Math Bridge: CoAP Message Charge and Sleep Current

← Back to CoAP Message Types
Math BridgeCoAPStruggle-friendly runway

Where does an eight-year NON lifetime really come from?

Add the current that flows between messages to the chapter's CON and NON active-charge rows.

Eddie, the electronics guideEddie guides
The one targetTurn active mAh/day plus sleep microamps into one complete average-current ledger.
The chapter case0.0136 mAh/day NON, 0.218 mAh/day CON, and a 1000 mAh cell.
What it buys youAn explanation for the chapter's roughly eight-year and five-year practical rows.

See the relationship before changing it

The figure reads from left to right. The blue card is sleep current. The middle card applies this page's rule. The green card is non total daily charge. 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 sleep current, so the numeric fixture does not switch without explanation.

Sleep current changes non total daily charge An input card leads through the rule total = 0.0136 + sleep current x 24 / 1,000 to the non total daily charge result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. Sleep current adds to active charge every hour, even when no packet moves.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 13.75 uA.

  2. 2

    Name the relationship. total = 0.0136 + sleep current x 24 / 1,000

  3. 3

    Substitute with units. 0.0136 + 13.75 x 24 / 1,000 = 0.3436 mAh/day

  4. 4

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

Predict, then change sleep current

Try Predict the direction of total = 0.0136 + sleep current x 24 / 1,000. Test another sleep current, then compare non total daily charge.

13.75 uA
Chapter baseline
NON total daily charge

Observe Sleep current adds to active charge every hour, even when no packet moves. Reset sleep current to 13.75 and compare non total daily charge.

Explain Sleep current adds to active charge every hour, even when no packet moves.

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 sleep current moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only sleep current. It is not a field prediction.

1. Start with the physical story

The transmitter is active for only a small part of each day. The radio, microcontroller, regulator, and sensors can still draw current between messages. Battery life must count both parts.

Eddie: Milliamp-hours per day and microamps can be joined after turning the sleep current into a daily charge.

2. Name every algebra move

1

Convert sleep currentMultiply µA by 24 hours and divide by 1,000 to obtain mAh/day.

2

Add active chargeAdd 0.0136 for NON or 0.218 for CON.

3

Recover average currentMultiply daily mAh by 1,000 and divide by 24.

4

Find lifetimeDivide 1000 mAh by daily charge, then divide days by 365.

5

Keep voltage separateUse IR for the fresh-cell transmit and ACK sag checks.

3. Reproduce the chapter case

sleep charge = 13.75 µA × 24/1000 = 0.330 mAh/day
NON total = 0.0136 + 0.330 = 0.3436 mAh/day
CON total = 0.218 + 0.330 = 0.548 mAh/day
NON life = 1000/0.3436/365 = 7.97 years
CON life = 1000/0.548/365 = 5.00 years

The hidden sleep term is most of the NON budget and still a large part of the CON budget. It reconciles the practical lifetimes without changing the active-message arithmetic.

4. Try one real input

TryMove background sleep current from 13.75 µA upward. Watch both lifetimes fall and the active-message shares shrink.

Sleep current
Sleep charge
NON daily charge
CON daily charge
NON average current
CON average current
NON lifetime
CON lifetime
NON active share
CON active share
NON active energy
CON active energy
TX pulse sag
ACK pulse sag

ObserveAt 13.75 µA, the calculated lifetimes are about 8.0 and 5.0 years. Raising sleep current harms both modes even though their packet costs stay unchanged.

ExplainSleep current is paid for every hour, so it can dominate a very efficient NON message path.

Technical boundaries.

This ledger reproduces the chapter's active-charge and practical-life reconciliation.

Background
The slider combines all between-message loads into one constant current.
Cell
Capacity is treated as fully usable; self-discharge, temperature, ageing, cutoff, and recovery are omitted.
Traffic
Retries, lost ACKs, changing intervals, and payload-dependent airtime are not added.

Correct, not complete: this ledger does not predict deployed battery life or choose CON versus NON by itself.

5. Use the result in the design

Measure sleep current on the assembled device, not just the radio datasheet. Then combine that trace with the actual CON/NON schedule, retry behaviour, and the cell's usable-capacity qualification.

6. Record the evidence state

Record firmware state, sensor and regulator modes, measured sleep current, packet interval, CON/NON choice, ACK timeout, retry count, pulse sag, temperature, and tested cutoff.

7. Check yourself

Why multiply sleep microamps by 24?
Answer: Current is charge per hour, so 24 hours turns the constant background current into one day's charge.
Why does NON benefit more from reducing sleep current?
Answer: NON's active charge is tiny, so background current is a larger fraction of its total.
Does the 4 mV fresh-cell sag prove the design is safe for years?
Answer: No. Resistance, voltage, temperature, wiring, and cutoff change as the cell and product age.
Honesty boundary.

This ledger reproduces the chapter's active-charge and practical-life reconciliation.

Background
The slider combines all between-message loads into one constant current.
Cell
Capacity is treated as fully usable; self-discharge, temperature, ageing, cutoff, and recovery are omitted.
Traffic
Retries, lost ACKs, changing intervals, and payload-dependent airtime are not added.

Correct, not complete: this ledger does not predict deployed battery life or choose CON versus NON by itself.

Return to CoAP Message Types with the maths unpacked →