$$P_{\text{avg}} \;=\; D \cdot P_{\text{active}} \;+\; (1-D)\cdot P_{\text{idle}}$$

Equation 6 · Edge AI & Electronics

Edge AI Electronics and Sensor Systems: A First-Principles Introduction

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

The average power such a system draws follows directly from how much time it spends in each state: $P_{\text{avg}} \;=\; D \cdot P_{\text{active}} \;+\; (1-D)\cdot P_{\text{idle}}$. where D is the fraction of time spent active. Because $P_{\text{active}}$ is typically one to three orders of magnitude larger than $P_{\text{idle}}$ for a real accelerator, battery life is dominated almost entirely by D and by $P_{\text{idle}}$ — not by how efficient the processor is once it wakes up. This is precisely why an always-on product design effort spends so much of its attention on cheap, low-power triggering stages (a simple always-listening front end that only wakes the expensive processor when something resembling the target event occurs) rather than on the…

Meanings in this article

• $D$: the fraction of time spent active.
• $P_{\text{active}}$: the because.

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