lecture 8 review: nodal analysis supernodes additional nodal analysis examples mesh analysis related...
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Lecture 8•Review:
•Nodal analysis•Supernodes•Additional nodal analysis examples
•Mesh Analysis•Related educational modules:
–Sections 1.6.2
Review: Nodal Analysis
1. Choose reference node2. Identify independent nodes3. Label “constrained” voltages4. Apply KCL at independent nodes5. Write the KCL equations in terms of node voltages6. Solve equations to determine the node voltages7. Determine desired circuit parameters from node
voltages
Supernodes
• In example 3 of lecture 7, we applied KCL at a supernode
V=0
Supernode
2mA
+ -3V
3kW 6kWi1 i2
Supernodes – continued
• A node is defined as having a single, unique voltage
• We can, however, apply KCL at supernodes which contain multiple nodes
• Example:
A Bi1 i2 i3
i4 i5
Supernodes in nodal analysis• Supernodes are especially useful in nodal analysis
when dependent nodes (voltage sources) are present
• Define a supernode containing the dependent nodes• The supernode contains the voltage source and the
nodes to which it is connected
• Apply KCL at the supernode
Supernodes are useful, but not required• Supernodes are not essential for nodal analysis, as
long as you account for all currents• Need to explicitly include currents through voltage sources
• Lecture 7, Example 3:
2mA
+ -3V
3kW 6kW
Lecture 7, Example 3 – alternate approach
2mA
+ -3V
3kW 6kW
Example 1• Determine the voltage across the 6W resistor
Example 1 – alternate approach
Example 2• Use nodal analysis to write a set of equations from which
you can determine the current through the 6W resistor.
Mesh analysis – review
• Identify mesh loops• The currents around these loops are the mesh currents
• Use Ohm’s Law to write KVL around each loop in terms of the mesh currents
• Solve these equations to determine the mesh currents
• Any desired circuit parameter can be determined from the mesh currents
Nodal and mesh analysis – comparison
• Nodal analysis:• Define independent
nodes
• Apply KCL at independent nodes
• Use Ohm’s Law to write KCL in terms of node voltages
• Mesh analysis:• Define “mesh loops”
• Apply KVL around the mesh loops
• Use Ohm’s Law to write KVL in terms of mesh currents
Mesh Analysis
• We will illustrate the mesh analysis technique in the context of an example circuit:
Mesh Analysis
• Step 1: Choose mesh loops and identify mesh currents• Kill sources (short
voltage sources, open-circuit current sources)
• Recommendation: mesh loops should not have other loops in their interior
•
Mesh Analysis
• Step 2: Replace sources and write constrained loops• Constrained loops go
through current sources• Constrained loops are
somewhat arbitrary, but their direction and magnitude must be consistent with the source through which they pass
Mesh Analysis
• Step 3: Apply KVL around the mesh loops• Use Ohm’s Law to write
voltage drops in terms of mesh currents
• Voltage polarities in KVL must be consistent with that loop’s mesh current
Mesh Analysis• Step 3: continued –
Mesh Analysis• Step 4: Solve the
equations for mesh currents• Use mesh currents to
determine the circuit parameters of interest
• Note: The total current in an element is the sum of the mesh currents in the element
•
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