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For any Linear Resistive Network there exists:
Thevenin Equiv. Network
Norton Equivalent Network
V
OC
 opencircuit voltage appearing across the terminals of the network, and
R
TH
 Thevenin equivalent resistance when all independent sources are deactivated.
I
SC
– current through load when replacing load with a short circuit
Equations
Solve for R
TH
1.
Deactivate all ind. srcs (leave dep. srcs)
2.
Remove the load R
L
*In circuits w. dependent sources, may need to apply a voltage or current source between A & B,
then apply the definition R
TH
= V
OC
/ I
SC
Finding V
TH
1.
Remove load R
L
AB
to rest of network.
a.
Sources remain unchanged.
b.
Use methods such as superposition, mesh, nodal, VDivision, etc…
Finding I
SC
1.
Replace load R
L
in original circuit with a short circuit.
a.
Sources remain unchanged.
Coefficient Approach
VI Char. Of Thev: V
AB
= R
TH
I
A
+ V
OC
VI Char. Of Nort: I
A
= (1/R
TH
)V
AB

I
SC
1.
Obtain an equation in one of the above forms allows us to match the coefficients of the
above equations to determine R
TH
, V
OC
, I
A
, or G
TH
.
Measured Data
1.
Substitute the given data into VI Char. Eqs: Thev: V
AB
= R
TH
I
A
+ V
OC
or Nort: I
A
=
(1/R
TH
)V
AB
 I
SC
2.
Put into matrix form
3.
Solve for remaining variables.
General Solving Procedures
1.
Have ways to find V
OC
, I
SC
, R
TH
directly using above techniques
2.
After solving for 2 of the 3, below are listed ways to solve for 3
rd
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*Extra condition for constructing Thev and Nort equivalents for active networks – all controlling
voltages
or currents must be within the 2terminal network whose Thev/Nort equiv are
being sought.
1. Since there are no ind. internal srcs, the Thev equiv. consists of a single resistance, R
TH
(V
OC
=
I
SC
= 0)
2.
Write an equation(s) to relate the terms in the 2terminal network via previous solving
techniques
(KCL, KVL, Mesh, Nodal, etc…)
3. If one equation, match coeficients with the VI char. equations of a Thev. Or Nort. Equiv.
network.
4. If set of equations, solve using matrix operations.
Maximum Power Transfer
Theorems, Requirements, Conditions, Assumptions, and Definitions
1.
Always put circuit in Thevenin or Norton Equivalent form
2.
Fixed R
TH
Equations
Always True Under M.P.T.
Inductors
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 Spring '08
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