ECE 2006Circuit TheoryLinearityLinearity Example:SuperpositionSuperposition RulesSuperposition in ActionSuperposition ContinuedSource TransformationThevenin’s TheoremNorton’s TheoremMaximum Power TransferECE 2006Lecture for Chapter 4S.NorrCircuit Theory•Linearity•Superposition•Source Transformation•Thevenin and Norton Transformation•Maximum Power TransferTHE INTENT IS TO MAKE CIRCUITS SIMPLER AND EASIERLinearity•In a Resistive Circuit governed by Ohm’s Law, Linearity implies both Homogeneity and Additivity:Homogeneity: If V=IR, then kV = kIRAdditivity: If V1 = I1R and V2 = I2R, then when I1 + I2 is applied through R, the resulting voltage is V, where V = (I1 + I2 )R = V1 + V2Linearity Example:•If a 1 volt source is scaled to 10 Volts, the circuit responses due to that source are also scaled by a factor of 10:Superposition•Given a Linear Circuit with multiple independent sources, any node voltage or branch current is the Algebraic Sum of the contributions from each source, evaluated one at a time.Superposition Rules•Turn off all but ONE independent source.•Always leave dependent sources on.•Find the desired node voltage (or branch current) contributed by that single source.•Repeat process for each independent source•Sum the contributions from each source•Turn off Voltage Sources with SHORT CIRCUIT •Turn off Current Sources with OPEN CIRCUITSuperposition in ActionSuperposition Continued•Total Node Voltage, V = V1 – V2 + V3•Total Branch Current, I = I1 – I2 + I3Source Transformation•It can be shown that a “Voltage behind a Series Resistance” affects a circuit in exactly the same manner as a “Current in parallel with a resistor”•These sources are “equivalent” when V = IR or conversely I = V/RThevenin’s Theorem•Any linear, One-Port Circuit can be represented by an equivalent circuit consisting of a Voltage Source (VTH) behind a Resistance (RTH).•VTH is the Open Circuit Voltage at the Port Terminals•RTH is Input Resistance at the Port Terminals with all Independent Sources Off.Norton’s Theorem•Any linear, One-Port Circuit can be represented by an equivalent circuit consisting of a Current Source (IN) in parallel with a Resistance (RN).•IN is the Short Circuit Current at the Port Terminals•RN is Input Resistance at the Port Terminals with all Independent Sources Off.Maximum Power Transfer•Power transferred from Source to Load is Maximized when R-Load equals
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