1EE141WiresEE141- Spring 2003Lecture 12EE141AnnouncementsMidterm results by next TuesdayStart of project on Tuesday as well2EE141Today’s lectureWire modelsInductanceEE141Interconnect3EE141The Lumped ModelVoutDrivercwireVinClum pe dRdriverVoutEE141The Distributed RC Line4EE141Step-response of RC wire as afunction of time and space0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 500.511.522.5time (nsec)voltage (V)x= L/10 x = L/4 x = L/2 x= L EE141RC Models5EE141Driving an RC-lineVinRsVout(rw,cw,L)EE141Design Rules of Thumbrc delays should only be considered whentpRC>> tpgateof the driving gateLcrit >> √ tpgate/0.38rcrc delays should only be considered when therise (fall) time at the line input is smaller thanRC, the rise (fall) time of the linetrise<RC» when not met, the change in the signal is slowerthan the propagation delay of the wire© MJIrwin, PSU, 20006EE141INTERCONNECTEE141Common Wire Cross-SectionsCoaxialCableTriplateStrip LineMicroStrip Wire aboveGround Planecl = εµ1212log2log2rrrrlcπµπε==c - capacitance/lengthl - inductance/length==WhlWhcµε7EE141Inductance of package pinsChipMountingCavityLead FrameBonding WirePinLL’MakeRise-andFallTimesasslowaspossibleEE141The Transmission LineVinrlcrlcrlcrlcVoutxg g g gThe Wave Equation8EE141Lossless Transmission Line -Parametersvacuumspeed of light inEE141Wave Propagation Speed9EE141Wave Reflection for DifferentTerminationsEE141Transmission Line Response (RL= ∞)0.01.02.03.04.05.0V0.01.02.03.04.0V0.0 5.0 10.0 15.0t(intlightf)0.02.04.06.08.0VRS=5Z0RS=Z0RS=Z0/5(a)(b)(c)VDestVSource10EE141Lattice DiagramVSourceVDest0.8333 V1.6666 V+ 0.8333+0.8333+ 0.5556+0.5556+ 0.3704+ 0.2469+0.3704+0.24692.2222 V3.1482 V3.7655 V...2.7778 V3.5186 V4.0124 VL/νtEE141Critical Line Lengths versus Rise Times(1990, Bakoglu)100-200ps todayLcrit~1cm11EE141Design Rules of ThumbTransmission line effects should be considered when therise or fall time of the input signal (tr,tf) is smaller than thetime-of-flight of the transmission line (tflight).tr(tf)<<2.5tflightTransmission line effects should only be considered whenthe total resistance of the wire is limited:R<5Z0The transmission line is considered lossless when the totalresistance is substantially smaller than the characteristicimpedance,R<Z0/2EE141Should we be worried?Transmission line effectscause overshooting and non-monotonic behaviorClock signals in 400 MHz IBM Microprocessor(measured using e-beam prober)
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