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 1 June 25, 2014
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Lecture 3:Resistive Circuits & Nodal AnalysisNilsson 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
Y T
π
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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 eitherMesh good for planar
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Identify
• 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