Day 23: November 3, 2010 Driving Large Capacitive Loads ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 23: November 3, 2010 Driving Large Capacitive Loads Penn ESE370 Fall2010 -- DeHon
Today How do we drive a large load? Stages and buffer sizing Minimum delay Penn ESE370 Fall2010 -- DeHon
Start Cdiff=0 Penn ESE370 Fall2010 -- DeHon
One Stage How size to minimize delay? Penn ESE370 Fall2010 -- DeHon
One Stage Delay equation? Penn ESE370 Fall2010 -- DeHon
Minimize Differentiate and set to zero. What’s WN? Penn ESE370 Fall2010 -- DeHon
Solving for size Penn ESE370 Fall2010 -- DeHon
N-stage Penn ESE370 Fall2010 -- DeHon
N-stage Delay Penn ESE370 Fall2010 -- DeHon
Size WNi to minimize delay Take partial derivative wrt WNi Penn ESE370 Fall2010 -- DeHon
Solving for WNi Penn ESE370 Fall2010 -- DeHon
Delay Penn ESE370 Fall2010 -- DeHon
Stage Delay Penn ESE370 Fall2010 -- DeHon
Stage Delay Penn ESE370 Fall2010 -- DeHon
Stage Delay Penn ESE370 Fall2010 -- DeHon
Total Delay Penn ESE370 Fall2010 -- DeHon
Minimize Penn ESE370 Fall2010 -- DeHon
Solve Penn ESE370 Fall2010 -- DeHon
Optimum Scale Up Penn ESE370 Fall2010 -- DeHon
Delay at Optimum Penn ESE370 Fall2010 -- DeHon
Cdiff=gCgate Penn ESE370 Fall2010 -- DeHon
N-stage Delay Penn ESE370 Fall2010 -- DeHon
N-stage Delay Penn ESE370 Fall2010 -- DeHon
Impact on Min Wni ? Partial Derivative unchanged Penn ESE370 Fall2010 -- DeHon
Total Delay Penn ESE370 Fall2010 -- DeHon
Stage Delay: N=7 N+1=8 Penn ESE370 Fall2010 -- DeHon
Stage Delay, g=0.5 N+1=8 Penn ESE370 Fall2010 -- DeHon
Stage Delay: N=6, g=0.5 N+1=7 Penn ESE370 Fall2010 -- DeHon
Stage Delay: N=5, g=0.5 N+1=6 Penn ESE370 Fall2010 -- DeHon
Stage Delay: N=4, g=0.5 N+1=5 Penn ESE370 Fall2010 -- DeHon
Optimal Staging g≠0 Penn ESE370 Fall2010 -- DeHon
Admin Friday Lecture HW5 due Proj2 out Penn ESE370 Fall2010 -- DeHon
Idea Drive large loads with geometrically sized buffer chain There is an optimal buffer ratio Technology/gate dependent Depends on self-loading Penn ESE370 Fall2010 -- DeHon