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7/30/2019 Nodal and Loop
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ECE 211 WORKSHOP: NODAL AND
LOOPANALYSIS
Tutor:Asad Akram
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AGENDA
Background: KCL and KVL.
Nodal Analysis:
Independent Sources and relating problems,
Dependent Sources and relating problems. Loop (Mesh Analysis):
Independent Sources and relating problems,
Dependent Sources and relating problems.
Practice Problems and solutions.
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KCLAND KVL REVIEW
Rule: Algebraic sum of
electrical current that
merge in a common
node of a circuit is zero.
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Rule: The sum of
voltages around a
closed loop circuit is
equal to zero.
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KCLAND KVL EXAMPLE
Find I and Vbd in
the following
circuit?
Solution:
Using KCL we know that
only 1 current Iflows in
the loop.
Then we apply Ohms law
to find the current I.
Lastly, we use KVL in the
single loop to evaluate the
voltage Vbd.
We therefore see how KCL
and KVL can used as
simple analysis tools.
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NODALANALYSIS
Nodal Analysis of electronic circuits is based on
assigning Nodal voltages at various nodes of the
circuit with respect to a reference and then
finding these nodal voltages to analyze the
circuit.
Simple representation of Nodal Voltages shown
below:
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As shown in Figure, a node is a point
in a circuit where two or more wires
meet. At these nodes one can assign
a nodal voltage with respect to the
reference ground shown.
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NODALANALYSIS: INDEPENDENT SOURCES ONLY
First we find the number of KCL equations (These are used to find
the nodal voltages). N -1 = n, here N = number of equations, n =
number of nodes.
Then we write the KCL equations for the nodes and solve them to
find the respected nodal voltages.
Once we have these nodal voltages, we can use them to further
analyze the circuit.
SuperNode: Two Nodes with a independent Voltage source
between them is a Super node and one forms a KVL equation for it.
Example1 (Circuit with Ind. Current Sources):
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Find the Nodal Voltages
in the circuit?
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In this example we write the
KCL equations at the nodes as
Shown, then solve them to find
The respected nodal voltages.
NODALANALYSIS: INDEPENDENT SOURCES ONLY
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NODALANALYSIS: INDEPENDENT SOURCES ONLY
Example2 (Ind. Voltage Sources Only):
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For this Problem, we first make the main
KCL equation at the only node 1.
Current is taken to be coming out of the nodeas positive. We solve this equation to find
The nodal voltage V1.
Once this is determined, Io is simply found
by using Ohms law at the sole resistor of
3KOhm.
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NODALANALYSIS: DEPENDENT SOURCES
Find Vo using Nodal Analysis?
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For this Circuit, We need to
Overlook the node with dependent
Source and form equations round
it. We use KCL at Nodes 1 and 2and derive the equations based on
Current flow.
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NODALANALYSIS: DEPENDENT SOURCES
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After setting up the Nodal Eqn.
For dependent Circuits, on has
To make the Controlling eqn.
This equation is made using the
Dependent source. Using theControlling equation we solve
For the nodal voltages.
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NODALANALYSIS: DEPENDENT SOURCES
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Using KCL at nodes 2 and
Forming a controlling equation
At node 1 we can simplify the
Problem into simple equations.
Current entering the node isSummed at the node to form
The equations.
Find Io in the circuit using Nodal Analysis?
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NODALANALYSIS: DEPENDENT SOURCES
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Simplify the circuit to
Obtain nodal voltage.
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MESHANALYSIS
Mesh Analysis involves solving electronic circuits
via finding mesh or loop currents of the circuit.
This is done by forming KVL equations for
respected loops and solving the equations to find
individual mesh currents.
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We simply assume clockwise current flow in
All the loops and find them to analyze the circuit.
Also any independent current source in a loopBecomes the loop current as current in series is
Same.
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MESHANALYSIS: INDEPENDENT SOURCES
Find Vo in the circuit?
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Using KVL at loops 1 and 2, we form
KVL equations using the current and
Components in the loops in terms of
The loop currents.
Important thing to look at it theSubtraction of the opposing loop
Current in the shared section of the
Loop.
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MESHANALYSIS: INDEPENDENT SOURCES
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The mesh equations are solved
Simultaneously and the required loop
Current is found. Then we use this loop
Current to find Vo in across the resistor.
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MESHANALYSIS: DEPENDENT SOURCES
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Find Vo in the circuit using Mesh Analysis?
Simplify the circuit using the
Independent sources by assigning
Them to the mesh currents for
The specific loop.
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MESHANALYSIS: DEPENDENT SOURCES
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`
Form KVL in Main loop 3.
Simplify Using Vx and I2.
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PRACTICE PROBLEMS
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PRACTICE PROBLEMS
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PRACTICE PROBLEMS
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PRACTICE PROBLEMS
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PRACTICE PROBLEMS
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PRACTICE PROBLEMS
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PRACTICE PROBLEMS
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END!!
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SOLUTIONS TO PRACTICE PROBLEMS
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