Slide 1Lecture Week 3aSuperpositionSuperposition ExampleEquivalent Circuit ConceptSource CombinationsThévenin Equivalent CircuitSlide 8Calculating a Thévenin EquivalentThévenin Equivalent ExampleAlternative Method of Calculating RThRTh Calculation Example #1Norton Equivalent CircuitFinding IN and RN = RThFinding IN and RNMaximum Power Transfer TheoremSlide 17Lecture 3a, Prof. WhiteEE 42/100, Spring 2006 1EE 42/100 Discussion sectionsSection Day/Time Room GSIDis 101 M 3-4pm 241 Cory Liu, VincentDis 102 W 4-5pm 241 Cory Li, LiDis 103 F 9-10am3108 Etcheverry Liu, VincentDis 104F 10-11am 71 Evans Liu, VincentDis ?105 Th 4-5pm3107 Etcheverry Li, LiDis 106Th 12-1pm 45 Evans Li, LiLecture 3a, Prof. WhiteEE 42/100, Spring 2006 2Lecture Week 3aOUTLINE•Superposition: Analysis method for circuits with sources and linear elements•Thévenin and Norton equivalent circuits•Maximum Power TransferLecture 3a, Prof. WhiteEE 42/100, Spring 2006 3SuperpositionA linear circuit is constructed only of linear elements (linear resistors, linear dependent sources*) and independent sources. * We’ll discuss dependent sources a bit laterPrinciple 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.Procedure:1. Determine contribution due to an independent source•Set all other independent sources to 02. Repeat for each independent source3. Sum individual contributions to obtain desired voltage or currentLecture 3a, Prof. WhiteEE 42/100, Spring 2006 4Superposition Example•Find Vo–+24 V2 4 4 A4 V+ –+Vo–Lecture 3a, Prof. WhiteEE 42/100, Spring 2006 5Equivalent 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)Lecture 3a, Prof. WhiteEE 42/100, Spring 2006 6•Voltage sources in series can be replaced by an equivalent voltage source:•Current sources in parallel can be replaced by an equivalent current source:Source Combinationsi1i2≡i1+i2–+–+v1v2≡–+v1+v2Lecture 3a, Prof. WhiteEE 42/100, Spring 2006 7Thévenin Equivalent Circuit•Any linear 2-terminal (1-port) network of independent voltage sources, independent current sources, and linear resistors can be replaced by an equivalent circuit consisting of an independent voltage source in series with a resistor without affecting the operation of the rest of the circuit.networkofsourcesandresistors≡–+VThRThRLiL+vL–abRLiL+vL–abThévenin equivalent circuit“load” resistorActual circuitLecture 3a, Prof. WhiteEE 42/100, Spring 2006 8Why use such equivalent circuits? They may be much easier to use than the actual circuits when doing circuit analysis Example: We can reduce the entire telephone network or the entire power system that delivers energy to an AC outlet to a Thevenin equivalent containing just one voltage source (Vth) and one resistor (Rth) [or one impedance Zth, which we’ll see a little later]Lecture 3a, Prof. WhiteEE 42/100, Spring 2006 9Calculating a Thévenin Equivalent1. Calculate the open-circuit voltage, voc2. Calculate the short-circuit current, isc•Note that isc is in the direction of the open-circuit voltage drop across the terminals a,b !networkofsourcesandresistorsab+voc–networkofsourcesandresistorsabiscscocThocThivRvVLecture 3a, Prof. WhiteEE 42/100, Spring 2006 10Thévenin Equivalent ExampleFind the Thevenin equivalent with respect to the terminals a,b:Lecture 3a, Prof. WhiteEE 42/100, Spring 2006 11Alternative Method of Calculating RThFor a network containing only independent sources and linear resistors:1. Set all independent sources to zerovoltage source short circuitcurrent source open circuit2. Find equivalent resistance Req between the terminals by inspectionOr, set all independent sources to zero1. Apply a test voltage source VTEST 2. Calculate ITESTeqRR ThTESTTESTThIVR network ofindependentsources andresistors, witheach sourceset to zeroReqnetwork ofindependentsources andresistors, witheach sourceset to zeroITEST–+VTESTLecture 3a, Prof. WhiteEE 42/100, Spring 2006 12RTh Calculation Example #1Set all independent sources to 0:Lecture 3a, Prof. WhiteEE 42/100, Spring 2006 13Norton equivalent circuitNorton Equivalent Circuit•Any linear 2-terminal (1-port) network of independent voltage sources, independent current sources, and linear resistors can be replaced by an equivalent circuit consisting of an independent current source in parallel with a resistor without affecting the operation of the rest of the circuit.networkofsourcesandresistors≡RLiL+vL–abaRLiL+vL–iNbRNLecture 3a, Prof. WhiteEE 42/100, Spring 2006 14Finding IN and RN = RThIN ≡ isc = VTh/RThAnalogous to calculation of Thevenin Eq. Ckt:1) Find open-circuit voltage and short-circuit current2) Or, find short-circuit current and Norton (Thevenin) resistanceLecture 3a, Prof. WhiteEE 42/100, Spring 2006 15Finding IN and RN•We can derive the Norton equivalent circuit from a Thévenin equivalent circuit simply by making a source transformation: RLRNiLiN+vL–ab–+RLiL+vL–vThRThscThThNscocThN ; iRviivRR abLecture 3a, Prof. WhiteEE 42/100, Spring 2006 16Maximum Power Transfer TheoremA resistive load receives maximum power from a circuit if the load resistance equals the Thévenin resistance of the circuit.Example: Maximizing power to speakers from music systemL2LThThL2LRRRVRip–+VThRThRLiL+vL–Thévenin equivalent circuit LThLThL2LTh4LThLThL2LTh2Th 02 02RRRRRRRRRRRRRRVdRdpLTo find the value of RL for which p is maximum, set to 0:Power absorbed by load resistor:LdRdpLecture 3a, Prof. WhiteEE 42/100, Spring 2006
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