ECE 1311: Electric Circuits
Chapter 3: Method of Analysis
Analysis Method Overview
 Solving linear equations
 Nodal Analysis
 Supernodes (Nodal analysis with voltage supply)
 Mesh Analysis
 Supermeshes (Mesh analysis with current source)
Recap
 What is vo in each case?
 What effect does the resistor has on the current flowing in
the circuit?
Recap
 What is io in each case?
 What effect does the resistor has on the voltage seen by the
circuit?
Networks terminology
 Planar circuit: a circuit that can be drawn on a plane with no
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crossing branches
Node: point of two or more elements are joined
Essential node: point of three or more elements are joined
Branches: path that connects two nodes
Loop: Path with last node same as starting node that does not
cross itself
Mesh: Loop that does not enclose any other loops
Practice 3.1
Nodal Analysis: Introduction
 Another easier way to solve for currents and voltages
 easier, more methodical
 Based on KCL
 Usually use to solve for voltages
 All voltages have a common reference point
Nodal Analysis: Review of steps
Practice 3.2
Nodal Analysis: Use of laws
 All three laws applied
 KCL applied at each n-1 non-reference node
 Ohm’s law to express the branch current in terms of node
voltages
 KVL when determining the voltage drop across the resistor
Practice 3.3
Solve:
answer v1= 4.8V, v2 = 2.4V, v3 = -2.4V
Practice
*Notice the dependent source
Supernodes (1)
 A super-node is formed by enclosing a (dependent or
independent) voltage source connected between two nonreference nodes and any elements connected in parallel with
it.
Note: We analyze a circuit with super-nodes using the same
steps mentioned in the nodal analysis except that the supernodes are treated differently.
Supernodes (2)
 Basic steps:
1.Take off all voltage sources in super-
nodes and apply KCL to super-nodes.
2.Put voltage sources back to the nodes
and apply KVL to relative loops.
Practice 3.4
Practice 3.5
Practice 3.6
Practice 3.7
Mesh Analysis: Introduction
 Applies KVL to solve for currents
 Work with imaginary currents
 Only apply to planar circuit
Mesh Analysis: Review of Steps
Practice 3.8
Practice
Supermesh (1)
 A super-mesh results when two meshes have a (dependent
or independent) current source in common as shown in (a).
We create a super-mesh by excluding the current source and
any elements connected in series with it as shown in (b).
Supermesh (2)
 The properties of a super-mesh:
1.The current source in the super-mesh is not
completely ignored; it provides the constraint
equation necessary to solve for the mesh
currents.
2. A super-mesh has no current of its own.
3. A super-mesh requires the application of
both KVL and KCL.
Practice 3.9
 On each resistor,
Practice 3.10
 Mesh analysis
Practice 3.11
 Mesh analysis
Practice 3.12
 Mesh analysis
Nodal vs Mesh Analysis