The Coin-Cell Beacon’s Duty-Cycle Budget

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

ADA · CALCULATION AUDIT

The Coin-Cell Beacon's Duty-Cycle Budget

A BLE temperature sensor advertises every 1,000 ms, drawing 15 mA for 2 ms and just 2 µA asleep from a 220 mAh CR2032 coin cell — a 0.2% duty cycle and a 0.032 mA average. That yields 6,875 hours of life, which the chapter rounds up toward “approximately 1 year.” This audit re-derives the cascade and asks whether those inputs honestly reach a year, or land closer to 286 days.

Companion to the chapter Quizzes and Practice Problems — every number here comes from that chapter.

Ada: The calculation problem builds a battery life from an advertising duty cycle. The duty-cycle and average-current steps are exactly right; the day count needs a careful look, so let me carry it through.

Starting from a 1,000 ms advertising period, 15 mA for 2 ms active, 2 µA (0.002 mA) asleep, and a 220 mAh cell:

• Duty cycle: 2 ms / 1,000 ms = 0.002 = 0.2%.
• Average current: (15 mA x 0.002) + (0.002 mA x 0.998) = 0.030000 + 0.001996 = 0.031996 mA, which rounds to the stated 0.032 mA.
• Battery life: 220 mAh / 0.032 mA = 6,875 hours, and 6,875 / 24 = 286.46 days.

So 6,875 hours is about 286 days – roughly 0.78 of a year. The chapter’s follow-on “286-365 days … approximately 1 year” is optimistic: real-world self-discharge (~15%/year) only subtracts from the 286-day figure, it cannot lift it toward 365. The honest, reproducible result from these inputs is 286 days. The design meaning is that the 0.2% duty cycle is what buys that life: the beacon is awake only 1/500 of the time, so the 15 mA active draw is diluted about 500-fold to the 0.032 mA average a coin cell can sustain for the better part of a year.

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