Math Bridge: FLiRS Battery Screen

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Math BridgeFLiRSBattery screen

What does frequent listening cost a battery endpoint?

Connect a listen interval to duty cycle, average current, usable charge, runtime, and the voltage sag that can break a radio burst.

Eddie, the electronics guideEddie guides
The one targetTurn a FLiRS listen interval into a bounded current and runtime ledger.
The chapter caseA 3 ms, 5 mA listen every 250 ms with 2 µA sleep current.
What it buys youA battery and route-health acceptance question that can be measured.

A field team has a real problem to settle: What does frequent listening cost a battery endpoint? They must decide what happens before they change listen interval on the device. Predict the direction first.

See the relationship first

The figure reads from left to right. The blue card is listen interval. The middle card uses this page's rule. The green card is listen duty. Follow the arrows: set the input, use the rule, then read the result and its unit.

The audit later on checks more than one number. Here, the added model uses the baseline named below and holds every other chapter value fixed. That sentence bridges the fixtures, so the numbers do not change without a reason.

Listen interval changes listen duty An input card leads through the page rule to the listen duty result. SET INPUT ONE CONTROL USE RULE predict calculate check units READ RESULT
Follow the arrows. Interval controls duty and average current. Sag stays tied to the separate transmit pulse and cell resistance assumptions.

Derive the baseline in four moves

  1. 1

    Name the input. The chapter baseline for listen interval is 250.

  2. 2

    Name the rule. duty = 3 / 250 = 1.20% I_avg = 0.012 x 5 + 0.988 x 0.002 = 0.06198 mA C_usable = 1500 x 0.99^2 x 0.80 = 1176.1 mAh runtime = 1176.1 / 0.06198 = 18,976 h = 2.17 years

  3. 3

    Put in the chapter value. Set listen interval to 250. The page rule gives listen duty as 1.20%.

  4. 4

    Read the result. Keep % next to the value. Use it only within the limits on this page.

Predict, then change listen interval

Try Predict what happens to listen duty. Move one control, calculate, then check your idea.

250
Chapter baseline
Listen duty

Observe Interval controls duty and average current. Sag stays tied to the separate transmit pulse and cell resistance assumptions. Reset to 250 and compare listen duty.

Explain Only listen interval moves here. The other chapter values stay fixed.

Check yourself

What should you do before you trust the result?
Answer: Predict its direction, use the shown rule, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only listen interval moves. Field effects named in the page limits stay fixed.

Honesty note. This teaching model changes only listen interval. It replays the chapter baseline; it is not a field prediction.

1. Start with the physical story

A listening endpoint saves charge by sleeping between brief checks. Shortening the interval increases checks and average current; an aged cell can also sag precisely during the high-current transmit pulse.

Eddie: Resting voltage and runtime arithmetic answer different questions, so keep both in the acceptance record.

2. Name every algebra move

1

Find dutyDivide listen duration by listen interval.

2

Average currentWeight listen and sleep currents by their time fractions.

3

Derate chargeApply self-discharge and the reserved design margin.

4

Screen runtimeDivide usable mAh by average mA.

5

Check sagUse ΔV = IR for fresh and aged internal resistance.

3. Reproduce the chapter case

duty = 3 / 250 = 1.20%
I_avg = 0.012 × 5 + 0.988 × 0.002 = 0.06198 mA
C_usable = 1500 × 0.99^2 × 0.80 = 1176.1 mAh
runtime = 1176.1 / 0.06198 = 18,976 h = 2.17 years

A 35 mA transmit burst sags 17.5 mV across 0.5 Ω but 175 mV across 5 Ω, leaving 2.825 V from the same nominal 3 V source.

4. Try one real input

TryMove the listen interval. Duty, daily checks, average current, and the listen/sleep-only runtime screen recompute together.

Listen interval
Listen duty
Average current
Usable charge
Runtime hours
Runtime days
Runtime years
Wake checks per day
Listen-cycle energy per day
Fresh-cell sag
Fresh loaded voltage
Aged-cell sag
Aged loaded voltage

ObserveAt 250 ms, 345,600 daily checks produce 0.06198 mA average current and a 2.17-year listen/sleep-only screen.

ExplainInterval controls duty and average current. Sag stays tied to the separate transmit pulse and cell resistance assumptions.

Technical boundaries.

This is a listen-current and sag screen, not a product battery claim.

Protocol
Actual FLiRS timing and radio work depend on certified device behavior and network state.
Cell
Capacity, resistance, temperature, discharge curve, and cutoff must come from the chosen cell and device.
Workload
Transmit, actuator, sensing, leakage, retries, and conversion losses are not included in runtime.

Correct, not complete: this ledger cannot certify a lock runtime or route.

5. Use the result in acceptance

Measure current and loaded voltage at the chosen interval, then repeat with aged-cell impedance and weak-route retries before accepting the endpoint placement.

6. Record the evidence state

Keep device role, firmware, interval, cell model and lot, age, temperature, current trace, brownout threshold, route, retries, and retest trigger.

7. Check yourself

Why does a longer listen interval improve this runtime screen?
Answer: The fixed listen window occupies less of each cycle, reducing average current.
Can resting voltage reveal the 175 mV transmit sag?
Answer: No. Loaded voltage must be captured during the current pulse.
Does 2.17 years predict the installed lock?
Answer: No. It includes only the named listen and sleep currents under illustrative cell assumptions.
Honesty boundary.

The ledger keeps duty-cycle runtime and pulse sag visible but separate.

Computed
Duty, average current, derated charge, runtime, and IR sag are reproducible.
Measured
Current pulses, cutoff, route retries, and aged-cell resistance require device evidence.
Excluded
Actuation, sensing, conversion, temperature, and ordinary network traffic remain outside runtime.

Correct, not complete: use this to shape acceptance tests, not advertise lifetime.

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