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Every circuit which is composed of Lecture 8: Linearity and Equivalent Circuits
(^) ideal independent voltage
resistors, and current sources, linear dependent sources, and has a linear I-V relationship.
There is a simpler circuit with the same I-V relationship.
I
v
The Thevenin equivalent Thevenin Equivalent Circuit
circuit is composed of a
current source, through choice of VIt can model any circuit except a pure independentvoltage source in series with a resistor:
T T and R. I
v TH V
THTH b^ -V/R^ a
The Norton equivalentNorton Equivalent Circuit
circuit is composed of a
voltage source, through choice of IIt can model any circuit except a pure independentcurrent source in parallel with a resistor:
N N and R. I
v
N^ -I NN IR
b a
Find the V Find the x-intercept and y-intercept of the graph. Set the current I and find the corresponding V Set the voltage V and find the corresponding I Find two points on the I-V graph for the circuit.circuit, all we need to do is: To find the Thevenin or Norton equivalent for a Two Points Define a Line
TH TH and R
N , or the I
N and Rthat
replicate this line.
Example
(Nilsson & Riedel text)
Norton circuits.Thevenin andFind the
Example
(Nilsson & Riedel text)
and Norton circuits.Find the Thevenin
TH Vand I
N Come From Independent Sources
in a circuit,^ ^ If there are no independent voltage or current sources
TH^ V= 0 V
N and^ I = 0 A
However, the slope of the graph, 1/Rthrough the origin. In this situation, you know that the I-V graph goes all currents and voltages in the circuit are zero. a circuit (only resistors and linear dependent sources), If there is no independent voltage or current present in
TH , still must be
determined. It cannot be found using R
TH TH = V/ I
N.
No Independent Sources? Test for R
TH
(^) Do the same to find Rcurrent to find resistance. (^) An ohmmeter applies a test voltage and measures the resultingcurrent—a resistor has no voltage or current on its own. (^) One cannot determine the resistance by measuring voltage andresistor. (^) A simple example of a circuit with no independent sources is a TH (^) : Set V using an independent voltage
(^) Here, you are finding an additional point on the I-V graph. TH (^) R= V / I (^) Or, set I using an independent current source, and measure V.source, and measure I.
Example
TH Find R.
One can change back and forth between Thevenin and Norton: Source Transformations
Example resistors. Remember that:circuit just like using series/parallel rules to simplify One can use source transformations to simplify a Source Transformations
(Nilsson & Riedel text)
Norton circuits.Thevenin andFind the
