Slide 1EE100 Summer 2008 Bharathwaj MuthuswamyEE100Su08 Lecture #5 (July 2nd2008)• Outline– Questions?– Lab notes:• Labs 2 and 3 have been shortened• Monday lab: go to your SECOND lab section next week.– Node-Voltage Analysis: wrap up– Mesh analysis: read it, OPTIONAL– Superposition– Thevenin’s TheoremSlide 2EE100 Summer 2008 Bharathwaj MuthuswamyV2V1R2R1R4R5R3I1VaNodal Analysis: Example #2Challenges: Determine number of nodes needed Deal with different types of sourcesSlide 3EE100 Summer 2008 Bharathwaj MuthuswamyA “floating” voltage source is one for which neither side is connected to the reference node, e.g. VLLin the circuit below:Problem: We cannot write KCL at nodes a or b because there is no way to express the current through the voltage source in terms of Va-Vb.Solution: Define a “supernode” – that chunk of the circuit containing nodes a andb. Express KCL for this supernode. Incorporate voltage source constraint into KCL equation. R4R2I2VaVb+-VLLI1Nodal Analysis w/ “Floating Voltage Source”Slide 4EE100 Summer 2008 Bharathwaj MuthuswamysupernodeEq’n 1: KCL at supernodeSubstitute property of voltage source:R4R2I2VaVb+-VLLI1Nodal Analysis: Example #3Slide 5EE100 Summer 2008 Bharathwaj MuthuswamySuperpositionA linear circuit is one constructed only of linear elements (linear resistors, and linear capacitors and inductors, linear dependent sources) and independent sources. Linearmeans I-V charcteristic of elements/sources are straight lines when plottedPrinciple of Superposition:• In any linear circuit containing multiple independent sources, the current or voltage at any point in the network may be calculated as the algebraic sum of the individual contributions of each source acting alone.Slide 6EE100 Summer 2008 Bharathwaj MuthuswamySuperpositionProcedure:1. Determine contribution due to one independent source• Set all other sources to 0: Replace independent voltagesource by short circuit, independent current source by opencircuit2. Repeat for each independent source3. Sum individual contributions to obtain desired voltage or currentSlide 7EE100 Summer 2008 Bharathwaj MuthuswamyOpen Circuit and Short Circuit• Open circuit Æ i=0 ; Cut offthe branch• Short circuit Æ v=0 ; replace the element by wire• Turn off an independent voltage source means –V=0 – Replace by wire – Short circuit• Turn off an independent current source means –i=0 – Cut off the branch– open circuitSlide 8EE100 Summer 2008 Bharathwaj MuthuswamySuperposition Example•Find Vo–+24 V2 Ω4 Ω4 A4 V+ –+Vo–Slide 9EE100 Summer 2008 Bharathwaj MuthuswamySlide 10EE100 Summer 2008 Bharathwaj MuthuswamySlide 11EE100 Summer 2008 Bharathwaj MuthuswamyEquivalent Circuit Concept• A network of voltage sources, current sources, and resistors can be replaced by an equivalent circuit which has identical terminal properties (I-V characteristics) without affecting the operation of the rest of the circuit.+vA_network AofsourcesandresistorsiA≡+vB_network BofsourcesandresistorsiBiA(vA) = iB(vB)Slide 12EE100 Summer 2008 Bharathwaj MuthuswamyThévenin Equivalent Circuit•Any* linear 2-terminal (1-port) network of indep. voltage sources, indep. current sources, and linear resistors can be replaced by an equivalent circuit consisting of an independent voltage source in series with a resistorwithout affecting the operation of the rest of the circuit.networkofsourcesandresistors≡–+VThRThRLiL+vL–abRLiL+vL–abThévenin equivalent circuit“load” resistorSlide 13EE100 Summer 2008 Bharathwaj MuthuswamyI-V Characteristic of Thévenin Equivalent• The I-V characteristic for the series combination of elements is obtained by adding their voltage drops:–+VThRThabii+vab–vab= VTh-iRI-V characteristic of resistor: v = iRI-V characteristic of voltage source: v = VThFor a given current i, the voltage drop vabis equal to the sum of the voltages dropped across the source (VTh)and across the resistor (iRTh)vSlide 14EE100 Summer 2008 Bharathwaj MuthuswamySlide 15EE100 Summer 2008 Bharathwaj MuthuswamySlide 16EE100 Summer 2008 Bharathwaj MuthuswamySlide 17EE100 Summer 2008 Bharathwaj MuthuswamySlide 18EE100 Summer 2008 Bharathwaj MuthuswamyThévenin Equivalent ExampleFind the Thevenin equivalent with respect to the terminals a,b:Slide 19EE100 Summer 2008 Bharathwaj MuthuswamyThévenin Equivalent Example (contd.)Slide 20EE100 Summer 2008 Bharathwaj MuthuswamyAside: Prelab 1, question 3Slide 21EE100 Summer 2008 Bharathwaj MuthuswamyThévenin Equivalent Example (contd.)Slide 22EE100 Summer 2008 Bharathwaj MuthuswamyThévenin Equivalent Example (contd.)Slide 23EE100 Summer 2008 Bharathwaj MuthuswamyThévenin Equivalent Example (contd.)Slide 24EE100 Summer 2008 Bharathwaj MuthuswamyRThCalculation Example #1Set all independent sources to
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