Measured State Ledger Calculation Audit

Measured State Ledger Calculation Audit

Ada recomputes the charge ledger, average current, and pack lifetime from the measured states

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Ada ADA · CALCULATION AUDIT

Measured State Ledger Calculation Audit

The chapter measures a node’s cycle: a WiFi burst of 150 mA for 1.5 s (225 mA-s), a short sense at 40 mA, and deep sleep at 12 uA — averaging 0.395 mA for about 211 days on a 2000 mAh pack. The radio burst alone is 94.9% of the cycle charge. This audit recomputes the measured state ledger to show why shortening association beats tuning the tiny sleep term.

Companion to the chapter Lab: Energy Measurement — every number here comes from that chapter.

A battery estimate is an area-under-the-current-curve problem. The chapter's measured states already give current and time, so the review can recompute the charge ledger instead of trusting the summary.

See the relationship before changing it

The figure reads from left to right. The blue card is wi-fi association time. The middle card applies this page's rule. The green card is cycle-average current. 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 wi-fi association time, so the numeric fixture does not switch without explanation.

Wi-Fi association time changes cycle-average current An input card leads through the rule average = (150 mA x association time + 4.8 + 7.1808 mA-s) / 600 s to the cycle-average current result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. Longer association time dominates the ten-minute cycle while the sense and sleep terms stay fixed.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 1.5 s.

  2. 2

    Name the relationship. average = (150 mA x association time + 4.8 + 7.1808 mA-s) / 600 s

  3. 3

    Substitute with units. (150 x 1.5 + 4.8 + 7.1808) / 600 = 0.395 mA

  4. 4

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

Predict, then change wi-fi association time

Try Predict the direction of average = (150 mA x association time + 4.8 + 7.1808 mA-s) / 600 s. Test another wi-fi association time, then compare cycle-average current.

1.5 s
Chapter baseline
Cycle-average current

Observe Longer association time dominates the ten-minute cycle while the sense and sleep terms stay fixed. Reset wi-fi association time to 1.5 and compare cycle-average current.

Explain Longer association time dominates the ten-minute cycle while the sense and sleep terms stay 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 wi-fi association time moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only wi-fi association time. It is not a field prediction.

TryMultiply the 150 mA Wi-Fi state by its 1.5 s duration before selecting Check derivation. Add the 40 mA sensing and 12 uA sleep plateaus over the same 600 s cycle.
ObserveThe ledger totals 236.9808 mA-s and averages 0.394968 mA. Shortening association to 0.5 s reduces the average far more than trimming the already-small sleep contribution.
ExplainState charge is current multiplied by residence time. The radio contributes 94.9% of this cycle, so reducing its 225 mA-s term changes lifetime by about 2.72×.

1. Convert every state into the same unit

Deep sleep is stated as 12 uA, so it must become 0.012 mA before multiplying by seconds.

12 uA = 0.012 mA; 0.012 mA x 598.4 s = 7.1808 mA-s, rounded to 7.2 mA-s
Review item Arithmetic shown Decision signal
WiFi associate + TX 150 mA x 1.5 s = 225 mA-s This is the dominant state in the measured cycle.
Wake + sense 40 mA x 0.12 s = 4.8 mA-s The current is high, but the duration is short.
Deep sleep 0.012 mA x 598.4 s = 7.1808 mA-s Long duration does not dominate when the current floor is truly low.
Cycle total and average 225 + 4.8 + 7.1808 = 236.9808 mA-s; 236.9808 / 600 = 0.394968 mA Rounded at the end, the chapter's 0.395 mA average is verified.
Pack lifetime 2000 mAh / 0.394968 mA = 5063.7 h; 5063.7 / 24 = 211.0 days The battery estimate follows from the measured average current.
Association improvement 150 mA x 0.5 s = 75 mA-s; 75 + 4.8 + 7.1808 = 86.9808 mA-s; 86.9808 / 600 = 0.144968 mA The proposed static-IP-style reduction gives about 0.394968 / 0.144968 = 2.72x improvement.
Board sleep-floor failure 10 mA x 598.4 s = 5984 mA-s; 5984 + 225 + 4.8 = 6213.8 mA-s; 6213.8 / 600 = 10.356 mA A board-level sleep floor moves lifetime to 2000 / 10.356 = 193.1 h, about 8 days.

2. The physics conclusion is state dominance, not peak current alone

The verified ledger says the radio burst is about 225 / 236.9808 = 94.9% of the cycle charge. That is why shortening association beats tuning the already-small sleep term on the bare module.

3. The claim is bounded to this measured trace

A different board, regulator, radio attach time, reporting interval, or battery capacity must be recomputed from its own measured state ledger.

Technical boundaries
The measured-state ledger deliberately does not simulate boot failures, retry traffic, regulator loss, battery voltage variation, temperature, or cycle-to-cycle spread; it integrates the four stated current plateaus over one 600-second trace.

Work the audit first, then check the displayed derivation.

Every number above is taken from this chapter's own worked example and re-derived step by step.