The Sweep Beats the Single Number

Ada re-derives this chapter’s own numbers step by step, at full precision

foundations
math-foundations
calculation-audit
energy-power
Ada ADA · CALCULATION AUDIT

The Sweep Beats the Single Number

The chapter’s headline is a tidy 4.2-year lifetime for a node that draws 50 mA for 0.5 s each hour and 20 uA asleep on a 1000 mAh cell. But the useful result is buried in the sweep: halving sleep buys +59% while halving the far larger active current buys only +15%, because the node sleeps for 74.2% of every hour. This audit rebuilds the ledger to show the sweep beats the single number.

Companion to the chapter Power Management Tools — every number here comes from that chapter.

Ada: This chapter’s headline is a tidy 4.2-year lifetime, but the useful claim is buried in the sweep: halving sleep buys +59% while halving the far larger active current buys only +15%. That ranking is what tells you where to spend measurement effort, so let me rebuild the once-per-hour ledger from the chapter’s own inputs (50 mA for 0.5 s, 20 uA sleep, 3600 s period, 1000 mAh cell) and carry full precision to the end.

  • Active charge: 50 mA x 0.5 s = 25.0 mA-s.
  • Sleep charge: 0.020 mA x 3599.5 s = 71.99 mA-s — sleep is 71.99 / 96.99 = 74.2% of the hourly budget.
  • Total and average: 96.99 mA-s / 3600 s = 0.0269417 mA = 26.94 uA.
  • Lifetime: 1000 mAh / 0.0269417 mA = 37,117 h = 4.24 years. (The chapter’s 37,175 h divides by the 3-significant-figure 26.9 uA; carrying full precision trims it by about 58 h, roughly 0.16% — both are “about 4.2 years.”)
  • Halve sleep to 10 uA: Iavg = 16.94 uA, life 59,021 h = 6.74 years — a 26.94 / 16.94 = +59.0% gain.
  • Halve active to 25 mA: Iavg = 23.47 uA, life 42,609 h = 4.86 years — only +14.8%.

The audit confirms the ranking and names why it holds: because the device sleeps for 3599.5 of every 3600 seconds, the 20 uA sleep term carries three-quarters of the average even though 50 mA is the bigger current on the trace. A lifetime figure alone would hide that — the sweep is the output that decides which input earns the careful bench measurement.

Every number above is taken from the chapter’s own material and re-derived step by step.