Intuition The one core ideaA chip is a giant collection of tiny switches; every time one flips it spends a fixed sip of energy, and how often they flip (frequency) times how big each sip is (voltage squared) sets the total power drain. Everything on the parent page is just this one story — energy per switch, times switches per second — measured against the useful work you get out.
This page assumes you have seen nothing . We name every letter and picture on the parent note before it is ever used, in an order where each idea leans on the one before it.
Before any chip talk, three plain words.
Definition Work, energy, power
Work = something useful got done (a calculation finished, a bit flipped). We count it in operations .Energy = the "fuel" spent doing it. Its unit is the joule (symbol J Power = how fast you burn fuel: joules per second . Its unit is the watt (symbol W 1 W = 1 J/s
Intuition The bucket-and-tap picturePicture a water bucket (your battery = a fixed pile of joules). Power is how wide you open the tap — litres leaving per second. Energy is the total water that left. You can drain the same bucket slowly (low power, long time) or fast (high power, short time). Energy is what actually runs out.
Why the topic needs this: performance/watt divides work by power . The seconds inside "work per second" and "energy per second" cancel , leaving work per joule. You cannot see that cancellation until you know power is literally joules ÷ seconds. See FLOPS and Benchmarking for how we count the "work" side.
A transistor is an electrically-controlled switch: a small voltage on its "gate" decides whether current can pass. A chip has billions of them wired into logic.
Definition Capacitor and the symbolC capacitor is two conducting plates that store electric charge when you put a voltage across them. The letter C capacitance — how much charge it holds per volt. Unit: the farad. On a chip, every gate behaves like a tiny capacitor: to make it a "1" you fill it with charge; to make it a "0" you empty it.
Intuition Why we picture a gate as a capacitorA capacitor is the simplest thing that must be charged and emptied to change state — exactly what a logic gate does when a bit flips. That "fill and empty" is where every joule of switching energy goes. Look at the amber charge dots filling the plate in the figure: each dot cost energy to push there.
Why the topic needs it: the parent's headline equation P dyn = α C V 2 f C C V 2
V Voltage (V
Intuition Why squared, in picturesCharge stored is proportional to voltage (more push, more charge). But energy is push × charge accumulated , and since charge itself grew with voltage, you multiply "push" by "amount that also grew with push" — a V V is that 2 1 C V 2 V quadruples .
Why the topic needs it: the parent's biggest "aha" — halving voltage quarters dynamic power — is nothing but this triangle area shrinking to a quarter. This is also the engine behind DVFS - Dynamic Voltage and Frequency Scaling .
f Frequency (f Hz 1 GHz = 1 0 9
Definition Activity factorα activity factor α fraction of gates that actually switch on a given tick. It's a number between 0 1 α = 0.1
Intuition Switches-per-second =α f α f α × f C V 2 watts . That is the whole recipe for dynamic power.
Why the topic needs it: without α all gates switch every tick and hugely over-estimate power. α
Now every letter is defined, so the parent's boxed equation reads like a sentence:
This is derived fully on the parent; here you now hold every symbol it uses. Contrast this switching drain with the always-on drain in Dynamic vs Static Power .
I I leak Current (I rate of charge flow . Leakage current I leak
Intuition Why it grows with heatHotter silicon lets more electrons sneak through, so I leak Leakage Current and Temperature .
Why the topic needs it: total power is P dynamic + P static
Intuition Why raising speed drags voltage upTo switch a gate quicker you must shove charge in faster , which needs a bigger push V V ∝ f physical constraint , not a choice — it's the fading half of Dennard Scaling .
Substituting V ∝ f P dyn = α C V 2 f V 2 f f 2 ⋅ f = f 3 f Watt Perf ∝ f 3 f = f 2 1 1/ f 2 Multicore and Parallelism and the budgeting number Thermal Design Power (TDP) .
FLOPS = Floating-point Operations Per Second — a way to count "useful work per second" for numeric machines. So 20 TFLOPS = 20 × 1 0 12
Recall Why "GFLOPS/W" secretly means "GFLOP per joule"Because J/s FLOP/s = J FLOP
Joule and Watt = energy and power
Gate acts like a capacitor C
Energy on capacitor = half C V squared
Voltage V = electrical push
Frequency f = ticks per second
Switches per second = alpha times f
Dynamic power = alpha C V squared f
Static power = V times I leak
Performance per watt = work per joule
Test yourself — cover the right side.
What unit is power measured in, and what does 1 watt equal? The watt; 1 W = 1 J/s
In plain words, what is capacitance C How much charge a gate holds per volt of push — its "size" as a tiny store of charge.
Why is the energy on a charged gate proportional to V 2 V Charge grows with V V V V 2
What does the activity factor α The fraction of gates that actually flip on a given clock tick (between 0 and 1).
What is α f The number of gate switches happening per second.
What is leakage current I leak A small unwanted current that flows even when transistors are "off," wasting power as V I leak
Why does raising frequency force voltage up? Faster switching needs charge pushed in faster, which needs a bigger voltage push, so roughly V ∝ f
Why do the "per second" units cancel in performance/watt? Performance is work/s and power is energy/s; dividing cancels the seconds, leaving work per joule.