Day 20: October 24, 2012 Driving Large Capacitive Loads ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 20: October 24, 2012 Driving Large Capacitive Loads Penn ESE370 Fall2012 -- DeHon

Today Back to CMOS today How do we drive a large load? Stages and buffer sizing Minimum delay Penn ESE370 Fall2012 -- DeHon

Message To drive large loads Scale factor: 3—4 typically Scale buffers geometrically Exponential scale up in buffer size Scale factor: 3—4 typically One origin of fanout 4 target Drains contribute capacitance, too Can formulate math to optimize Penn ESE370 Fall2012 -- DeHon

(same model we’ve been assuming) Start Cdiff=0 (same model we’ve been assuming) Penn ESE370 Fall2012 -- DeHon

One Stage How size to minimize delay? Penn ESE370 Fall2012 -- DeHon

One Stage Delay equation? Penn ESE370 Fall2012 -- DeHon

Minimize Differentiate and set to zero. What’s WN? Penn ESE370 Fall2012 -- DeHon

Solving for size Penn ESE370 Fall2012 -- DeHon

Concrete? What is WN for Cload=4x104? Penn ESE370 Fall2012 -- DeHon

N-stage Penn ESE370 Fall2012 -- DeHon

N-stage Delay Penn ESE370 Fall2012 -- DeHon

Size WNi to minimize delay How minimize? Penn ESE370 Fall2012 -- DeHon

Size WNi to minimize delay Take partial derivative wrt WNi Penn ESE370 Fall2012 -- DeHon

Solving for WNi Penn ESE370 Fall2012 -- DeHon

Delay Penn ESE370 Fall2012 -- DeHon

Stage Delay Penn ESE370 Fall2012 -- DeHon

Stage Delay Penn ESE370 Fall2012 -- DeHon

Math Penn ESE370 Fall2012 -- DeHon

Total Delay Penn ESE370 Fall2012 -- DeHon

Total Delay Penn ESE370 Fall2012 -- DeHon

How many stages? How does this trend with N? Penn ESE370 Fall2012 -- DeHon

Plot Delay vs. N Delay (t units) N Penn ESE370 Fall2012 -- DeHon

Zoom Delay vs. N Penn ESE370 Fall2012 -- DeHon

Minimize Penn ESE370 Fall2012 -- DeHon

Solve Penn ESE370 Fall2012 -- DeHon

Concrete What is optimal N for Cload=4x104C0? Penn ESE370 Fall2012 -- DeHon

Zoom Delay vs. N Penn ESE370 Fall2012 -- DeHon

Optimum Scale Up What is f? Penn ESE370 Fall2012 -- DeHon

Optimum Scale Up Deep result – take time to digest. Penn ESE370 Fall2012 -- DeHon

Delay at Optimum Penn ESE370 Fall2012 -- DeHon

Cdiff=gCgate Penn ESE370 Fall2012 -- DeHon

Contact Capacitance n+ contacts are formed by doping = diffusion Day 11 Contact Capacitance n+ contacts are formed by doping = diffusion Depletion under contact Contact-Body capacitance Depletion around perimeter of contact Also contact-Body capacitance Penn ESE370 Fall2012 -- DeHon

Contact/Diffusion Capacitance Day 11 Contact/Diffusion Capacitance Cj – diffusion depletion Cjsw – sidewall capacitance LS – length of diffusion LS Penn ESE370 Fall2012 -- DeHon

Capacitance Roundup CGS=CGCS+CO CGD=CGCD+CO CGB=CGCB CSB=Cdiff Day 11 Capacitance Roundup CGS=CGCS+CO CGD=CGCD+CO CGB=CGCB CSB=Cdiff CDB=Cdiff Penn ESE370 Fall2012 -- DeHon

Impact on Capacitance Penn ESE370 Fall2012 -- DeHon

Contact/Diffusion Capacitance Cj – diffusion depletion Cjsw – sidewall capacitance LS – length of diffusion LS Penn ESE370 Fall2012 -- DeHon

Diffusion Capacitance What does this do to t model? Delay of middle stage? Penn ESE370 Fall2012 -- DeHon

Stage Delay Penn ESE370 Fall2012 -- DeHon

Stage Delay Penn ESE370 Fall2012 -- DeHon

N-stage Delay Penn ESE370 Fall2012 -- DeHon

N-stage Delay Penn ESE370 Fall2012 -- DeHon

Impact on Min Wni ? Partial Derivative unchanged What does this say about f? Penn ESE370 Fall2012 -- DeHon

Stage Delay: f unchanged (fixed N) Penn ESE370 Fall2012 -- DeHon

Total Delay Penn ESE370 Fall2012 -- DeHon

Impact of Gamma g=1.5 g=1.0 g=0.5 g=0 Penn ESE370 Fall2012 -- DeHon

Impact of Gamma g=1.5 g=1.0 g=0.5 g=0 Penn ESE370 Fall2012 -- DeHon

Minimize Penn ESE370 Fall2012 -- DeHon

Solve Penn ESE370 Fall2012 -- DeHon

Solve Penn ESE370 Fall2012 -- DeHon

Optimum Scale Up Penn ESE370 Fall2012 -- DeHon

Optimal Staging g≠0 Penn ESE370 Fall2012 -- DeHon

F and gamma? f=4 is optimal for what g? f=3 is optimal for what g? Penn ESE370 Fall2012 -- DeHon

Optimal Fanout Clearer why we use f=4 as our benchmark? Remember HW3.5 Penn ESE370 Fall2012 -- DeHon

Idea To drive large loads Scale factor: 3—4 typically Scale buffers geometrically Exponential scale up in buffer size Scale factor: 3—4 typically One origin of fanout 4 target Drains contribute capacitance, too Can formulate math to optimize Penn ESE370 Fall2012 -- DeHon

Admin Project: Milestone due tomorrow Jan Rabaey talk tomorrow at 11am Udit office hours today Jan Rabaey talk tomorrow at 11am One of textbook authors Penn ESE370 Fall2012 -- DeHon