16 WSN Duty Cycle Worked Examples

16.1 Start With the Field Story

Treat each duty-cycle example as a small energy ledger. List the states, attach a current draw and time share to each one, include wake and communication overhead, then ask whether the resulting average current matches the lifetime claim.

16.2 In 60 Seconds

Duty-cycle examples are useful when each calculation is tied to an evidence record. A reviewable example lists the states, current draw, active interval, cycle length, omitted overhead, average-current result, and retest trigger.

This chapter uses supplied exercise values only. The goal is not to promise an operating interval for a particular node. The goal is to show how to check a duty-cycle claim, find missing states, and write a bounded decision.

Phoebe’s Field Notes: The mA Ledger Hides A Volt And A Band Choice

The mathematical gist. The chapter’s 160-bit, 24 mA transmit at 4,000 bit/s lasts 40.0 ms and spends 960 mA·ms. A catalog-typical depleted CR2032 sags 0.480 V to 2.52 V, only 0.12 V above a 2.4 V brownout line. After explicit retention, cold, and cutoff factors, 157 mAh at the chapter’s 0.213 mA average gives about 739 h or 30.8 days. Charge, energy, voltage sag, and airtime are separate checks.

Math Bridge · guided foundationsWill the radio survive its 24 mA burst, not just average it?Let Packet Pete turn payload bits into airtime, sag, usable charge, and bounded runtime. Learn the maths

16.3 Learning Objectives

By the end of this chapter, you will be able to:

• Build a state ledger for a duty-cycled sensor node.
• Compute average current from active, wake, transmit, listen, and sleep states.
• Solve for a cycle length from a current budget.
• Compare a simple calculation with a measured trace and explain the gap.
• Record validation evidence and retest triggers for duty-cycle examples.

16.4 Quick Check: Duty Cycle Worked Examples

16.5 Minimum Viable Understanding

Duty cycle is an active fraction, but average current depends on every state in the cycle. Sleep current is small per instant but can dominate a long cycle. Wake, listen, guard, and transmit states should not be hidden inside a single active number. A current budget can be used to solve for the longest acceptable cycle length. Weighted mode examples must state how much of the record is spent in each mode. A calculation is not accepted until the record states what was measured, assumed, and excluded.

16.6 Prerequisites

• WSN Energy Duty Cycling: active fraction, sleep states, average-current basics, and schedule evidence.
• WSN Energy Management: why battery, current, latency, and measurement records belong in the same design review.
• Topology Management Techniques: follow-on review of topology policies.

16.7 Review Pattern

Worked examples matter because duty-cycle decisions usually fail in the gap between a neat percentage and an operating record. Treat each example as a small audit trail: follow the numbers, then ask what the calculation proves, what it leaves out, and what field evidence would confirm that the schedule is still acceptable.

Each worked example should produce a short review record:

Question: what claim is being checked? State ledger: which states occur in one cycle? Inputs: current draw, active interval, cycle length, and units. Calculation: current-time sum divided by the full cycle length. Evidence: trace, log, or inspection that supports the inputs. Decision: accept, revise, or retest. Retest trigger: the change that makes the calculation stale.

Make Review Pattern testable with the visual in Figure 16.1. The Duty-Cycle Worked Example: State Ledger and Exercise question checkpoints frame the evidence behind Review Pattern.

In the Figure 16.1 visual, Duty-Cycle Worked Example: State Ledger exposes energy cost. The next element, Exercise question, names a responsibility; State names a responsibility. Retaining both Duty-Cycle Worked Example: State Ledger and State makes 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 auditable. The Review Pattern evidence record should retain Exercise question.

Concrete example context: treat each exercise as a review of a battery-powered status node, such as a leak detector or soil-moisture node, before its schedule is accepted for a field trial. The arithmetic is useful only because the ledger explains what the node actually does during wake, sense, listen, transmit, and sleep states.

16.8 Example 1: Expand A Simple Cycle

Question

A learner claims that a node uses only its sensing and transmit states during a repeating cycle. Check the average-current result after adding wake and sleep states.

Given exercise record

• Sensing state: 80 ms at 12 mA.
• Transmit state: 40 ms at 24 mA.
• Wake overhead: 10 ms at 6 mA.
• Sleep state: remaining interval at 0.015 mA.
• Full cycle length: 10,000 ms.

Step 1: compute the known current-time terms

sensing  = 80 ms  x 12 mA  = 960 mA*ms
transmit = 40 ms  x 24 mA  = 960 mA*ms
wake     = 10 ms  x 6 mA   = 60 mA*ms

Step 2: compute the sleep interval

sleep interval = 10,000 ms - 80 ms - 40 ms - 10 ms
sleep interval = 9,870 ms
sleep term     = 9,870 ms x 0.015 mA = 148.05 mA*ms

Step 3: divide by the full cycle length

current-time sum = 960 + 960 + 60 + 148.05
current-time sum = 2,128.05 mA*ms
average current  = 2,128.05 / 10,000
average current  = 0.213 mA

Decision

Revise the original claim if it omitted wake or sleep states. The corrected average current for this exercise record is 0.213 mA.

Retest trigger

Repeat the review if any state interval, current draw, cycle length, or radio behavior changes.

16.9 Example 2: Solve For The Cycle Length

Question

A review record gives the maximum average current as 0.080 mA. Determine the cycle length that keeps the example at or below that budget.

Given exercise record

• Wake state: 15 ms at 8 mA.
• Sensing state: 120 ms at 10 mA.
• Transmit state: 60 ms at 28 mA.
• Sleep current: 0.012 mA.
• Maximum average current: 0.080 mA.

Step 1: compute active current-time sum

wake     = 15 ms  x 8 mA  = 120 mA*ms
sensing  = 120 ms x 10 mA = 1,200 mA*ms
transmit = 60 ms  x 28 mA = 1,680 mA*ms
active current-time sum = 3,000 mA*ms
active interval = 195 ms

Step 2: solve for cycle length

Let T be the full cycle length in milliseconds.

0.080 = (3,000 + 0.012 x (T - 195)) / T
0.080T = 3,000 + 0.012T - 2.34
0.068T = 2,997.66
T = 44,083 ms

Step 3: interpret the answer

The cycle length must be at least about 44.1 s for the supplied values to meet the current budget. A shorter cycle can still work if another state is reduced, but that new design needs its own record.

Decision

Accept the schedule only if the implementation actually uses a cycle length at or above the computed value and the trace confirms the listed states.

Retest trigger

Repeat the review if the current budget, active interval, transmit interval, or sleep current changes.

16.10 Example 3: Weighted Modes

Question

A node has three operating modes during an observation record. Compute the weighted average current and decide whether the record supports the current budget.

Given exercise record

• Baseline mode: fraction 0.80, average current 0.050 mA.
• Watch mode: fraction 0.15, average current 0.200 mA.
• Event mode: fraction 0.05, average current 1.000 mA.
• Current budget: 0.150 mA.

Step 1: multiply each mode by its fraction

baseline contribution = 0.80 x 0.050 mA = 0.040 mA
watch contribution    = 0.15 x 0.200 mA = 0.030 mA
event contribution    = 0.05 x 1.000 mA = 0.050 mA

Step 2: add the contributions

weighted average current = 0.040 + 0.030 + 0.050
weighted average current = 0.120 mA

Decision

Accept the calculation for the supplied observation record because 0.120 mA is below the 0.150 mA budget. The decision is bounded to the stated mode fractions.

Retest trigger

Repeat the review if event mode becomes more common, if any mode current changes, or if the mode classification rule changes.

16.11 Example 4: Explain A Measurement Gap

Question

A simple ledger predicts 0.210 mA, but a measured trace shows 0.300 mA. Find a plausible missing state before changing the schedule.

Given exercise record

Simple ledger result: 0.210 mA. Measured trace result: 0.300 mA. Full cycle length: 10,000 ms. Trace inspection finds a guard-listen state: 60 ms at 15 mA.

Step 1: compute the missing guard-listen contribution

guard-listen term = 60 ms x 15 mA = 900 mA*ms
guard-listen average contribution = 900 / 10,000
guard-listen average contribution = 0.090 mA

Step 2: add it to the simple ledger

corrected average current = 0.210 mA + 0.090 mA
corrected average current = 0.300 mA

Decision

The measured trace is consistent with the missing guard-listen state. Revise the ledger rather than treating the measurement as a fault.

Retest trigger

Repeat the review if guard-listen length, synchronization policy, radio state, or cycle length changes.

Evidence for Example 4: Explain A Measurement Gap starts in Figure 16.2. Look at Duty-Cycle Worked Example Review Loop beside Inspect the ledger for before accepting the evidence behind Example 4: Explain A Measurement Gap.

At Figure 16.2, Duty-Cycle Worked Example Review Loop exposes energy cost; moving to Inspect the ledger for shows how it names a responsibility. The missing states before label names a responsibility. Retaining both Duty-Cycle Worked Example Review Loop and missing states before makes Duty-cycle worked example review loop: six stages with the Example 4 guard-listen arithmetic that closes a 0.210-to-0.300 mA gap auditable. The Example 4: Explain A Measurement Gap review can now test Inspect the ledger for directly.

16.12 Example 5: Budget A Multi-Component Device

Question

The first four examples ledger one radio’s states inside a single repeating cycle. A field device usually has several independently switchable subsystems instead of one radio, and the record has to show which combination of subsystems is active, not just how long any one of them runs. A cold-chain tracker tag has temperature, vibration, humidity, and light sensors plus a Bluetooth Low Energy (BLE) radio, a GPS receiver, and an LTE radio, each of which can be on or off separately. Compare four operating modes and decide which ones meet a 30-day shipment requirement.

Given exercise record

• Battery: a 0.2 Wh coin cell (the record’s whole usable-energy budget for the trip).
• Always-on sensor draw (temperature, vibration, humidity, light together): 0.199 mW.
• BLE beacon: 10 ms of radio-on time once per hour.
• GPS fix: 10 s of radio-on time once every 3 hours.
• LTE upload: 50 ms of radio-on time once every 24 hours.
• Mode A — System on: every subsystem left active continuously, measured at 2,180.66 mW.
• Mode B — Sensors only: sensors active, BLE/GPS/LTE off, measured at 0.199 mW.
• Mode C — Sensors + BLE beacon: adds the hourly BLE beacon, measured at 0.229 mW.
• Mode D — Sensors + BLE + GPS + LTE: adds the periodic GPS fix and daily LTE upload, measured at 0.428 mW.

Step 1: convert each mode’s average power to a lifetime

lifetime (hours) = battery energy (Wh) / average power (W)

Mode A: 0.2 Wh / 2.18066 W   = 0.0917 h  = 5.5 minutes
Mode B: 0.2 Wh / 0.000199 W  = 1,005 h   = 41.8 days
Mode C: 0.2 Wh / 0.000229 W  = 873 h     = 36.4 days
Mode D: 0.2 Wh / 0.000428 W  = 467 h     = 19.4 days

Step 2: read the ledger as a budget, not a single number

Mode A is what the tag would draw if nothing were ever switched off: every sensor, the BLE radio, the GPS receiver, and the LTE modem left running. At 2,180.66 mW that mode empties a 0.2 Wh coin cell in about five and a half minutes, which is a useful ceiling to keep in the record but not a mode any real shipment would run in. Modes B through D are the actual candidates, and each adds one more periodically-on subsystem to the always-on sensor baseline: Mode C’s only addition over Mode B is a 10 ms BLE beacon once an hour, and Mode D’s only addition over Mode C is a 10 s GPS fix every three hours plus a 50 ms LTE upload once a day. The ledger shows that those two small additions — a few seconds of radio time per hour, spread across a day — are what cut the lifetime from 41.8 days to 19.4 days, not the always-on sensors.

Decision

For a shipment leg that must report location and status for at least 30 days, Mode B (sensors only, no telemetry) and Mode C (sensors plus hourly BLE beacon) both clear the requirement with margin, but Mode D (adds GPS fix and daily LTE upload) does not: 19.4 days is short of the 30-day claim. Accept Mode C only if an hourly beacon without GPS or cellular upload still satisfies the shipment’s tracking requirement; otherwise the design needs a lower GPS/LTE duty cycle, a larger cell, or a shorter accepted shipment leg before Mode D can be approved.

Retest trigger

Repeat the review if the GPS fix interval, LTE upload interval, BLE beacon interval, sensor set, or battery capacity changes, and re-measure rather than reuse these currents if the tag design or firmware changes.

16.13 Review Checklist

Before accepting a duty-cycle worked example, check:

Is the question stated? Are all state intervals listed with units? Are current values recorded in a consistent unit? Does the calculation divide by the full cycle length? Are wake, listen, guard, and transmit states included when present? Is the evidence source named? Is the decision bounded to the supplied record? Is the retest trigger explicit?

16.14 Knowledge Check

16.15 Matching Quiz

16.16 Ordering Quiz

16.17 Duty Cycle Becomes A Battery-Life Claim

Duty-cycle arithmetic is useful only when it stays tied to the review record. The short chain is: a duty cycle sets an average current, average current divided into battery capacity gives lifetime, and the evidence record states which states were included or excluded. A node that sleeps 99% of the time may move from days to years of operation, but only if the ledger includes wake, listen, transmit, and sleep behavior instead of just the headline active fraction.

To challenge Duty Cycle Becomes A Battery-Life Claim, examine the visual at Figure 16.3. Its Duty Cycle Impact on Battery Life and Always-On labels reveal the comparison behind Duty Cycle Becomes A Battery-Life Claim.

At Figure 16.3, Duty Cycle Impact on Battery Life exposes energy cost; moving to Always-On shows how it names a responsibility. The 100% Duty Cycle label exposes energy cost. Keeping Duty Cycle Impact on Battery Life distinct from 100% Duty Cycle explains Duty cycle impact on battery life: for a 2000 mAh battery, always-on versus a 1% duty cycle changes the average current and extends lifetime from days to years. A later Duty Cycle Becomes A Battery-Life Claim review can recheck Always-On.

Read the ledger left to right: name the state, multiply current by time, add every contribution, and divide by the full period. The formula is reviewable only when the state rows are visible.

The same average-current ledger can support an operating-life estimate, but the estimate inherits every assumption in the ledger. A field note that says “2% duty cycle” is not enough if the node also wakes an oscillator, waits through a guard interval, listens for a parent, retries a transmit, or leaves a sensor rail biased after the sample.

For a novice, the easiest mental model is a phone that spends most of the day with its screen off. The screen-off time helps, but the phone still drains if background radios, sensors, or apps keep running. A sensor node is the same kind of accounting problem at smaller currents. The ledger is not extra paperwork; it is the place where hidden always-on behavior becomes visible. If the ledger says “sleep” but a pull-up, regulator, or sensor bias remains on, the battery-life claim is already optimistic.

That is why the worked examples in the body stop at bounded decisions instead of announcing a universal lifetime. Each arithmetic answer is a claim about one record, one set of states, and one evidence source. When the hardware or schedule changes, the record must be rerun before the lifetime story is reused.

16.18 Average Current To Lifetime

Average current blends the active and sleep states weighted by duty cycle D:

I_avg = D x I_active + (1 - D) x I_sleep

Then lifetime = battery capacity / I_avg. Take a node with I_active = 20 mA, I_sleep = 5 uA, a 2000 mAh battery, and a 1% duty cycle:

Two practical details keep this calculation honest. First, the units must agree: battery capacity in mAh divided by average current in mA gives hours, not seconds or cycles. Second, the capacity number is not a perfect fuel tank. Temperature, battery chemistry, regulator efficiency, cutoff voltage, pulse current, and ageing can reduce usable capacity, so a production record should treat the arithmetic lifetime as an upper-bound estimate unless the battery test supports it.

The calculation also tells the practitioner which measurement to improve next. If active current dominates, shortening transmit time or reducing radio current can move the result. If sleep current dominates, a better active routine may barely matter; the useful work is finding leakage, sleep-mode mistakes, or always-on peripherals. A reviewable example names that controlling term so the next lab measures the right state instead of repeating the same average-current calculation.

The same node at 100% duty draws 20 mA and lasts about 100 hours, roughly four days. Dropping to a 1% duty cycle multiplies lifetime by nearly 100x, but the decision is still bounded to this battery, this active current, this sleep current, and this duty cycle. If any of those terms changes, the lifetime estimate needs a new record.

Practitioner check: when a worked example solves for cycle length, state the result as a constraint, not a promise. “At least 44.1 s for this ledger” is reviewable; “the node lasts long enough” is not.

16.19 Sleep Current Sets The Floor

Look again at the numbers as the duty cycle keeps falling. At 1% duty the active term (0.20 mA) still dominates the sleep term (0.005 mA). At 0.01% duty the active contribution drops to about 0.002 mA, below the 0.005 mA sleep current. Beyond that point, cutting the duty cycle further barely helps because the node’s lifetime is set by what it draws while asleep. Sleep current becomes the floor on average current, and therefore the ceiling on battery life.

This reframes low-power engineering. Once your duty cycle is very low, the payoff moves from “wake less often” to “sleep more deeply”: a microcontroller sleep mode of 5 uA versus 50 uA changes the lifetime floor by 10x at those duty cycles, while shaving the active time does almost nothing. It also explains why designers scrutinize leakage, brown-out circuitry, and always-on peripherals: at aggressive duty cycles, the microamps you cannot switch off are the whole game. The worked numbers are not just a lifetime estimate; they tell you which parameter to optimize next.

Worked example: the crossover point. The active term equals the sleep term when D x Iactive = (1 - D) x Isleep. With Iactive = 20 mA and Isleep = 0.005 mA, the crossover is approximately D = 0.005 / (20 + 0.005) = 0.00025, or 0.025%. Above that duty cycle, the active burst is still the larger contributor. Below it, sleep current dominates. A 0.01% duty cycle is below the crossover, so a designer should first audit leakage, sleep-mode selection, regulator quiescent current, pull-up paths, and sensors left biased during sleep.

The floor also explains why measurement traces can disagree with tidy ledgers. A meter set to average current may hide a short 24 mA transmit pulse, while a slow logging interval may miss a 6 mA wake ramp. Conversely, an unexpected 10 uA leakage path can double a nominal 5 uA sleep floor and erase the benefit of rare wakeups. Under the hood, duty-cycle examples are not just algebra: they are a model of where current flows in time, which instrument can see it, and which omitted state would change the final decision.

16.20 Summary

Duty-cycle worked examples should preserve the evidence behind the arithmetic. A complete review record states the question, lists every state, computes current-time terms, divides by the full cycle length, compares the result with evidence or a current budget, and records a retest trigger. Missing wake, listen, guard, or transmit states are common reasons a simple calculation disagrees with a measured trace.

16.21 Key Takeaway

Duty-cycle worked examples should show the energy, latency, sensing, communication, and failure assumptions behind each schedule.

16.22 Concept Relationships

Duty Cycle Fundamentals define active fraction and average-current vocabulary. State ledgers make each operating state visible. Weighted modes connect adaptive schedules to observed mode fractions. Trace comparison separates missing states from measurement faults. Retest triggers keep calculations tied to the current design record.

16.23 What’s Next

Previous: WSN Duty Cycling

Next: WSN Deployment Sizing

Use WSN Duty Cycling to review sleep/wake scheduling and measurement evidence. Continue to WSN Deployment Sizing to connect energy records with field deployment constraints.