Modeling System Longevity Based on Power Budgeting

In this lesson, you will learn how to synthesize your knowledge of duty-cycling, regulator efficiency, and peripheral power profiles to accurately predict the total operational lifespan of an embedded device.

The Physics of the Power Budget

System longevity is not merely Battery Capacity / Average Current. It is an integration of dynamic states over time, adjusted by the realities of power conversion. To build a robust model, you must calculate the total energy consumed across your system's duty cycle.

If your device spends time in various states (e.g., Deep Sleep, Active Processing, Data Transmission), your total energy consumption per cycle ($E_{cycle}$) is defined as:

$E_{cycle} = \sum (I_n \times V_{sys} \times t_n) / \eta_n$

Where:

• $I_n$: Current draw in state $n$.
• $t_n$: Time spent in state $n$.
• $\eta_n$: The efficiency of your regulator (e.g., switching vs. linear) at that specific current load.

Integrating the Variables

Consider a sensor node where the MCU wakes, samples a sensor, and transmits via BLE. You must account for the conversion efficiency ($\eta$) of your DC-DC converter, which changes significantly when transitioning from sleep currents (µA range) to active transmission (mA range). Using a static efficiency value will lead to an optimistic, incorrect longevity estimate.

// Simplified longevity estimation logic
float calculate_longevity(float battery_mah, float duty_cycle_hours) {
    // Account for 85% utilization of battery capacity due to self-discharge 
    // and voltage drop-off characteristics.
    float usable_capacity = battery_mah * 0.85;
    
    // Total average current including regulator efficiency losses
    float avg_current = (active_time * active_i / eff_active) + 
                        (sleep_time * sleep_i / eff_sleep);
    
    return usable_capacity / avg_current; // Returns operational hours
}

Refining the Estimate

When modeling, treat your battery as a non-ideal source. As your device approaches the end of its life, the battery’s internal resistance increases, and voltage drops, often forcing your switching regulator to pull more current to maintain a stable output. Your model must be iterative; if your system’s "Brown-Out" threshold is reached while your battery still holds 10% capacity, that 10% must be excluded from your longevity calculation.

Key Takeaway: Accurate system longevity modeling requires weighting your average current draw against the non-linear efficiency curves of your power supply and the realistic usable capacity of the battery under load.