
ADA · CALCULATION AUDIT
Antenna Scale, Airtime, and EIRP Limits
Four short calculations, ~4 minutes
Band reviews are easier to audit when the physics and regulatory arithmetic are written next to the claim: wavelength sets antenna scale, duty cycle sets airtime, and antenna gain changes radiated power.
License-exempt bands carry rules a radio setting alone cannot satisfy. The chapter converts each band to an antenna scale — a 915 MHz quarter-wave is about 8.2 cm, a 2.4 GHz one about 3.1 cm — then meters airtime: a 1% duty cycle allows only 36 s per hour, so firmware sending one status frame a minute burns about 54 s and blows the budget. It also warns that 14 dBm into a 2 dBi antenna radiates 16 dBm EIRP, over a 14 dBm cap. This audit re-derives those antenna, airtime, and EIRP numbers to show where a compliant-looking design still fails.
Companion to the chapter IoT Frequency Bands and Licensing — every number here comes from that chapter.
1. Turn frequency into antenna scale
Using the wave relation λ = c / f with c ≈ 3.0×108 m/s, the quarter-wave length is one fourth of the wavelength:
| Band example | Calculation | Quarter-wave result |
| 915 MHz sub-GHz | 3.0×108 / (4×915×106) = 0.0820 m | 8.2 cm |
| 2.4 GHz shared spectrum | 3.0×108 / (4×2.4×109) = 0.03125 m | 3.1 cm |
The smaller 2.4 GHz antenna is easier to package, but that does not prove the installed link or coexistence story. It only closes the antenna-size part of the review.
2. Convert the duty-cycle rule into seconds
A duty-cycle limit is a fraction of time, so the hourly budget is direct:
A stricter 0.1% sub-band would give 0.001 × 3600 = 3.6 s/hour, which is why the exact regional sub-band matters.
3. Test a proposed uplink schedule
With 900 ms = 0.9 s on air per uplink:
| Question | Calculation | Result |
| Maximum 0.9 s uplinks in a 1% hour | 36 / 0.9 | 40 uplinks/hour before overhead |
| One status frame per minute | 60 × 0.9 | 54 s/hour |
| Budget check | 54 s − 36 s | 18 s/hour over the limit |
| Relative load | 54 / 36 | 1.5× the 1% airtime budget |
That is why a schedule that sounds modest in software can still fail a radio-regulation review.
4. Add antenna gain to conducted power
For the chapter’s example, negligible cable loss means:
If the allowed EIRP is 14 dBm, the configuration is 2 dB high. In linear power terms, 10^(2/10) = 1.58, so the radiated power is about 58% above that limit even though the transmitter setting alone says 14 dBm.
Every number above is taken from the chapter’s own band examples and re-derived step by step.