Circuits Lecture Slides Module5Handouts

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


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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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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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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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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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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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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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


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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


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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


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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


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