Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.002 Fall 2000 Lecture 136.002CIRCUITS ANDELECTRONICSDigital CircuitCite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.002 Fall 2000 Lecture 13C+–CvIv+–RtCvOVIV()RCtIOICeVVVv−−+=1()OCVv =0tIVIv0Reviewtime constant RCRCCite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.002 Fall 2000 Lecture 13Let’s apply the result to an inverter.ABVSVSXCGStAvV501 Æ 0 at AABXFirst, rising delay trat BCite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.002 Fall 2000 Lecture 13ABVSVSXCGSidealtAvV501 Æ 0 at AFirst, rising delay trat BobservedtBvV50Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.002 Fall 2000 Lecture 13ABVSVSXCGStAvV501 Æ 0 at AOHVrtrising delay of XFirst, rising delay trat BtBvV50Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.002 Fall 2000 Lecture 13Equivalent circuit for 0Æ1 at B+–BvSIVv =+–LRGSC()GSLCRtSSBeVVv−−+= 01FromNow, we need to find t for whichvB= VOH.SIVv=for t ≥ 0()00=BvCite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.002 Fall 2000 Lecture 13GSLCRtSSOHeVVv−−=OrFind tr:OHSCRtSVVeVGSLr−=−SOHSGSLrVVVCRt−=−lnSOHSGSLrVVVCRt−−= lnCite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.002 Fall 2000 Lecture 13GSLCRtSSOHeVVv−−=OrFind tr:OHSCRtSVVeVGSLr−=−SOHSGSLrVVVCRt−=−lnSOHSGSLrVVVCRt−−= lne.g.KRL1=pFCGS1.0=VVS5=VVOH4=545ln101.0101t123r−×××−=−ns16.0=!1.0 nsRC=Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.002 Fall 2000 Lecture 13Falling Delay tfSV+–LR+–BvGSCONR()()VVvSB50 =XFalling delay tfis thet for which vBfalls to VOLEquivalent circuit for 1 Æ 0 at BCite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.002 Fall 2000 Lecture 13Falling Delay tfEquivalent circuit for 1 Æ 0 at BONLTHRRR||=LONONSTHRRRVV+=Thévenin replacement …+–BvTHVTHRGSC+–SV+–LR+–BvGSCONR()()VVvSB50 =XCite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.002 Fall 2000 Lecture 13()GSTHCRtTHSTHBeVVVv−−+=1FromFalling decay tfis thet for which vBfalls to VOL()GSTHfCRtTHSTHOLeVVVV−−+=orTHSTHOLGSTHfVVVVCRt−−−= lnCite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.002 Fall 2000 Lecture 13THSTHOLGSTHfVVVVCRt−−−= lne.g.51ln101.01012−⋅⋅−=ftps6.1=!1psRC =KRL1=pFCGS1.0=VVS5=VVOL1=Ω= 10ONRVVRTHTH0,10≈Ω≈Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.002 Fall 2000 Lecture 13For recitation: Slow may be betterProblempin 2pin 1chipLCSo the engineers decided to speed it up…made RLsmallmade RONsmallRLRONidealslow!observedv:vCite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.002 Fall 2000 Lecture 13For recitation: Slow may be betterProblempin 2pin 1chipLCidealslow!observed…but, disaster!expectedv:v:vVILobservedCite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.002 Fall 2000 Lecture 13Why? Consider…1Case1R0Rpin1okDemoCite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.002 Fall 2000 Lecture 13Why? Consider…2Case1R0Rpin12Rpin2PCcrosstalk!Demomodel for crosstalk:+–vRPC+–Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.002 Fall 2000 Lecture 133Case…6.002 expert saw the solutionDetailed analysis in recitation.PC1R0R2R+–slower
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