ECE 2006
Lecture for Chapter 5
S.Norr
Circuit Theory
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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.