Antenna Scale, Airtime, and EIRP Limits

Antenna Scale, Airtime, and EIRP Limits

Ada re-derives this chapter’s own numbers step by step, at full precision

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Ada 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.

See the relationship before changing it

The figure reads from left to right. The blue card is uplink airtime. The middle card applies this page's rule. The green card is airtime used each hour. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only uplink airtime, so the numeric fixture does not switch without explanation.

Uplink airtime changes airtime used each hour An input card leads through the rule hourly airtime = 60 uplinks x airtime per uplink to the airtime used each hour result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. Longer packets consume more of the fixed hourly duty-cycle allowance.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 0.9 s.

  2. 2

    Name the relationship. hourly airtime = 60 uplinks x airtime per uplink

  3. 3

    Substitute with units. 60 x 0.9 s = 54.0 s/hour

  4. 4

    Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.

Predict, then change uplink airtime

Try Predict the direction of hourly airtime = 60 uplinks x airtime per uplink. Test another uplink airtime, then compare airtime used each hour.

0.9 s
Chapter baseline
Airtime used each hour

Observe Longer packets consume more of the fixed hourly duty-cycle allowance. Reset uplink airtime to 0.9 and compare airtime used each hour.

Explain Longer packets consume more of the fixed hourly duty-cycle allowance.

Check yourself

What should you do before trusting a moved-control result?
Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only uplink airtime moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only uplink airtime. It is not a field prediction.

TryRun Check derivation for 915 MHz, a 1% duty cycle, and 14 dBm conducted power into a 2 dBi antenna.
ObserveThe evidence shows an 8.2 cm quarter-wave, only 36 s/hour of airtime, and 16 dBm EIRP.
ExplainFrequency fixes antenna scale, duty-cycle percentage limits accumulated transmit seconds, and antenna gain adds to conducted power when checking the EIRP cap.

Ready: use the stated baseline inputs, then compare each displayed result.

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:

λ/4 = c / (4f)
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:

1% of one hour = 0.01 × 3600 s = 36 s/hour

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:

EIRP = 14 dBm + 2 dBi − 0 dB = 16 dBm

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.

Technical boundaries. Antenna efficiency, clutter, scheduler bursts, certification tolerances, and jurisdiction-specific exceptions remain outside this fixed-frequency compliance screen.