6.4.10
Intuition Ek-sentence ideaRaw speed ka koi fayda nahi agar aap bijli ka bill ya cooling afford nahi kar sakte — isliye hum hardware ko measure karte hain ki woh har joule (ya watt) mein kitna useful work karta hai , na ki sirf yeh ki woh kitna fast hai.
Intuition Yeh kaunsi problem solve karta haiEk datacenter ka bill aur ek phone ki battery life dono energy se dominate hoti hain, raw clock speed se nahi. Do chips same benchmark score hit kar sakti hain, lekin agar chip A yeh 100 W par karti hai aur chip B 50 W par, toh chip B practically twice as valuable hai. Hume ek aisa number chahiye tha jo performance aur power ko fuse kare , taaki engineers fairly compare kar sakein.
Yeh tension hai:
Performance chahti hai high clock frequency f V Power dono f V tezi se badhti hai (hum derive karenge kyun).Ek "sweet spot" ke baad, performance push karna disproportionately zyada power cost karta hai — isliye performance/watt ek design target ke roop mein exist karta hai.
Definition Performance per wattPerformance per Watt = Power Performance Performance throughput hai (operations/second, jaise FLOPS ya instructions/sec) aur Power average electrical power watts mein hai (joules/sec).
Kyunki performance work per second hai aur power energy per second hai:
Power Perf = energy / sec work / sec = energy work = joule operations
Intuition Seconds cancel ho jaate hain!Performance/watt secretly operations per joule hai — total useful work jo aap ek fixed energy budget (jaise battery) se nikal sakte hain. Isliye yeh honest efficiency number hai.
CMOS chip mein total power:
P total = P dynamic + P static
Intuition Physically kya ho raha haiHar logic gate basically ek chhoti capacitor C V charge karte ho phir charge dump karte ho. Capacitor par stored energy hai E = 2 1 C V 2 aur discharge karna dono milake ek full cycle mein C V 2
Derivation:
Ek capacitor ko V E stored = 2 1 C V 2
Discharge par resistive path mein utni hi energy dissipate hoti hai, isliye har switching event mein hum E = 2 1 C V 2 2 1 C V 2
Agar gates activity factor α f α f
P dynamic = α C V 2 f
Intuition Yeh kyun exist karta haiJab kuch bhi switch nahi ho raha tab bhi, transistors ek trickle current I leak P static = V I leak
Intuition High speed par efficiency kyun collapse ho jaati haiFaster run karne ke liye aapko f f V f ∝ V V ∝ f P dyn = α C V 2 f P dyn ∝ f ⋅ f 2 = f 3 Power roughly frequency ke cube ke saath scale karta hai. Performance sirf linearly f
Watt Perf ∝ f 3 f = f 2 1
Worked example Example 1 — Operations per joule compute karoEk GPU 20 TFLOPS 250 W
Step 1: 250 W 20 × 1 0 12 FLOP/s = 8 × 1 0 10 FLOP/(s⋅W) = 80 GFLOPS/W Yeh step kyun? Perf/watt literally yeh division hai; units ban jaate hain FLOP per joule.
Step 2: Energy per FLOP = 8 × 1 0 10 1 = 12.5 pJ/FLOP Yeh step kyun? ops/joule ka reciprocal = joules/op. Confirm karta hai ki perf/watt ≡ work/energy.
Worked example Example 2 — Voltage scaling payoff (DVFS)Ek core V = 1.0 V f = 2 GHz V = 0.8 V f = 1.6 GHz f ∝ V
Step 1 — naya power: P ∝ V 2 f = ( 1.0 0.8 ) 2 ⋅ 2.0 1.6 = 0.64 × 0.8 = 0.512 Yeh step kyun? Sirf relative factors matter karte hain, isliye ratios ko V 2 f 51% tak drop ho jaata hai.
Step 2 — nayi performance: ∝ f = 0.8 Yeh step kyun? Throughput frequency ko track karta hai.
Step 3 — perf/watt ratio: 0.512 0.8 = 1.5625 Yeh step kyun? Perf/watt = perf ÷ power. Hume +56% efficiency mila sirf 20% kam speed ke liye. Isliye phones load ke neeche throttle down karte hain.
Worked example Example 3 — Do chips ke beech choose karnaChip A: 100 GFLOPS @ 40 W. Chip B: 160 GFLOPS @ 80 W. Kaun zyada energy-efficient hai?
Step 1: A → 100/40 = 2.5 160/80 = 2.0 Yeh step kyun? Direct perf/watt comparison absolute size ko ignore karta hai aur fair hai.
Conclusion: A efficiency mein jeetta hai (har joule mein zyada work karta hai), bhaley hi B faster ho. Battery/thermal budget ke hisaab se chunein, raw speed se nahi.
Common mistake "Faster chip = zyada efficient chip."Kyun sahi lagta hai: Speed aur quality synonymous lagte hain; ek faster CPU task "jaldi" finish karta hai, toh surely woh kam energy use karta hai?
Fix: Jaldi finish karna (race-to-idle) kabhi kabhi help karta hai, lekin high f V P ∝ V 2 f badh sakta hai bhaley hi time kaam ho. Hamesha operations/joule compute karo, sirf speed nahi.
Common mistake "Voltage aadha karna power bhi aadhi kar deta hai."Kyun sahi lagta hai: Ohm's-law reflex: P = V I V Fix: Dynamic power α C V 2 f V quadratic . V
Common mistake "Sirf dynamic power matter karta hai."Kyun sahi lagta hai: Textbooks α C V 2 f Fix: Modern deep-nanometer chips mein, leakage (P static = V I leak
Recall Feynman: ek 12-saal ke bachche ko explain karoSocho tumhara toy car battery se chalta hai. Ek car super fast jaati hai lekin 5 minute mein battery khatam kar deti hai. Doosri thodi slower hai lekin ek ghante tak chalti hai. "Performance per watt" yeh pooch raha hai: tumhe battery ke har bit se kitna maza (kaam) milta hai? Slow-and-steady aksar zyada total maza deta hai. Aur yeh trick hai: do guna fast jaana do guna battery cost nahi karta — yeh chaar ya aath guna zyada cost kar sakta hai, kyunki speed badhane ke liye zyada "push voltage" chahiye, aur battery drain voltage ke saath squared badhta hai. Isliye fast gadgets garam ho jaate hain aur jaldi mar jaate hain.
Mnemonic Power law yaad rakho"Alpha Cats Voltage-Squared Frequency" → P = α C V 2 f "Volts hurt squared, Hertz hurt cubed" (kyunki f V P ∼ f 3
Performance/watt mein "per second" units kyun cancel ho jaate hain?
Voltage-frequency scaling ke under derive karo ki P dyn ∝ f 3
Jab aap V
Performance per watt kaunsi aur zyada fundamental quantity ke equivalent hai? Operations per joule (work per unit energy), kyunki performance aur power mein "per second" cancel ho jaata hai.
CMOS ke liye dynamic power equation? P d y n = α C V 2 f
Dynamic power V 2 Energy stored/dissipated on a gate capacitor 2 1 C V 2
Clock speed push karne par total power f 3 Zyada f V V ∝ f V 2 f f 3
Agar voltage aadha karo (frequency hold karte hue), dynamic power ka kya hoga? Yeh one quarter ho jaata hai (V
Static/leakage power kya hai aur uska formula kya hai? Idle hone par bhi leakage current se hone wala power loss: P s t a t i c = V I l e ak
Chip A: 100 GFLOPS @ 40 W, Chip B: 160 GFLOPS @ 80 W — kaun zyada efficient hai? A (2.5 GFLOPS/W) B (2.0 GFLOPS/W) se jeetta hai, bhaley hi B faster ho.
Industry ever-higher clocks ki jagah multicore par kyun gayi? High frequency par Perf/watt 1/ f 2 f , V
DVFS kya exploit karta hai? Dynamic Voltage & Frequency Scaling V
Steel-man: "faster = more efficient" sahi kyun lagta hai, aur fix kya hai? Race-to-idle ki wajah se sahi lagta hai; fix: total energy = power×time, aur high f V ∝ V 2 f
Capacitor energy half C V squared
Voltage and frequency sweet spot
