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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