6 002 CIRCUITS AND ELECTRONICS Incremental Analysis 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 7 Review Nonlinear Analysis X Analytical method X Graphical method Today X Incremental analysis Reading Section 4 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 7 Method 3 Incremental Analysis Motivation music over a light beam Can we pull this off iD vD LED light intensity I D iD vI music signal iR vI t t vI t iD t light AMP iR I R light intensity IR in photoreceiver LED Light Emitting expoDweep iR t sound nonlinear linear problem will result in distortion 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 7 Problem The LED is nonlinear distortion iD iD vD vD vI t vD t iD vD t 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 7 Insight iD small region looks linear about VD ID ID VD vD DC offset or DC bias Trick vi t vI VI iD I D id vD LED vD VD vd VI vi 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 7 Result iD id ID vD VD vd very small 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 7 Result vD vI vd vD VD t iD id iD linear ID t Demo 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 7 The incremental method or small signal method 1 Operate at some DC offset or bias point VD ID 2 Superimpose small signal vd music on top of VD 3 Response id to small signal vd is approximately linear Notation iD I D id total DC small variable offset superimposed signal 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 7 What does this mean mathematically Or why is the small signal response linear nonlinear iD f vD We replaced vD VD vD large DC vd increment about VD using Taylor s Expansion to expand f vD near vD VD iD f VD df vD vD dvD vD VD 1 d 2 f v D 2 dvD 2 v 2 vD D VD neglect higher order terms because vD is small 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 7 iD f VD constant w r t vD d f v D vD d vD vD VD constant w r t vD slope at VD ID We can write X I D iD f VD d f v D vD d vD vD VD equating DC and time varying parts I D f VD operating point d f v D iD vD d vD vD VD constant w r t vD so iD vD By notation iD id v D vd 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 7 In our example iD a e bv D From X I D id a e bVD a e bVD b vd Equate DC and incremental terms I D a ebVD operating point aka bias pt aka DC offset id a ebVD b vd id I D b vd constant small signal behavior linear 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 7 Graphical interpretation operating point I D a ebVD id I D b vd A slope at VD ID iD ID id B VD operating point vd vD we are approximating A with B 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 7 graphically mathematically now circuit We saw the small signal Large signal circuit ID VI LED VD I D a ebVD Small signal reponse id I D b vd vd behaves like id R small signal circuit 1 ID b id vi vd 1 I Db Linear 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 7
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