Transcript ECE 201 Exam #2 Review

Exam #2 Review
Dr. Holbert
March 27, 2006
ECE201 Exam #2 Review
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Don’t Forget the Fundamentals
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Polarity and Passive Sign Convention
Ohm’s Law; KCL; KVL
Voltage and Current Division
Phasors, Impedance, and Complex numbers
ECE201 Exam #2 Review
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Steps of Nodal Analysis
1. Choose a reference (ground) node, V=0.
2. Assign node voltages to the other nodes.
3. Apply KCL to each node
V1
V2
but the reference node;
Z
express currents in terms
of node voltages.
V1  V2
4. Solve the resulting system
I
Z
of linear equations.
ECE201 Exam #2 Review
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Steps of Mesh/Loop Analysis
1. Identify mesh (loops).
2. Assign a current to each mesh.
I2
3. Apply KVL around each
VZ +
–
loop to get an equation in
Z
terms of the loop currents.
I1
4. Solve the resulting system
VZ = (I1 - I2 ) Z
of linear equations.
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Nodal and Loop Analyses
Nodal Analysis Recipe
1&2) Identify and label
N nodal voltages plus
the ground node (V=0)
3) Apply KCL at N
nodes (supernode
makes constraint eq.)
4) Solve for the nodal
voltages
Loop Analysis Recipe
1&2) Identify and label
N mesh currents
3) Apply KVL at the N
meshes
4) Solve for the mesh
currents
ECE201 Exam #2 Review
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Linearity
• More important as a concept than as an
analysis methodology, but allows scaling of
current/voltage values
• Leads to superposition:
“In any linear circuit containing multiple independent
sources, the current or voltage at any point in the circuit
may be calculated as the algebraic sum of the individual
contributions of each source acting alone.”
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Superposition Procedure
1. For each independent voltage and current source (repeat the
following):
a) Replace the other independent voltage sources with a
short circuit (i.e., V = 0).
b) Replace the other independent current sources with an
open circuit (i.e., I = 0).
Note: Dependent sources are not changed!
c) Calculate the contribution of this particular voltage or
current source to the desired output parameter.
2. Algebraically sum the individual contributions (current
and/or voltage) from each independent source.
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Source Transformation
Z
VS
+
–
IS
Z
VS = Z IS
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Thevenin/Norton Analysis
1. Pick a good breaking point in the circuit (cannot split a
dependent source and its control variable).
2. Thevenin: Compute the open circuit voltage, VOC.
Norton: Compute the short circuit current, ISC.
For case 3(b) both VOC=0 and ISC=0 [so skip step 2]
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Thevenin/Norton Analysis
3. Compute the Thevenin equivalent resistance, RTh (or
impedance, ZTh).
(a) If there are only independent sources, then short
circuit all the voltage sources and open circuit the current
sources (just like superposition).
(b) If there are only dependent sources, then must use a
test voltage or current source in order to calculate
RTh (or ZTh) = VTest/Itest
(c) If there are both independent and dependent sources,
then compute RTh (or ZTh) from VOC/ISC.
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Thevenin/Norton Analysis
4. Thevenin: Replace circuit with VOC in series with RTh, ZTh.
Norton: Replace circuit with ISC in parallel with RTh, ZTh.
Note: for 3(b) the equivalent network is merely RTh (or ZTh),
that is, no voltage (or current) source.
Only steps 2 & 4 differ from Thevenin & Norton!
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Thevenin/Norton Analysis
ZTh
Voc
+
–
Isc
Thevenin equivalent
circuit
ECE201 Exam #2 Review
ZTh
Norton equivalent
circuit
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