The Cellular Energy Ledger

The Cellular Energy Ledger

Ada audits the cellular energy ledger — one unit conversion, two ledger equations

foundations
math-foundations
cellular-iot
energy
advanced
Ada ADA · CALCULATION AUDIT

Foundations · optional mathematics and physics

The Cellular Energy Ledger

A cellular IoT device cycles through sleep, wake, network registration, payload transfer, a downlink listening window, and return to sleep, and in PSM its reachability hinges on the network-granted T3412 and T3324 timers. The chapter converts each measured state into a charge term to build daily and maintenance ledgers, yet it publishes no measured-current table to plug in. This audit works those ledgers symbolically and asks whether any trustworthy battery-life claim is possible before real trace values replace the symbols.

Companion to the chapter Cellular IoT Power Optimization — every number here comes from that chapter.

One unit conversion, two ledger equations, ~4 minutes

The physics is charge over time. A cellular battery model is only trustworthy when every measured state in the trace becomes a charge term, and when granted timers and retry behavior stay visible instead of being averaged away.

See the relationship before changing it

The figure reads from left to right. The blue card is measured state duration. The middle card applies this page's rule. The green card is state charge at 100 ma. 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 measured state duration, so the numeric fixture does not switch without explanation.

Measured state duration changes state charge at 100 ma An input card leads through the rule state charge = 100 mA x duration / 3,600 s per hour to the state charge at 100 ma result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. A longer measured state adds charge before daily retries and host overhead enter the ledger.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 4 s.

  2. 2

    Name the relationship. state charge = 100 mA x duration / 3,600 s per hour

  3. 3

    Substitute with units. 100 mA x 4 s / 3,600 = 0.111 mAh

  4. 4

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

Predict, then change measured state duration

Try Predict the direction of state charge = 100 mA x duration / 3,600 s per hour. Test another measured state duration, then compare state charge at 100 ma.

4 s
Chapter baseline
State charge at 100 mA

Observe A longer measured state adds charge before daily retries and host overhead enter the ledger. Reset measured state duration to 4 and compare state charge at 100 ma.

Explain A longer measured state adds charge before daily retries and host overhead enter the ledger.

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 measured state duration moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only measured state duration. It is not a field prediction.

Try

A cellular IoT device cycles through sleep, wake, network registration, payload transfer, a downlink listening window, and return to sleep, and in PSM its reachability hinges on the network-granted T3412 and T3324 timers. Calculate this case.

Observe

This audit works those ledgers symbolically and asks whether any trustworthy battery-life claim is possible before real trace values replace the symbols. Check shows this.

Explain

The calculation is deliberately symbolic because the chapter has no measured current table to reuse. The release decision should therefore demand real trace values before turning these equations into a battery-life claim. Check confirms it.

Technical boundaries

Beyond the scope of “The Cellular Energy Ledger” sit network attach retries, coverage-dependent transmit power, paging, signalling, battery ageing, regulator loss, or measured modem current transients; “The Cellular Energy Ledger” therefore reports only its named fixtures.

Convert each measured state

The chapter's formula uses current in milliamps and duration in seconds, so the hour conversion is explicit.

state_mAh = current_mA x duration_seconds / 3600
because 1 hour = 3600 seconds, mA x seconds / seconds_per_hour = mAh

That unit check is the guardrail: sleep, wake, registration, transfer, listening, retry, and host cleanup each need their own term before the daily average is credible.

Keep rare events in the ledger

Carry the same charge terms into the daily and maintenance ledgers.

normal_day_mAh = sleep_state_mAh + wake_cycles_per_day x measured_wake_and_send_mAh + granted_active_window_mAh + expected_retry_mAh + host_and_sensor_mAh + self_discharge_allowance
maintenance_day_mAh = normal_day_mAh + update_transfer_mAh + diagnostic_session_mAh + retry_margin_mAh
usable_life_days = usable_battery_capacity_mAh / measured_daily_mAh

If weak coverage adds an extra retry term, the denominator becomes larger.

new_denominator = measured_daily_mAh + extra_retry_mAh; when extra_retry_mAh > 0, usable_life_days falls

The calculation is deliberately symbolic because the chapter has no measured current table to reuse. The release decision should therefore demand real trace values before turning these equations into a battery-life claim.

Every symbol above is taken from the chapter's own cellular energy example and re-derived step by step.