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Equation 6 · Edge AI Electronics and Sensor Systems in Practice: Quantization, Power Budgets, and Sensor Front Ends

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Ecycle=Psleep tsleep+Pactive tactive+ninf Einf,E_{\mathrm{cycle}} = P_{\mathrm{sleep}} \, t_{\mathrm{sleep}} + P_{\mathrm{active}} \, t_{\mathrm{active}} + n_{\mathrm{inf}} \, E_{\mathrm{inf}},

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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EcycleE_{\mathrm{cycle}}

Symbol E_cycle

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 ninfn_{\mathrm{inf}} inferences each cost a measured EinfE_{\mathrm{inf}}.

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PsleepP_{\mathrm{sleep}}

Symbol P_sleep

PsP_sleep is one of the signed contributions combined to compute the quantity on the left.

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tsleept_{\mathrm{sleep}}

Symbol t_sleep

tst_sleep is one of the signed contributions combined to compute the quantity on the left.

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PactiveP_{\mathrm{active}}

Symbol P_active

PaP_active is one of the signed contributions combined to compute the quantity on the left.

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tactivet_{\mathrm{active}}

Symbol t_active

tat_active is one of the signed contributions combined to compute the quantity on the left.

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ninfn_{\mathrm{inf}}

Symbol n_inf

nin_inf is one of the signed contributions combined to compute the quantity on the left.

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EinfE_{\mathrm{inf}}

Symbol E_inf

EiE_inf is one of the signed contributions combined to compute the quantity on the left.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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addition

addition

Add the term after the plus sign to the term or group before it.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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How to interpret it

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What the article says around this equation

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: Ecycle=Psleep tsleep+Pactive tactive+ninf EinfE_{\mathrm{cycle}} = P_{\mathrm{sleep}} \, t_{\mathrm{sleep}} + P_{\mathrm{active}} \, t_{\mathrm{active}} + n_{\mathrm{inf}} \, E_{\mathrm{inf}}. where EcycleE_{\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 ninfn_{\mathrm{inf}} inferences each cost a measured…
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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: Ecycle=Psleep tsleep+Pactive tactive+ninf EinfE_{\mathrm{cycle}} = P_{\mathrm{sleep}} \, t_{\mathrm{sleep}} + P_{\mathrm{active}} \, t_{\mathrm{active}} + n_{\mathrm{inf}} \, E_{\mathrm{inf}}. where EcycleE_{\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 ninfn_{\mathrm{inf}} inferences each cost a measured EinfE_{\mathrm{inf}} . Every term in that expression should be a number taken off a current probe at the actual rail, not a value copied from a component’s datasheet, because sleep current in particular is notorious for being dominated not by the processor but by whichever peripheral, pull-up, or leakage path the design forgot to disable.

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