Math Bridge: Z-Wave Endpoint Budget

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Math BridgeZ-WaveSleepy endpoint

Can the endpoint meet its life target in the right region?

Put the charge budget, wake schedule, regional carrier, and quarter-wave antenna target on one ledger.

Eddie, the electronics guideEddie guides
The one targetCompare modeled average current with the derated service-life budget.
The chapter caseAn 850 mAh CR2-class cell, five years, and EU/US/ANZ carriers.
What it buys youA bounded battery and regional-RF review before hardware approval.

See the relationship before changing it

The figure reads from left to right. The blue card is five-year current budget. The middle card applies this page's rule. The green card is hours supported by retained 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 five-year current budget, so the numeric fixture does not switch without explanation.

Five-year current budget changes hours supported by retained charge An input card leads through the rule runtime = 646,670 uAh / current to the hours supported by retained charge result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. Larger average current consumes the retained CR2-class charge sooner.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 14.76 uA.

  2. 2

    Name the relationship. runtime = 646,670 uAh / current

  3. 3

    Substitute with units. 646,670 / 14.76 = 43,812 hours

  4. 4

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

Predict, then change five-year current budget

Try Predict the direction of runtime = 646,670 uAh / current. Test another five-year current budget, then compare hours supported by retained charge.

14.76 uA
Chapter baseline
Hours supported by retained charge

Observe Larger average current consumes the retained CR2-class charge sooner. Reset five-year current budget to 14.76 and compare hours supported by retained charge.

Explain Larger average current consumes the retained CR2-class charge sooner.

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 five-year current budget moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only five-year current budget. It is not a field prediction.

1. Start with the physical story

A sleepy endpoint can miss its life target through current draw and miss its network through a region-mismatched radio. Both checks belong in architecture review.

Eddie: Battery charge and antenna length use different equations, but both are fixed by explicit design choices.

2. Name every algebra move

1

Derate chargeCompound self-discharge and reserve margin.

2

Set the ceilingDivide usable mAh by all service hours.

3

Average modesTurn supervisory, event, and sleep states into mAh/day.

4

Size the waveDivide wave speed by each regional frequency, then by four.

3. Reproduce the chapter case

Cusable = 850(0.99)⁵(0.80) = 646.67 mAh
Ibudget = 646.67 / 43,800 = 14.76 µA; Imodeled = 2.37 µA
λ/4 = 8.64 cm EU; 8.26 cm US; 8.14 cm ANZ

The example uses 16.04% of the five-year average-current ceiling before unmodeled sensor, regulator, temperature, and ageing loads.

4. Try one real input

TryMove the service target while the cell, wake schedule, and regional carriers stay fixed.

Service target
Service hours
Usable charge
Average-current budget
Modeled average
Budget used
EU wavelength
US wavelength
ANZ wavelength
EU quarter wave
US quarter wave
ANZ quarter wave

ObserveAt five years the modeled 2.37 µA is 16.04% of a 14.76 µA ceiling; longer targets shrink the ceiling.

ExplainService time changes charge headroom, while the regional wavelengths remain fixed by their carrier plans.

Technical boundaries.

This combines an average-current screen with ideal free-space antenna lengths.

Battery
Temperature, pulse sag, regulator loss, ageing, sensor bias, retries, and cutoff require component data and traces.
Schedule
Hourly supervision and ten events/day are illustrative catalog-style assumptions, not a traffic guarantee.
Antenna
A quarter wave is a starting scale; enclosure, ground, matching, certification, and region rules control the released RF design.

Correct, not complete: this screen does not approve battery life or regional hardware.

5. Use the result in the lab

Measure sleep, supervision, event, retry, and fault modes; then verify the exact regional part and antenna match in the enclosure.

6. Record the evidence state

Keep cell lot, temperature, cutoff, current traces, wake schedule, firmware, region code, RF part, antenna match, certification, and failure triggers.

7. Check yourself

Does 16% budget use prove five-year life?
Answer: No. Important loads and real cell behavior still need measurement.
Why is a US device not just an EU device on another channel?
Answer: Its RF front end, matching, antenna target, certification, and allowed frequencies differ.
Does λ/4 specify the final antenna?
Answer: No. It is an ideal scale before enclosure and matching effects.
Honesty boundary.

The bridge keeps the battery and regional-RF claims explicit and separately testable.

Computed
Derated charge, current ceiling, modeled average, use fraction, wavelengths, and quarter waves are reproducible.
Specified
Cell, schedule, carrier plan, antenna implementation, and release margin come from the selected product.
Observed
Current traces, resets, RF match, range, retries, and certification evidence decide the release.

Correct, not complete: prove the endpoint in its claimed region and service conditions.

Return to Z-Wave Architecture with both budgets visible →