The Duty-Cycle Ledger
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.
See the relationship before changing it
The chapter figure below shows: Duty-cycle worked example state ledger (Example 1): sensing, transmit, wake, and sleep terms sum to 2,128.05 mA·ms, divided by the 10,000 ms cycle for a 0.213 mA average.
The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only watch and event share, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 10 %.
- 2
Name the relationship. average = 0.050 mA + 0.0095 mA per active percent
- 3
Substitute with units. 0.050 + 0.0095 x 10 = 0.145 mA
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change watch and event share
Try Predict the direction of average = 0.050 mA + 0.0095 mA per active percent. Test another watch and event share, then compare illustrative average current.
Observe More time in higher-current modes raises the weighted current above its floor. Reset watch and event share to 10 and compare illustrative average current.
Explain More time in watch and event operation replaces low-current baseline operation, so the illustrative average current rises linearly with that active share.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
Rebuild Example 1 from 80 mA × 12 ms, 40 mA × 24 ms, 10 mA × 6 ms, and 0.015 mA sleep over a 10000 ms cycle.
The current-time sum is 2128.05 mA·ms and Iavg = 0.212805 mA; adding Example 4's 15 ms guard listen raises 0.210 mA to 0.300 mA.
Each state contributes physical charge equal to current times duration, so a short omitted high-current state can materially change the cycle's weighted average.
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.
Technical boundaries: These deterministic state ledgers omit wake and radio transients, regulator efficiency, retry distributions, clock drift, battery voltage and temperature, leakage paths, and variation between devices.