Transcript ppt
ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 39: December 5, 2014 Repeaters in Wiring 1 Penn ESE370 Fall2014 -- DeHon Previously • Transmission line (LC wire) wire delay scales as Length • Unbuffered RC wire delay scales as Length2 – 0.5 Rwire Cwire – 0.5 L2 Ru Cu 2 Penn ESE370 Fall2014 -- DeHon Today • RC (on-chip) Interconnect Buffering 3 Penn ESE370 Fall2014 -- DeHon Back to RC Wire (on-chip, no inductance, L) 4 Penn ESE370 Fall2014 -- DeHon Delay of Wire • • • • Long Wire: 1mm Ru = 60K W per 1mm of wire Cu = 0.16 pF per 1mm of wire Driven by inverter – R0 = 25K W – C0 = 0.01 fF – Assume velocity saturated, sized Wp=Wn=1 • Loaded by identical inverter Penn ESE370 Fall2014 -- DeHon 5 Should be able to do these calculations on final. Formulate Delay Delay of inverter driving wire? Rbuf Cself Cwire Cload 0.5Rwire Cwire Rwire Cload 6 Penn ESE370 Fall2014 -- DeHon Calculate Delay • Cload = 2 C0 • Rbuf = R0 • Cself = g 2 C0 = 2 C0 Rbuf Cself Cwire Cload 0.5Rwire Cwire Rwire Cload 7 Penn ESE370 Fall2014 -- DeHon Buffering Wire • Complete Preclass Table 8 Penn ESE370 Fall2014 -- DeHon N Buffers • Delay Equation for N buffers? Rwire Cwire Rwire Cwire N Rbuf Cself Cload 0.5 Cload N N N N N Rbuf Cself Cload Rbuf Rwire Cwire Cwire 0.5 Rwire Cload N 9 Penn ESE370 Fall2014 -- DeHon Minimize Delay N Rbuf Cself Cload Rbuf Rwire Cwire Cwire 0.5 Rwire Cload N • How determine N to minimize delay? • Derivative with respect to N Rbuf Cself Cload Rwire Cwire 0.5 0 2 N 10 Penn ESE370 Fall2014 -- DeHon Solve for N Rbuf Cself Cload Rwire Cwire 0.5 0 2 N Rwire Cwire N 0.5 R C C self load buf 11 Penn ESE370 Fall2014 -- DeHon Minimize Delay Rwire Cwire N 0.5 R C C self load buf N Rbuf Cself Cload Rbuf Rwire Cwire Cwire 0.5 Rwire Cload N Rbuf Cself Cload Rbuf Cwire Rwire Cload 2 0.5Rwire Cwire Penn ESE370 Fall2014 -- DeHon Equalizes delay in buffer and wire 12 Calculate: Delay at Optimum Stages for Example • • • • Ru = 60K W per 1mm of wire Cu = 0.16 pF per 1mm of wire Rbuf=R0 = 25K W Cself=Cload=2(C0 = 0.01 fF)=0.02fF 2 0.5Rwire Cwire Rbuf Cself Cload Rbuf Cwire Rwire Cload 13 Penn ESE370 Fall2014 -- DeHon Segment Length • Rwire = L×Runit • Cwire = L×Cunit Rwire Cwire N 0.5 R C C self load buf Ru Cu N L 0.5 R C C self load buf 14 Penn ESE370 Fall2014 -- DeHon Optimal Segment Length • Delay scales linearly with distance once optimally buffered * seg L R C C L buf self load 2 N Ru Cu Ru Cu N L 0.5 R C C self load buf Penn ESE370 Fall2014 -- DeHon 15 Buffer Size? • How big should buffer be? – Rbuf = R0/W – Cload = 2 W C0 (assuming velocity saturation) – Cself = g 2 W C0 2 0.5Rwire Cwire Rbuf Cself Cload Rbuf Cwire Rwire Cload R0 R0 2 0.5Rwire Cwire 1 g 2WC0 Cwire Rwire 2WC0 W W 16 Penn ESE370 Fall2014 -- DeHon Implication W • Rwire = L×Runit • Cwire = L×Cunit • W independent of Length – Depends on technology R0 Cwire W Rwire 2C0 17 Penn ESE370 Fall2014 -- DeHon Delay at Optimum W 2 0.5Rwire Cwire R0 1 g 2C0 2 R0 Cwire Rwire 2C0 • With g=1, 1+g=2 • Same size as first term 4 R0 Cwire Rwire 2C0 18 Penn ESE370 Fall2014 -- DeHon Ideas • Wire delay linear once buffered • Optimal buffering matches – Buffer delay – Delay on wire between buffers – Delay of wire driving buffer 19 Penn ESE370 Fall2014 -- DeHon Final • Everything – Including today • Focus on wiring, memory – Crosstalk – Transmission lines • Delay • Energy • • • • • • • Static CMOS Precharge Pass Transistors Ratio Clocking Restoration Buffering 2010, 2011, 2012, 2013 finals all good content --2011 many “small” problems – good coverage Penn ESE370 Fall2014 -- DeHon 20 Admin • Ron Review Monday (12/8) – Talk with him about final Q&A session • Final (12/18) noon Towne 303 21 Penn ESE370 Fall2014 -- DeHon