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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 Fall DeHon
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Today Back to CMOS today How do we drive a large load?
Stages and buffer sizing Minimum delay Penn ESE370 Fall DeHon
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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 Fall DeHon
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(same model we’ve been assuming)
Start Cdiff=0 (same model we’ve been assuming) Penn ESE370 Fall DeHon
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One Stage How size to minimize delay? Penn ESE370 Fall DeHon
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One Stage Delay equation? Penn ESE370 Fall DeHon
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Minimize Differentiate and set to zero. What’s WN?
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Solving for size Penn ESE370 Fall DeHon
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Concrete? What is WN for Cload=4x104? Penn ESE370 Fall DeHon
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N-stage Penn ESE370 Fall DeHon
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N-stage Delay Penn ESE370 Fall DeHon
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Size WNi to minimize delay
How minimize? Penn ESE370 Fall DeHon
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Size WNi to minimize delay
Take partial derivative wrt WNi Penn ESE370 Fall DeHon
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Solving for WNi Penn ESE370 Fall DeHon
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Delay Penn ESE370 Fall DeHon
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Stage Delay Penn ESE370 Fall DeHon
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Stage Delay Penn ESE370 Fall DeHon
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Math Penn ESE370 Fall DeHon
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Total Delay Penn ESE370 Fall DeHon
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Total Delay Penn ESE370 Fall DeHon
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How many stages? How does this trend with N?
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Plot Delay vs. N Delay (t units) N Penn ESE370 Fall DeHon
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Zoom Delay vs. N Penn ESE370 Fall DeHon
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Minimize Penn ESE370 Fall DeHon
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Solve Penn ESE370 Fall DeHon
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Concrete What is optimal N for Cload=4x104C0?
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Zoom Delay vs. N Penn ESE370 Fall DeHon
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Optimum Scale Up What is f? Penn ESE370 Fall DeHon
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Optimum Scale Up Deep result – take time to digest.
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Delay at Optimum Penn ESE370 Fall DeHon
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Cdiff=gCgate Penn ESE370 Fall DeHon
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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 Fall DeHon
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Contact/Diffusion Capacitance
Day 11 Contact/Diffusion Capacitance Cj – diffusion depletion Cjsw – sidewall capacitance LS – length of diffusion LS Penn ESE370 Fall DeHon
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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 Fall DeHon
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Impact on Capacitance Penn ESE370 Fall DeHon
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Contact/Diffusion Capacitance
Cj – diffusion depletion Cjsw – sidewall capacitance LS – length of diffusion LS Penn ESE370 Fall DeHon
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Diffusion Capacitance
What does this do to t model? Delay of middle stage? Penn ESE370 Fall DeHon
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Stage Delay Penn ESE370 Fall DeHon
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Stage Delay Penn ESE370 Fall DeHon
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N-stage Delay Penn ESE370 Fall DeHon
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N-stage Delay Penn ESE370 Fall DeHon
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Impact on Min Wni ? Partial Derivative unchanged
What does this say about f? Penn ESE370 Fall DeHon
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Stage Delay: f unchanged (fixed N)
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Total Delay Penn ESE370 Fall DeHon
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Impact of Gamma g=1.5 g=1.0 g=0.5 g=0 Penn ESE370 Fall DeHon
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Impact of Gamma g=1.5 g=1.0 g=0.5 g=0 Penn ESE370 Fall DeHon
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Minimize Penn ESE370 Fall DeHon
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Solve Penn ESE370 Fall DeHon
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Solve Penn ESE370 Fall DeHon
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Optimum Scale Up Penn ESE370 Fall DeHon
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Optimal Staging g≠0 Penn ESE370 Fall DeHon
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F and gamma? f=4 is optimal for what g? f=3 is optimal for what g?
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Optimal Fanout Clearer why we use f=4 as our benchmark? Remember HW3.5
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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 Fall DeHon
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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 Fall DeHon
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