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 26.002CIRCUITS ANDELECTRONICSBasic 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 20=∂∂tBφ0=∂∂tqOutside elementsInside elementsAllows us to create the lumped circuitabstractionwiresresistorssourcesReviewLumped Matter Discipline LMD:Constraints we impose on ourselves to simplify our analysisCite 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 2LMD allows us to create the lumped circuit abstractionLumped circuit element+-vipower consumed by element =viReviewCite 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 2KVL:0loopKCL:node=∑jjν0=∑jjiReviewReviewMaxwell’s equations simplify to algebraic KVL and KCL under LMD!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 2KVL0=++bcabcavvv0=++badacaiiiKCLDEMO1R2R4R5R3Rabdc+–ReviewCite 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 2Method 1:Basic KVL, KCL method ofCircuit analysisGoal: Find all element v’s and i’swrite element v-i relationships(from lumped circuit abstraction)write KCL for all nodeswrite KVL for all loops1.2.3.lots of unknownslots of equationslots of funsolveCite 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 2Method 1:Basic KVL, KCL method ofCircuit analysisFor R,For voltage source,For current source,Element RelationshipsIRV=0VV=0II=3 lumped circuit elementsR0VoI+ –JCite 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 2KVL, KCL ExampleThe Demo Circuit+–1R2R4R5R3Rabdc00V=ν+–1ν+–5ν+–3ν+–2ν+–4ν+–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 2Associated variables disciplineνi+-Element eThen power consumedby element eiν=is positiveCurrent is taken to be positive going into the positive voltage terminalCite 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 2KVL, KCL ExampleThe Demo Circuit+–1R2R4R5R3Rabdc00V=ν+–1ν+–5ν+–3ν+–1L2L4L3L2ν+–4ν+–2i1i0i5i3i4iCite 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 2Analyze12 unknowns5050,ιινν……1. Element relationships3. KVL for loops 00Vv =111Riv =222Riv =333Riv=444Riv=555Riv=given2. KCL at the nodesredundant0431=−+ vvv0210=++− vvv0253=−+ vvv0540=++− vvvredundant0410=++ iii0132=−+ iii0435=−− iii0520=−−− iiia:b:d:e:6 equations3 independentequations3 independentequations12 unknowns12 equations/ugh @#!()iv,L1:L2:L3: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 2Other Analysis MethodsMethod 2—Apply element combination rulesBCD⇔NRRR+++21⇔1G2GNGNGGG++ 21iiRG1=⇔+ –+ –+ –1V2V21VV+⇔JJ1I2I21II+JA1R2R3RNR…Surprisingly, these rules (along with superposition, whichyou will learn about later) can solve the circuit on page 8Cite 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 2Other Analysis MethodsMethod 2—Apply element combination rulesVI3232RRRR+VI32321RRRRRR++=+–V?=I1R3R2R+–+–RExample1RRVI =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 21.2.3.4.5.Select reference node ( ground)from which voltages are measured.Label voltages of remaining nodeswith respect to ground.These are the primary unknowns.Write KCL for all but the groundnode, substituting device laws andKVL.Solve for node voltages.Back solve for branch voltages andcurrents (i.e., the secondary unknowns) Particular application of KVL, KCL methodMethod 3—Node analysisCite 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 2Example: Old Faithful plus current source0V1R2R4R5R3RJ1I0V+–1e2eStep 1Step 2Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
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