Penn ESE370 Fall DeHon 1 ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 19: October 15, 2014 Energy and Power Optimization

Previously Three components of power –Static –Short circuit –Capacitive switching P tot = P static + P sc + P dyn Penn ESE370 Fall DeHon 2

Static Penn ESE370 Fall DeHon 33 CMOS circuit in steady-state –Leaks subthreshold current determined by off device –P static = V dd × I static

Switching (Charging) Penn ESE370 Fall DeHon 44 CMOS circuit switching output from 0  1 –Spends energy CV dd 2 charging load

Switching (Short Circuit) P=IV When: Vin=Vdd/2 Vth<Vin<Vdd-|Vthp| Penn ESE370 Fall DeHon 5

Today Power Sources –Static –Short Circuit –Capacitive Switching Reducing Switching Energy Energy-Delay tradeoffs (time permit) Penn ESE370 Fall DeHon 6

Switching Quick Review Penn ESE370 Fall DeHon 7

Switching Currents I switch (t) = I sc (t) + I dyn (t) I(t) = I static (t)+I switch (t) Penn ESE370 Fall DeHon 8 I sc I static I dyn

Charging I dyn (t) –I ds = f(V ds,V gs ) –and V gs, V ds changing Penn ESE370 Fall DeHon 9

Look at Energy [focus on I dyn (t)] Penn ESE370 Fall DeHon 10

Energy to Switch Penn ESE370 Fall DeHon 11

Capacitor Charge Penn ESE370 Fall DeHon 12

Capacitor Charging Energy Penn ESE370 Fall DeHon 13

Switching Power Every time output switches 0  1 pay: –E = CV 2 P dyn = (# 0  1 trans) × CV 2 / time # 0  1 trans = ½ # of transitions P dyn = (# trans) × ½CV 2 / time Penn ESE370 Fall DeHon 14

Short Circuit Power Penn ESE370 Fall DeHon 15

Preclass 1 Current flow during switching? Penn ESE370 Fall DeHon 16

Short Circuit Power Between V TN and V dd -V TP –Both N and P devices conducting Roughly: Penn ESE370 Fall DeHon 17

Peak Current Penn ESE370 Fall DeHon 18 I peak around V dd /2 –If |V TN |=|V TP | and sized equal rise/fall

Short-Circuit Energy Penn ESE370 Fall DeHon 19

Short-Circuit Energy Penn ESE370 Fall DeHon 20

Short Circuit Energy Looks like a capacitance –Q=I×t –Q=CV Penn ESE370 Fall DeHon 21

Short Circuit Energy and Power Every time switch –Also dissipate short-circuit energy: E = CV 2 –Different C = C sc –C cs “fake” capacitance (for accounting) Largely same dependence as charging Penn ESE370 Fall DeHon 22

Switching Energy Penn ESE370 Fall DeHon 23

Reminder Output switches 0  1 charge output from Vdd Output switches 1  0 discharge output to ground – no current from Vdd Penn ESE370 Fall DeHon 24

Data Dependent Activity Consider an 8b counter –How often do each of the following switch? Low bit? High bit? –Average switching across all 8 output bits? Assuming random inputs –Activity at output of nand4? –Activity at output of xor4? Penn ESE370 Fall DeHon 25

Gate Output Switching (random inputs) Penn ESE370 Fall DeHon 26 Prev. Next 0 1

Charging Power P dyn = (# trans) × ½CV 2 / time Often like to think about switching frequency Useful to consider per clock cycle –Frequency f = 1/clock-period P dyn = (#trans/clock) ½CV 2 f Penn ESE370 Fall DeHon 27

Switching Power P dyn = (#trans/clock) ½CV 2 f Let a = activity factor a = average #tran/clock P dyn = a½CV 2 f P sc = aC sc V 2 f Penn ESE370 Fall DeHon 28

Total Power P tot = P static + P sc + P dyn P dyn + P sc = a(½C load +C sc )V 2 f P tot ≈ a(½C load +C sc )V 2 f+VI ’ s (W/L)e -Vt/(nkT/q) Penn ESE370 Fall DeHon 29

Dynamic Power Penn ESE370 Fall DeHon 30

Reduce Dynamic Power? P dyn = a × ½CV 2 f How do we reduce dynamic power? Penn ESE370 Fall DeHon 31

Slow Down What happens to power contributions as reduce clock frequency? What suggest about V th ? Penn ESE370 Fall DeHon 32

Reduce V What happens as reduce V? –Delay? –Energy? Static Switching Penn ESE370 Fall DeHon 33

Penn ESE370 Fall DeHon 34 Old Reduce V (no vsat)   gd =Q/I=(CV)/I  I d =(  C OX /2)(W/L)(V gs -V TH ) 2   gd impact?   gd α 1/V

Saturation Observe Ignoring leakage Penn ESE370 Fall DeHon 35

Penn ESE370 Fall DeHon 36 Reduce V (velocity saturation)   gd =Q/I=(CV)/I  I ds =( sat C OX )(W)(V gs -V TH -V DSAT /2)

Reduce Short-Circuit Power? P sc = aC sc V 2 f Penn ESE370 Fall DeHon 37

Energy vs. Power? Which do we care about? –Battery operated devices? –Desktops? –Pay for energy by kW-Hr? Penn ESE370 Fall DeHon 38

Increase V th ? What is impact of increasing threshold on –Delay? –Leakage? Penn ESE370 Fall DeHon 39

Penn ESE370 Fall DeHon 40 Increase V th   gd =Q/I=(CV)/I  I ds =( sat C OX )(W)(V gs -V TH -V DSAT /2)

Idea Short circuit energy looks like more capacitance for switching energy Tradeoff –Speed –Switching energy –Leakage energy Energy-Delay tradeoff: E  2 ? E  Penn ESE370 Fall DeHon 41

Admin HW6 Due tomorrow Project 1 out –Milestone piece due in one week –Full Report in two weeks –That means you need to be starting on it now…and working on it all next week Read assignment today Lecture Friday Penn ESE370 Fall DeHon 42