Two Budgets a Coin Cell Must Pass

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

Two Budgets a Coin Cell Must Pass

The chapter’s sharpest claim is that a CR2032’s real limit is its resistance, not its 225 mAh: a 10 mA radio pulse sags 0.1 V on a fresh 10-15 ohm cell but 0.4 V on a 40-ohm aged one, near brownout with most charge still inside. The cell easily passes a 2.6 uA energy check yet can still reset on every transmission. This audit runs both budgets a coin cell must pass, energy and pulse-sag, together.

Companion to the chapter Battery-Life Target Contracts — every number here comes from that chapter.

Ada: This chapter’s sharpest claim is that a CR2032’s real limit is its resistance, not its milliamp-hours. The number that proves it is a 0.4 V pulse sag on an aged cell. Let me run both budgets the chapter insists must pass together — the energy check and the pulse-sag check — using its stated values (225 mAh label, 10 mA / 5 ms radio pulse, 10-15 ohm fresh rising to 40 ohm aged).

  • Energy check: a ten-year average allowance is 225 mAh / (10 x 8,760 h) = 0.00257 mA = 2.6 uA — easily met by a mostly-sleeping beacon.
  • Pulse sag, fresh: V = I x R = 0.010 A x 10 ohm = 0.1 V, so a 3.0 V terminal holds 2.9 V under the burst.
  • Pulse sag, aged: 0.010 A x 40 ohm = 0.4 V, dropping a 2.7 V open-circuit cell to 2.3 V — near a 2.0-2.2 V brownout with most of the charge still inside.
  • Brownout headroom (2.6 V cell, 10 mA pulse): a 2.4 V threshold allows only (2.6 - 2.4) / 0.010 = 20 ohm, while a 2.0 V threshold allows (2.6 - 2.0) / 0.010 = 60 ohm of internal resistance before reset.
  • Reservoir fix: for a 0.2 V droop, C = I x t / dV = 0.010 A x 0.005 s / 0.2 V = 250 uF — but its leakage counts too: 1 uA x 10 yr x 8,760 h/yr = 87.6 mAh, about 87.6 / 225 = 39% of the cell.

The audit confirms the whole message: the cell clears the energy check by a wide margin (2.6 uA against a tiny average) yet can still reset on every transmission once resistance climbs, because 0.4 V of sag is set by Ohm’s law, not by remaining charge. Usable capacity is therefore a design variable — a lower brownout threshold triples the resistance headroom (60 ohm versus 20 ohm) and unlocks charge that a higher threshold would strand.

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