Introduction

Modern IoT devices, wearables, and embedded systems present unique challenges when estimating battery life. Unlike older devices with steady power consumption, today’s smart devices feature spiky loads – brief high-current events followed by long sleep periods. This pattern makes traditional battery life calculations inaccurate.

Accurate estimation requires understanding duty cycle, sleep current, the Peukert effect, self-discharge, and coulomb counting. Simply averaging power consumption leads to significant errors for devices with bursty consumption patterns.

This guide provides a systematic approach that engineers and product designers can implement, combining duty cycle modeling with precise coulomb counting and corrections for various battery effects.

Understanding the Challenge of Spiky Loads

Spiky loads occur when devices draw brief bursts of high current interspersed with low-power states. Common examples include:

• Radio transmission bursts (12-50mA for milliseconds)
• Sensor reading events (5-20mA for seconds)
• Data processing spikes (multiple mA for variable duration)

Traditional estimation methods fail for several reasons:

• Naive averaging ignores internal resistance effects during current spikes
• Simple calculations miss voltage sag that can trigger early device shutdown
• Averaging doesn’t account for the Peukert effect where higher discharge rates reduce effective capacity
• Long-term effects like self-discharge and sleep current are often overlooked

The difference between a device’s actual current profile and its average can be dramatic, leading to estimates that are off by 30% or more.

Battery Basics Relevant to Estimation

Capacity Fundamentals

A battery’s capacity represents the total charge (mAh) it can deliver. However, usable capacity is always less than rated capacity due to cutoff voltage limitations. Standard capacity ratings assume specific discharge conditions that rarely match real device usage patterns.

Internal Resistance (ESR)

Internal resistance causes voltage to drop during high-current events according to the formula: ΔV = Ipeak × ESR. This voltage sag can trigger device shutdown before the battery’s capacity is fully used.

Chemistry-Specific Considerations

The Peukert effect varies by chemistry:

• Lead-acid: Strong (exponent 1.2-1.3)
• Alkaline: Moderate (1.1-1.2)
• Lithium: Weaker but present (1.05-1.1)

For lithium cells, this effect manifests more as “derating” at high discharge rates.

Self-Discharge

Batteries lose charge even when not used. Typical rates:

• Li-ion: 2-3% per month
• Alkaline: 2-3% per year
• Lead-acid: 5-15% per month

Temperature significantly affects self-discharge rates, with higher temperatures accelerating the process.

Modeling Workload with Duty Cycle

Duty cycle represents the ratio of time spent in active states versus sleep states. For battery estimation, you need to identify all system states:

• Deep sleep: Typically <10μA, often the dominant state for IoT devices
• Idle/standby: Intermediate power mode, usually 10-500μA
• Active processing: CPU/MCU running, typically 1-50mA
• Radio/sensor activity spikes: Brief high-current events (10-200mA)

To measure each state’s contribution:

1. Measure current draw in each state using a DMM or oscilloscope
2. Record duration of each state
3. Calculate frequency of transitions
4. Determine time fraction for each state

For a first approximation, calculate: Average current = Σ(Current_i × Time fraction_i)

This is only a starting point that will need refinement with the following steps.

Step-by-Step Battery Life Estimation Method

Step 1: Gather All Required Inputs

Battery specifications:

• Rated capacity in mAh
• Internal resistance/ESR
• Peukert exponent (if applicable)
• Self-discharge rate
• Operating temperature range
• Cutoff voltage

System specifications:

• Current consumption in each state
• Spike characteristics (amplitude, duration, frequency)
• Regulator quiescent current
• Any known leakage paths

Step 2: Apply Coulomb Counting Over One Cycle

Coulomb counting integrates current over time to determine charge used:

• Q = I × t (where Q is charge in coulombs, I is current in amps, t is time in seconds)
• 1 mAh = 3.6 coulombs

For each state: Qi = Ii × ti

For the full cycle: Qtotal = ΣQi

This method is superior to averaging for spiky loads because it accounts for the exact charge used in each state and captures the actual impact of brief high-current events.

Step 3: Account for Spiky Loads Explicitly

For peak currents:

1. Calculate voltage sag during spikes: ΔV = Ipeak × ESR
2. Check if minimum voltage (Vbatt – ΔV) stays above system cutoff voltage
3. If not, the battery will appear “dead” during spikes before capacity is fully used

Batteries can deliver more total energy when high-current pulses are interspersed with rest periods. This effect is strongest in alkaline and zinc-carbon chemistries, but present to some degree in all types.

When modeling pulses, treat each spike as a discrete event rather than part of an average.

Step 4: Apply Peukert/Derating Effects

The Peukert effect means higher discharge rates reduce effective capacity:

Ceff = Crated × (Irated/Iactual)^(n-1)

Where n is the Peukert exponent, Irated is the current at which capacity was rated, and Iactual is the actual discharge current.

Different chemistries require different approaches:

• Lead-acid: Apply full Peukert calculation (n = 1.2-1.3)
• Alkaline: Apply modified Peukert (n = 1.1-1.2)
• Lithium primary: Use lighter correction (n = 1.05-1.1)
• Li-ion: Use manufacturer derating curves

Step 5: Add Sleep Current and Baseline Losses

Sleep current is critical in long-life applications. Even 1μA consumes 8.76mAh per year – significant for coin cells. Calculate total sleep consumption as:

Sleep charge = Sleep current × Sleep time fraction × Total time

Also account for:

• Regulator quiescent current
• Board leakage through pull-up resistors and reverse diode leakage
• Self-discharge (convert from %/month to mA equivalent)

Step 6: Consider Environmental and Aging Factors

Temperature has major effects:

• Cold temperatures (below 0°C) can reduce capacity by 10-50%
• Hot temperatures accelerate self-discharge rates
• Rule of thumb: Self-discharge doubles with every 10°C increase

Aging effects include:

• Cycle aging for rechargeable batteries
• Calendar aging for all battery types
• Shelf life limitations

Multiply rated capacity by appropriate derating factors based on expected operating conditions.

Step 7: Compute Final Battery Life

Battery Life (hours) = Usable capacity (after all derating) / Total average current

Where total average current includes all active states, spikes, sleep, and self-discharge.

Always build in a 20-30% margin for real-world variation and present results as a range rather than a single value.

Worked Example

Consider an IoT sensor with a CR2032 coin cell (220mAh nominal, 10Ω ESR, 2.0V cutoff)

System states:

• Sleep mode: 1μA for 99.9% of time
• MCU active + sensor reading: 1mA for 9ms every 10 seconds
• Radio transmission: 12mA for 1ms every 10 seconds

Step-by-step calculation:

1. Coulomb counting:
   • Sleep: 1μA × 99.9% = 0.999μA average
   • MCU: 1mA × 9ms/10s = 0.9μA average
   • Radio: 12mA × 1ms/10s = 1.2μA average
   • Raw total: 3.099μA average
2. Peukert correction:
   • Apply n=1.05 to radio transmissions
   • Effective radio contribution becomes 1.3μA
   • Adjusted total: 3.199μA
3. Self-discharge:
   • 1%/month = 0.31μA equivalent
4. Temperature derating:
   • 10% capacity reduction at 10°C
   • Usable capacity = 198mAh
5. Final calculation:
   • Battery life = 198mAh / 0.00352mA = 56,250 hours (6.4 years)

A naive approach using simple averaging would estimate 8.1 years – a 20% overestimation that could lead to field failures.

Common Pitfalls to Avoid

1. Ignoring sleep current in long-life designs
   • Even “zero power” circuits have leakage
   • 1μA over a year is 8.76mAh – significant for coin cells
2. Overlooking self-discharge for multi-month/year applications
   • Can reduce life by 30%+ over years
   • Varies significantly with temperature
3. Treating spiky loads as simple averages
   • Misses voltage sag effects that cause early shutdown
   • Solution: Use proper coulomb counting
4. Misapplying Peukert’s law
   • Using lead-acid exponents for lithium chemistries
   • Solution: Use chemistry-specific corrections
5. Forgetting regulator losses
   • Quiescent current can exceed sleep current
   • Efficiency varies with load current

Summary

Effective battery life estimation requires:

• Proper duty cycle modeling to identify all system states
• Coulomb counting to precisely account for charge in each state
• Corrections for Peukert effect, self-discharge, and sleep current
• Validation and iteration to improve confidence

Follow this checklist:

1. Identify all operational states and their current consumption
2. Measure actual current profiles, especially for spiky loads
3. Apply coulomb counting across a full operational cycle
4. Account for battery-specific effects
5. Include environmental factors
6. Validate with real-world measurements
7. Apply appropriate safety margins

Implementing this systematic approach will help you achieve reliable, long-life battery-powered designs and prevent field failures and customer disappointment.

FAQ

Q1: Why are traditional battery life estimations inaccurate for modern devices?

A1: Modern devices have “spiky loads” with brief, high-current events and long sleep periods, which traditional averaging methods fail to account for accurately, missing effects like voltage sag and the Peukert effect.

Q2: What is the Peukert effect and why is it important?

A2: The Peukert effect describes how a battery’s usable capacity decreases at higher discharge rates. It’s crucial because if ignored, it can lead to overestimates of battery life, especially for devices with high-current bursts.

Q3: How does internal resistance (ESR) affect battery life?

A3: ESR causes voltage drops (sag) during high-current events. If this voltage drops below the device’s minimum operating voltage, the device can shut down prematurely, even if the battery still has significant charge remaining.

Q4: Why is accounting for sleep current so important in long-life designs?

A4: Even very small sleep currents (e.g., 1μA) accumulate significantly over months or years, consuming substantial battery capacity that can drastically reduce the overall device lifespan, especially for coin cell devices.

Q5: What margin should I build into my battery life estimates?

A5: It’s recommended to build in a 20-30% safety margin. This accounts for real-world variations in battery manufacturing, environmental conditions, and slight discrepancies between theoretical models and actual device performance.