Math Bridge: NFC Wake Budget

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Math BridgeNFCEnergy budget

Does an NFC wake device spend nothing between taps?

Put five years of quiet detector current beside the energy used by every wake-and-store event.

Eddie, the electronics guideEddie guides
The one targetSeparate stored charge, waiting energy, and event energy.
The chapter caseA 220 mAh coin cell, 0.6 µA detector, and 2.8 mA, 50 ms wake.
What it buys youA life-budget hypothesis that reveals the quiet load a demo hides.

A field team faces an unresolved physical question: Does an NFC wake device spend nothing between taps? They must answer it before changing taps/day 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 taps/day. The middle card applies this page's relationship. The green card is service hours. 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.

Taps/day changes service hours An input card leads through the page relationship to the service hours result. SET INPUT ONE CONTROL APPLY RULE predict calculate check units READ RESULT
Walk the arrows. Tap count changes event energy, but the five-year quiescent line stays fixed because it is paid continuously.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline for taps/day is 2.

  2. 2

    Name the relationship. Cusable = 220(0.99)⁵(0.80) = 167.37 mAh; Eusable = 502.12 mWh Esleep = 0.0006x3x43,800 = 78.84 mWh Eevent = 2.8x3x0.050 = 0.420 mJ; 3,650 events = 0.426 mWh

  3. 3

    Substitute the chapter fixture. Set taps/day to 2. The page ledger gives service hours as 43800 hours.

  4. 4

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

Predict, then change taps/day

Try Predict the direction of service hours. Move one control, calculate, then check your prediction.

2
Chapter baseline
Service hours

Observe Tap count changes event energy, but the five-year quiescent line stays fixed because it is paid continuously. Reset the control to 2 and compare service hours.

Explain Only taps/day 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 taps/day moves. Field effects named in the page's technical boundary stay fixed.

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

1. Start with the physical story

The NFC field may trigger the device, but a battery-backed microcontroller keeps paying for its detector every hour between taps.

Eddie: A tiny current multiplied by 43,800 hours can outweigh thousands of short events.

2. Name every algebra move

1

Derate chargeCompound self-discharge, then hold back the design reserve.

2

Convert to energyMultiply usable amp-hours by cell voltage.

3

Count waitingMultiply detector current, voltage, and all service hours.

4

Count eventsMultiply current, voltage, duration, and tap count.

3. Reproduce the chapter case

Cusable = 220(0.99)⁵(0.80) = 167.37 mAh; Eusable = 502.12 mWh
Esleep = 0.0006×3×43,800 = 78.84 mWh
Eevent = 2.8×3×0.050 = 0.420 mJ; 3,650 events = 0.426 mWh

The five-year waiting cost is 185.14 times the active cost at two taps per day.

4. Try one real input

TryMove taps per day while the cell, detector, event, and five-year interval stay fixed.

Taps/day
Service hours
Usable charge
Usable energy
Waiting energy
One event
Tap count
Active energy
Active share
Total modeled spend
Waiting/active ratio

ObserveAt two taps/day, active events spend 0.426 mWh while the detector spends 78.84 mWh waiting.

ExplainTap count changes event energy, but the five-year quiescent line stays fixed because it is paid continuously.

Technical boundaries.

This is a constant-current ledger, not a coin-cell discharge model.

Cell
Capacity, voltage, leakage, and self-discharge vary with part, temperature, age, and load pulse.
Electronics
Regulator loss, MCU boot, radio bridge, retries, storage, and sensing require measured traces.
Traffic
Taps/day is an average; commissioning bursts and faults need their own evidence.

Correct, not complete: this ledger does not predict field life or approve a battery.

5. Use the result in the lab

Measure detector current between taps and integrate a complete wake, parse, store, bridge, and return-to-sleep trace.

6. Record the evidence state

Keep cell part and lot, temperature, detector state, firmware, tap waveform, boot path, retries, storage action, and current integration window.

7. Check yourself

Does a battery-less NFC tag have this coin-cell budget?
Answer: No. This case is for a battery-backed field-detection design.
Why does 0.6 µA matter?
Answer: It flows for every service hour, so a small current accumulates into substantial energy.
Do more taps change self-discharge?
Answer: Not in this screen. Self-discharge is a separate fixed fractional assumption.
Honesty boundary.

The bridge exposes which part of the five-year budget comes from waiting and which comes from taps.

Computed
Derated charge, waiting energy, event energy, tap total, ratio, and shares are reproducible.
Specified
Cell curves, detector current, event duration, and reserve come from the selected design.
Observed
Current traces, resets, tap success, and retained events determine release evidence.

Correct, not complete: measure the complete device over the claimed temperature and service interval.

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