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 36.002CIRCUITS ANDELECTRONICSSuperposition, Thévenin and NortonCite 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 30=∑loopiVReviewCircuit Analysis Methodsz Circuit composition rulesz Node method – the workhorse of 6.002KCL at nodes using V ’s referenced from ground(KVL implicit in “ ”) ()jiee−Gz KVL: KCL:0=∑nodeiIVICite 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 3ConsiderLinearityWrite node equations –VI1R2R+–J021=−+−IReRVeNotice:linear inIVe ,,VI,eVNo termseCite 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 3ConsiderLinearityWrite node equations --Rearrange --VI1R2R+–J021=−+−IReRVeIRVeRR+=⎥⎦⎤⎢⎣⎡+12111GeS=conductancematrixnodevoltageslinear sumof sourceslinear inIVe ,,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 3Linearityor IRRRRVRRRe2121212+++=…… +++++=22112211IbIbVaVaeWrite node equations --Rearrange --021=−+−IReRVeIRVeRR+=⎥⎦⎤⎢⎣⎡+12111GeS=conductancematrixnodevoltageslinear sumof sourceslinear inIVe ,,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 3LinearityHomogeneitySuperposition⇒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 3LinearityHomogeneitySuperpositionHomogeneity1x2x...y1xα2xαyα...⇓⇒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 3LinearityHomogeneitySuperpositionSuperpositionax1ax2ay......bx1bx2by⇒baxx11+baxx22+bayy +⇓...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 3LinearityHomogeneitySuperpositionSpecific superposition example:1V01y02V2y01+V20V+21yy+⇓⇒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 3Method 4: Superposition methodThe output of a circuit isdetermined by summing theresponses to each sourceacting alone.independent sourcesonlyCite 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 3i+–0=V+-vishort+-vi0=IJ+-viopen+-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 3Back to the exampleUse superposition methodVI1R2R+–JeCite 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 3Back to the exampleUse superposition methodV acting aloneV0=I2R+–e1RI acting alone0=VI1R2RJeVRRReV212+=IRRRReI2121+=IRRRRVRRReeeIV2121212+++=+=sum superpositionVoilà !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 3saltwateroutput showssuperpositionDemoconstant+–sinusoid+–?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 3ConsiderYet another method…resistorsnounitsBy setting0,0==∀iInn0,0==∀iVmmAll0,0=∀=∀mmnnVIJ+–mVnIArbitrarynetwork NBy superpositionRiIVvnnnmmm++=∑∑βα+-vJiiresistanceunitsindependent of external excitation and behaves like a voltage “ ”THvalsoindependentof externalexcitement &behaves likea resistorCite 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 3OriRvvTHTH+=As far as the external world is concerned (for the purpose of I-V relation), “Arbitrary network N” is indistinguishable from:i+–THRTHvJ+-vThéveninequivalentnetworkTHRTHvopen circuit voltageat terminal pair (a.k.a. port)resistance of network seenfrom port( ’s, ’s set to 0)mVnINCite 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 3Method 4:The Thévenin
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