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 146.002CIRCUITS ANDELECTRONICSState and MemoryCite 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 14C+–CvIv+–R1RecallReading: Sections 10.3, 10.5, and 10.7ReviewVvII0t≥=for()RCtIICeVVv−−+=()Cv 0()Cv 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 14tIv0tCv0IV()0CvIvIVThis lecture will dwell on the memory property of capacitors.For the RC circuit in the previous slideNotice that the capacitor voltage for is independent of the form of the input voltage before . Instead, it depends only on the capacitor voltage at , and the input voltage for .0t≥0t=0t=0t≥()0t≥RCtIICeVVv−−+=()Cv 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 14VCq =for linear capacitors,capacitor voltage Vis also state variablestate variable, actuallyState : summary of past inputs relevantto predicting the futureStateCite 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 14()()RCtICICeVvVv−−+= 01Back to our simple RC circuit()()()tvvfvICC,0=StateSummarizes the past input relevant to predicting future behaviorCite 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 14We are often interested in circuitresponse for zero state vC(0) = 0 zero input vI(t) = 0 zero input response or ZIR()RCtCCevv−= 0RCtIICeVVv−−=Correspondingly, zero state response or ZSR23StateCite 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 14Why memory?Or, why is combinational logic insufficient?One application of STATEDIGITAL MEMORYExamples Consider adding 6 numbers on yourcalculator “Remembering” transient inputs2 + 9 + 6 + 5 + 3 + 8M+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 14A 1-bit memory elementMemory AbstractionRemembers input when store goes high.Like a camera that records input (dIN) when the user presses the shutter release button.The recorded value is visible at dOUT.INdOUTdstore MINdstoreOUTdremembers the 1The6.004viewTheNECView☺$¥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 14AFirst attemptBuilding a memory element …storestoragenodedINdOUTC*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 14AStored value leaks awaystore pulse width >> RON CBuilding a memory element …CRtCLev−⋅= 55lnOHLVCRT −=2fromvCtT5VVOHvCstore = 1dINdOUTC*vCstore = 0dINdOUTC*RLCite 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 14Input resistance RINBSecond attempt bufferRINstorebufferdINdOUTC*5lnOHINVCRT −=LINRR>>Better, but still not perfect.DemoBuilding a memory element …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 14Does this work?CThird attempt buffer + refreshstoredINdOUTC*storeBuilding a memory element …No. External value caninfluence storage node.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 14Works!DFourth attempt buffer + decoupled refreshstoredINdOUTC*storeBuilding a memory element …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 14A Memory ArrayDecoderAddressINdOUTdS MINdOUTdS MINdOUTdS MINdOUTdS MABCD00100111INstoreOUTa0a12ABCDstore4-bit memoryAddressINOUTCite 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 14Truth table for decodera0a1AB CD0010 000101 001000 101100 01Cite 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 14Agarwal’s top 10 list on memory10 I have no recollection, Senator.9 I forgot the homework was due today.8 Adlibbing
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