ECE 2006 Lecture for Chapter 5 S Norr

Circuit Theory • • • Linearity Superposition Source Transformation Thevenin and Norton Transformation Maximum

Linearity • In a Resistive Circuit governed by Ohm’s Law, Linearity implies both Homogeneity

Linearity Example: • If a 1 volt source is scaled to 10 Volts, the

Superposition • Given a Linear Circuit with multiple independent sources, any node voltage or

Superposition Rules • Turn off all but ONE independent source. • Always leave dependent

Superposition Continued • Total Node Voltage, V = V 1 – V 2 +

Source Transformation • It can be shown that a “Voltage behind a Series Resistance”

Thevenin’s Theorem • Any linear, One-Port Circuit can be represented by an equivalent circuit

Norton’s Theorem • Any linear, One-Port Circuit can be represented by an equivalent circuit

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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 • In a Resistive Circuit governed by Ohm’s Law, Linearity implies both Homogeneity and Additivity: Homogeneity: If V=IR, then k. V = k. IR Additivity: If V 1 = I 1 R and V 2 = I 2 R, then when I 1 + I 2 is applied through R, the resulting voltage is V, where V = (I 1 + I 2 )R = V 1 + V 2

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:

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 CIRCUIT

Superposition in Action

Superposition Continued • Total Node Voltage, V = V 1 – V 2 + V 3 • Total Branch Current, I = I 1 – I 2 + I 3

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

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 • 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.