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ECE 2006

ECE 2006. Lecture for Chapter 5 S.Norr. Circuit Theory. Linearity Superposition Source Transformation Thevenin and Norton Transformation Maximum Power Transfer THE INTENT IS TO MAKE CIRCUITS SIMPLER AND EASIER. Linearity.

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ECE 2006

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  1. ECE 2006 Lecture for Chapter 5 S.Norr

  2. Circuit Theory • Linearity • Superposition • Source Transformation • Thevenin and Norton Transformation • Maximum Power Transfer THE INTENT IS TO MAKE CIRCUITS SIMPLER AND EASIER

  3. Linearity • In a Resistive Circuit governed by Ohm’s Law, Linearity implies both Homogeneity and Additivity: Homogeneity: If V=IR, then kV = kIR Additivity: 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 + V2

  4. Linearity 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:

  5. 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.

  6. 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 CIRCUIT

  7. Superposition in Action

  8. Superposition Continued • Total Node Voltage, V = V1 – V2 + V3 • Total Branch Current, I = I1 – I2 + I3

  9. Source 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/R

  10. Thevenin’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 • RTHis Input Resistance at the Port Terminals with all Independent Sources Off.

  11. 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 • RNis Input Resistance at the Port Terminals with all Independent Sources Off.

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