Post on 03-Jun-2018
8/11/2019 Circuits Lecture Slides Module5Handouts
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Linear Circuits
An introduction to linear electric components and a study of circuitscontaining such devices.
Dr. Bonnie FerriProfessor
School of Electrical and
Computer Engineering
School of Electrical and Computer Engineering
Concept Map
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Concept Map: Power
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Concept Map: Power
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Nathan V. ParrishPhD Candidate & GraduateResearch AssistantSchool of Electrical and ComputerEngineering
School of Electrical and Computer Engineering
Root Mean Square
Introduce the root mean square statistic and how to calculate it.
Identify the equation for calculating root meansquare (RMS) value
Calculate the RMS values of simple periodic
functions Find peak value from RMS
Lesson Objectives
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Average of a Sinusoid
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Root Mean Square
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Root Mean Square Example
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The voltage that goes into your home isdescribed by the root-mean-squarevoltage. In the US, the voltage issinusoidal with 120V rms at 60 Hz.
What is the peak amplitude?
Example
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Defined the root mean square calculation
Calculated the RMS values of
Sinusoidal functions
Triangular functions
Applied to home power voltages
Summary
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Nathan V. ParrishPhD Candidate & GraduateResearch AssistantSchool of Electrical and ComputerEngineering
School of Electrical and Computer Engineering
Power Factor and
Power Triangles
Part 1
Gain an understanding of the way that sinusoidal power is analyzed.
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Identify average power in resistive andreactive devices
Calculate complex power
Lesson Objectives
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Instantaneous Power
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Average Power
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Average Power
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Complex Power
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What Complex Power Represents
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Calculated complex power
Identified the meaning behind complex power
Summary
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Nathan V. ParrishPhD Candidate & GraduateResearch AssistantSchool of Electrical and ComputerEngineering
School of Electrical and Computer Engineering
Power Factor and
Power Triangles
Part 2
Gain an understanding of the way that sinusoidal power is analyzed.
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Use power triangles
Calculate
Power angle and power factor
Real and reactive power
Apparent power
Lesson Objectives
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Review of Complex Power
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Power Factor
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Complex Power for Impedances
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Complex Power for Impedances
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Complex Power for Impedances
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Complex Power for Impedances
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Complex Power for Impedances
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Nathan V. ParrishPhD Candidate & GraduateResearch AssistantSchool of Electrical and ComputerEngineering
School of Electrical and Computer Engineering
Transformers
Present transformers, a circuit device commonly used in powerapplications.
Identify physical transformers and theircircuit representations
Describe the physical function oftransformers
Lesson Objectives
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Transformer
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Amperes Law
Faradays Law of Induction
Relationship of Magnetic Field and Current
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Linear Transformer Model Used primarily for communications applications
Uses impedances for analysis
Ideal Transformer Model Used primarily for power transfer
Uses voltages and number of coil turns
Two Transformer Models
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Introduced transformers as a circuit device
Described the physical behavior of thesedevices
Introduced two analysis models
Summary
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Nathan V. ParrishPhD Candidate & GraduateResearch AssistantSchool of Electrical and ComputerEngineering
School of Electrical and Computer Engineering
Linear Model ofTransformers
Present linear model for analyzing transformers.
Identify the linear model of transformers
Use circuit analysis to analyze the behavior ofa transformer system
Apply this analysis to solving a transformercircuit problem
Lesson Objectives
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Linear Transformer
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Transformer Example
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Nathan V. ParrishPhD Candidate & GraduateResearch AssistantSchool of Electrical and ComputerEngineering
School of Electrical and Computer Engineering
Ideal Transformers
Use the ideal transformer model for transformer analysis.
Identify the assumptions used for the idealtransformer model
Use the ideal transformer model for doingsimple circuit analysis
Describe the importance of transformers inpower transmission
Lesson Objectives
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k: Coefficient of Coupling
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Coupling coefficient k=1
L1 = L2 =
Losses from coil
resistances arenegligible
The Ideal Transformer
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Properties of the Ideal Transformer
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Example
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Transformers allow a change from onevoltage to another voltage
High-voltage low-current power transmissionallows long-distance power distribution
systems
Implications
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Showed the ideal transformer model
Used the model to solve an examplesystem
Identified the usefulness of transformersfor power transmission
Summary
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Nathan V. ParrishPhD Candidate & GraduateResearch AssistantSchool of Electrical and ComputerEngineering
School of Electrical and Computer Engineering
Linear VariableDifferential
Transformer
Explore LVDT sensors devices which use mutual inductance formeasurement.
Explain how LVDT sensors work
Identify relative position measured by a
LVDT based on magnitude and phase
Lesson Objectives
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Linear Variable Differential Transformer
Amplitude showsdisplacement
Phase showsdirection
Capable of very high precision Completely electrically shielded
Can operate in extreme conditions
Benefits of LVDT
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Described the behavior of LVDT sensors
Described how to identify the position bymeasuring the voltage and phase
Described the benefits of such a sensor
Summary
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Presented the linear model
Derived the phenomenon of reflectedimpedance
Used circuit analysis to analyze an exampletransformer circuit
Summary
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Concept Map: Power
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Be able to calculate the root-mean square of a periodicfunction
Recognize that RMS is invariant to frequency
Use known RMS value equations to find RMS values
given peak values Use known RMS value equations to find peak value
given RMS values
Important Concepts and Skills
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Calculate the complex power from either equations or phasors Generate power triangles Using power triangles, be able to find
Apparent power, |S|
Real (or average) power, P
Reactive power, Q
Power factor Power angle
Important Concepts and Skills
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Using the phase angle, identify if a load is resistive,capacitive, or inductive
From equations, identify if a load is resistive,capacitive, or inductive
From a plot of current and voltage, identify if a load isreactive, capacitive, or inductive
Recognize if a system is leading or lagging
Important Concepts and Skills
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Calculate the impedance which gives maximal powertransfer
Calculate the average power consumed when the loadgives maximal power transfer
Find the optimal purely resistive load for constrained
maximal power transfer Calculate average power for purely resistive load
Important Concepts and Skills
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Describe the physical effects which make transformers work Use the linear model to analyze a circuit with a transformer Use the ideal model to analyze a circuit with a transformer Identify circumstances when a transformer is an appropriate device to be
used in a system Explain how the use of transformers allow long-distance power
distribution
Describe why transformers do not typically function for direct currentsystems
Identify, from amplitude and phase, the relative displacement for an LVDTtransformer
Important Concepts and Skills
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