6 002 CIRCUITS AND ELECTRONICS Basic Circuit Analysis Method KVL and KCL method 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 2 Review Lumped Matter Discipline LMD Constraints we impose on ourselves to simplify our analysis B 0 t q 0 t Outside elements Inside elements wires resistors sources Allows us to create the lumped circuit abstraction 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 2 Review LMD allows us to create the lumped circuit abstraction i v Lumped circuit element power consumed by element 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 2 Review Review Maxwell s equations simplify to algebraic KVL and KCL under LMD KVL j j 0 loop KCL jij 0 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 2 Review a R1 b R4 R3 R2 d R5 c DEMO vca vab vbc 0 KVL ica ida iba 0 KCL 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 2 Method 1 Basic KVL KCL method of Circuit analysis Goal Find all element v s and i s 1 write element v i relationships from lumped circuit abstraction 2 write KCL for all nodes 3 write KVL for all loops lots of unknowns lots of equations lots of fun solve 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 2 Method 1 Basic KVL KCL method of Circuit analysis Element Relationships For R V IR For voltage source V V0 R V0 For current source I I 0 J Io 3 lumped circuit elements 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 2 KVL KCL Example a 1 0 V0 R3 b 2 4 R1 3 R2 R4 d 5 R5 c The Demo Circuit 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 2 Associated variables discipline i Element e Current is taken to be positive going into the positive voltage terminal Then power consumed by element e i is positive 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 2 KVL KCL Example a 0 V0 1 i0 L1 2 i4 i1 L 2 R1 4 R4 R3 b i3 d 3 i2 i5 R2 5 R5 L3 c The Demo Circuit L4 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 2 Analyze 0 5 0 5 1 Element relationships v i given v3 i3 R3 v0 V0 v4 i4 R4 v1 i1 R1 v5 i5 R5 v2 i2 R2 12 unknowns 6 equations 2 KCL at the nodes a i0 i1 i4 0 3 independent b i2 i3 i1 0 equations d i5 i3 i4 0 e i0 i2 i5 0 redundant 3 KVL for loops L1 v0 v1 v2 0 3 independent equations L2 v1 v3 v4 0 s L3 v3 v5 v2 0 n o L4 v0 v4 v5 0 redundant ati s n w u no k eq n u 2 2 1 1 ugh 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 2 Other Analysis Methods Method 2 Apply element combination rules A B C R1 R2 R3 G1 G2 V1 V2 RN GN RN GN V1 V2 J J J I2 G1 G2 1 Gi Ri D I1 R1 R2 I1 I 2 Surprisingly these rules along with superposition which you will learn about later can solve the circuit on page 8 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 2 Other Analysis Methods Method 2 Apply element combination rules I Example R1 V R3 R2 I I V R1 V R2 R3 R2 R3 R R1 R R2 R3 R2 R3 V I R 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 2 Method 3 Node analysis Particular application of KVL KCL method 1 Select reference node ground from which voltages are measured 2 Label voltages of remaining nodes with respect to ground These are the primary unknowns 3 Write KCL for all but the ground node substituting device laws and KVL 4 Solve for node voltages 5 Back solve for branch voltages and currents i e the secondary unknowns 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 2 Example Old Faithful plus current source V0 R2 R5 J e2 V e1 0 Step 1 R4 R1 R 3 I1 Step 2 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 2 Example Old Faithful plus current source V0 V e1 0 R2 R4 e2 R5 J R1 R 3 for I1 convenience write 1 Gi Ri KCL at e1 e1 V0 G1 e1 e2 G3 e1 G2 0 KCL at e2 e2 e1 G3 e2 V0 G4 e2 G5 I1 0 Step 3 Cite as Anant Agarwal and Jeffrey Lang course materials for …
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