Linear Circuits€¦ · · 2014-01-08Linear Circuits An introduction to linear electric...

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Linear Circuits

An introduction to linear electric components and a study of circuits containing such devices.

Dr. Bonnie FerriProfessor

School of Electrical and

Computer Engineering

School of Electrical and Computer Engineering

Concept Map

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BackgroundResistive

Circuits

Reactive

CircuitsFrequency

Analysis

Power

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3 4

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Concept Map: Power

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BackgroundResistive

Circuits

Reactive

CircuitsFrequency

Analysis

Power

Impedance,

phasors

Max power

transfer

Power

Concept Map: Power

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BackgroundResistive

Circuits

Reactive

CircuitsFrequency

AnalysisImpedance,

phasors

Max power

transfer

Power• Apparent power

• Reactive power

• Power factor

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Nathan V. ParrishPhD Candidate & Graduate Research AssistantSchool 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 mean

square (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 is

described by the root-mean-square

voltage. In the US, the voltage is

sinusoidal 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 and

reactive 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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� Only real power is being transformed to heat/light/etc.

� Reactive power causes increased current, so more power is consumed by resistive transmission lines

� Private customers generally only charged for real power, industrial customers charged for both

Implications

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� Defined

� Power angle and power factor

� Real and reactive power

� Apparent power

� Illustrated using power triangles

Summary

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Transformers

Present transformers, a circuit device commonly used in power applications.

� Identify physical transformers and their

circuit representations

� Describe the physical function of

transformers

Lesson Objectives

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Transformer

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Primary Winding Secondary Winding

� Ampere’s Law

� Faraday’s Law of Induction

Relationship of Magnetic Field and Current

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Transformers are AC

devices

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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 these

devices

� Introduced two analysis models

Summary

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Linear Model of

Transformers

Present linear model for analyzing transformers.

� Identify the linear model of transformers

� Use circuit analysis to analyze the behavior of

a transformer system

� Apply this analysis to solving a transformer

circuit problem

Lesson Objectives

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Linear Transformer

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Reflected

impedance

Transformer Example

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Ideal Transformers

Use the ideal transformer model for transformer analysis.

� Identify the assumptions used for the ideal transformer model

� Use the ideal transformer model for doing simple circuit analysis

� Describe the importance of transformers in power 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 are

negligible

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 one

voltage to another voltage

� High-voltage low-current power transmission

allows long-distance power distribution

systems

Implications

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� Showed the ideal transformer model

� Used the model to solve an example

system

� Identified the usefulness of transformers

for power transmission

Summary

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Linear Variable

Differential

Transformer

Explore LVDT sensors – devices which use mutual inductance for measurement.

� 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 shows displacement

� Phase shows direction

� 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 by

measuring the voltage and phase

� Described the benefits of such a sensor

Summary

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� Presented the linear model

� Derived the phenomenon of reflected

impedance

� Used circuit analysis to analyze an example

transformer circuit

Summary

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Power

Concept Map: Power

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BackgroundResistive

Circuits

Reactive

CircuitsFrequency

AnalysisImpedance,

phasors

Max power

transfer

Power• Apparent power

• Reactive power

• Power factor

• Transformers

� Be able to calculate the root-mean square of a periodic function

� 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 is reactive, capacitive, or inductive

� Recognize if a system is “leading” or “lagging”


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� Calculate the impedance which gives maximal power transfer

� Calculate the average power consumed when the load gives 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 current systems

� Identify, from amplitude and phase, the relative displacement for an LVDT transformer


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Linear Circuits€¦ · · 2014-01-08Linear Circuits An introduction to linear electric...

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