The Context-Weighted Current Blend

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

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Ada ADA · CALCULATION AUDIT

The Context-Weighted Current Blend

The chapter’s office node reports every 30 s when a room is occupied and every 600 s when vacant, blending its two context currents by time to reach an average of 147 uA on a 2,200 mAh pack — a claimed 2.3x battery-life improvement. That whole figure rests on weighting the busy and idle currents by their 0.375 occupied fraction rather than averaging them. This audit rebuilds the context-weighted current blend to test whether the 2.3x holds.

Companion to the chapter Context-Aware Energy Management — every number here comes from that chapter.

Ada: The battery-life claim here is a 2.3x improvement, and it stands or falls on blending the two context currents by time rather than averaging them. Let me rebuild the office-node ledger from the chapter’s own inputs (40 mA for a 250 ms burst, 12 uA deep sleep, report every 30 s when occupied and every 600 s when vacant, 0.375 occupied fraction) and carry every state to the end.

  • Occupied per cycle: active 40 mA x 0.25 s = 10 mA-s; sleep 0.012 mA x 29.75 s = 0.357 mA-s; average 10.357 / 30 = 0.345233 mA = 345.2 uA.
  • Vacant per cycle: active 10 mA-s; sleep 0.012 mA x 599.75 s = 7.197 mA-s; average 17.197 / 600 = 0.028662 mA = 28.7 uA.
  • Time-weighted blend: 0.375 x 345.2 + 0.625 x 28.7 = 129.5 + 17.9 = 147.4 uA, the chapter’s 147 uA.
  • Battery life on a 2,200 mAh pack: fixed 30 s schedule 2,200 / 0.345 = 6,377 h; context-aware 2,200 / 0.147 = 14,966 h; ratio 14,966 / 6,377 = 2.35x, rounding to the stated 2.3x.

One caution the chapter is right to raise: the always-on context sensor is not free. Add a 50 uA watcher floor to every state and the blend rises to 0.375 x 395 + 0.625 x 78.7 = 197 uA, shrinking the saving from 198 uA to 148 uA. That is the honest reading of context-aware duty cycling — the blend is only as good as the low-activity number, and a standing watcher hurts exactly the cheap context the whole scheme depends on.

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