Ada’s Calculation Audit: Transition Cost

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

Ada's Calculation Audit: Transition Cost

A BLE node that wakes once per second sleeps for 999.6 ms at 4.8 µA, then spends 0.3 ms active at 14.6 mA and 0.14 ms moving the radio into transmit at 7 mA. That last radio-transition term is easy to fold into the active bucket — and doing so quietly hides about 9.7% of the cycle's real average current. This audit keeps the transition as its own ledger line to show why it belongs there.

Companion to the chapter Low-Power Design Strategies — every number here comes from that chapter.

Ada: Use the same one-second BLE cycle from the chapter above. Convert every duration to seconds, convert every current to microamps, then multiply current by time to get charge. Keep the radio-transition term on its own line instead of folding it into “active” – that is the whole point of this audit.

  • Sleep: 999.6 ms = 0.9996 s, so 4.8 uA x 0.9996 s = 4.79808 uA-s.
  • Active transmit and CPU: 14.6 mA = 14,600 uA and 0.3 ms = 0.0003 s, so 14,600 uA x 0.0003 s = 4.38 uA-s.
  • Radio transition: 7 mA = 7,000 uA and 0.14 ms = 0.00014 s, so 7,000 uA x 0.00014 s = 0.98 uA-s.
  • Total with transition: 4.79808 + 4.38 + 0.98 = 10.15808 uA-s; over the 1 s cycle, that averages to about 10.16 uA.
  • Total without transition: 4.79808 + 4.38 = 9.17808 uA-s; over the same 1 s cycle, that averages to about 9.18 uA.
  • Difference: 10.15808 - 9.17808 = 0.98 uA, and 0.98 / 10.15808 = 0.0965, so omitting the transition hides about 9.7% of the measured average current.

The engineering lesson is not that every BLE product has this exact budget. It is that short transition states can be large enough to change a release decision, so a current trace should label them instead of folding them into a vague active bucket.

What the audit buys you: the transition term is small in isolation (0.98 µA-s) but it sits right next to a sleep term of similar size (4.79808 µA-s), so leaving it out understates the cycle's average current by nearly a tenth. Label every state that has its own current and duration -- sleep, active, and transition -- and sum them separately before averaging.

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