Before you can read the parent note, you need to earn every symbol it throws at you. This page starts from absolute zero — no prior electronics assumed — and builds each idea onto the last. Read top to bottom; nothing is used before it is defined.
Picture a tap. Energy is the total amount of water in the bucket; power is how fast the water is pouring out right now. A chip that "uses 100 watts" is pouring out energy at a fixed rate every second — and every one of those watts turns into heat inside a fingernail-sized square of silicon.
Why does the parent topic care? Because heat is the enemy. If a chip makes heat faster than the cooling can carry it away, the silicon cooks itself. So there is a ceiling on watts — and that ceiling is the whole story.
Picture a stadium of people flipping cards. One person flipping once uses almost nothing. A billion people flipping billions of times per second? That adds up to a furnace.
This gives us our first symbol.
Why the topic needs α: power depends on how busy the chip is, not just how big it is. α is the knob that captures "busyness."
Picture two water tanks at different heights. The height difference is voltage — the higher the drop, the harder the water pushes. Higher voltage makes transistors switch faster and more reliably, but (as we'll see) it costs power squared.
Picture the OFF transistor as a closed but slightly dripping valve. Multiply that drip by a billion transistors and it becomes a real river of wasted power.
Why the topic needs Ileak: it explains the parent note's warning that dark silicon still costs power. A switched-off region isn't free — it leaks. That's why we need Power-gating to fully cut its supply.
Picture each transistor as a little bucket. To turn it ON you must fill the bucket; to turn it OFF you empty it. A bigger bucket takes more water (energy) to fill each time.
Why the topic needs C: every switch dumps the energy stored in this bucket as heat. More capacitance → more heat per flip.
Now every symbol in the parent note's central equations is defined. Let's read them out loud.
Read it as a story: to spend dynamic power you need transistors that are busy (α), each with a bucket to fill (C), pushed by voltage — and because both filling and emptying scale with the push, voltage enters squared — happening f times each second.
Picture a hotplate. Ten watts spread over a dinner plate is warm; ten watts focused on a pinhead melts metal. It's not total watts that burn the chip — it's watts per square millimetre. Shrinking transistors packs the same watts into less area, so density climbs.
Why the topic needs it: this is exactly why Dennard-scaling mattered — it was the rule that kept power density constant as transistors shrank. When it broke, density began to rise, and dark silicon was born.
Picture the circuit breaker in the kitchen analogy from the parent note. You own 16 burners but the breaker trips past 4-burners-worth of power. TDP is that breaker. See TDP-and-power-budget.
That s2 for area (versus s1 for a single length) is the key to reading Dennard's cancellation in the parent note. See Mores-law for why s keeps shrinking.
Why the topic needs it: you can't run half a core. If the power budget allows 4.7 cores, you actually run 4. The bracket enforces "cores are whole things."
