6 002 CIRCUITS AND ELECTRONICS Superposition Th venin and Norton 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 3 Review Circuit Analysis Methods z KVL Vi 0 loop KCL Ii 0 VI node z Circuit composition rules z Node method the workhorse of 6 002 KCL at nodes using V s referenced from ground KVL implicit in ei e j G 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 3 Linearity R1 V R2 e J Consider I Write node equations e V e I 0 R1 R2 Notice linear in e V I No eV VI terms 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 3 Linearity R1 Consider V J R2 Write node equations e V e I 0 R1 R2 Rearrange 1 1 R R e 1 2 conductance matrix G I linear in e V I V I R1 node linear sum voltages of sources e S 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 3 Linearity Write node equations e V e I 0 R1 R2 Rearrange 1 1 R R e 1 2 conductance matrix G or linear in e V I V I R1 node linear sum voltages of sources e S R2 R1 R2 e V I R1 R2 R1 R2 e a1V1 a2V2 b1 I1 b2 I 2 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 3 Linearity Homogeneity Superposition 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 3 Linearity Homogeneity Superposition Homogeneity x1 x2 y x1 x2 y 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 3 Linearity Homogeneity Superposition Superposition x1a x2 a ya x1b x2 b yb x1a x1b x2 a x2 b y a yb 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 3 Linearity Homogeneity Superposition Specific superposition example V1 0 0 V2 y1 y2 V1 0 0 V2 y1 y2 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 3 Method 4 Superposition method The output of a circuit is determined by summing the responses to each source acting alone s e c r u so t n e nd e p e i nd only 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 3 i V 0 i v v short I 0 J i i v v open 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 3 Back to the example Use superposition method V e R2 J R1 I 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 3 Back to the example Use superposition method V acting alone e R1 V I 0 eV R2 I acting alone R2 V R1 R2 e R2 V 0 sum J R1 I R1 R2 eI I R1 R2 superposition R2 R1 R2 e eV eI V I R1 R2 R1 R2 Voil 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 3 Demo salt water constant output shows superposition 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 3 Yet another method Consider By superposition v mVm n I n Ri m n no resistance units units By setting n I n 0 mVm 0 i 0 i 0 i v J y network r a r t i N Arb resistors Vm In J i also independent of external excitement behaves like a resistor All n I n 0 mVm 0 independent of external excitation and behaves like a voltage vTH 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 3 Or v vTH RTH i As far as the external world is concerned for the purpose of I V relation Arbitrary network N is indistinguishable from RTH Th venin equivalent network vTH RTH vTH v J N i open circuit voltage at terminal pair a k a port resistance of network seen from port Vm s I n s set to 0 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 3 Method 4 The Th venin Method J i N v E v E Th venin equivalent RTH vTH i Replace network N with its Th venin equivalent then solve external network E 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 3 Example V R2 J i1 R1 I i1 R1 RTH V VTH i1 I V VTH R1 RTH Cite as Anant Agarwal and Jeffrey Lang course materials for 6 …
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