The Duty-Cycle Formulas

Ada re-checks this chapter’s own formulas step by step, with no invented constants

ADA · CALCULATION AUDIT

The Duty-Cycle Formulas

This chapter defines duty cycle as the active part of a repeating schedule, where the cycle splits into an active window and a sleep window that is not optional bookkeeping. Because the chapter gives no measured currents or exact cycle windows, the arithmetic here stays symbolic rather than inventing values. This audit lays out the duty-cycle formulas — cycle time, average current, and the schedule limits — so numbers can be added only from a real trace.

Companion to the chapter Duty Cycle Fundamentals — every number here comes from that chapter.

Active fraction, charge balance, and schedule limits, no invented constants

Duty-cycle math is a charge ledger. Current multiplied by time is charge, so the average-current estimate must account for the whole cycle, not just the convenient active state.

1. Split the cycle before using a percentage

The chapter defines duty cycle as the active part of a repeating schedule. That means the sleep window is not optional bookkeeping.

T_cycle = T_active + T_sleep
D = T_active / T_cycle
T_sleep = T_cycle - T_active

2. Derive the average-current shortcut from charge balance

Substitute the active and sleep fractions into the weighted average. The units stay consistent because each current is weighted by a fraction of the same full cycle.

I_avg = D I_active + (1 - D) I_sleep
I_avg = (I_activeT_active + I_sleepT_sleep) / T_cycle

3. Expand active time when the node has real states

If wake, sense, listen, communicate, and decide states all occur, a review should not hide them inside one active-current term.

Review term	Formula shown	Why it matters
Active window	Tactive = twake + tsense + tlisten + tcomm + tdecide	Every active state named in the chapter gets a time slot.
Cycle charge	Qcycle = Iwaketwake + Isensetsense + Ilistentlisten + Icommtcomm + Idecidetdecide + IsleepTsleep	Current times time is charge; missing states understate the cycle cost.
Average current	Iavg = Qcycle / Tcycle	The denominator is the full repeating cycle, including sleep.
Schedule limit	Detection wait and communication wait are bounded by the wake schedule, not by battery arithmetic alone.	A lower average current can still fail the latency or rendezvous requirement.

The chapter does not provide measured currents, exact cycle windows, or exact latency limits, so this panel stays symbolic. Add numeric values only from a lab trace, datasheet-backed exercise, or the worked-examples chapter where the arithmetic record is supplied.

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