subscript

The passage around this formula

A power budget derived only from a datasheet’s typical operating current is a guess, and it is usually an optimistic one, because the datasheet number rarely includes the device’s actual duty cycle, its radio’s transmit spikes, or the current the sensor’s analog front end draws while settling before a reading is valid. The more defensible starting point is a duty-cycle energy model built from measured, not assumed, currents at each state: $E_{\mathrm{cycle}} = P_{\mathrm{sleep}} \, t_{\mathrm{sleep}} + P_{\mathrm{active}} \, t_{\mathrm{active}} + n_{\mathrm{inf}} \, E_{\mathrm{inf}}$. where $E_{\mathrm{cycle}}$ is the energy spent in one full wake-sense-infer-sleep cycle, the first two terms are housekeeping power integrated over the time spent in each state, and $n_{\mathrm{inf}}$ inferences each cost a measured…

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