9  Duty Cycle Worked Examples

Keywords

duty cycle worked examples, average current, sensor node sleep schedule, wake overhead, current ledger, retest trigger

9.1 Start With the Review Record

Worked examples matter because duty-cycle decisions often fail in the gap between a neat percentage and an operating record. A reviewer needs to see the states, durations, overheads, assumptions, and retest triggers that turn arithmetic into a trustworthy claim.

Use 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.

9.2 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.

9.3 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.

9.4 First Step: Make The Claim Reviewable

9.5 Minimum Viable Understanding

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

9.6 Prerequisites

• Duty Cycle Fundamentals: active fraction, sleep states, and average-current basics.
• Duty-Cycling and Topology Management: why node schedules affect network behavior.
• Topology Management Techniques: follow-on review of topology policies.

9.7 Review Pattern

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.

Figure 9.1: 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.

Use Figure 9.1 as the structure for each example. The important move is to keep omitted states visible. If a radio listen window, sensor warm-up, or wake overhead is present, it belongs in the ledger.

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.

9.8 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.

9.9 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.

9.10 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.

9.11 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.

Figure 9.2: 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.

Use Figure 9.2 when a calculation and trace disagree. The first response should be to inspect the ledger for missing states before changing the schedule.

9.12 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?

9.13 Knowledge Check

9.14 Matching Quiz

9.15 Ordering Quiz

9.16 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.

9.17 Key Takeaway

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

9.18 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.

9.19 What’s Next

Previous: Duty Cycle Fundamentals

Next: Topology Management Techniques

Use Duty Cycle Fundamentals to review the base concepts. Continue to Topology Management Techniques to connect duty-cycle schedules with topology behavior.