ECE 2006 Lecture for Chapter 5 S.Norr. Circuit Theory Linearity Superposition Source Transformation...

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 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

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 = V1 – V2 + V3

• Total Branch Current, I = I1 – I2 + I3

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.