ECE 4991 Electrical and Electronic ECE 4991 Electrical and Electronic CircuitsCircuits

Chapter 3Chapter 3

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Where are we?Where are we?• Chapter 2 - The basic concepts and practice at

analyzing simple electric circuits with sources and resistors

• Chapter 3 – More harder networks to analyze and the notion of equivalent circuits

• Chapter 4 – Capacitors and inductors added to the mix

• Chapter 5 – Analyzing transient situations in complex passive networks

• Chapter 8 – New subject – the wonders of operational amplifiers as system elements

• Chapter 9 – Introduction to semiconductors – the basics and diodes – more network analysis

• Chapter 10 – Bipolar junction transistors and how they work – now you can build your own op amp

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What’s Important in What’s Important in Chapter 3Chapter 3

1. Definitions

2. Nodal Analysis

3. Mesh Analysis

4. The Principle of Superposition

5. Thevenin and Norton Equivalent Circuits

6. Condition for Maximum Power Transfer

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1. Definitions1. Definitions• Node voltages• Branch currents• “Ground”• KCL• Nodal Analysis• Mesh currents• KVL• Mesh Analysis

• Principle of Superposition

• Equivalent circuit• Thevenin theorem• Norton theorem• One-port networks• Source loading

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2. Nodal Analysis2. Nodal Analysis• Used to “analyze” circuits

• Solve for currents, voltages, power, etc., throughout circuits

• Applies KCL to nodes– Often used in concert with Ohm’s Law

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Node MethodNode Method• Find nodes – Identify ground node• Label branch currents & node voltages• Node voltages, if not defined by a voltage

source, are independent variables• Write KCL for nodes• Solve for unknowns

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Working with Nodal Working with Nodal AnalysisAnalysis

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Working with Nodal Working with Nodal AnalysisAnalysis

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R1

R2

R3

R4

V

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Working with Nodal Working with Nodal AnalysisAnalysis

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R1

R2

R3

R4

V

R5 R6

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Working with Nodal Working with Nodal AnalysisAnalysis

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For Next TimeFor Next Time

1. Sign onto Blackboard, if still have not

2. Practice Nodal Analysis

3. Learn about rest of chapter 3, particularly about mesh analysis

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3. Mesh Analysis3. Mesh Analysis• Also used to “analyze” circuits

• Solve for currents, voltages, power, etc., throughout circuits

• Applies KVL to meshes– Often used in concert with Ohm’s Law

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Node MethodNode Method• Identify meshes and mesh currents• For n meshes and m current sources, there

are n-m independent variables• Write KVL for all meshes with unknown

mesh currents• Solve for unknowns

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Working with Mesh Working with Mesh AnalysisAnalysis

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Working with Mesh Working with Mesh AnalysisAnalysis

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R1

R2

R3

R4

V

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Working with Mesh Working with Mesh AnalysisAnalysis

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R1

R2

R3

R4

VR5

R6

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Working with Mesh Working with Mesh AnalysisAnalysis

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For Next TimeFor Next Time

1. Sign onto Blackboard, if still have not

2. Keep practicing Nodal Analysis

3. Practice Mesh Analysis

4. Learn about rest of chapter 3, particularly about equivalent circuits

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4. The Principle of 4. The Principle of SuperpositionSuperposition

• When working with linear circuits, can find the solution for each energy source and combine the results

• Procedure:– Remove all but one energy source

• V sources wires• I sources opens

– Solve the circuit– Repeat for a different energy source– Add up the solutions

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5. Th5. Théévveenin and Norton nin and Norton Equivalent CircuitsEquivalent Circuits

• Thévenin Theorem When viewed from the load, any network

composed of ideal voltage and current sources and of linear resistors, may be represented by an equivalent circuit consisting of an ideal voltage source VT in series with an equivalent resistance RT

I VT

RT

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ThThéévveenin and Norton nin and Norton Equivalent CircuitsEquivalent Circuits

• Norton Theorem When viewed from the load, any network

composed of ideal voltage and current sources and of linear resistors, may be represented by an equivalent circuit consisting of an ideal current source IN in parallel with an equivalent resistance RN

I IN RN

I

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ThThéévenin Equivalencevenin Equivalence• Equivalent Resistance

1. Remove load2. Zero all current and voltage sources

• V sources wires• I sources opens

3. Compute the resistance between the load terminals

• Equivalent Voltage1. Remove the load

2. Define VOC as the open-circuit voltage across the load terminals

3. Solve for VOC

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ThThéévenin Equivalent venin Equivalent CircuitsCircuits

R1

R2 RL

V

RT = ? VT = ?

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ThThéévenin Equivalent venin Equivalent CircuitsCircuits

VT

RT

VR2

R1

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Working with ThWorking with Théévenin venin Equivalent CircuitsEquivalent Circuits

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R1

R2

R3

V

RT = ? VT = ?

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Working with ThWorking with Théévenin venin Equivalent CircuitsEquivalent Circuits

VT

RT

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Practice with ThPractice with Théévenin venin Equivalent CircuitsEquivalent Circuits

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R1

R3

R5

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RT = ? VT = ?

R4

R2

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Practice with ThPractice with Théévenin venin Equivalent CircuitsEquivalent Circuits

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Chapter 2 and 3 Practice Chapter 2 and 3 Practice for Testfor Test

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Chapter 2 and 3 Practice Chapter 2 and 3 Practice for Testfor Test

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Chapter 2 and 3 Practice Chapter 2 and 3 Practice for Testfor Test

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Chapter 2 and 3 Practice Chapter 2 and 3 Practice for Testfor Test

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Chapter 2 and 3 Practice Chapter 2 and 3 Practice for Testfor Test

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Chapter 2 and 3 Practice Chapter 2 and 3 Practice for Testfor Test