479 Duty Cycle Worked Examples
479.1 Learning Objectives
By the end of this chapter, you will be able to:
- Calculate battery life: Perform step-by-step energy budget analysis for sensor deployments
- Account for wake-up overhead: Include fixed costs that affect real-world battery consumption
- Design adaptive strategies: Configure duty cycles that respond to environmental conditions
- Diagnose synchronization issues: Identify and fix clock drift problems in coordinated sleep schedules
- Apply to real scenarios: Use these calculations for fire monitoring, agricultural sensing, and industrial deployments
Core concept: Real-world battery life depends on wake-up overhead, synchronization costs, and adaptive strategies—not just the duty cycle percentage. Why it matters: Naive duty cycle calculations overestimate battery life by 20-50%. Including overhead gives accurate predictions for deployment planning. Key takeaway: Always calculate average current including all overhead costs, and consider adaptive duty cycling for applications with variable event rates.
479.2 Prerequisites
Before working through these examples, you should understand:
- Duty Cycle Fundamentals: Basic duty cycle concepts, power states, and protocol comparison
- Wireless Sensor Networks: Network topologies and energy constraints
479.3 Worked Example: Forest Fire Monitoring
This worked example demonstrates how duty cycle dramatically affects battery life in a practical deployment scenario, including often-overlooked factors like synchronization overhead and realistic battery capacity.
Context: You are designing a forest fire monitoring network with battery-powered sensor nodes that must operate unattended for at least one year. Each node measures temperature and humidity, then transmits data via a low-power radio to a gateway.
479.3.1 Given Parameters
| Parameter | Value | Notes |
|---|---|---|
| Battery | 2000 mAh (2× AA alkaline) | Typical capacity; usable ~80% due to voltage cutoff |
| Active current | 25 mA | Sensing (5 mA) + Radio TX (20 mA) |
| Sleep current | 10 µA | Deep sleep mode with RTC running |
| Active time per cycle | 100 ms | Sensor read (50 ms) + transmit (50 ms) |
| Sync/wake overhead | 5 ms at 15 mA | Clock sync + peripheral initialization |
| Target lifetime | 1 year minimum | Fire season monitoring requirement |
479.3.2 Solution: Step-by-Step Analysis
Step 1: 100% Duty Cycle (Always On)
In always-on operation, the node continuously monitors and transmits:
\[ I_{avg} = 25 \text{ mA (constant)} \]
\[ \text{Battery Life} = \frac{2000 \text{ mAh}}{25 \text{ mA}} = 80 \text{ hours} = \mathbf{3.3 \text{ days}} \]
Verdict: Completely impractical for remote deployment.
Step 2: 10% Duty Cycle (Wake Every 1 Second)
The node wakes every 1 second, active for 100 ms + 5 ms overhead:
- Cycle period: 1000 ms
- Active time: 105 ms (100 ms sensing/TX + 5 ms wake overhead)
- Sleep time: 895 ms
Calculate average current:
\[ I_{avg} = \frac{(105 \text{ ms} \times 25 \text{ mA}) + (5 \text{ ms} \times 15 \text{ mA}) + (895 \text{ ms} \times 0.01 \text{ mA})}{1000 \text{ ms}} \]
\[ I_{avg} = \frac{2625 + 75 + 8.95}{1000} = \frac{2708.95}{1000} = 2.71 \text{ mA} \]
\[ \text{Battery Life} = \frac{2000 \text{ mAh}}{2.71 \text{ mA}} = 738 \text{ hours} = \mathbf{30.8 \text{ days}} \]
Verdict: Better, but still far from 1-year target.
Step 3: 1% Duty Cycle (Wake Every 10 Seconds)
The node wakes every 10 seconds:
- Cycle period: 10,000 ms
- Active time: 105 ms
- Sleep time: 9,895 ms
\[ I_{avg} = \frac{(100 \text{ ms} \times 25 \text{ mA}) + (5 \text{ ms} \times 15 \text{ mA}) + (9895 \text{ ms} \times 0.01 \text{ mA})}{10000 \text{ ms}} \]
\[ I_{avg} = \frac{2500 + 75 + 98.95}{10000} = 0.267 \text{ mA} = 267 \text{ µA} \]
\[ \text{Battery Life} = \frac{2000 \text{ mAh}}{0.267 \text{ mA}} = 7,491 \text{ hours} = \mathbf{312 \text{ days}} \]
Verdict: Close to 1 year but not quite meeting the requirement.
Step 4: 0.1% Duty Cycle (Wake Every 100 Seconds)
The node wakes every 100 seconds (~1.7 minutes):
- Cycle period: 100,000 ms
- Active time: 105 ms
- Sleep time: 99,895 ms
\[ I_{avg} = \frac{(100 \text{ ms} \times 25 \text{ mA}) + (5 \text{ ms} \times 15 \text{ mA}) + (99895 \text{ ms} \times 0.01 \text{ mA})}{100000 \text{ ms}} \]
\[ I_{avg} = \frac{2500 + 75 + 998.95}{100000} = 0.0357 \text{ mA} = 35.7 \text{ µA} \]
\[ \text{Battery Life} = \frac{2000 \text{ mAh}}{0.0357 \text{ mA}} = 56,022 \text{ hours} = \mathbf{6.4 \text{ years}} \]
Verdict: Exceeds 1-year requirement with significant margin!
479.3.3 Summary: Duty Cycle Comparison Table
| Duty Cycle | Sample Rate | Avg Current | Battery Life | Life vs Always-On | Meets 1-Year? |
|---|---|---|---|---|---|
| 100% | Continuous | 25 mA | 3.3 days | 1× (baseline) | ❌ No |
| 10% | 1/second | 2.71 mA | 30.8 days | 9.3× | ❌ No |
| 1% | 1/10 sec | 267 µA | 312 days | 94.5× | ❌ Close |
| 0.1% | 1/100 sec | 35.7 µA | 6.4 years | 708× | ✅ Yes |
479.3.4 Key Insights
1000× duty cycle reduction ≈ 700× battery life increase
Going from always-on (100%) to 0.1% duty cycle extends battery life from 3.3 days to 6.4 years—a factor of 708×.
Why not exactly 1000×? Three factors reduce the theoretical improvement:
- Sleep current is not zero: Even at 10 µA, sleep mode consumes energy over long periods
- Wake-up overhead: Each wake cycle costs ~5 ms at 15 mA regardless of active time
- Fixed active time: The 100 ms sensing/transmit time doesn’t scale down with duty cycle
Application-Specific Trade-offs:
| Application | Recommended Duty Cycle | Rationale |
|---|---|---|
| Fire detection | 0.1% (100s interval) | Temperature changes slowly; fires take minutes to spread |
| Intrusion detection | 1% (10s interval) | Need faster response to intruders |
| Structural monitoring | 0.01% (1000s interval) | Building stress changes over hours/days |
| Real-time tracking | 10% (1s interval) | Location updates needed frequently |
Design Recommendation for Fire Monitoring: Use 0.1% duty cycle with event-triggered wake-up. If temperature exceeds threshold, switch to 10% duty cycle to track fire progression rapidly.
479.4 Worked Example: Adaptive Duty Cycling for Agricultural Monitoring
Context: A vineyard deploys 200 soil moisture sensors across 50 hectares. The sensors must operate for 2 years on a single AA battery (2400 mAh) while providing timely irrigation alerts.
Given:
- Battery capacity: 2400 mAh (usable: 2000 mAh accounting for 80% depth of discharge)
- Active current: 18 mA (sensing + transmission)
- Sleep current: 8 µA
- Active time per wake cycle: 150 ms (sensor read: 100 ms, transmission: 50 ms)
- Required lifetime: 2 years (17,520 hours)
Steps:
Calculate maximum average current for 2-year lifetime: \[I_{max} = \frac{2000 \text{ mAh}}{17520 \text{ hours}} = 0.114 \text{ mA} = 114 \text{ µA}\]
Calculate required duty cycle: \[I_{avg} = D \times I_{active} + (1-D) \times I_{sleep}\] \[114 \text{ µA} = D \times 18000 \text{ µA} + (1-D) \times 8 \text{ µA}\] \[114 = 18000D + 8 - 8D\] \[106 = 17992D\] \[D = 0.0059 = 0.59\%\]
Calculate wake interval for 0.59% duty cycle with 150 ms active time: \[\text{Wake interval} = \frac{150 \text{ ms}}{0.0059} = 25.4 \text{ seconds}\]
Validate with adaptive strategy (normal vs. dry conditions):
- Normal: Wake every 60 seconds (0.25% duty cycle) → 48 µA average
- Dry alert: Wake every 10 seconds (1.5% duty cycle) → 270 µA average
- If dry conditions occur 10% of time: \(0.9 \times 48 + 0.1 \times 270 = 70.2\) µA → exceeds 2-year target with margin
Result: Configure sensors to wake every 60 seconds during normal conditions, switching to 10-second intervals when soil moisture drops below 30%. This provides 2.5+ year battery life while ensuring rapid response during irrigation-critical periods.
Key Insight: Adaptive duty cycling based on environmental conditions can provide both energy efficiency and application responsiveness. The key is identifying which conditions require faster sampling and keeping those periods short.
479.5 Worked Example: Synchronization Overhead in Coordinated Sleep Schedules
Context: A factory floor WSN uses S-MAC protocol with synchronized sleep schedules. Engineers notice battery life is 40% shorter than duty cycle calculations predict. Diagnose and fix the synchronization overhead problem.
Given:
- 50 sensor nodes with 10-second sleep/wake cycle
- Expected 1% duty cycle (100 ms active per 10 seconds)
- Measured battery consumption: 0.35 mA average (expected: 0.21 mA)
- S-MAC synchronization: SYNC packet every cycle
- Clock drift: 30 ppm (parts per million)
Steps:
Calculate daily clock drift: \[\text{Drift per day} = 30 \times 10^{-6} \times 86400 \text{ s} = 2.59 \text{ seconds/day}\]
Calculate SYNC overhead per wake cycle:
- SYNC packet transmission: 20 ms at 20 mA
- SYNC reception window (guard time for drift): 50 ms at 15 mA
- Total sync overhead: 70 ms additional per 10-second cycle
- Sync energy per cycle: \((20 \times 20 + 50 \times 15) = 1150\) µAs
Calculate actual duty cycle including sync:
- Data active time: 100 ms
- Sync overhead: 70 ms
- Total active: 170 ms per 10 seconds = 1.7% actual duty cycle
Calculate corrected average current: \[I_{avg} = \frac{100 \text{ ms} \times 18 \text{ mA} + 70 \text{ ms} \times 17.5 \text{ mA} + 9830 \text{ ms} \times 0.008 \text{ mA}}{10000 \text{ ms}}\] \[I_{avg} = \frac{1800 + 1225 + 78.6}{10000} = 0.31 \text{ mA}\]
Implement fix: Reduce sync frequency:
- Sync every 60 seconds instead of every 10 seconds
- Sync overhead now: 70 ms per 60 s = 0.12% additional
- New average: 0.23 mA (meets design target)
Result: Reducing SYNC frequency from every wake cycle to every 6th cycle (60 seconds) reduces average current from 0.35 mA to 0.23 mA, improving battery life by 52% while maintaining acceptable schedule alignment.
Key Insight: Synchronization protocols have hidden energy costs that often exceed the data transmission energy in low-traffic WSNs. Always account for protocol overhead when calculating duty cycle energy budgets, and tune synchronization frequency based on clock drift requirements rather than defaulting to per-cycle sync.
479.6 Common Pitfalls in Duty Cycle Calculations
The Mistake: Developers configure nodes to wake every 10 seconds using their local oscillators, assuming all nodes stay synchronized after initial setup. Within days, packets are lost and the network fragments.
Why It Happens: Low-cost crystal oscillators drift 20-100 ppm (parts per million). At 50 ppm, clocks drift 4.32 seconds per day. After one week, nodes are 30+ seconds out of sync—their wake windows no longer overlap, so receivers are asleep when senders transmit.
The Fix: Implement periodic resynchronization based on your oscillator quality and wake window size: - Guard time formula: Guard_time = Clock_drift_ppm × Sync_interval × 2 - Example: 50 ppm drift, 60-second sync interval → Guard time = 50×10⁻⁶ × 60 × 2 = 6 ms minimum - Resync frequency: With 100 ms wake windows and 50 ppm drift, resync every 1000 seconds (16.7 min) to keep drift under 50 ms - Protocol choice: Use X-MAC or ContikiMAC (asynchronous) if synchronization overhead exceeds 5% of energy budget; use S-MAC (synchronous) only with accurate clocks (<30 ppm) and stable topologies
The Mistake: Engineers calculate that 0.1% duty cycle will provide 10-year battery life, but the network dies in 18 months. They assume energy scales linearly with duty cycle percentage.
Why It Happens: Every wake cycle has fixed overhead costs that don’t scale with duty cycle: oscillator stabilization (1-5 ms), radio PLL lock (0.5-2 ms), microcontroller boot (10-50 ms), and synchronization beacon transmission. At very low duty cycles, these fixed costs dominate.
The Fix: Calculate actual average current including wake overhead: - Formula: I_avg = (T_wake × I_wake + T_overhead × I_overhead + T_sleep × I_sleep) / T_cycle - Example breakdown for 0.1% duty cycle (wake every 100s): - Active sensing: 100 ms × 25 mA = 2.5 mAs - Wake overhead: 50 ms × 15 mA = 0.75 mAs (fixed per wake!) - Sleep: 99.85s × 10 µA = 0.999 mAs - Total per cycle: 4.25 mAs → 42.5 µA average (not 25 µA as naive calculation suggests) - Diminishing returns: Below 0.1% duty cycle, overhead typically exceeds 30% of active energy. Calculate your specific break-even point before targeting ultra-low duty cycles.
The Misconception: Many IoT practitioners assume that minimizing duty cycle (e.g., 0.01% vs 1%) always maximizes network lifetime.
Why It’s Wrong: Ultra-low duty cycles can reduce overall energy efficiency due to hidden overheads:
Energy breakdown for typical sensor node:
| Component | Power (mA) | Time (ms) | Energy (mJ @ 3.3V) |
|---|---|---|---|
| Sleep mode | 0.01 | - | 0.000033/s |
| Wake-up overhead | 15 | 50 | 2.475 |
| Sensing | 5 | 100 | 1.65 |
| Radio TX (10 bytes) | 30 | 5 | 0.495 |
| Total active cycle | - | 155 | 4.62 mJ |
1% Duty Cycle (36s active/hour, 100 wake cycles/hour): - Wake overhead: 100 × 2.475 mJ = 247.5 mJ/hour - Sensing/TX: 100 × (1.65 + 0.495) = 214.5 mJ/hour - Sleep: 0.000033 mJ/s × 3564s = 0.12 mJ/hour - Total: 462.1 mJ/hour
0.1% Duty Cycle (3.6s active/hour, 10 wake cycles/hour): - Wake overhead: 10 × 2.475 mJ = 24.75 mJ/hour - Sensing/TX: 10 × (1.65 + 0.495) = 21.45 mJ/hour - Sleep: 0.000033 mJ/s × 3596.4s = 0.12 mJ/hour - Total: 46.3 mJ/hour (10× improvement ✓)
0.01% Duty Cycle (0.36s active/hour, 1 wake cycle/hour) - THE TRAP: - Wake overhead: 1 × 2.475 mJ = 2.475 mJ/hour - Sensing/TX: 1 × (1.65 + 0.495) = 2.145 mJ/hour - Sleep: 0.000033 mJ/s × 3599.6s = 0.12 mJ/hour - Total: 4.74 mJ/hour - But: Single reading may be insufficient for reliable event detection - Reality: Need redundancy → 3 readings/hour = 14.2 mJ/hour (worse than 0.1% with better coverage!)
The Real Problem: At ultra-low duty cycles (<0.1%), wake-up overhead dominates, and you sacrifice detection reliability. Network may miss critical events, requiring denser deployment (more nodes = more total energy).
Quantified Impact - Agricultural Monitoring (100-node network, 1-year deployment):
| Strategy | Per-Node Energy | Detection Reliability | Nodes Needed | Total Network Energy |
|---|---|---|---|---|
| 1% duty cycle | 4.05 kWh/year | 99.9% | 100 | 405 kWh |
| 0.1% duty cycle | 405 Wh/year | 95% | 100 | 40.5 kWh |
| 0.01% duty cycle | 41.5 Wh/year | 60% (unacceptable) | 250 | 103.8 kWh (worst!) |
Optimal design: 0.1% duty cycle provides 90% energy savings vs 1% while maintaining reliability. Going lower requires 2.5× node density, negating energy benefits.
Best Practice: Choose duty cycle based on application requirements (detection probability, latency tolerance), not just minimal energy per node. Consider network-wide energy including deployment density.
479.7 Summary
This chapter provided detailed worked examples for duty cycle battery life analysis:
- Forest fire monitoring: Step-by-step calculation showing how 0.1% duty cycle extends battery life from 3.3 days to 6.4 years
- Agricultural adaptive cycling: Designing sensors that wake more frequently during dry conditions while maintaining 2+ year battery life
- Synchronization overhead diagnosis: Identifying and fixing hidden energy costs in coordinated sleep schedules
- Common pitfalls: Clock drift issues and wake-up overhead that cause real-world battery life to fall short of predictions
479.8 What’s Next
Continue to CoRAD Drone Flight Planning to learn how drones can collect data from isolated sensor nodes when normal wireless communication fails.