Lighting control-technology and applications

L i g h t i n g C o n t r o l - T e c h n o l o g y a n d A p p l i c a t i o n s
This Page Intentionally Left Blank
Robert S. Simpson
L i g h t i n g C o n t r o l – T e c h n o l o g y a n d A p p l i c a t i o n s
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CONTENTS
Focal Press An imprint of Elsevier Linacre House, Jordan Hill, Oxford OX2 8DP 200 Wheeler Road, Burlington MA 01803
First published 2003
Copyright© 2003, Robert S. Simpson. All rights reserved
The right of Robert S. Simpson to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988
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British Library Cataloguing in Publication Data Simpson, Robert S.
Lighting control : technology and applications 1.Electric lighting – Control I.Title 621.3’2
Library of Congress Cataloguing in Publication Data A catalogue record for this book is available from the Library of Congress
ISBN 0 240 51566 8
Printed and bound in Italy
For information on all Focal Press publications visit our website at: www.focalpress.com
CONTENTS
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Part 1 Foundation chapters
1 Electricity and light 1
1.1 Electricity 1 1.2 Electrical units and components 4 1.3 Electrical distribution 15 1.4 Power factor 24 1.5 Control of electric power 29 1.6 Electromagnetic compatibility (EMC) 36 1.7 Light 39 1.8 The eye, how we see light 44 1.9 Measurement of light 45 1.10 Color 50 1.11 Measurement of color 53
2 Lighting electronics 58
2.1 Electronic principles 58 2.2 The diode 63 2.3 The transistor 68 2.4 The thyristor, triac and GTO 81 2.5 Analog and digital 85 2.6 The integrated circuit and ASIC 93 2.7 The microprocessor 102 2.8 Programmable devices 110
Part 2 Lamps
3 Everyday lamps 112
3.1 Non-electric lighting 112 3.2 The incandescent lamp 113 3.3 Tungsten halogen lamps 115 3.4 The fluorescent lamp 119 3.5 Compact fluorescent lamps 123 3.6 Special purpose fluorescent lamps 124
4 Arc lamps 130
4.1 High intensity discharge lamps 130 4.2 Mercury vapor lamps 130 4.3 Sodium and high pressure sodium lamps 133 4.4 Metal halide lamps 136 4.5 Compact source metal halide lamps 138 4.6 High pressure mercury vapor lamps 139 4.7 Xenon arc lamps 140 4.8 Arc lamp classification 141
5 Special purpose lamps 144
5.1 Induction lamps 144 5.2 Flat lamps 148 5.3 Neon lamps 149 5.4 Electroluminescent lamps 151 5.5 Light emitting diodes (LEDs) 153 5.6 Lasers 159 5.7 Ultra-violet lamps 162 5.8 Infra-red lamps 163 5.9 Flash tubes 164 5.10 Fiber optics and lightguides 166 5.11 Video displays as lightsources 171
Part 3 Lighting components
6 Electromagnetic components 172
6.1 Principles of transformers and inductors 172 6.2 Transformers for lighting 186 6.3 Ballasts for fluorescent lamps 192 6.4 Ballasts for HID and arc lamps 204 6.5 Ignitors and starters 207 6.6 Lighting control by transformers
and ballasts 210 6.7 Power factor correction 211
7 Electronic components 215
7.1 Circuit elements 215 7.2 Electronic ballasts for fluorescent lamps 219
C o n t e n t s
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CONTENTS
7.3 Electronic ballasts for HID and arc lamps 242 7.4 Electronic transformers 245 7.5 Lighting control by electronic transformers
and ballasts 248
8 Dimmers 250
8.1 Introduction to dimmers 250 8.2 Non-electronic dimming 252 8.3 Thyristor and triac dimmers 257 8.4 Transistor dimmers 269 8.5 Electromagnetic compatibility (EMC) 272 8.6 New developments in electronic dimming 276
9 Control signals and protocols 280
9.1 Introduction 280 9.2 Analog control 280 9.3 Digital control 283 9.4 Standard protocols for lighting control 288 9.5 Networks and buses 303 9.6 Computers in lighting control 332 9.7 Cordless control 334
10 Why lighting control? 343
10.1 The practical role 343 10.2 The esthetic role 344 10.3 The energy management role 345 10.4 Influence of legislation 348 10.5 Lighting design 351
11 Stage and entertainment lighting control systems 353
11.1 Basis of stage lighting control 353 11.2 Simple multichannel controls for
entertainment 354 11.3 Memory consoles 356 11.4 Live versus automatic 362 11.5 Control of moving lights 363 11.6 Control of color 370 11.7 Large scale entertainment lighting control 372
12 Architectural lighting control systems 374
12.1 “Setting the scene” 374 12.2 Manual versus automatic control 375 12.3 Single channel control 376 12.4 Small multi-channel control systems 377 12.5 Large multi-channel control systems 381 12.6 Switching systems 383 12.7 Centralized versus distributed systems 390 12.8 Emergency and safety 391
13 The merging of “architectural” and “entertainment” lighting control 396
13.1 User demands and the influence of designers 396
13.2 Automatic lighting control in public shows and public areas 398
13.3 Control of exterior lighting 400
14 Energy management and building control systems 402
14.1 Principles 402 14.2 Sensors and timers 403 14.3 Switching versus dimming, control
algorithms 412 14.4 Local versus central control 417 14.5 Impact of lighting on HVAC 417 14.6 Power quality 417 14.7 Integrated versus separate lighting control 418 14.8 Monitoring systems 418
Part 5 Applications
15 Architectural applications 420
15.1 The home 420 15.2 Integrated home control systems 428 15.3 The workplace 431 15.4 Meeting rooms, conference centers, and
auditoria 436 15.5 Places of worship 447 15.6 Museums, art galleries and libraries 449 15.7 Visitor centers and exhibitions 454
CONTENTS
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15.8 Hotels, hospitals and institutions 459 15.9 Restaurants, bars and pubs 463 15.10 Illuminated signs 464
17 Entertainment applications 510
Trade marks and disclaimer
In order to ensure that this book can be of practical use, it has been necessary to mention many commercial products by name. The inclusion or omission of any particular company’s products does not imply any endorsement or comment by the publisher. Where summaries are given of manufacturers of different kinds of equipment, these are intended as examples only, no claim is made that such summaries represent any kind of comprehensive directory.
This book is intended as a source of information only. Care has been taken to verify the accuracy of all information contained herein, but neither the author nor the publisher can take responsibility for the consequences of using the information, or for any errors or omissions.
Example circuits, devices and techniques may be the subject of patent protection or patent application. Their publication in this book does not imply any license for their use.
Any references to standards and protocols (whether public or proprietary) are intended to give readers an introduction to their nature and operation. There is no implication of any license to use them, and current standards specifications and details of any licensing associated with them must be obtained from the sponsoring body concerned.
All trade marks are acknowledged. Where known they are identified in the text by TM or ®.
17.1 Small stages 510 17.2 Large stages 514 17.3 Television 520 17.4 Touring shows 524 17.5 Outdoor shows, Son et Lumière,
pyrotechnics 526 17.6 Stadia, arenas, sporting facilities 534 17.7 Theme parks 539 17.8 Entertainment within retail 542 17.9 Discotheques, dancefloors and clubs 544 17.10 Conclusion 546
Some suggestions for further reading 547 Table of acronyms 550 Index 552
16 Functional applications 469
16.1 Retail spaces 469 16.2 Agriculture and horticulture 472 16.3 Manufacturing processes 473 16.4 Healthcare 474 16.5 Simulation 475 16.6 On water 476 16.7 In the air 481 16.8 On the road 490 16.9 On railways 505 16.10 Control rooms 508
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CONTENTS
The author acknowledges the help given to him in prepar- ing this book by many industry colleagues from around the world. As far as possible application illustrations and case histories are acknowledged within the text. Unac- knowledged diagrams and photographs are mostly from Helvar and Electrosonic. Among the many individuals who have contributed information and help, special thanks are due to to the following, arranged in company alphabetical order:
Individual independent consultants Brian Legge Thomas Baenziger
ADB (aviation lighting) Ira Jackson AIM Aviation (Jecco) Ltd Rolf Startin Anytronics Ltd Bob Hall Artistic License Wayne Howell Art2Architecture Peter Fink Arup Acoustics Sam Wise Arup (Manchester office) John Waite Avolites Richard Salzedo British Library Michael Wildsmith Building Research Establishment Michael Perry Carr & Angier Paul Covell CCT Lighting David Manners Claude Lyons Jim McIlfatrick Color Kinetics Melissa Connor The Deep (Hull, UK) Dr David Gibson Delmatic Stephen Woodnutt Derungs Licht Claudio Roth DHA Lighting Design Adam Grater Dynalite Dannielle Furness ECS Philips Lighting Controls Chris Holder Electrosonic Ltd Yvonne Hegarty, Daniela Simonides ETC Fred Foster Firework Shop John Stapleton Fisher Marantz Stone Scott Hershman
Rob Schoenbohm Focus Lighting Inc Paul Gregory Genlyte Controls Jason Moreno Helvar (Finland) Teijo Viljanen, Markku Nohiu
Eeva Harjula Helvar (Germany) Ingo Sommer Helvar (UK) Alan Jackson, Trevor Forrest
Austen Conway, Dr Scott Wade, Mel Collins Howard Industries Mike Dodds
IBL Peter Saunders Leviton Breda Potter Lighting Architects Group Jonathan Speirs
Mark Major, Iain Ruxton LSI Projects Ltd Nick Mobsby Lumisphere Products Bob Myson Lutron Brian McKiernan MEM and MEM250 Richard Hunt, H. Milligan Osram Hans Jörg Schenkat, Verena Roemer P. Ducker Systems Ltd Richard Thomas Philips Marc Segers, Holger Moench
Peter Woodward, John Rothery Pinniger & Partners Miles Pinniger Project Interational Richard Dixon Pulsar Light Cambridge Andy Graves, Paul Marden Pyrodigital Consultants Ken Nixon Quo Vadis Ltd Michael Stott Relco Daria Fossati repas AEG Dirk Buchholz Royal National Theatre Great Britain MikeAtkinson Schott Fibre Optics UK John Meadows Starfield Controls Wayne Morrow Strand Lighting Vic Gibbs, Ivan Myles Sutton Vane Associates Mark Sutton Vane Technical Marketing Ltd Andy Collier Teknoware Jari Tabell Thorlux Lighting Terry Fletcher Tunewell Transformers Derek Price, Glen McGovern Tridonic Stewart Langdown Kate Wilkins Lighting Design Kate Wilkins Vantage Controls Andy North Vari-Lite Europe Ltd Samantha Dean,Colin Brooker Waltzing Waters Douglas Tews, Michael Przystawik The Watt Stopper Inc Joy Cohen WRTL Exterior Lighting Tom Thurrell Wynne Willson Gottelier Tony Gottelier Wybron Inc Brandon James Young Electric Sign Co Graham Beland, Blake Gover
In addition, grateful thanks to Paul Ashford for driving “Pagemaker”, Noel Packer (of Helvar UK) and Paul Ashford for drawing most of the diagrams and Maggie Thomas (of Electrosonic) for help thoughout the project. Finally, thanks to the staff at Focal Press for their support over three years.
A c k n o w l e d g e m e n t s
CONTENTS
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Artificial lighting is part of our daily lives; in the modern world there are few activities which take place without it. While there are many books on the subjects of light and lighting, there are few that cover the subject of lighting control. Those that do look at the subject from a limited perspective, for example that of stage lighting.
Within the practical limits set by its size, this book is intended as a review of all methods of lighting control. It covers all the current technologies, and gives application examples from many aspects of our daily lives. It is intended for all those who already work in the lighting industry, for designers and consultants, and for the sophisticated end user. It is also intended as a training resource for those new to the industry.
No significant prior technical knowledge is assumed. The book is written for the “intelligent layman”, and mathematics are kept to a minimum. In order to make it a complete resource Part 1 is in the nature of a “foundation course” to give the necessary background to those with limited (or no) knowledge of the basics of light, electricity and electronics. It can be skipped by engineers and techni- cians who already have this knowledge.
Part 2 is a review of light sources. Unless you understand how a particular light source works, you cannot appreciate how to control it. Again much of the information in Part 2 may be well known to some readers, although there could be a few surprises arising from recent developments in traditional sources, and from the arrival of completely new sources.
P r e f a c e
Most light sources need some kind of “load interface”, for example a ballast or transformer, between them and the electricity supply. Part 3 reviews these “lighting components”, most of which are available in both electromagnetic and electronic form. In recent years there have been major advances in electronic lighting components, and they now form an essential part of many lighting control systems.
Part 4 is the technical heart of the book, covering dimmers and control systems. The dimmer or dimming interface is now only part of lighting control. With modern systems often embracing thousands of lighting “channels” spread over a large building com- plex, a basic knowledge of network and computer technology becomes necessary.
Lighting control is used for practical, esthetic and energy management reasons. Part 5 reviews how the technologies described in the first four parts of the book are applied in practice. The aim here has been to cite examples, without attempting to be exhaus- tive, representing best practice from different parts of the world.
Lighting control has been part of my life for over 50 years, from operating slider dimmers for school plays, to being a member of a specifying team for the latest generation of digital dimmers. I hope that my enthusiasm for the subject is reflected in this book, and that even if you are an experienced lighting practioner, you will find something useful or unex- pected within it.
R.S.S.
ELECTRICITY AND LIGHT
1.1 Electricity
Both electricity and light are mysterious. We are well aware of their effect, but, if asked the question “what is electricity?” or “what is light?”, we have difficulty giving a convincing answer. We find it easiest to think in terms of a model, or models, which make it possible for us to understand how an electrical or optical device works. Provided the model, or “mind picture”, is consistent, this is a quite acceptable way to proceed – indeed it is the only way for the layman to get an insight into physical processes. In this chapter we describe the simplest models of electricity and light to the point where the methods of controlling them can be understood.
The first model we need is that of the structure of matter. The atomic theory holds that the smallest unit of matter is the atom. In a compound there are several different kinds of atom, but in an element all the atoms are the same. All atoms are themselves made up of fundamental particles. Modern physics has produced an alarmingly long list of these, but for our purposes it is sufficient to know of only three: • the proton, a massive particle which carries a
positive electric charge • the neutron which has the same mass as the
proton, but has no charge • the electron which carries a negative electric
charge equal and opposite to that of the proton.
The model of atomic structure which is sufficient for our purposes imagines that atoms have a planetary structure: a heavy nucleus consisting of a mixture of protons and neutrons, surrounded by orbiting electrons. The resulting atom is electrically neutral since the number of electrons in orbit exactly matches the number of protons.
Figure 1.1 gives some examples of elements which are relevant to our subject. An important point to notice is that the electron orbits are not haphazard. The model shows that the electrons occupy “shells”, each one of which can only contain a defined number of electrons. As we move through the elements, from hydrogen the lightest, through to the heavy elements such as uranium, one unit of charge is added for each element. The shells get filled up in sequence, and this has the result that only some elements have a “complete” outer shell. It is the nature of the outer shell of electrons which determines many of the electrical and chemical properties of different elements.
When an atom, for example a copper atom, has only a single electron in its outer shell, this electron can be easily dislodged – a so-called “free” electron. Such a free electron can be influenced by an electric charge. Electric charges have as their principal characteristic the fact that like charges repel each other, and unlike charges attract each other. An atom which has “lost” its free electron will itself aquire a
E l e c t r i c i t y a n d l i g h t
C h a p t e r 1
Part 1 – Foundation chapters
The first two chapters are intended for those who have little or no knowledge of light, electricity and electronics. They include definitions and background technical information which is assumed in the succeeding chapters. Restrictions on space, and the use of only the simplest mathematics, mean that the introduction is cursory, but nonetheless it should help those new to the subject (and those of us who have forgotten our school physics and simple electronics, and just want a reminder!). Readers with a technical qualification in electronics or electrical engineering can safely omit the sections on electricity and electronics, but may still find the sections on light and color useful.
LIGHTING CONTROL – TECHNOLOGY AND APPLICATIONS
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positive charge and is said to be positively ionized; it will then tend to attract a free electron to balance the charge again. However, free electrons are quite mobile in metals, and if an electric charge is applied across a length of metal, it results in a movement of free electrons; which we now identify as an electric current.
Figure 1.2 shows the idea of an electron flow within a metal wire or conductor. The measure of the rate of flow of electric current is the Ampere, often abbreviated to Amp. For our mind picture of electricity it can be thought of as a flow of 6.26 1018 (that is 6.26 multiplied by 1,000,000,000,000,000,000) electrons per second, although for reasons explained later this is not the actual definition of an Ampere.
The measure of electrical charge is the Coulomb. It is defined as the charge transferred when a current of one ampere flows for one second. Since the free electrons creating an electric current are themselves charged particles, the coulomb is equal to the total charge carried by 6.26 1018 electrons.
Next for our model of electricity flow we need to have an idea of what can “push” the free electrons along the conductor. Figure 1.3 shows a simple electrical circuit where a battery is the source of electro-motive force or e.m.f. measured in Volts. When the first electrical discoveries were made, it was a convention that electric current flowed from the positive terminal of a battery to the negative terminal. This convention remains today, even though our “electron flow” model of electricity
×
×
3
shows the free electrons flowing the other way. The more volts applied, the stronger the current. It is also
found that the conductor heats up while the current flows, and that this heating effect is proportional to the square of the current.
The tendency for an electrical conductor to restrict current flow is called its resistance and is measured in Ohms. Table 1.4 shows how the Ohm is defined by the amount of heat produced by a current of one Ampere, and how in turn the Volt is defined as the Potential Difference across a resistance of one Ohm when it is carrying a current of one Ampere. The most useful and most easily remembered relationships which link the main electrical units together are:
Ohm’s Law (Volts = Current in Amps × Resistance in Ohms) which can also be expressed:
and
and the power dissipated in a resistance:
Figure 1.3 The concept of potential difference down the length of a uniform conductor. At any point in the wire, the potential difference is proportional to the length of wire. On the right a hydraulic analogy shows that water pressure drops in a pipe in a similar way. If the tap is closed, then the level in all the columns would rise to match the level in the tank.
Figure 1.2 The idea of free electron flow creating an electric current. At the positive end of the conductor there is a deficiency of electrons, so the free electrons move to fill the space. Conversely at the negative end, there is a sur- plus of electrons “pushing”.
IRV =
RIW 2=
+- Electron flow
= Nucleus with full inner shells and free electron in outer shell
Wire Conductor POSITIVE CHARGE THIS END attracts electrons
Conventional current flow
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(Power in Watts = Current in Amps squared × Resistance in Ohms)
which Ohm’s Law allows us to more conveniently remember as:
(Power in Watts = Potential Difference in Volts × Current in Amps)
Figure 1.3 shows the battery as a source of e.m.f. (measured in Volts) providing a potential difference (also measured in Volts) across the electrical conductor which we can think of as being some kind of heating element. Down the length of the conductor the potential drops in proportion to the length – if you take a Voltmeter to measure the voltage it gets lower along the length of the conductor. A simple hydraulic analogy is shown of water from a header tank losing pressure down the length of a pipe.
In the real world the e.m.f of the battery measured on open circuit (nothing connected) only equals the p.d. across the load resistance when connected if the
battery itself has no internal resistance. If it does have internal resistance, then the actual voltage across the load will be lower. An automobile battery is an example of a battery with very low internal resistance; it can deliver a current of several hundred Amperes at 12 Volts to run a starter motor. A battery set for a portable compact disc player may also deliver 12V as an open circuit e.m.f., but its internal resistance limits the current available (and the actual p.d. at the load). See Figure 1.4.
Figure 1.4 A car battery has negligible internal resistance, so can deliver a full 12V to a lamp load. The same lamp load connected to a small 12V battery might show only half the current flowing through it because of the battery’s internal resistance. (The value shown here has been chosen for simplicity) Thus the p.d. across the load is much less then the e.m.f. of the open circuit battery. The idea that a source of power can itself limit the available current is important.
VAW =
1.2.1 Units
Having introduced the concept of the flow of electricity, it is now necessary to be more rigorous about how it is measured.
The way in which we measure things depends finally on having agreed reference standards, so that
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Quantity Unit Symbol Defined as Length Meter m The length of the path travelled by light in a vacuum during a
time interval of 1/299,792,458 of a second. Mass Kilogram kg The mass of the prototype kilogram kept at Sèvres in France Time Second s 9,192,631,770 periods of vibration of the Caesium 133 atom
(formerly 1/86,400 of the mean solar day). Plane angle Radian rad The angle subtended at the center of a circle by an arc of equal
length to the radius (r). The ratio of a circle's circumference to its diameter (which equals 2r) is . Thus 360° is equivalent to 2 radians, and one radian = approximately 57.3°.
Solid angle Steradian sr The solid angle subtended at the center of a sphere by an area numerically equal to the square of its radius. Since the surface area of a sphere is 4 r2, a sphere subtends 4 steradians.
Temperature Degree Kelvin
K The temperature scale where each degree is numerically the same size as that on the Celsius scale (i.e. there are 100 degrees between the freezing and boiling points of water) but whose zero point is Absolute Zero (the lowest temperature possible where all molecular movement ceases) 0K = 273°C approximately.
Table 1.1 Fundamental units
there is consistency between different methods of arriving at the same result. For example the heat generated by a gas heater or an electric heater must be measured in the same units; or the power developed by an electric motor must be comparable to the power developed by a gasoline engine. It would be very confusing if we had different units for both, although in practice this can happen! For example most people like to talk in terms of horsepower (derived from “imperial” units of measurement) for the capability of a motor, whereas it is in fact easier to work in kilowatts (derived from metric units) when working as an engineer.
Most electrical engineering is now based on SI (Système International d’Unités) units. These are based on the MKS or meter, kilogram, second system, whereby the primary units of length, mass and time are used as the basis of all other units. Thus, while we could define the flow of electric current in terms of the number of electrons passing a particular point per second, it is actually agreed to define it in terms of the mechanical force created by a current carrying conductor, because this way we can relate it back to the MKS primary units.
Originally the meter was related to the dimensions of the earth, and represented by a
physical standard of platinum–iridium kept in Paris. Similarly the second was related to the mean solar day. However, the demand for greater accuracy in measurement has resulted in the meter being related to the velocity of light, and the second to the emission of radiation from a particular atom.
Table 1.1 lists the fundamental SI or MKS units, and Table 1.3 shows how other commonly required
Prefix Symbol Multiplier Example
Pico- p 10-12 Picosecond Nano- n 10-9 Nanometer Micro- 10-6 Microfarad Milli- m 0.001 Millisecond Centi- c 0.01 Centiliter Deci- d 0.1 Decibel Unit- - 1 - Deka- da 10 - Hekto- h 100 Hectoliter Kilo- k 1000 Kilogram Mega- M 106 Megawatt Giga- G 109 Gigahertz Tera- T 1012 Terabyte
Table 1.2 The common unit modifiers.
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mechanical units are derived from them. Table 1.4 then shows the main electrical units, and here it can be seen that by relating the unit of electric current to physical force, and the unit of resistance to measurable heat energy, all the electrical units are “tied back” to the SI fundamental units.
Many of the standard units are inconveniently big or small for certain types of measurement. They are modified by prefixes denoting powers of ten. Some of particular interest to lighting are frequencies such as kHz and MHz; and short wavelengths such as nanometers. Table 1.2 summarizes these prefixes.
1.2.2 Conductors and insulators
In Section 1.1 we identified copper and other metals as being good conductors of electricity, because of the availability of free electrons. Different metals have different conductivity, for example copper, silver and aluminum are good conductors; iron is a conductor, but is poor compared with copper.
The opposite of a conductor is an insulator which in theory should not carry any electricity at all. In Figure 1.1 the gas Neon is shown as an insulator, because its electron shells are full and tightly bound to the nucleus. However, the perfect insulator does not exist. A very strong electric field can “break down” an insulator, or alternatively an insulating gas or compound can be ionized under certain conditions
of heat or pressure so that it becomes conducting. This will be discussed further in Chapter 3.
Another category is the semi-conductor, the best known example of which is silicon. Pure silicon at room temperature is an insulator. But under certain conditions of heat or local impurities it is possible to detach a free electron from the incomplete M shell, at which point silicon becomes a conductor. Semi- conductors are the basis of modern electronics, and are discussed further in Chapter 2.
1.2.3 Resistors
While we usually want a conductor to conduct electricity as well as possible, and an insulator not to conduct it at all, there are times that we need to limit the current flowing in a circuit. This is done with a resistor, which is simply a device which has a known resistance in ohms. Resistors take many forms (Figure 1.5.) At one extreme a heating element for a cooker or electric fire is a resistor, at the other modern electronic circuits use tiny resistors often with values in the kilohm or megohm range. The size of a resistor will depend on the way in which it is to be used.
Because a resistor dissipates heat in direct proportion to its resistance in ohms, and in proportion to the square of the current going through it; it must be designed to get rid of this heat. A resistor in an
Quantity Unit Symbol Defined as Frequency Hertz Hz The number of repetitions of a regular occurrence within one second.
Formerly cycles per second. Force Newton N The force which, when applied to a mass of one kilogram, gives it an
acceleration of one meter per second per second. Force in N = Mass in kg Acceleration in m/s2
Energy (or Work)
Joule J The work done when a force of one Newton acts for a distance of one meter in the direction of the force. Energy and heat are directly equivalent, so heat is also measured in Joules. (The SI avoids the use of the calorie; but a Kilogram-calorie, beloved of dieticians and the heat required to raise a kilogram of water by one degree Celsius, is found by experiment to equal 4187 Joules.)
Power (or the rate of doing work)
Watt W Work being done at the rate of one Joule per second. (The imperial based horsepower is 550 ft lb/sec, which converts to 746 watts.)
Pressure (force per unit area)
Pascal Pa When a force of one Newton is applied across an area of one square meter, the force is one Pascal. (One Bar is 105 Pa. Comparing with imperial measurement, one Pa is 1.45 10-4 lb/sq. in.)
Table 1.3 Derived units (mechanical).
Electric Current I
Ampere A One Ampere is the constant current which, if flowing in two infinitely long parallel conductors, of negligible cross-sectional area, in a vacuum and placed one meter apart, creates between them a force of 2 10-7 Newton per meter length.
Electric Charge Q
Coulomb C The quantity of electricity transported when a current of one Ampere flows for one second.
Electric Resistance R
Ohm The resistance of a conductor is one Ohm if a current of one Ampere flowing for one second generates one Joule of heat energy.
Electric Potential V
Volt V When a resistance of one Ohm carries a current of one Ampere, the potential difference across the resistance is one Volt. Ohm's Law can be stated as V=IR
Electric Energy E
Joule J The physicist James Joule determined that the heating effect in a wire conductor was proportional to the square of the current flowing I, to the resistance of the wire R, and to the time the current flows t, i.e.
E I2Rt (symbol means “proportional to”)
As shown above the definition of the Ohm is based on E = I2Rt when E is in Joules, I is in Amperes and t in seconds
Electric Power P Watt W One Joule per second, so, from the basis of E above Power in Watts = I2R
Applying Ohm's Law, the alternative Power in Watts =
Current in Amperes Potential Difference in Volts
Or Watts = Amps Volts
is the more convenient and easiest form to remember. Electric Capacitance C
Farad F If the potential across the plates of a capacitor rises to one volt as a result of being charged with one coulomb, then its capacitance is one Farad. In practice this unit is too large for most purposes. The microfarad ( F), and nanofarad (nF) are common measures in electronics.
Electrical Inductance L
Henry H A circuit (or coil) has an inductance of one Henry if an e.m.f. of one volt is induced across it when the current changes at the rate of one Ampere per second. Again this is a large unit and mH and
H are widely used. Magnetic Flux
Weber Wb The magnetic flux which, linking a circuit of one turn, produces in it an e.m.f. of one volt as it is reduced to zero in one second at a uniform rate. But more strictly derived from the definition of flux density.
Magnetic Flux Density B
Wb/m2
(or T) A magnetic field has a flux density of one Weber per square meter if a conductor placed at right angles to the field and carrying a current of one Ampere, has a force of one Newton per meter acting on it.
Table 1.4 Electrical and magnetic units, showing how they are derived from the mechanical units in Tables 1.1 and 1.3
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Figure 1.5 Examples of resistors. The circuit symbols for resistance, and some simple laws about using resistances in series and parallel. A variable resistor is a two terminal device; a potentiometer has a similar construction but is a three terminal device; a voltage is applied across the ends of the resistance element, and the moving contact has a varying potential difference (voltage) according to its position along the resistance.
Figure 1.6 Resistance varies with temperature. On the left a 100W tungsten lamp has the voltage presented to it changed by a variable resistor. Current through, and voltage across, the lamp are measured by A and V. The resistance can be calculated, and plotted against the voltage, and this shows that at proper operating temperature the filament has more than ten times the resistance it does when cold.
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electronic circuit may only need to dissipate a few microwatts, or at most a watt or so. A resistor for use as a current limiter in a lighting or motor circuit may have to dissipate a kilowatt.
There is a complication about resistance which is highly significant in lighting. In most materials it varies with temperature. Figure 1.6 shows a simple experiment in which a 100W light bulb is connected to a 230V mains supply via a suitable variable resistance to change the potential across the lamp. A voltmeter measures the volts across the lamp, and an ammeter measures the current through it. Using Ohm’s law it is possible to calculate the resistance for different voltages. The graph shows that when no current is flowing the lamp has a resistance of 50 ohms – but when the lamp filament is running at its rated operating temperature, its resistance has risen to over 500 ohms.
The variation of resistance with temperature is defined by the temperature coefficient of resistance. The resistance of pure metals rises with temperature; whereas the resistance of carbon, silicon and insulating materials drops with temperature. Special alloys (such as Eureka, a 60/40 mixture of copper and nickel) have practically no change in resistance over a wide range of temperature and are used in applications where the resistance must remain constant.
1.2.4 Capacitors
A capacitor (also formerly known as a condenser) consists of two conducting surfaces separated by an insulating layer called the dielectric. The plates (or electrodes) can be flat metal plates, and the insulator between them can be air; but as a practical component capacitors usually consist of thin plastic films on which layers of aluminum have been deposited, or are thin metal sheets with an electrochemically derived insulating layer – see Figure 1.7.
An “empty” capacitor has no potential difference between its electrodes, but if an electric field is applied across them the capacitor “charges up”. The process is shown in Figure 1.8(a).
R VI =
Figure 1.7 The principle of a capacitor (a), and (b) a possible construction using metallized film or paper.
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At first the switch S is in a center-off position. There is no voltage across the capacitor C. If the switch is closed to terminal b, a battery is connected to the capacitor through a resistance R. Measurement of the current through the capacitor by ammeter A, and the voltage across it by Voltmeter V, gives the curves shown in Figure 1.8(b) with respect to time.
The initial current is high, but as the voltage across the capacitor rises, the current drops to zero. The “charging time” is found to be limited by the resistor R. Double the resistor value, and the initial charging current halves, and the time to full charge is doubled. If the switch is returned to its center-off position, the voltmeter V will continue to show the full battery voltage across the capacitor – and in a perfect capacitor it will hold the charge indefinitely. Now if the switch is turned to the d position, the current and voltage will behave as shown in Figure 1.8(c) as the capacitor discharges.
Figure 1.8(d) shows a hydraulic analogy of the operation of a capacitor. In the top cylindrical chamber there is a rubber diaphragm stretched across the cylinder (= the dielectric). In the bottom cylinder the piston can increase the pressure on one side of the diaphragm and move more fluid into the top chamber (= the battery applying an e.m.f.)
If the force is removed from the piston, the diaphragm springs back and forces the fluid back again (= capacitor discharging). No fluid can get from one side of the diaphragm to the other under normal circumstances. However, if it is subjected to excessive pressure, it bursts. Exactly what happens when a capacitor is subjected to too high a voltage.
Table 1.3 defines the ability to store charge in a way which can be expressed as a simple equation:
or
Practical capacitors used in lighting and electronics are usually measured in microfarads or mF. Their capacity can be related to their physical dimensions by the equation:
Figure 1.8 Charging and discharging a capacitor. Fig- ure described in the main text.
Capacitance in Farads
C V Q =
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where C is the capacitance in Farads, A is the area of the capacitor plates in square meters, and d is the distance between the plates in meters.
εεεεε0 is the permittivity of free space (or vacuum) a quantity which can be determined experimentally as having a value of about 8.85 × 10-12 F/m. It relates the electric force, or field strength across the capacitor plates measured in V/m to the electric flux density measured in Coulombs per square meter. (It also has a deeper significance, referred to in Section 1.6.)
εεεεεr is the relative permittivity of the dielectric material. For a vacuum this is unity (one). For other materials it is higher, for example for paper it is 2- 2.5. Plastic films have a relative permittivity of 4-6.
Sometimes ε0εr is shortened to ε and is referred to as the dielectric constant of the material concerned. From an electrical power point of view a most important characteristic of a capacitor is that in any practical circuit containing even the smallest amount of resistance, it is not possible to change the voltage across a capacitor instantaneously. Figure 1.9 gives some more summary information about capacitors.
1.2.5 Inductors
Electricity and magnetism are inextricably mixed. The fundamental discoveries of electromagnetism were: • when a conductor carries an electric current a magnetic field surrounds the length of the conductor. • if a conductor is moved in a stationary magnetic field, then an electric current is induced in it. Conversely if a magnetic field moves with respect to a stationary conductor, an electric current is induced in the conductor. This is the basis of electricity generation. • if a conductor carrying an electric current is placed across a magnetic field, a force is exerted on the conductor. This is the basis of electric motors.
Any magnet has a “north” and “south” pole (named after the way small magnets align themselves with the earth’s magnetic field, as in a compass) and we are all familiar, from magnetic toys, with the way that like poles repel, and unlike poles attract. The
same happens with magnetic fields produced electrically – a force is produced which causes the affected items to repel or attract each other.
The definition of the ampere given in Table 1.4 is based on the idea that any current carrying conductor creates a magnetic field, but also a conductor carrying a current in a magnetic field has a force exerted on it.
An inductor consists of a coil of wire, usually, but not necessarily, wound on a core with
Figure 1.9 More about capacitors.
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it is sufficient to see what happens when an inductor is placed in a simple circuit – in the same way we considered capacitors in 1.2.4 above.
Figure 1.10 shows a simple inductor, and the way a magnetic field is created by it. In Figure 1.11(a) a circuit is shown containing an iron cored inductor, arranged in a way that confines the magnetic field largely within the core. The circuit also contains a resistor R and two ammeters, one of which is “center-zero”.
Closing the switch S connects the battery to both the resistor and the inductor, and results in the currents shown in Figure 1.11(b). The current through R jumps immediately to the value determined by Ohm’s law. But that through the inductor takes time to reach a steady level (which does indeed reach a value limited by the resistance of the coil – but only when the steady state is reached does Ohm’s law apply as usual).
What slows the current rise? The current produces a magnetic flux in the core; but because this flux is changing, it itself introduces an e.m.f. back in the coil. Lenz’s Law states that when this happens, the e.m.f. is always in the opposite direction to that which is creating the flux. This effect limits how fast the current can rise in the coil – in an inductor it is not possible to change the current
Figure 1.10 A simple inductor, showing the magnetic field. The field is more intense when there is an iron core, and the iron magnetizes.
Figure 1.11 Experimental circuit showing the effect of inductance in a DC circuit (a). The switch on and switch off currents are shown in (b). IL is the switch-on current through the inductor, and IR the switch-on current through the resistor. Ib is the switch-off current, which goes through the resistor in the opposite direction to IR and arises from the back e.m.f. of the inductor. The magnetic flux in the inductor core builds up during switch-on, and collapses at switch- off.
ferromagnetic (or iron-like) magnetic properties. The details of different kinds of inductors relevant to lighting control are given in later chapters, for now
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instantaneously (compare the capacitor – where it is not possible to change the voltage instantaneously).
If switch S is now opened, an interesting thing happens. The original source of e.m.f. has gone, so the current drops in the coil – but this creates a change in flux again and, therefore, an e.m.f. The only way for its resulting current to go is through the resistance R – the center-zero ammeter now shows a decaying current in the opposite direction to that originally flowing through R.
What happens if there is no resistance R in the circuit? Opening the switch S produces a rapid current change, therefore a rapid flux change. Therefore, in turn, a big “back e.m.f.” which in practical circuits can result in arcing (sparks!) at the switch. Even in the simplest circuits using inductive components precautions have to be taken to limit the effects of back e.m.f.
1.2.6 Magnetic units
In the discussion on capacitors, the concept of permittivity was introduced to describe how different materials are affected by an electric field. A similar idea applies to inductors and magnetism, where permeability is the description of how materials are affected by magnetic fields. Since magnetic properties are fundamental to ballasts and transformers used in lighting control, some understanding of magnetic units is important.
We have described an electric current in a circuit as being due to the presence of electromotive force. In electromagnetism we can postulate that in a magnetic circuit a magnetic flux is created by the presence of magnetomotive force (or m.m.f.) caused by a current flowing through one or more turns in a coil. Since the m.m.f. is proportional both to the current and the number of turns, the unit of m.m.f. in the MKS system is the ampere-turn.
Figure 1.12 shows a toroidal coil with T turns carrying a current I. The mean length of the magnetic circuit is l meters. The magnetizing force H is defined as the m.m.f. per unit length, so:
H = IT/l ampere turns/meter
The strength of a magnetic field is termed its magnetic flux density B. This is measured in Webers per square meter, or Tesla, and is defined by relation to the ampere, see Table 1.4. To see how B and H are related we need to do a small thought experiment.
Figure 1.13 shows a long thin conductor in a vacuum A. It is carrying current of one ampere in the direction of the paper. Let us suppose that the return path of this current is a long distance away, so any magnetic field the return path generates does not affect things.
The magnetic flux created by the current is in the form of concentric circles. What is sometimes referred to as Maxwell’s corkscrew rule says that the direction of the flux is clockwise if the current is flowing away from you as in Figure1.13. In this figure just one line of flux is shown, at a distance of one meter from the conductor.
Since the conductor (and its return partner) form one turn, the m.m.f. acting on the flux path is one ampere-turn. The length of the flux path (2πr where r is one meter) is 2π meters. Thus the magnetizing force acting at one meter radius is:
or:
Now let us imagine a second conductor A´ sited one meter away from A, and also carrying one
Figure 1.12 Defining the magnetizing force H. Here a toroidal inductor has magnetic circuit length L meters, has a coil of T turns and is carrying a current I Amperes.
H=1/2π ampere-turn/meter
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ampere. The definition of magnetic flux density gives us the equation:
Force on conductor in Newtons = Flux density in Wb/m2 X length in meters X current in amperes.
So for A´ we have:
Force per meter = B (Wb/m2) × 1 m × 1 A = B Newtons
But we know the force acting under these circumstances, because our thought experiment has replicated the conditions which define the ampere (see Table 1.3). The force is 2 X 10-7 N. So now we can say that:
the flux density B at one meter radius from a conductor carrying a current of one ampere is 2×10-7 Wb/m2.
And further, if we compare the flux density at A´ to the magnetizing force at A´, we now have:
represented by the symbol μ0 and applies not only to vacuum but also to non-magnetic materials.
The magnetic flux inside a coil such as that in Figure 1.12 or 1.10 is greatly increased if an iron or other magnetic core is introduced. Magnetic materials are defined by their relative permeability, μr such that:
B= μrμ0H
While the relative permeability of air and other non magnetic materials is 1, that for special nickel– iron alloys can be as high as 100,000.
If measurements are made on different materials of the effect of increasing magnetizing force H on the flux density B, a graph of the kind shown in Figure 1.14 is found. Here it is assumed that the experiments started with unmagnetized material. The increase in flux density follows the curve OAC, but beyond a certain value of H the value of B reaches a limit. The material is said then to be magnetically saturated.
If H is now reduced to zero, the value of B does not go down to zero, but retains a remanent flux density OD (usually between 60 and 75% of the maximum). A reverse magnetizing force OE, known as the coercive force is required to return B to zero. If the reverse force is increased, point F can be reached where the material is now saturated in the other direction.
If the cycle is continued, by reversing H again, the curve follows FGC. The complete loop resulting from a double reversal of magnetizing force is called the hysteresis loop. The “fatter” the curve, the more effort is needed to take the magnetic material through a flux reversal.
1.2.7 Inductance
The unit of measurement of the ability of an inductor to slow down a rise in current, its inductance, is the Henry, defined in Table 1.4. For an air cored coil of the kind shown in Figure 1.12 the inductance is: • proportional to the square of the number of turns
of wire T. • proportional to the cross sectional area of the core
a.
Figure 1.13 Defining the magnetic flux density B. Imagine the conductor A as perpendicular to the paper, with current flowing into the paper. Maxwell’s corkscrew rule says the magnetic flux is in a clockwise direction.
7104 H B −×π=
or
The ratio B/H for the conditions we have defined is referred to as the permeability of free space. It is
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• inversely proportional to the length of the magnetic circuit l. In fact:
When the air core is replaced by an iron or other magnetic core, the situation becomes very complicated. The magnetization curve Figure 1.14 shows that the variation of flux is not linearly proportional to the current (which causes the magnetizing force) – so a coil can have a lot of different inductance values depending on the range of current variation.
However, our interest in inductance is primarily concerned with alternating current (described in Section 1.3.2) where the current changes direction repeatedly. If μr is the relative permeability of the core material corresponding to the maximum value of the flux (point C on Figure 1.14) and it is understood that the relevant use of the inductance involves repeated flux reversals (to point F) then it is assumed that the value of the inductance is the
same as if the flux varied linearly along FOC, and, therefore, that the inductance of the coil becomes:
1.3 Electrical distribution
1.3.1 Direct current sources
In the concepts presented so far, only circuits using Direct Current or DC have been mentioned. With the exception of the changes in current or voltage introduced by capacitors or inductors, the circuits have been “steady state” with current flow conventionally seen as flowing from positive to negative.
DC is essential for the operation of most electronic components, and is most familiar to us as being supplied by batteries. A battery is in fact a group of electrochemical cells whose action is to convert chemical energy to electrical energy. Primary cells or batteries are “use once” devices, exemplified by the common zinc/carbon dry battery. Secondary cells are rechargeable devices, where the chemical reactions leading to the generation of electricity can be reversed, and are exemplified by the standard automobile battery.
Figure 1.14 The relationship between flux density B and magnetizing force H is not linear, and displays hysteresis.
Figure 1.15 Examples of batteries. Battery capacity is given in ampere-hours, thus a 2Ah battery can sustain a current of 2A for one hour or 500mA for 4 hours.
1.2v 300mAh battery used in cordless control
3.6V 4Ah rechargeable battery used in emergency
light fitting
Henrys l
aT104 LcetanInduc
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Trigonometry
In our treatment of electrical units and electricity, we are keeping mathematics to a minimum; using where possible simple algebraic formulae with each symbol clearly defined. In describing alternating current it is necessary to use simple trigonometry. For those who have forgotten the basic relationships, here they are:
In the right angled triangle in Figure 1.16 the angle θθθθθ is identified, as are the three sides of the triangle:
• the hypotenuse which is the longest side opposite the right angle, the length of which is identified here as H.
• the adjacent side which is the side next to the angle θθθθθ. Identified here as having length A.
• the opposite side, which is the side opposite to the angle θθθθθ, identified here as having length O.
The following relationships apply:
O2 + A2 = H2 (Pythagoras’s Theorem)
The Sine of the angle θ = O/H The Cosine of the angle θ = A/H The Tangent of the angle θ = O/A
Sine, Cosine and Tangent are abbreviated to Sin, Cos and Tan in mathematical expressions. A mnemonic for remembering the above is:
Old Always Other Hands Help AviatorsFigure 1.16 Simple trigonometry. Defining the sine, co-
sine and tangent of angle θ.
Figure 1.17 A force F acts on an object at angle θ to the horizontal. If the line OF represents the magnitude and direction of the force; it can be resolved into horizontal and vertical components of forces H and V, represented by the lengths of OH and OV. Conversely, if there are two forces acting on an object, there is a resultant force whose magnitude and direction lies between them.
Figure 1.15 shows some examples of batteries. The demands of portable electronic equipment, emergency power supplies and electric traction have resulted in considerable developments in battery technology.
DC is also derived by power conversion from AC, and this is described in Chapter 2. It can also be generated by DC generators or dynamos, but this is not now generally relevant to lighting.
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F cos θ is the horizontal component, and F sin θ is the vertical component
But there is an important concept here, which will be appreciated as we look further into how alternating current, described in the next section, behaves. That is that, if you have two vector components acting in two different directions, you have a resultant single vector – and while this is quite easy to appreciate when dealing with a force, it may not be so obvious when you are dealing with an electric current.
1.3.2 Alternating current
The electricity which arrives in our home is Alternating Current or AC. The reason for this is that it is both easier to generate, and easier to distribute. To understand why this is so, it is necessary to understand how an alternator (or AC Generator) works.
Figure 1.18 shows a rectangular loop conductor rotating in a magnetic field. A conductor cutting magnetic flux generates an e.m.f. but here the conductor is not always cutting the flux at the perpendicular. When the loop is vertical the conductors are parallel with the flux, and no e.m.f. is generated, when the loop is rotated 90° the loop is cutting across the flux and maximum e.m.f. is generated. The instantaneous e.m.f. is proportional to the sine of the angle at which the conductor cuts the magnetic flux.
Figure 1.19 shows how a sine wave is produced by this action. It also shows another “mind picture” of how a rotating vector produces the sine wave. A vector quantity is one which has both magnitude and direction (for example speed is a scalar quantity, having magnitude only, whereas velocity is a vector quantity which must always be specified in both magnitude and direction). The magnitude in both cases can be km/hour or m/s or m.p.h. as appropriate.
Notice here how the use of angular velocity ω, measured in radians per second simplifies the mathematics, since there are 2π radians in each revolution.
A version of the device shown in Figure 1.18 could be used for generating AC by connecting pick- up brushes to both ends of the conducting loop as shown in the diagram. (Indeed a very rough DC could be derived by having a “commutator” arrangement which switched the direction of current to the outgoing circuit every half revolution.) However “real” alternators of any size work the other way round. They have static conductor coils, which are then easily connected to the outside world without the need for any pick up brushes; and the moving magnetic field is produced by rotating electromagnets. These are powered by DC, traditionally generated by a dynamo on the same shaft as the main alternator, but now also derived by converting from AC.
An important use of trigonometry is in “resolving” forces, and in defining the contribution of a vector quantity (a vector quantity is one which has both magnitude and direction) in a particular direction.
Figure 1.17 shows the principle of resolving a force into two different components. A force of F Newtons is acting on an object at an angle θθθθθ. If we want to know the horizontal and vertical components of the force, we draw the rectangle shown, with the length of the diagonal corresponding to the magnitude of the force. The lengths of the sides of the rectangle now represent the horizontal and vertical components of the force, and it can be seen that:
e.m.f. generated in one side of loop = Blv sin θθθθθ volts
Where B is the flux in Wb/m2, l is the length of one side of the loop, v is the velocity of the conductor through the flux and sin θθθθθ is the resolved component of that velocity perpendicular to the magnetic field.
Without needing to worry too much about the details of this equation, it is clear that the more and longer conductors there are, and the faster the loop rotates, the more volts will be produced.
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Figure 1.18 Creating an alternating current. On the left a loop conductor being rotated in a magnetic field (shown in the position of rotation θ=90°). On the right it is shown that maximum e.m.f. is generated when the conductor cuts the flux at right angles (rotation angle 90°) and no e.m.f. is generated when the conductor is moving in the same direction as the flux lines (rotation angle 0°).
Figure 1.19 If the value of r sin θ is plotted at equal increments along an axis, a sine wave is the result, as shown on the left. On the right we see the idea of a rotating vector producing a sine wave. The horizontal axis can represent both the angle of rotation and time (if the angular velocity is known). If the vector length represents a current of maximum value IM the waveform is that of an alternating current.
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Figure 1.20 shows the principle of an alternator. AC does not have to be sinusoidal (sine wave shaped) and many other waveforms exist, especially in electronics. But for power distribution it is the most efficient waveform, so alternators are designed to give a sinusoidal output. (To be technically correct it should be noted that the alternator construction implied by the two arrangements shown in Figure 1.20 would not give sinusoidal output without some refinement.)
To make better use of the alternator frame, and to assist with power distribution, AC is often produced in three phase form. Here the alternator simultaneously produces three different sine waves, but each of these is timed to peak at different times. The idea is shown in Figure 1.21, and a real alternator is shown in Figure 1.22.
In the USA, electricity is generated at 60Hz (cycles per second) in Europe it is generated at 50Hz.
1.3.3 AC circuits
In Section 1.2 many of the basic rules about electricity were given in relation to DC circuits. Unfortunately they need some “tweaking” when applied to AC.
First we need to know if Ohm’s law and the simple power calculation rules still apply. Clearly it is no use taking “average” current and voltage, since these are both zero if the waveform is symmetrical.
The way forward is to say that the effective value of an alternating current is that which produces the same heating effect in a resistance as does a direct current of the same numerical value. We can do a comparison by “slicing up” an AC waveform.
In Figure 1.23 we show n instants at which current is measured in a half cycle. The instantaneous heating effect at each instant is in
2R. So we can say
Figure 1.20 The single phase alternator. The left hand diagram shows the principle with a single 2-pole magnet. The right hand diagram shows an 8-pole magnet system. In a real alternator the magnets are electromagnets fed by a DC supply.
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that the average heating effect over the whole half cycle is:
Now if we say that I amperes is the Direct Current through the same resistance R which gives the same heating effect as the average heating effect of the AC, we have:
Therefore:
In words, the current equals the square root of the mean of the squares of the current.
The r.m.s. or root mean square values of current and voltage are used whenever AC supplies are specified. Ohm’s Law and the relationship Watts = Amps × Volts both work when applied to resistive loads.
Some other aspects of the sine wave are shown in Figure 1.24.
An interesting point arises with 3-phase AC. Usually each phase can be considered as an independent supply, requiring two wires. In most electrical systems one side of the supply is connected to earth or “ground”. It is referred to as the Neutral connection, and the other side is called the Live (or “Hot”) connection. You get an electric shock off the live connection, but not off the neutral connection (provided it is well bonded to earth) because the neutral is at the same potential as you are if you are standing on the ground.
In a 3-phase system the three neutrals are obviously joined together if they are all to be at ground potential. If you look carefully at a 3 phase waveform as in Figure 1.21 you can see that at any instant the three currents add up to zero – for example if at any one moment there are two positive currents and one negative, the sum of the two positives
Figure 1.21 The principle of the 3-phase alternator. The top diagram shows how the three sets of stator coils are set at 120° (or 2π/3 radians) apart, the bottom diagram shows the relationship of the three waveforms.
Figure 1.22 A power station generator under construction. This one is from Siemens AG, and is rated at 1,000 MVA, with output at 27 kV. It uses hydrogen cooling to achieve a comparatively small frame size. The rotor carrying the rotating electromagnets is being inserted into the stator assembly, the coils of which collect the induced alternating current.
n Ri.................RiRiRi 2
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exactly equals the negative. The vector representation of currents helps make this clear.
A 3-phase system with common neutral is referred to as a “star” or “Y” system, and its feature is that if the load on all phases is equal there is no neutral current. Power system design usually calls for balancing the load on the three phases in order to minimize or preferably eliminate neutral current. This is of great significance in lighting systems.
While the r.m.s value of the voltage on a single phase in a 3-phase system is the same for each phase
Figure 1.23 Finding the heating effect of AC. Imagine the sine wave to be divided into many small sections, of current value i1 i2 i3 and so on to in. Each little chunk of current will make its own i2R heating contribution.
Figure 1.24 Peak, r.m.s. and half wave average values of a sine wave. For all symmetrical waveforms the form factor is the ratio of r.m.s value to average value (1.11 for a sine wave) and the crest or peak factor is the ratio of the peak value to r.m.s. value (1.414 for a sine wave).
Figure 1.25 3-phase electricity. (a) shows the concept of three simultaneous rotating vectors, 120° apart. (b) shows a 3-phase alternator with Y output and Y connected loads; and (c) shows a 3-phase alternator with delta output ( ) and delta connected loads.
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(for example 230V in Europe and 115V in USA in the home) the voltage across phases is much higher (and more dangerous). The r.m.s voltage across two phases is √3 × the single phase voltage (about 398V when the single phase voltage is 230V).
There is another way of distributing 3-phase AC, arising from the fact that the vector sum of the e.m.f.’s is zero. This is to do away with the “neutral” connection altogether, and connect the alternator windings in a “mesh” or “delta” format. Figure 1.25 shows the idea. Vector considerations of the current show that the current in each load line is √3 times the current in the phase winding of the alternator. The arrangement is particularly suitable for powering big electrical motors. It is also encountered in some electical distribution systems (for example in Norway and on board many ships) and this has some consequences for lighting control systems.
1.3.4 Transformers
In any simple electrical system, the power delivered to the load is the product of the voltage and the current. If we want to transfer 10kW of power, we can do it in several ways:
• at 10 Volts, we would need a current of 1,000A • at 200 Volts, the current is a reasonable 50A • at 10,000 Volts, the current is only 1A
High currents mean very big conductors if there is not to be significant heat loss in the conductor due to the conductor’s resistance. The heat effect is proportional to the square of the current, so a cable resistance of one ohm would result in 2,500W being dissipated by the 50A current, but only 1W by the 1A current.
Thus for electrical distribution the power generated at the power station’s alternator at around 20,000 Volts (20kV) is “stepped up” for primary distribution to as much as 400kV. Local distribution may be done at 11kV or 33kV, requiring a “step down”. Final distribution to the home and office requires a further step down to 230V or 115V depending on where you live.
The voltage conversion process is done by a transformer. A transformer extends the principle of the inductor described earlier. A typical construction is shown in Figure 1.26. A coil is wound on an iron core and is fed from an AC supply. A second coil is mounted on the same core. When the current changes in the first coil or primary winding, it produces a change in magnetic flux, and this flux change must cut the conductors of the second coil. A current is, therefore, induced in the secondary winding, through mutual inductance – the process where two coils share the same magnetic flux.
In the description of the inductor in Section 1.2.5 its behavior was discussed in relation to the application or removal of a direct current. This showed that the current reached a steady value and the coil circuit obeyed Ohm’s law once the steady state was reached. If we were to apply DC to a transformer, the same thing would apply. The current induced in the secondary would be momentary, and all that would happen is that the transformer would cook due to the high current and low coil resistance of the primary.
Figure 1.26 Construction of a transformer.
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But with AC the current, and, therefore, the magnetic flux, is constantly changing. There is a continuous back e.m.f. limiting the current in the primary, and the current in the secondary follows that of the primary.
In a perfect transformer (and in fact most power transformers are quite efficient) all power put into the primary can be extracted from the secondary. For reasons explained in Section 1.4, transformer ratings are always given in VA (or VoltAmps). Figure 1.27 shows a 300VA transformer intended for use for lighting operating at 12V. This means that if it is fed with AC at 230V, the primary current is 300/230 = 1.3A. At the secondary, rated for 12V, there is a total of 300/12 = 25A available.
The Ampere/Turns must be the same for the primary and secondary (clearly the transformer cannot actually create energy). Therefore:
But also:
So:
In the example transformer, the 230V primary winding might have 400 turns, thus to give 12V at the secondary, the secondary winding needs only 21 turns. The turns ratio determines the voltage ratio.
Good transformer design confines most of the magnetic flux close to the transformer core, so all of it is used to induce e.m.f.’s into the conductors. Power transformers working at 50 or 60Hz use special transformer iron alloy to provide the core. Being metal, this is a conductor – therefore the moving magnetic flux must induce electric current into it.
The current so induced is called an eddy current because it circulates within the metal. Eddy currents cause heating, like any other current, and could be responsible for serious losses in transformers (and, of course, other electromagnetic devices, including alternators and motors). The problem is solved, if not entirely eliminated, by using a laminated construction for the transformer core. See Figure 1.28.
The laminations are insulated from one another, and in this way any eddy current is confined to a single lamination. An example illustrates how effective the technique is.
Suppose we substitute a single core piece with ten laminations: • the e.m.f. per lamination is only one tenth of that
generated in the solid core.
Figure 1.27 Example of a transformer used for lighting – a step-down transformer for low voltage tungsten halogen lamps. (Photo from Relco.)
Figure 1.28 Electromagnetic devices working at 50/60Hz use iron alloy laminations to minimize the effect of eddy currents.
voltsPrimary turnsPrimary turnsSecondary
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• the cross sectional area is also reduced to one tenth, so the resistance goes up ten times; this reduces the current by a further factor of ten.
The current per eddy path is thus reduced to 1/100th of what it would be in the solid core. In fact the eddy current loss is proportional to the square of the thickness of the laminations, so within reason the aim is to use the thinnest laminations practicable.
An important feature of most transformers is that primary and secondary windings are completely separate; the power transfer is achieved entirely by induction. For many applications this is essential for safety or signal isolation reasons. In an autotransformer only a single tapped winding is used (Figure 1.29).
Transformers used at high frequencies work on the same principle but use a different construction, described in Chapters 6 and 7. The iron alloy used in low frequency transformers has pronounced hysteresis, making it unsuitable for high frequency operation.
1.4 Power factor
1.4.1 Reactance
The description of the transformer has introduced the idea that some loads may behave differently to simple resistances when connected to an AC supply. If we consider what happens when a pure inductance (i.e. an inductor with no resistance and no capacitance) or a pure capacitance (a capacitor with no inductance and no resistance) is connected to an AC supply we find the voltage and current get “out of phase”.
In an AC circuit with a resistive load, the current in the load is exactly in phase or “in step” with the applied voltage. But this is not the case with capacitance and inductance.
Figure 1.30 shows a sine wave of current flowing through a pure inductance. The instantaneous value of current is Imax sin ωt. Now the voltage across an inductance is given by the inductance multiplied by the rate at which the current is changing. Mathematically this can be stated as:
Where e is the voltage, L the inductance in Henrys, and di the change of current in small time dt. The negative sign arises because the induced e.m.f. is in the opposite direction to the applied current.
The rate at which the current is changing at any instant corresponds to the instantaneous slope on our sine wave current curve. If we plot the value of this
Figure 1.29 The autotransformer has only a single tapped winding.
Figure 1.30 AC flowing through an inductance. The top sine wave is the current. The bottom curve is a plot of the gradient (or slope, or rate-of-change, whichever you find easiest to imagine) of the current sine wave. It turns out to be a cosine wave, which is simply another sine wave 90° (or π/2 radians) out of phase with the first one.
dt diLe −=
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slope against time, we find we get another curve looking the same, but out of phase with the current curve. It is a cosine curve, which is exactly the same as a sine curve, but 90° (or π/2 radians) out of phase. It is at its maximum when the current is zero, and at zero when the current is at its maximum.
This sounds counter-intuitive, but what is happening is that the external AC supply puts energy into the inductance, but the induced e.m.f. puts the energy back into the supply. A mechanical analogy is that of the pendulum – when the pendulum bob is stationary, as it is changing direction at its highest point, it has maximum potential energy (voltage) but no movement (current); and as it passes through its lowest point, it is moving fastest (highest current) but has no potential energy (voltage).
What limits the current through a perfect inductor? Is there an equivalent of resistance? There is, it is called the inductive reactance with symbol XL. It is the ratio of r.m.s. voltage to r.m.s. current, and is, therefore, measured in ohms.
We can derive the formula for reactance in several ways, but the easiest is using simple calculus. Start with the equation:
Which is the description of our current sine wave. Differentiate this with respect to time to obtain the slope of the curve at any time (remember this is the rate of change of current with time).
(This is a mathematical shorthand for describing the lower curve in Figure 1.30. It says that any point on the curve representing a particular value of di/dt, or rate of change of current, can be calculated by the instantaneous value of ωImax cos ωt.)
Going back to the equation e = - L di/dt, we can substitute the general expression for rate of change with the curve value (ignoring the - sign):
For any angle θ, Cosine θ = Sine (θ + 90°) so we can write:
But in magnitude terms we know that Imax sin (ωt + 90°) is the same as Imax sin ωt (but advanced by 90°) and this equals the instantaneous current i. So we have in magnitude:
We have defined the inductive reactance XL as e/i so we have:
Now ω is the angular velocity of the current vector in radians per second, but this is the same as 2πf, where f is the frequency of the supply.
Even if you have not followed the mathematics completely, the end result
is interesting. It tells us that the reactance is not simply proportional to the inductance, but also to the frequency of the AC supply. The higher the frequency, the higher the reactance.
The same kind of analysis can be applied to a pure capacitance. This time we start with the equation:
That is to say, the instantaneous current equals the capacitance multiplied by the rate of change of voltage dv/dt. This time it is easiest to start with the voltage sine wave, and create the the current waveform from it (by the same procedure of plotting the new curve of instantaneous dv/dt).
We find that, whereas with inductance the current lags the voltage by 90°, with a capacitance the current leads the voltage by 90°, and that the capacative reactance XC is defined by:
tsinIi max ω=
tcosI dt di
fL2X L π=
dt dvCi =
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Again the reactance depends on frequency. This time, however, it is inversely proportional – the higher the frequency the lower the reactance.
Our “mind picture” of what is happening with reactive loads such as capacitors and inductors must not get carried away. It is easy to think of a capacitor “carrying” current through itself, but actually charge is building up cyclically on either side and then falling away. With an inductor, current flows in, to be returned by the back e.m.f. Both devices are temporary stores of energy, and in their pure form do not take heat energy from the supply.
The fact that in both cases the current is 90° out of phase with the voltage means that average VA product is zero. Pure inductive and capacitive loads are sometimes referred to as “wattless”.
1.4.2 Impedance
In any real circuit there is no such thing as a pure inductor or a pure capacitor. Any such device, including any real-world connections to it, includes resistance. Depending on the frequency of operation, an inductor may include significant, in the sense of reactive, capacitance and a capacitor may exhibit some inductance.
The combination of the reactance and resistance in a circuit is referred to as impedance, and is frequency dependent. It is represented by symbol Z. The rules for calculating impedance, and for calculating currents in an AC circuit are more complicated than for simple DC circuits. We could use several different mathematical treatments to explain them, but the simplest way to visualize what is happening is the vector method.
Let us start with the problem of adding two AC voltages, which are not in phase, but separated by a phase difference of angle φφφφφ. What is the resultant voltage? In the vector model we imagine two rotating vectors, each generating a sinusoidal AC voltage. We draw a line OE1 representing the first voltage. The length of the line represents the peak voltage E1, and the instantaneous voltage we designate e1. Figure 1.31(a) shows the idea. (At this stage we are
not bothered about the instantaneous phase situation of e1 but at any time e1 = E1 sin θ, where θ is the instantaneous phase angle.)
Now we do the same for the other voltage, which we envisage as having a peak value of E2 and an instantaneous value of e2. The instantaneous sum of the two voltages can be expressed as:
e = e1 + e2
If we create a parallelogram from the two original vectors, we see that the diagonal of the parallelogram has an instantaneous value corresponding to e. Therefore we can say that the resultant voltage has a peak value E, corresponding to the length OE of the
Figure 1.31 Adding two vector quantities (AC voltages) by the parallelogram method. (a) shows the principle for two rotating voltage vectors with phase difference φ. (b) shows an r.m.s. vector diagram, where V = 0.707E, and the vectors are stationary because time is not involved with r.m.s. values.
)ohms( fC2
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diagonal. Its phase relationship to the constituent voltages clearly depends on both their respective magnitudes and the phase relationship between them, and can be measured directly from the parallelogram model.
We can generalize this approach for r.m.s. voltages and currents. Figure 1.31(b) shows the corresponding r.m.s. vector diagram (where r.m.s. values are 0.707 of peak) and the vectors are considered stationary.
In practice an inductor is a device that has both inductive reactance and resistance, and can be considered as an inductance and resistance in series as shown in Figure 1.32(a). Figure 1.32(b) shows the vector relationship between the resistive voltage (which must be in phase with the current) and the pure inductive voltage, which lags 90° behind it. The line voltage V is the diagonal of the rectangle, and leads the current by φ°.
The figure may be re-drawn as a “voltage triangle” as Figure 1.32(c). But we know in each case that the relationship between voltage and current is V = IR for a resistance, V = IX for a reactance and V = IZ for the circuit impedance. Pythagoras’ theorem gives us:
(IZ)2 = (IR)2 + (IX)2
Z2 = R2 + X2 or Z = √ (R2 + X2)
From the above, the “voltage triangle” idea applies equally to impedance, as Figure 1.32(d).
1.4.3 Power factor
In a typical AC circuit with reactance present, a vector calculation of the resultant current and voltages done on the basis of Figure 1.32 will usually yield a VA product which is higher than the power in watts being delivered to the resistive load.
The power factor in an AC circuit is defined as:
Figure 1.32 (a) shows a resistance and inductance in series. (b) shows the applied voltage V being made up of V1 across the resistance, in phase with the current; and V2 across the inductance, 90° ahead of the current. (c) shows the corresponding voltage triangle, from which we can derive the impedance triangle (d).
Amps.s.m.rVolts.s.m.r watts
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So power factor = R/Z, and from the impedance triangle we can see that:
Power factor = cos φφφφφ
where φ is the phase angle difference between current and voltage.
When the current follows, or lags, the voltage, there is said to be a lagging power factor – as is the case with inductive loads. A leading power factor applies for capacitive loads. Table 1.5 shows the impedance and power factor for the common circuit elements.
Any circuit involving inductance, especially electric motors and electromagnetic fluorescent lamp ballasts, will have a poor power factor of, typically, around 0.5. Why “poor”? Electric utilities companies don’t like low power factors because it means that their generation and distribution plant must be rated for the maximum VA product taken, but their customers only pay for the watts actually used. In practice inductive loads, with lagging power factor,
are the problem – and the problem is solved by applying power factor correction using capacitors to restore the power factor to near unity. This is an important technique for most kinds of discharge lighting.
Today the term “power factor” is used to cover all “wattless” activity. As will be discussed later, many modern power control systems introduce harmonics onto the power line, or, looked at another way, they switch the power on and off very rapidly. The power company only gets paid for the “on” time, and cannot divert the resource during the “off” time which is measured in milliseconds. So they don’t like harmonics, any more than they like their fundamental sinusoidal current and voltage being out of phase.
These factors are highly significant in lighting. When cos φ is quoted on a piece of electrical equipment (typically a fluorescent lighting ballast) it is defining power factor in the traditional way described above, related to a standard power frequency of 50 or 60Hz. The alternative power
Table 1.5 Impedance formulae and power factors.
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factor symbol is λ which is the ratio of watts to all wattless components however they arise.
1.5 Control of electrical power
The control of electric power is divided into two: • at its simplest to be able to connect power to a device (whether it be a giant electric motor, an electric kettle or a bedside lamp) and, just as important, the ability to disconnect it. • at a more sophisticated level, the ability to regulate a power flow. In this case we may want to adjust the speed of the motor, adjust the temperature of the water in the kettle, or the brightness of the lamp.
In this section we review some of the control elements which are relevant to lighting.
1.5.1 Switches
The humble light switch is the most familiar electrical control device. It is no more than a device which makes a physical break in the electrical circuit. However: • The switch contacts must not only be able to carry the running current, they may have to absorb an “inrush” current on switching on (and, indeed, must be able to withstand a short circuit current matching the rating of the fuse or circuit breaker protecting it) and, more importantly, suffer some arcing when switching off. This is particularly the case for DC, and also for inductive AC loads like fluorescent lamps and motors. • The switch contact must have negligible resistance. If it gets corroded by arcing, its resistance goes up, I2R heating sets in, and its resistance goes up still further. Eventually it fails, but it may have caused a fire in the meanwhile. For this reason switch contacts are usually made with precious metal alloys, and are constructed with a “wiping” action to assist maintaining a clean connection. A spring “snap action” is also included to make a fast circuit break. • High power switches used in electrical distribution have their contacts immersed in an insulating oil; or are mounted in an inert or otherwise controlled atmosphere. Any “open air” switches are
mechanically power assisted, and have arrangements for arc quenching.
Figure 1.33 Power factor correction capacitors, as used in fluorescent and high intensity discharge lamp circuits.
Where there is to be a repeated switching action at comparatively high frequency (for example in animating an electric sign) the ordinary switch is no longer appropriate. Before the advent of electronic switches the best that could be done was the use of motor diven switches with “brushgear” contacts or of mercury switches where connection was made through a “liquid contact” of mercury.
Today all high speed switching is done by power electronic components such as the thyristor or power transistor, described in Chapter 2.
1.5.2 Fuses and circuit breakers
All electrical circuits require protection against faults which might either damage equipment or injure people. Fault protection is divided into different types:
Short circuit protection. This protects against short circuits. For example a stage lighting dimmer needs good short circuit protection if a badly wired temporary cable creates a “short”. Short circuits can result in v

Lighting control-technology and applications

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