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 46.002CIRCUITS ANDELECTRONICSThe Digital AbstractionCite 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 4Reviewz Discretize matter by agreeing to observe the lumped matter disciplinezAnalysis tool kit: KVL/KCL, node method, superposition, Thévenin, Norton (remember superposition, Thévenin, Norton apply only for linear circuits)Lumped Circuit AbstractionCite 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 4Discretize value Digital abstractionInterestingly, we will see shortly that the tools learned in the previous three lectures are sufficient to analyze simple digital circuitsReading: Chapter 5 of Agarwal & LangTodayCite 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 4Analog signal processingBut first, why digital?In the past…By superposition,The above is an “adder” circuit.221112120VRRRVRRRV+++=If,21RR =2210VVV+=1V1R2R+–2V+–0Vandmight represent the outputs of two sensors, for example.1V2VCite 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 4Noise Problem…noise hampers our ability to distinguishbetween small differences in value —e.g. between 3.1V and 3.2V.Receiver:huh?add noise onthis wiretCite 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 4Value DiscretizationWhy is this discretization useful?Restrict values to be one of twoHIGH5VTRUE1LOW0VFALSE0…like two digits 0 and 1(Remember, numbers larger than 1 can be represented using multiple binary digits and coding, much like using multiple decimal digits to represent numbers greater than 9. E.g., the binary number 101 has decimal value 5.)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 4Digital SystemsenderreceiverSVRVnoiseSV“0” “0”“1”0V2.5V5VHIGHLOWtRV“0” “0”“1”0V2.5V5VtVVN0=NVSV“0” “0”“1”2.5VtWith noiseVVN2.0=SV“0” “0”“1”0V2.5V5Vt0.2VtCite 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 4Digital SystemBetter noise immunityLots of “noise margin”For “1”: noise margin5V to 2.5V = 2.5VFor “0”: noise margin 0V to 2.5V = 2.5VCite 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 4Voltage Thresholds and Logic Values1010senderreceiver100V2.5V5VCite 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 4forbiddenregionVHVL3V2VBut, but, but …What about 2.5V?Hmmm… create “no man’s land”or forbidden regionFor example,senderreceiver0V5V1100“1” V 5V“0” 0V VHLCite 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 4senderreceiverBut, but, but …Where’s the noise margin?What if the sender sent 1: ?VHHold the sender to tougher standards!5V0V1100V0HV0LVIHVILCite 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 4senderreceiver5V0VVHBut, but, but …Where’s the noise margin?What if the sender sent 1: ?Hold the sender to tougher standards!“1” noise margin:“0” noise margin:VIH-V0HVIL-V0L1100V0HV0LVIHVILNoise marginsCite 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 4Digital systems follow static discipline: if inputs to the digital system meet valid input thresholds, then the system guarantees its outputs will meet valid output thresholds.senderreceiver0 1 0 1t5VV0HV0L0VVIHVIL0 1 0 1t5VV0HV0L0VVIHVILCite 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 4Processing digital signalsRecall, we have only two values —Map naturally to logic: T, FCan also represent numbers1,0Cite 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 4Processing digital signalsBoolean LogicIf X is true and Y is trueThen Z is true else Z is false.Z
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