Fundamentals of alternating current technology - Festo · PDF fileThe training package...

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With CD-ROM

Festo Didactic

567217 EN

Fundamentals of alternating current technology

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Order No.: 567217

Edition: 10/2010

Author: Christine Löffler

Graphics: Thomas Ocker, Doris Schwarzenberger

Layout: 03/2011, Susanne Durz

© Festo Didactic GmbH & Co. KG, 73770 Denkendorf, Germany, 2011

Internet: www.festo-didactic.com

e-mail: [email protected]

The copying, distribution and utilization of this document as well as the communication of its contents to

others without expressed authorization is prohibited. Offenders will be held liable for the payment of

damages. All rights reserved, in particular the right to carry out patent, utility model or ornamental design

registration.

© Festo Didactic GmbH & Co. KG 567217 III

Contents

Use for intended purpose __________________________________________________________________ IV Preface ______________________________________________________________________________ V Introduction ____________________________________________________________________________ VII Work and safety instructions ______________________________________________________________ VIII Training package Fundamentals of alternating current technology (TP 1011) _______________________ IX Learning objectives – Fundamentals of alternating current technology _______________________________X Allocation of learning objectives and exercises – Fundamentals of AC technology _____________________ XI Equipment set __________________________________________________________________________ XIII Allocation of components and exercises – Fundamentals of alternating current technology ___________ XVII Notes for the teacher/trainer ______________________________________________________________ XVIII Structure of the exercises _________________________________________________________________ XIX Component designations __________________________________________________________________ XIX CD-ROM contents ________________________________________________________________________ XX

Exercises and solutions

Exercise 1: Recording and representing characteristics used in AC technology _______________________ 1

Exercise 2: Investigating the behaviour of a capacitor _________________________________________ 19

Exercise 3: Selecting a suitable capacitance for a high-pass filter ________________________________ 39

Exercise 4: Reducing voltage peaks when switching a solenoid coil ______________________________ 51

Exercise 5: Determining the inductance of a coil ______________________________________________ 65

Exercise 6: Investigating RC elements by measurement ________________________________________ 77

Exercise 7: Tracing the frequency response of a high-pass and low-pass filter ______________________ 89

Exercise 8: Compensating the reactive power for an electric motor ______________________________ 101

Exercise 9: Selecting a three-phase circuit for connecting a storage heater _______________________ 113

Exercise 10: Generating different output stages for a heater ____________________________________ 127

Exercises and worksheets

Exercise 1: Recording and representing characteristics used in AC technology _______________________ 1

Exercise 2: Investigating the behaviour of a capacitor _________________________________________ 19

Exercise 3: Selecting a suitable capacitance for a high-pass filter ________________________________ 39

Exercise 4: Reducing voltage peaks when switching a solenoid coil ______________________________ 51

Exercise 5: Determining the inductance of a coil ______________________________________________ 65

Exercise 6: Investigating RC elements by measurement ________________________________________ 77

Exercise 7: Tracing the frequency response of a high-pass and low-pass filter ______________________ 89

Exercise 8: Compensating the reactive power for an electric motor ______________________________ 101

Exercise 9: Selecting a three-phase circuit for connecting a storage heater _______________________ 113

Exercise 10: Generating different output stages for a heater ____________________________________ 127

IV © Festo Didactic GmbH & Co. KG 567217

Use for intended purpose

The training package Fundamentals of electrical engineering/electronics may only be used:

• For its intended purpose in teaching and training applications

• When its safety functions are in flawless condition

The components included in the training package are designed in accordance with the latest technology

as well as recognised safety rules. However, life and limb of the user and third parties may be endangered,

and the components may be impaired if they are used incorrectly.

The learning system from Festo Didactic has been developed and produced exclusively for training

and further education in the fields of automation and technology. The training companies and/or

trainers must ensure that all trainees observe the safety instructions described in this workbook.

Festo Didactic hereby excludes any and all liability for damages suffered by trainees, the training

company and/or any third parties, which occur during use of the equipment sets in situations which

serve any purpose other than training and/or vocational education, unless such damages have been

caused by Festo Didactic due to malicious intent or gross negligence.

© Festo Didactic GmbH & Co. KG 567217 V

Preface

Festo Didactic's learning system for automation and technology is geared towards various educational

backgrounds and vocational requirements. The learning system is therefore broken down as follows:

• Technology-oriented training packages

• Mechatronics and factory automation

• Process automation and control technology

• Mobile robotics

• Hybrid learning factories

The learning system for automation and technology will be updated and extended in parallel

with developments in the area of training and professional practice.

The technology packages deal with various technologies including pneumatics, electropneumatics,

hydraulics, electrohydraulics, proportional hydraulics, programmable logic controllers, sensors,

electrical engineering, electronics and electric drives.

The modular design of the learning system allows for applications which go above and beyond

the limitations of the individual training packages. For example, PLC actuation of pneumatic,

hydraulic and electric drives is possible.

VI © Festo Didactic GmbH & Co. KG 567217

All training packages feature the following components:

• Hardware

• Media

• Seminars

Hardware The hardware in the training packages consists of industrial components and systems that are

specially designed for training purposes. The components contained in the training packages

are specifically designed and selected for the projects in the accompanying media.

Media The media provided for the individual topics consist of a mixture of teachware and software.

The teachware includes:

• Technical books and textbooks (standard works for teaching basic knowledge)

• Workbooks (practical exercises with supplementary instructions and sample solutions)

• Glossaries, manuals and technical books (providing more in-depth information on the various topics)

• Sets of transparencies and videos (for clear and dynamic instruction)

• Posters (for clear-cut illustration of facts)

Within the software, the following programs are available:

• Digital training programs (learning content specifically prepared for the purpose of virtual training)

• Simulation software

• Visualisation software

• Software for acquiring measurement data

• Project engineering and design engineering software

• Programming software for programmable logic controllers

The teaching and learning media are available in several languages. They are intended for use in classroom

instruction, but are also suitable for self-study.

Seminars A wide range of seminars covering the contents of the training packages round off the system for training

and vocational education.

If you have any suggestions or feedback about this manual,

please send us an e-mail at: [email protected]

The authors and Festo Didactic look forward to your comments.

© Festo Didactic GmbH & Co. KG 567217 VII

Introduction

This workbook is part of the learning system for automation and technology by Festo Didactic

GmbH & Co. KG. The system provides a solid basis for practice-oriented basic and further training. The

training package Fundamentals of electrical engineering/electronics TP 1011 covers the following topics:

• Fundamentals of direct current technology

• Fundamentals of alternating current technology

• Fundamentals of semiconductors

• Basic electronic circuits

The workbook Fundamentals of alternating current technology continues on from the introduction

to electrical engineering/electronics. It focuses primarily on teaching about the behaviour of resistors,

capacitors and coils in an AC circuit. In addition, it also focuses on circuits with capacitor and coil is phase

shifting of current and voltage in AC circuits. The representation and evaluation of phase shifts is dealt

with in detail in hybrid circuits. The electrical variables of active power, reactive power and apparent

power are also investigated. Finally, it looks at power in the context of star and delta circuits in

three-phase AC voltage systems.

A laboratory workstation equipped with a protected power supply, two digital multimeters,

a storage oscilloscope and safety laboratory cables is needed to build and evaluate the circuits.

All circuits for the 10 exercises in Fundamentals of alternating current technology are built using

the equipment set TP 1011. The basic theoretical principles needed to understand these exercises

are covered by technical textbooks.

Technical data for the individual components (linear and non-linear resistors, capacitors, coils,

light emitting diodes, measuring equipment, etc.) is also available.

VIII © Festo Didactic GmbH & Co. KG 567217

Work and safety instructions

General information • Trainees should only work with the circuits under the supervision of a trainer.

• Observe the specifications included in the technical data for the individual components

and in particular all safety instructions!

• Faults which may impair safety must not be generated in the training environment and must

be eliminated immediately.

Electrical components • Risk of fatal injury from interrupted protective earth conductor

– The protective earth conductor (yellow/green) must not be interrupted either outside or inside

the device.

– The insulation of the protective earth conductor must not be damaged or removed.

• In industrial facilities, the regulations BGV A3 "Electrical systems and equipment" of the German

institute for health and safety must be observed.

• In schools and training facilities, the operation of power supply units must be responsibly monitored

by trained personnel.

• Caution! The capacitors in the device can still be charged even if the device has been disconnected

from all power sources.

• When replacing fuses: only use specified fuses with the correct rated current.

• Never switch on the power supply unit immediately after it has been moved from a cold room

to a warm one. The condensate that forms can, under unfavourable conditions, damage your

device. Leave the device switched off until it has reached room temperature.

• Only use voltages of max. 60 V DC and 25 V AC as the operating voltage for the circuits in the individual

exercises. Note also the information on the maximum operating voltage of the components used.

• The power must be disconnected before establishing electrical connections.

• The power must be disconnected before breaking electrical connections.

• Only use connecting cables with safety plugs for electrical connections.

• Only pull the safety plugs when disconnecting connecting cables – never pull the cable.

• Always connect the storage oscilloscope to the power supply using an isolating transformer.

© Festo Didactic GmbH & Co. KG 567217 IX

Training package Fundamentals of alternating current technology

(TP 1011)

The training package TP 1011 consists of a multitude of individual training materials. This part

of the training package TP 1011 deals with the fundamentals of alternating current technology.

Individual components included in the training package TP 1011 can also be included in other packages.

Important components of TP 1011 • Permanent workstation with EduTrainer® universal patch panel

• Component set for electrical engineering/electronics with jumper plugs and safety laboratory cables

• Basic power supply unit EduTrainer®

• Complete set of laboratory equipment

Media The teachware for the training package TP 1011 consists of technical textbooks, books of tables and workbooks.

The textbooks clearly communicate the fundamentals of alternating current technology. The workbooks

contain the worksheets for each of the exercises, the solutions to each individual worksheet and a CD-ROM.

A set of ready-to-use exercise sheets and worksheets for each exercise is supplied with each workbook.

Technical data for the hardware components is made available along with the training package

and on the CD-ROM.

Media

Textbooks Technical expertise for electrical professions

Electrical engineering

Book of tables Electrical engineering/electronics

Workbooks Fundamentals of direct current technology

Fundamentals of alternating current technology

Fundamentals of semiconductors

Basic electronic circuits

Digital learning programs WBT Electrical engineering 1 – Fundamentals of electrical engineering

WBT Electrical engineering 2 – Direct and alternating current circuits

WBT Electronics 1 – Fundamentals of semiconductor technology

WBT Electronics 2 – Integrated circuits

WBT Electrical protective measures

Overview of media for the training package TP 1011

The digital learning programs Electrical engineering 1, Electrical engineering 2, Electronics 1, Electronics 2

and Electrical protective measures are available as software for the training package TP 1011. These

learning programs deal in detail with the fundamentals of electrical engineering/electronics. The learning

content is conveyed both by descriptions of the topics and by application using practical case studies.

The media are offered in numerous languages. You'll find further training materials in our catalogue

and on the Internet.

X © Festo Didactic GmbH & Co. KG 567217

Learning objectives – Fundamentals of alternating current technology

• You will be able to describe the characteristics used in AC technology and perform calculations using

these characteristics.

• You will be familiar with the different representations used for variables associated with alternating current.

• You will be able to record characteristics used in connection with alternating current by using an

oscilloscope and evaluate them.

• You will be familiar with how an ohmic resistor behaves in an AC circuit.

• You will be able to describe the behaviour of a capacitor in an AC circuit.

• You will be able to determine and calculate the capacitive reactance of a capacitor.

• You will be able to determine the phase shift of current and voltage at the capacitor in the AC circuit

by measurement and evaluate it.

• You will be able to determine and calculate the capacitive reactive power.

• You will be able to calculate the capacitance of capacitors connected in series and in parallel.

• You will be able to investigate capacitors connected in series and in parallel by measurement and

extrapolate laws.

• You will be familiar with the structure, application and characteristics of a coil.

• You will be able to analyse the switch-on and switch-off behaviour of a coil by measurement.

• You will know what effect the self-induction of a coil has on its behaviour.

• You will be able to describe the behaviour of a coil in an AC circuit.

• You will be able to determine the inductance and inductive reactance of a coil.

• You will be able to determine the phase shift of current and voltage at the coil in the AC circuit

by measurement and evaluate it.

• You will be able to use phasor and linear diagrams to add alternating variables in RC circuits.

• You will be familiar with RC elements as frequency-dependent voltage dividers.

• You will be able to use RC elements as high-pass and low-pass filters.

• You will be familiar with the importance of reactive power in the public electricity supply system.

• You will be able to measure and apply the power factor cos φ.

• You will be able to calculate and apply the RLC parallel circuit as a compensating circuit for

reactive power.

• You will be familiar with the relationship between effective power, reactive power and apparent

power and how they are represented.

• You will be able to use phasor and linear diagrams to add alternating variables in hybrid circuits.

• You will be familiar with the principle of generation of three-phase AC voltage.

• You will be familiar with the basic circuits (star circuit and delta circuit) in three-phase current

systems and be able to build them.

• You will be able to measure and calculate the power in star and delta circuits.

• You will be able to selectively use individual phases in a three-phase current system to generate power.

• You will know what effect the failure of a phase will have on the power of a consuming device

in a star circuit.

© Festo Didactic GmbH & Co. KG 567217 XI

Allocation of learning objectives and exercises – Fundamentals

of AC technology

Exercise 1 2 3 4 5 6 7 8 9 10

Learning objective

You will be able to describe the characteristics used in AC

technology and perform calculations using these characteristics. •

You will be familiar with the different representations used

for variables associated with alternating current. •

You will be able to record characteristics used in connection with

alternating current by using an oscilloscope and evaluate them. •

You will be familiar with how an ohmic resistor behaves in

an AC circuit. •

You will be able to describe the behaviour of a capacitor

in an AC circuit. •

You will be able to determine and calculate the capacitive

reactance of a capacitor. • •

You will be able to determine the phase shift of current

and voltage at the capacitor in the AC circuit by measurement

and evaluate it.

•

You will be able to determine and calculate the capacitive

reactive power. •

You will be able to calculate the capacitance of capacitors

connected in series and in parallel. •

You will be able to investigate capacitors connected in series and

in parallel by measurement and extrapolate laws. •

You will be familiar with the structure, application and

characteristics of a coil. •

You will be able to analyse the switch-on and switch-

off behaviour of a coil by measurement. •

You will know what effect the self-induction of a coil has

on its behaviour. •

XII © Festo Didactic GmbH & Co. KG 567217

Exercise 1 2 3 4 5 6 7 8 9 10

Learning objective

You will be able to describe the behaviour of a coil in an AC circuit. •

You will be able to determine the inductance and inductive

reactance of a coil. •

You will be able to determine the phase shift of current and voltage

at the coil in the AC circuit by measurement and evaluate it. •

You will be able to use phasor and linear diagrams to add

alternating variables in RC circuits. • •

You will be familiar with RC elements as frequency-dependent

voltage dividers. •

You will be able to use RC elements as high-pass and

low pass filters. •

You will be familiar with the importance of reactive power in the

public electricity supply system. •

You will be able to measure and apply the power factor cos φ. •

You will be able to calculate and apply the RLC parallel circuit as

a compensating circuit for reactive power. •

You will be familiar with the relationship between effective power,

reactive power and apparent power and how they are represented. •

You will be able to use phasor and linear diagrams to add

alternating variables in hybrid circuits. •

You will be familiar with the principle of generation of three-phase

AC voltage. •

You will be familiar with the basic circuits (star circuit and delta

circuit) in three-phase current systems and be able to build them. •

You will be able to measure and calculate the power in star and

delta circuits. •

You will be able to selectively use individual phases in a three-

phase current system to generate power. •

You will know what effect the failure of a phase will have on the

power of a consuming device in a star circuit. •

© Festo Didactic GmbH & Co. KG 567217 XIII

Equipment set

The workbook Fundamentals of alternating current technology covers the structure and function

of capacitors and coils as well as the behaviour of these components in basic circuits and simple

application circuits.

The equipment set Fundamentals of electrical engineering/electronics TP 1011 contains all the

components required to achieve the specified learning objectives. Two digital multimeters and

safety laboratory cables are also needed for building and evaluating functioning circuits.

Equipment set Fundamentals of electrical engineering/electronics, order no. 571780

Component Order no. Quantity

Basic power supply unit EduTrainer® 567321 1

Universal patch panel EduTrainer® 567322 1

Component set for electrical engineering/electronics 567306 1

Jumper plug set, 19 mm, grey-black 571809 1

Overview of the component set for electrical engineering/electronics, order no. 567306

Component Quantity

Resistor, 10 Ω/2 W 1








Resistor, 1 kΩ/2 W 3

Resistor, 2.2 kΩ/2 W 2






Resistor, 1 MΩ/2 W 1

XIV © Festo Didactic GmbH & Co. KG 567217

Component Quantity

Potentiometer, 1 kΩ/0.5 W 1

Potentiometer, 10 kΩ/0.5 W 1

Resistor, temperature-dependent (NTC), 4.7 kΩ/0.45 W 1

Resistor, light-dependent (LDR), 100 V/0.2 W 1

Resistor, voltage-dependent (VDR), 14 V/0.05 W 1

Capacitor, 100 pF/100 V 1

Capacitor, 10 nF/100 V 2


Capacitor, 0.1 μF/100 V 2




Capacitor, 10 μF/250 V, polarised 2



Coil, 100 mH/50 mA 1

Diode, AA118 1

Diode, 1N4007 6

Zener diode, ZPD 3.3 1

Zener diode, ZPD 10 1

DIAC, 33 V/1 mA 1

NPN transistor, BC140, 40 V/1 A 2

NPN transistor, BC547, 50 V/100 mA 1

PNP transistor, BC160, 40 V/1 A 1

P-channel JFET transistor, 2N3820, 20 V/10 mA 1

N-channel JFET transistor, 2N3819, 25 V/50 mA 1

UNIJUNCTION transistor, 2N2647, 35 V/50 mA 1

P channel MOSFET transistor, BS250, 60 V/180 mA 1

Thyristor, TIC 106, 400 V/5 A 1

TRIAC, TIC206, 400 V/4 A 1

Transformer coil, N = 200 1


Transformer iron core with holder 1

Indicator light, 12 V/62 mA 1

Light emitting diode (LED), 20 mA, blue 1

Light emitting diode (LED), 20 mA, red or green 1

Changeover switch 1

© Festo Didactic GmbH & Co. KG 567217 XV

Graphical symbols for the equipment set

Component Graphical symbol Component Graphical symbol

Resistor Zener diode

Potentiometer DIAC

Resistor, temperature-

dependent (NTC) NPN transistor

Resistor, light-dependent

(LDR) PNP transistor

Resistor, voltage-dependent

(VDR)

U

P-channel JFET transistor

Capacitor N-channel JFET transistor

Capacitor, polarised UNIJUNCTION transistor

Coil P-channel MOSFET transistor

Diode Thyristor

XVI © Festo Didactic GmbH & Co. KG 567217

Component Graphical symbol Component Graphical symbol

TRIAC Blue LED

Transformer coil Red or green LED

Indicator light Changeover switch

© Festo Didactic GmbH & Co. KG 567217 XVII

Allocation of components and exercises – Fundamentals of alternating

current technology

Exercise 1 2 3 4 5 6 7 8 9 10

Component


Resistor, 470 Ω/2 W 1 1

Resistor, 1 kΩ/2 W 1 1 1 1 1 1 3 3




Resistor, voltage-dependent (VDR), 14 V/0.05 W 1

Capacitor, 100 pF/100 V 1

Capacitor, 10 nF/100 V 1 1



Capacitor, 0.22 μF/100 V 1 1 1 1



Coil, 100 mH/50 mA 1 1 1


Transformer coil, N = 600 1 1

Digital multimeter 1 1 1 1 1 1 1

Oscilloscope, 2-channel 1 1 1 1 1 1 1

Basic power supply unit EduTrainer® 1 1 1 1 1 1 1 1 1 1

XVIII © Festo Didactic GmbH & Co. KG 567217

Notes for the teacher/trainer

Learning objectives The main objective of this workbook is to explain how to analyse and evaluate simple AC circuits

with a resistor, capacitor and coil. It does this through a combination of theoretical questions and

practical exercises where the students are required to build the circuits and measure electrical variables.

The combination of both theory and practice ensures faster progress and longer-lasting learning. The more

specific learning objectives are documented in the matrix. Concrete, individual learning objectives are

assigned to each exercise.

Required time The time required for working through the exercises depends on the student’s previous knowledge

of the subject matter. Each exercise should take approx. 1 to 1.5 hours.

Equipment set components The workbook, set of exercises and equipment match each other. All 10 exercises can be completed using

components from one equipment set TP 1011.

Standards The following standards are applied in this workbook:

EN 60617-2 to EN 60617-8 Graphical symbols for circuit diagrams

EN 81346-2 Industrial systems, installations and equipment and industrial products;

structuring principles and reference designations

IEC 60364-1 Low-voltage electrical installations – Fundamental principles,

assessment of general characteristics, definitions

IEC 60364-4-41 Low-voltage electrical installations – Protective measures –

Protection against electric shock

Classifications in the workbook Solutions and supplements in graphics or diagrams are in red.

Exception: Information and evaluations relating to current are always in red, information and evaluations

relating to voltage are always in blue.

Classifications in the set of exercises Texts which require completion are identified with a grid or grey table cells.

Graphics which require completion include a grid.

Notes for the lesson These provide additional information about the training approach, method or about the components.

These notes are not included in the set of exercises.

© Festo Didactic GmbH & Co. KG 567217 XIX

Solutions The solutions specified in this workbook are the results of test measurements. The results of your

measurements can deviate from these data.

Learning topics The training subject "Fundamentals of direct current technology" is part of the learning topics in technical

colleges for electronic engineering.

Structure of the exercises

All 10 exercises have the same structure and are broken down into:

• Title

• Learning objectives

• Problem description

• Circuit or positional sketch

• Project assignment

• Work aids

• Worksheets

The workbook contains the solutions for each worksheet in the set of exercises.

Component designations

The components in the circuit diagrams are identified in accordance with DIN EN 81346-2. Letters are

assigned as appropriate to each component. Multiple components of the same type within a circuit are

numbered.

Resistors: R, R1, R2, etc.

Capacitors: C, C1, C2, etc.

Coils: L, L1, L2, etc.

Signalling devices: P, P1, P2, etc.

Note

If resistors, capacitors or coils are being interpreted as physical variables, the letter identifying them

is shown in italics (symbols). If numbers are required for numbering, these are treated like indices and

subscript is used.

XX © Festo Didactic GmbH & Co. KG 567217

CD-ROM contents

The workbook is included on the CD-ROM as a PDF file. The CD-ROM also provides you with

additional media.

The CD-ROM contains the following folders:

• Operating instructions

• Images

• Product information

Operating instructions Contains operating instructions for various components in the training package. These instructions

are helpful when using and commissioning the components.

Images Contains photos and graphics of components and industrial applications. These can be used

to illustrate individual tasks or to supplement project presentations.

Product information Contains the manufacturer's product information for selected components. The representations

and descriptions of the components in this format are intended to demonstrate how they are presented

in an industrial catalogue. Additional information regarding the components is also included.

© Festo Didactic GmbH & Co. KG 567217 1

Exercise 1

Recording and representing characteristics used in AC technology

Learning objectives After completing this exercise:

• You will be able to describe the characteristics used in AC technology and perform calculations using

these characteristics.

• You will be familiar with the different representations used for variables associated with alternating current.

• You will be able to record characteristics used in connection with alternating current using the

oscilloscope and evaluate them.

• You will be familiar with how an ohmic resistor behaves in an AC circuit.

Problem description You are to start work in the Quality Assurance department, where you will be testing faulty

electronic circuits.

In preparation, you will perform measurements on simple AC circuits.

Circuit

RLUG

AC circuit with oscilloscope

Exercise 1: Recording and representing characteristics used in AC technology

2 © Festo Didactic GmbH & Co. KG 567217

Project assignments 1. Describe what AC voltage is.

2. Answer the questions on phasor and linear representation of alternating variables.

3. Explain the main characteristics used in connection with alternating current.

4. Familiarise yourself with the operation of the oscilloscope and answer the questions.

5. Perform the initial measurements using the oscilloscope.

6. Investigate the current, voltage and power waveform in a simple resistance circuit.

Work aids • Textbooks, books of tables

• Data sheets

• WBT Electrical engineering 1

• Internet

Note

Do not switch on the electrical power supply until you have made and checked all the connections. Once

you have completed the exercise, switch off the power supply again before dismantling the components.



Describing AC voltage

– Describe what AC voltage is.

AC voltage is a voltage that periodically changes its polarity (direction) and value.

The illustration shows three frequent temporal waveforms of alternating variables.

– Enter the name of the waveform in the table.

Signal waveform Designation

u

u

u

t

t

t

T

T

T

T2

T2

T2

Sinusoidal waveform

Triangular waveform

Square-wave waveform

Typical electrical signal shapes



Explaining phasor and linear representation of alternating current

The sinusoidal line for the AC voltage can be constructed from the rotating phasor in the circle.

The radius of the circle corresponds to the amplitude of the sinusoidal oscillation and is called UP.

α

u

u

α, t180° 360°90° 270°α

UP

-UP

UP

π

2π 2π3π

2

Phasor representation and linear representation of a sinusoidal AC voltage

– Specify the formula for calculating the momentary voltage value u.

The formula is:

P

OppositesidesinHypotenuse

uU

α = =

The momentary value u is therefore:

P sinu U= ⋅ α

The higher the frequency of the sinusoidal oscillation, the shorter the periodic duration and the faster

the rotation of the associated phasor. The angular frequency ω is used as a measure for the speed

of the phasor movement.

– Specify the formula for calculating the momentary value u as a function of ω.

– To do this, also add the sinusoidal curve to the graph. Under the angle value in degrees, enter

the corresponding value in radians.

Formula for calculating the momentary value u:

P sinu U ( t )= ⋅ ω



Describing the characteristics used in connection with alternating current

To work in the field of AC technology, you will need to be familiar with the characteristics used in connection

with alternating current.

– Briefly describe the main characteristics used in connection with AC technology. To do this, complete

the corresponding fields in the table.

Characteristic Symbol or formula Description

Peak voltage UP

UP Highest or lowest AC voltage value, also called amplitude or peak value.

Peak current IP

IP Highest or lowest alternating current value.

Peak-to-peak voltage UPP PP P2U U= ⋅ Difference between the positive and negative peak value.

With sinusoidal voltage: UPP is twice the amplitude.

Effective voltage Ueff

Peff 2

UU =

The effective value is the AC voltage value that will give the same power

at an ohmic resistor as a DC voltage with this value.

Effective current Ieff

P

eff 2I

I = The effective value is the alternating current that will give the same power

at an ohmic resistor as a direct current with this value.

Periodic duration T in s

T A period (full wave with positive and negative half-wave) lasts a certain

amount of time. This time is called the periodic duration T.

Frequency f in Hz

1fT

=

Number of periods per second.

Angular frequency ω in 1s

2 fω = ⋅ π⋅

Angle covered per time unit in radians.

Momentary value u

P sinu U ( t )= ⋅ ω Time-dependent momentary value of a sinusoidal AC voltage.

Momentary value i

P sini I ( t )= ⋅ ω Time-dependent momentary value of a sinusoidal alternating current.

Characteristics used in AC technology



– Add some of the characteristics to the representation of the sinusoidal AC voltage. To do this, match

the characteristics with the numbers.

u

t0

3 1

4

2

Sinusoidal AC voltage

Number Designation

1 Peak value UP

2 Peak-to-peak value UPP

3 Effective voltage Ueff

4 Periodic duration T

Describing the basic functions of an oscilloscope

Oscilloscopes offer many adjustment and connection options, which differ depending on the design

and model. Certain basic settings, however, are common to all oscilloscopes.

USB

Flash Drive

PRINT

SAVE

CH1

MENU

MATH

MENU

CH2

MENU

VOLT/DIV

CH1 CH2 EXT.TRIG.

SEC/DIV

HORIZ

MENU

SET TO

ZERO

VERTICAL

POSITION

HORIZONTAL

POSITION

TRIGGER

LEVEL

TRIG

MENU

SET TO

50%

FORCE

TRIG

TRIG

VIEW

REF

MENU

SINGLE

SEQ

RUN/

STOP

AUTOSETHELP

DEFAULT SETUP

AUTORANGE SAVE/RECALL MEASURE ACQUIRE

UTILITY CURSOR DISPLAY

Example of an oscilloscope



– Find out how the oscilloscope that you will be using for your measurements works.

– Complete the table with the names of the controls that trigger the described functions.

Control Brief description

Switch 0/I Mains switch

Rotary knob POSITION CH1 Positions the signal from channel 1 (CH1) vertically.

Rotary knob VOLTS/DIV (CH1) Sets the sensitivity of the CH1 input signal vertically.

Button CH1 MENU Switches the display of channel 1 on or off.

Rotary knob POSITION Positions all signals horizontally.

Rotary knob SEC/DIV Sets the time-base sweep for the signals.

Button CH1 MENU -> Probe Probe setting for channel 1.

Button CH1 MENU -> Coupling Sets the following for channel 1: DC, AC, Ground.

Ground means: switches the channel to ground.

Button CH1 MENU -> Invert Inverts the signal from channel CH1.

Button TRIG MENU Trigger settings

Button TRIG MENU -> Edge Sets Edge as the trigger type.

Input connector EXT. TRIG. Input connector for an external trigger source.

CH1 Measurement channel 1

CH2 Measurement channel 2

Basic oscilloscope functions

Note for the lesson

The basic functions and controls are illustrated using the 2-channel digital storage oscilloscope

Tektronix TDS 1002B as an example.

– Describe the effect of the trigger function on oscilloscope traces.

The trigger function can be used with periodic signals to set the start time of the beam

on the oscilloscope's display to the same amplitude value as for the previous signal.

This produces a seemingly stationary image.



Proceed as follows when creating an oscilloscope trace: • Make sure that the X and Y deflections are calibrated.

• Make sure that the zero line is where you want it.

• If you are setting a frequency on the function generator, measure the frequency using the

oscilloscope to make sure it matches.

• Always portray at least one period when performing a trace.

• Always enter the zero line in the trace.

• Always enter the time-base sweep in the trace.

• Always enter the voltage sweep of each channel used (CH1 and CH2) in the trace.

• Pay attention to the reciprocal time references of the signals when tracing.

• Always use the slowest signal as the trigger.

TUPP

Settings on the oscilloscope:

Y = 2 V/DIV

X = 0.1 ms/DIV

Measurement example for the oscilloscope

– Evaluate the measurement results of the oscilloscope trace. Determine the peak-to-peak voltage

UPP and the periodic duration T.

Peak-to-peak voltage UPP:

UPP corresponds to 4 scale divisions (DIV).

PPV4 DIV 2 8 V

DIVU = ⋅ =

Periodic duration T:

T corresponds to 6 scale divisions.

ms6 DIV 0 1 0 6 ms

DIV= ⋅ =T . .



Performing a measurement using the oscilloscope

Investigate the temporal waveform of an AC voltage using the oscilloscope display.

– Build the circuit.

Y1

UG

Circuit for tracing a sinusoidal AC voltage using an oscilloscope

Identifier Designation Values

– Oscilloscope 2-channel

– Basic power supply unit EduTrainer® –

Equipment list

– Connect the function generator.

– Make the settings for the measuring ranges on the oscilloscope as specified.

– Set the frequency and voltage on the function generator to get a voltage waveform similar to that in the

oscilloscope graph shown below.



0 (Y )1

Settings on the oscilloscope

Channel 1:

Y1 = 1 V/DIV

Time-base sweep:

X = 0.1 ms/DIV

Oscilloscope graph for the AC voltage to be investigated

– Measure the peak-to-peak voltage UPP and the periodic duration T.

Peak-to-peak voltage UPP:

PPV6 DIV 1 6 V

DIVU = ⋅ =

Periodic duration T:

ms10 DIV 0 1 1 ms

DIV= ⋅ =T .

– Determine the peak voltage UP, the effective voltage Ueff and the frequency f from the measured values

mathematically.

Peak voltage UP:

PPP

6 V 3 V2 2

UU = = =

Effective voltage Ueff:

Peff

3 V 2 12 V2 2

UU .= = =

Frequency f:

31 1 11 10 1 kHz1 ms s

fT

= = = ⋅ =



– Measure the effective value Ueff using the digital multimeter.

– Compare the measured effective value and the mathematically determined effective value.

Measured Ueff:

Ueff = 2.01 V

Calculated Ueff:

Ueff = 2.12 V

Slight deviations between the measured values and the calculated values are due to measuring errors

and component tolerances.

Measuring voltage, current and power at the ohmic resistor

Represent the temporal waveform of AC voltage and alternating current at an ohmic resistor. Construct the

power curve for the resistor from the momentary values for current and voltage. Compare this power curve

with the power curve at a comparable DC voltage.

– Describe how to represent the waveform of currents using the oscilloscope.

To be able to measure the current, a current measurement resistor RM must be added to

the electrical circuit. The voltage drop URM at the current measurement resistor is determined

using the oscilloscope and used as a basis for calculating the current flowing through the circuit.

– Describe what is meant by an active resistor.

In AC technology, an ohmic resistor is called an active resistor. The active resistor has the same

effect in the AC circuit as in the DC circuit. It acts on the electrical energy and converts it into heat,

light or mechanical energy. The power converted at the active resistor is also called effective power.



– Specify the formula for calculating the current I at the active resistance R.

= UIR

Voltage and current at the active resistor

Y1

Y2

URM

U

f

P = 6.6 V(sinusoidal)

= 1 kHz

URL

G

RL

RM

Resistance circuit with RL = 1 kΩ, RM = 100 Ω, UP = 6.6 V, f = 1 kHz


RL Resistor 1 kΩ/2W

RM Resistor 100 Ω/2 W

– Oscilloscope 2-channel


Equipment list

Note To enable the voltages URL and URM to be represented simultaneously on the oscilloscope, the reference

point of the two voltages is placed between the two resistances. As a result, the voltage signal URM

must be inverted.

Make sure that no ground loops occur across the protective earth conductors when the two measurement

channels are connected to the oscilloscope. Connect an isolating transformer to prevent this.



– Build the circuit.

– Connect the function generator.

– Set a sinusoidal voltage UP = 6.6 V with the frequency f = 1 kHz.

– Make the necessary settings for the measurements on the oscilloscope.

– Measure the sinusoidal voltage URL at the resistor RL using the oscilloscope.

– Transfer the voltage waveform to the oscilloscope graph.

– Measure the voltage URM at the measuring resistor RL using the oscilloscope.

– Transfer this voltage waveform to the oscilloscope graph too.

0 (Y ),1 (Y )2

Y2

Y1

Settings on the oscilloscope

Channel 1:

Y1 = 2 V/DIV

Channel 2:

Y2 = 0.5 V/DIV

(invert)

Time-base sweep:

X = 0.1 ms/DIV

Centre zero lines of channel 1

and channel 2

Trigger: Y1

Oscilloscope graph for uRL and uRM

– Determine the momentary values uRL and uRM for the times specified in the measurement log.

Enter the momentary values in the measurement log.

– Calculate the current i and the effective power p for the times specified in the measurement log.

Enter these values too. Also specify the formula for calculating p.

Formula for calculating the momentary values for power:

p u i= ⋅

– Represent the current values i, the voltage values u and the power waveform p in the prepared graph.



Time t (ms) Voltage uRL (V) Voltage uRM (V) Current i (mA) Effective power p (mW)

0 0 0 0 0

0.1 3.8 0.38 3.8 14.4

0.15 5.0 0.5 5.0 25.0

0.25 6.0 0.6 6.0 36.0

0.35 5.0 0.5 5.0 25.0

0.4 3.8 0.38 3.8 14.4

0.5 0 0 0 0

0.6 -3.8 -0.38 -3.8 14.4

0.65 -5.0 -0.5 -5.0 25.0

0.75 -6.0 -0.6 -6.0 36.0

0.85 -5.0 -0.5 -5.0 25.0

0.9 -3.8 -0.38 -3.8 14.4

1.0 0 0 0 0

Measurement log

tTime

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ms

-10-25

00

VmA

615

410

25

-2-5

-4-10

-6-15

-8-20

1025

1.0

Vo

lta

ge

u

Cu

rre

nt

i

Po

we

rp

-50

0

mW

30

20

10

-10

-20

-30

-40

50

u

p

i

Voltage, current and power waveform at the ohmic resistor RL



– Describe the waveform of the current and voltage curve.

Current and voltage are in phase. They reach their zero crossovers and peak values at the same time.

– Describe the waveform of the power curve.

The waveform of the power curve is also sinusoidal, but has no negative components. The frequency

is twice that of the voltage and current waveform.

The waveform of the effective power at the ohmic resistor can be replaced with a constant mean value.

It is the effective value of the power.

– Specify the formula for calculating the effective value of the power P.

eff eff effP U I= ⋅

Ohm's law gives two further formulae for calculating the power:

2eff effP R I= ⋅ or

2eff

effU

PR

=

– Specify the effective value of the power for the resistance circuit.

eff eff eff6 V 6 mA 18 mW

2 2 2 2= ⋅ = ⋅ = ⋅ =P PU I

P U I



Power in the DC and AC circuit To be able to compare the power in the DC and AC circuit, determine the power output at the ohmic resistor

RL = 1 kΩ at a DC voltage of U = 4.24 V.

– Explain why the comparison measurement for direct current is performed at a DC voltage of U = 4.24 V.

The sinusoidal AC voltage with UP = 6 V has the effective value:

eff6 V 4 24 V

2 2= = =PU

U .

A DC voltage of U = 4.24 V gives the same power at an ohmic resistor as the effective value

Ueff = 4.24 V of an AC voltage.

– Measure the power of the illustrated circuit in the DC circuit using the indirect method and write

down the measured values.

U = 4.24 V URLRL

Resistance circuit with RL = 1 kΩ, U = 4.24 V


RL Resistor 1 kΩ/2W

– Digital multimeter –


Equipment list for the resistance circuit connected to direct current

Measured values of the electrical variables for calculating power:

U = 4.24 V

I = 4.19 mA



– Calculate the electrical power at the ohmic resistor in the DC circuit from the measured values.

4 24 V 4 19 mA =17.8 mWP U I . .= ⋅ = ⋅ &

– Enter the waveform of the measured electrical variables and the calculated electrical power

in the corresponding graph.

DC circuit AC circuit

U = 4.24 V URLRL UP = 6 V URLRL

G

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ms00

VmA

410

25

-2-5

-4-10

-6-15

-8-20

1.0

Vo

lta

ge

U

Cu

rren

tI U

I

tTime

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ms00

VmA

410

25

-2-5

-4-10

-6-15

-8-20

1.0

Vo

lta

ge

u

Cu

rre

nt

i

u

i

tTime

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ms 1.0

P

Po

wer

P

0

mW

30

20

10

tTime

50

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ms 1.0

p

Po

we

rp

0

mW

30

20

10

50

tTime

Comparison: Power in the DC circuit and AC circuit for RL = 1 kΩ



– Describe the relationship between the two power curves.

• A constant, invariable power is output in the DC circuit.

• The power output fluctuates greatly in the AC circuit.

• With a sinusoidal AC voltage, both sources output the same power on average if the maximum

value of the power output for the AC voltage is exactly twice the temporally constant power

of the DC voltage source.


Exercise 2

Investigating the behaviour of a capacitor

Learning objectives After completing this exercise:

• You will be able to describe the behaviour of a capacitor in an AC circuit.

• You will be able to determine and calculate the capacitive reactance of a capacitor.

• You will be able to determine the phase shift of current and voltage at the capacitor by measurement

and evaluate it.

• You will be able to determine and calculate the capacitive reactive power.

Problem description A series resistor is needed in an AC circuit for an LED. The series resistor should release as little

electrical energy as possible in the form of heat. At your disposal are ohmic resistors and capacitors.

Investigate the behaviour of the capacitor connected to AC voltage and examine whether the capacitor

can be used as a loss-free series resistor.

Positional sketch

PE

L1

L1

L2

L2

L3

L3

N

N

EMERGENCY

STOP

PE

Power supply unit for three-phase alternating current with LED indicator

Exercise 2: Investigating the behaviour of a capacitor


Work assignments 1. Compare the behaviour of the capacitor connected to AC and DC voltage.

2. Investigate the behaviour of the capacitor in the AC circuit by measuring the charging and

discharging process.

3. Examine the current and voltage waveform at the capacitor in the AC circuit.

4. Investigate the frequency dependence of a capacitor's capacitive reactance. To do this, trace

the resistance curve.

5. Trace the capacitor's power curve and decide whether the capacitor can be used as a series resistor.

Work aids • Textbooks, books of tables

• Data sheets

• WBT Electrical engineering 2

• Internet

Note for the lesson

There are two ways of completing the exercise:

• First, research the basic behaviour of the capacitor in the AC circuit,

• then check the results through an experiment

or vice versa.

If the decision about the order is left to the student, he can take his individual needs into consideration.

Note

Do not switch on the electrical power supply until you have made and checked all the connections. Once

you have completed the exercise, switch off the power supply again before dismantling the components.

Fundamentals of alternating current technology - Festo · PDF fileThe training package...

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Transcript of Fundamentals of alternating current technology - Festo · PDF fileThe training package...