The Duty-Cycle Ledger
Ada re-derives this chapter’s own numbers step by step, at full precision
ADA · CALCULATION AUDIT
The Duty-Cycle Ledger
Charge per state, average current, and budget margin, ~4 minutes
Duty-cycle math is physics bookkeeping: current multiplied by time is charge moved through the device, and average current is that charge spread across the whole cycle.
A device ledger splits operation into baseline (fraction 0.80 at 0.050 mA), watch (0.15 at 0.200 mA), and event (0.05 at 1.000 mA) modes against a 0.150 mA current budget, while a separate trace shows a simple ledger predicting 0.210 mA but a measured trace reading 0.300 mA until a 60 ms guard-listen state at 15 mA is added back across the 10,000 ms cycle. This audit asks the question those numbers invite: does the weighted-mode average really clear the budget, and does the guard-listen state fully explain the 0.300 mA measurement gap?
Companion to the chapter WSN Duty Cycle Worked Examples — every number here comes from that chapter.
1. The core equation is a weighted average
Each state contributes a current-time term. Divide the full current-time sum by the full cycle length, including sleep, wake, transmit, and guard states.
Because 1 mA for 1 ms equals 1 microcoulomb of charge, the ledger is not just arithmetic decoration. It is the physical charge budget for one cycle, written in reviewable units.
The worked-example ledger
| Review question | Arithmetic shown | Audit result |
| Example 1 current-time sum | 80 x 12 = 960; 40 x 24 = 960; 10 x 6 = 60; sleep = (10,000 - 80 - 40 - 10) x 0.015 = 148.05 | 960 + 960 + 60 + 148.05 = 2,128.05 mA*ms |
| Example 1 average current | 2,128.05 / 10,000 | 0.212805 mA, rounded to 0.213 mA |
| Example 2 active ledger | 15 x 8 = 120; 120 x 10 = 1,200; 60 x 28 = 1,680 | 3,000 mA*ms over 195 ms of active states |
| Example 2 cycle-length solve | 0.080T = 3,000 + 0.012(T - 195); 0.068T = 2,997.66 | T = 44,083 ms, about 44.1 s |
| Example 3 weighted modes | 0.80 x 0.050 + 0.15 x 0.200 + 0.05 x 1.000 | 0.040 + 0.030 + 0.050 = 0.120 mA, which uses 80% of the 0.150 mA budget |
| Example 4 missing guard-listen state | 60 x 15 / 10,000 | 0.090 mA; 0.210 + 0.090 = 0.300 mA |
What the audit buys you: each example now has a reproducible physical ledger. If a reviewer changes a state current, duration, mode fraction, or cycle length, the decision changes immediately and the retest trigger is no longer optional.
Every number above is taken from the chapter’s own worked examples and re-derived step by step.