Download ENG17 - SS14 - Lecture 3 - Resistive Circuits and Nodal

Lecture 3:
Resistive Circuits & Nodal Analysis
Nilsson 3.3, 3.4, 3.7, 4.1-4.4
ENG17 (Sec. 1): Circuits I
Summer 1 2014
June 25, 2014
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Overview
• Voltage Divider
• Current Divider
• Voltage / Current
Division
• Δ-to-Y Equivalent
Circuits
• Node Voltage Method
• NVM w/Dependent
Sources
• NVM Special Cases
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Voltage Divider
• One voltage supply, multiple voltage levels
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Load
• RL = load = 1+ circuit elements that draw
power from circuit
– May alter voltage across parallel element
– But not if RL >> R2
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Example
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Example
• Wheatstone Bridge
– 2 voltage dividers in parallel
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Overview
• Voltage Divider
• Current Divider
• Voltage / Current
Division
• Δ-to-Y Equivalent
Circuits
• Node Voltage Method
• NVM w/Dependent
Sources
• NVM Special Cases
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Current Divider
• One current supply, multiple current levels
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Example
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Example
• Similar analysis
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Overview
• Voltage Divider
• Current Divider
• Voltage / Current
Division
• Δ-to-Y Equivalent
Circuits
• Node Voltage Method
• NVM w/Dependent
Sources
• NVM Special Cases
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Voltage Division
• Generalization of voltage divider circuit
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Current Division
• Generalization of current divider circuit
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Example
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Overview
• Voltage Divider
• Current Divider
• Voltage / Current
Division
• Δ-to-Y Equivalent
Circuits
• Node Voltage Method
• NVM w/Dependent
Sources
• NVM Special Cases
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Unable to get Req
• For example, Wheatstone bridge circuit
(below) cannot be simplified with standard
parallel/series rules
• Must use circuit transformation
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Defining Delta/Pi and Y/T
Δ
π
Y
T
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Delta-to-Wye Circuit Transformation
• Equivalent resistance between nodes
• Note: resistor values are NOT THE SAME
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Apply to Wheatstone Bridge
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Recap
• Voltage Divider
• Current Divider
• Voltage / Current
Division
• Δ-to-Y Equivalent
Circuits
• Node Voltage Method
• NVM w/Dependent
Sources
• NVM Special Cases
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Planar Circuit
Planar
Not Planar
Nodal good for either
Mesh good for planar
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Identify
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•
•
•
•
•
•
Node
Essential Node
Path
Branch
Essential Branch
Loop
Mesh
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Simultaneous Equations
• How many unknown currents?
• How many equations needed?
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Node Voltage Method – Setting Up
• Identify essential nodes
• Define reference node
• Apply KCL to each non-reference node,
express current in terms of node voltages
• Solve simultaneous equations
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Node Equations
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Example
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Overview
• Voltage Divider
• Current Divider
• Voltage / Current
Division
• Δ-to-Y Equivalent
Circuits
• Node Voltage Method
• NVM w/Dependent
Sources
• NVM Special Cases
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Dependent Sources
• Only need to add equation to describe
relationship of the dependent source
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Example
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Overview
• Voltage Divider
• Current Divider
• Voltage / Current
Division
• Δ-to-Y Equivalent
Circuits
• Node Voltage Method
• NVM w/Dependent
Sources
• NVM Special Cases
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Source Between Essential Nodes
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w/Dependent Source
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Supernode
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Example
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Recap
• Voltage Divider
• Current Divider
• Voltage / Current
Division
• Δ-to-Y Equivalent
Circuits
• Node Voltage Method
• NVM w/Dependent
Sources
• NVM Special Cases
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