Math Bridge: LoRaWAN ADR Retry Energy

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Math BridgeLoRaWANADR energy

What energy does one failed ADR guess waste?

Carry symbol time through a short-packet energy screen and its retry tax.

Eddie, the electronics guideEddie guides
The one targetCompare one SF8 packet with a failed SF7 try plus SF8 retry.
The chapter case125 kHz, 14 dBm, and 15 illustrative symbols.
What it buys youA physical energy reason for margin hysteresis.

A field team faces an unresolved physical question: What energy does one failed ADR guess waste? They must answer it before changing selected sf on the real device. Predict the direction first.

See the relationship before changing it

The figure reads from left to right. The blue card is selected sf. The middle card applies this page's relationship. The green card is selected symbol time. 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 added model holds every other chapter fixture fixed, so the numeric fixture does not switch without explanation.

Selected SF changes selected symbol time An input card leads through the page relationship to the selected symbol time result. SET INPUT ONE CONTROL APPLY RULE predict calculate check units READ RESULT
Walk the arrows. Margin hysteresis helps ADR settle instead of paying for repeated boundary crossings and retries.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline for selected sf is 8.

  2. 2

    Name the relationship. T7 = 2^7/125000 = 1.024 ms T8 = 2^8/125000 = 2.048 ms P = 10^(14/10) = 25.12 mW E = P x 15 x T

  3. 3

    Substitute the chapter fixture. Set selected sf to 8. The page ledger gives selected symbol time as 2.05 ms.

  4. 4

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

Predict, then change selected sf

Try Predict the direction of selected symbol time. Move one control, calculate, then check your prediction.

8
Chapter baseline
Selected symbol time

Observe Margin hysteresis helps ADR settle instead of paying for repeated boundary crossings and retries. Reset the control to 8 and compare selected symbol time.

Explain Only selected sf moves here. The other chapter fixtures remain fixed.

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 selected sf moves. Field effects named in the page's technical boundary stay fixed.

Honesty note. This teaching model changes only selected sf. It replays the chapter fixture; it is not a field prediction.

1. Start with the physical story

A higher spreading factor stretches every symbol. At fixed transmit power, longer airtime means more energy. If ADR guesses too aggressively at the margin, a missed cheap packet must be paid for before the safer retry.

Eddie: The failed packet did no useful work, but the battery still paid for every millisecond.

2. Name every algebra move

1

Find symbol timeDivide 2^SF by 125,000 Hz.

2

Undo dBmTurn 14 dBm into 25.12 mW.

3

Find packet energyMultiply power, 15 symbols, and symbol time.

4

Price the retryAdd failed SF7 energy to the selected packet and compare with one selected packet.

3. Reproduce the chapter case

T7 = 2^7/125000 = 1.024 ms
T8 = 2^8/125000 = 2.048 ms
P = 10^(14/10) = 25.12 mW
E = P × 15 × T

SF7 costs 0.386 mJ and SF8 costs 0.772 mJ. A failed SF7 attempt plus SF8 retry costs 1.158 mJ, 50% more than sending SF8 once.

4. Try one real input

TryMove the selected spreading factor while the failed reference remains SF7.

Selected SF
Selected symbol time
Transmit power
Selected packet energy
SF7 symbol time
Failed SF7 energy
Retry total
Retry tax
Energy ratio to SF7

ObserveAt SF8, the failed SF7 packet adds 50% to the safe packet's energy; at higher SF the same failed try is a smaller fraction but still wasted.

ExplainMargin hysteresis helps ADR settle instead of paying for repeated boundary crossings and retries.

Technical boundaries.

This is a short-symbol energy screen, not a packet-airtime calculator.

Packet
Preamble, headers, coding, payload, low-data-rate optimization, and receive windows add energy.
Power
Battery energy includes regulator, startup, MCU, PA efficiency, and receive current.
ADR
Use the implemented algorithm, evidence window, commands, acknowledgements, and retry policy.

Correct, not complete: use the measured state named above before release.

5. Use the result in ADR review

Set an evidence window and hysteresis that avoid rapid switching, then verify packet delivery, total airtime, receive windows, retries, battery current, and recovery after the path changes.

6. Record the evidence state

Record SF, bandwidth, packet settings, power and PA current, margin target, ADR window, commands, missed attempts, retries, delivery, airtime, and measured energy.

7. Check yourself

Why does SF8 use twice the symbol energy of SF7 here?
Answer: It doubles symbol time while power and symbol count stay fixed.
Where does the 50% retry tax come from?
Answer: The failed SF7 packet costs half as much as the successful SF8 packet, so it adds 50%.
Does this screen predict battery life?
Answer: No. Complete packet timing, receive windows, electronics, retries, sleep, and battery behavior remain.
Honesty boundary.

The bridge keeps ideal transmit energy separate from device and ADR evidence.

Computed
Symbol time, ideal power, packet energy, retry total, retry tax, and SF ratio.
Specified
Bandwidth, conducted power, symbol count, reference SF, ADR policy, and margin target.
Observed
Current trace, full airtime, commands, retries, delivery, path changes, and battery state.

Correct, not complete: this page does not certify ADR, packet energy, battery life, capacity, or deployment.

Return to LoRaWAN Link Budget and ADR with margin and retry energy connected →