Download Methods of Analysis

Methods of Analysis
ELEC 202
Electric Circuit Analysis II
Nodal Analysis
1. For an AC circuit, transform the circuit
into the phasor domain.
2. Identify every node in the circuit.
3. Label each node with a node voltage.
The node with the highest number of
branches connected should be labeled as
the ground node having zero potential.
Nodal Analysis (Cont’d)
4. At a particular node of interest (except
ground), use Ohm’s law to express the
current through any branch connected to
that node as the difference between the
two node voltages at both end of that
branch divided by the branch impedance.
The voltage at the node of interest is
always considered to be at higher
potential than the rest of the node
voltages.
Nodal Analysis (Cont’d)
5. Apply KCL to sum all currents at that
node of interest. The resulting algebraic
equation (called nodal equation) has all
node voltages as its unknowns.
6. Repeat steps 4 and 5 until all nodes
except ground are accounted for. The
number of equations must be equal to
the number of node voltages.
Nodal Analysis (Cont’d)
7. If a branch not connected to ground
contains a voltage source, the two nodes
at both ends are collapsed into a single
node called a supernode, and the voltage
source and any elements connected in
parallel with it removed. However, KCL
must still be satisfied at a supernode
using the old node voltage labels. Also,
the removal of the voltage source
provides another nodal equation.
Nodal Analysis (Cont’d)
8. If a branch connected to ground contains
a voltage source, the non-ground node
voltage is equal to the source voltage, and
KCL is not applied to this node.
9. Solve the resulting simultaneous nodal
equations to obtain the values of the
unknown node voltages.
10. Use the values of node voltages above to
find voltages and/or currents throughout
the rest of the circuit.
Example 1
Find ix in the circuit using nodal analysis.
Example 1 (cont’d)
The resulting circuit in the phasor domain.
Example 2
Compute v1 and v2 in the circuit.
Example 3
Compute V1 and V2 in the circuit.
Example 3 (Cont’d)
Example 4
Compute V1 and V2 in the circuit.
Mesh Analysis
1. For an AC circuit, transform the circuit
into the phasor domain.
2. Identify every mesh in the circuit.
3. Label each mesh with a mesh current.
It is recommended that all mesh
currents be labeled in the same direction
(either clockwise (CW) or counterclockwise (CCW)).
Mesh Analysis (Cont’d)
4. Within a particular mesh of interest, use
Ohm’s law to express the voltage across
any element within that mesh as the
difference between the two mesh
currents of contiguous meshes shared by
the element times the element impedance.
The current within the mesh of interest is
always considered to be larger than the
rest of the mesh currents.
Mesh Analysis (Cont’d)
5. Apply KVL to sum all voltages in that
mesh of interest. The resulting algebraic
equation (called mesh equation) has all
mesh currents as its unknowns.
6. Repeat steps 4 and 5 until all meshes are
accounted for. The number of equations
must be equal to the number of mesh
currents.
Mesh Analysis (Cont’d)
7. If a current source exists between two
contiguous meshes, the two meshes are
collapsed into a single mesh called a
supermesh, and the current source and
any elements connected in series with it
removed. However, KVL must still be
satisfied within a supermesh using the
old mesh current labels. Also, the
removal of the current source provides
another mesh equation.
Mesh Analysis (Cont’d)
8. If a current source exists only in one
mesh, the mesh current is equal to the
source current, and KVL is not applied to
this mesh.
9. Solve the resulting simultaneous mesh
equations to obtain the values of the
unknown mesh currents.
10. Use the values of mesh currents above
to find voltages and/or currents
throughout the rest of the circuit.
Example 5
Find I0 in the circuit using mesh analysis.
Example 6
Find I0 in the circuit using mesh analysis.
Example 7
Find V0 in the circuit using mesh analysis.
Example 7 (cont’d)