ElectroMag Survey of Electromagnetic

8/8/2019 ElectroMag Survey of Electromagnetic

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DRAFT 1 July 2004, R.Levine page 1

SOUTHERN METHODIST UNIVERSITY

Department of Electrical Engineering

EETS8302 Advanced Telecommunications Technology

Fall 2004

2004 by Richard Levine

In some cases, students hold concepts that are general and vague. For example, students may

talk about electricity, a word that for them has elements of current, voltage, energy and power all

muddled together. Quoted from Prof. Diane J. Grayson, Centre for the Improvement of

Mathematics, Science and Technology Education, University of South Africa, inAmerican Journal

of Physics, Vol. 72 , No. 8, August 2004, page 1127.

Introduction: Survey of ElectroMagnetic

Theory and Technology

The purpose of this document, and other course

notes, is to give the reader a briefsurvey of basicelectromagnetic science and technology used in

telecommunications. Most of the information inthis document is given without proof. Moredetails will follow in later course notes documents.

Some readers already have a strong background itthese topics, while others do not. What is the bestmethod for explaining these topics to such a

diverse group of readers? There are severaldifferent ways to explain the so-called laws1 of

physics. Some of these descriptions or methodsseem very different from each other at first glance.For example, when studying mechanical systems,

such as a group of objects held together byattractive forces due to mechanical springs, we can

say that objects that exert forces on each other arestationary or are in equilibrium when the sumof all theforces acting on each pair of objects in

the system combine to produce a zero net force, ortotal force, on each object. We can alternatively

say that the system of objects is in equilibriumwhen the energy related to all the interactions is ata local minimum, that is: the total system energy is

smallest when all objects are at equilibriumposition, compared to the energy associated with

any small movement of any object(s) away fromtheir equilibrium positions. Of course, if you are areader with little scientific background, you may be

1Most laws used in engineering or science are valid only

for a limited range of the data involved. An example of this

type is Ohms law. That is why we use quotation marks

around the word. There are also a few true scientific laws that

appear to have no limitation on their range of applicability

and accuracy. The law of conservation of energy is of this

latter type.

a little unsure of the precise meaning of the wordsforce and energy, but we will explain them in alater document.

In any case, the two descriptions call for different

values (zero force vs. minimum -- but notnecessarily zero -- energy) of different scientific

parameters, so they are different statements aboutwhat equilibrium means. If alternative methodsproduce the same correct results, they are both

equally correct, but some methods are easier tounderstand or use for certain purposes, while othermethods are easier to use for other purposes.

Some alternative methods for analyzing and

explaining electromagnetism. When the theory ofelectromagnetic interactions is presented, the moretraditional classic method is to use the four

celebrated equations developed by the Britishscientist James Clerk Maxwell in the mid 19th

century. Maxwells equations describe theinteraction between various types of electric andmagnetic fields. We will explain the term field

more fully later in the section on vectors and vectorfields. From Maxwells equations we can indirectly

analyze electrostatic and electromagnetic forceinteractions between sources of these fields(electric charges and currents) and the fields

themselves, and ultimately the forces on other

electric charges that act as the receiver ordestination of these forces. As some readers mayknow, there are also other methods as well. Forexample, a scientist may also calculate the forces

on electric charges by first calculating a theoreticalintermediate vector field called the vector

potential, a vector that traditionally has thesymbol A. From the vector field A one can thenderive the electric and magnetic fields and the

forces acting on charges and currents. We will notdelve into all of the alternative methods, but we


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mention them just to show that there are manydifferent methods, and some people find the

availability of these different methods puzzling.

Because of the specific objectives in this course to

understand (but not to create or design)telecommunications systems, we will begin with a

specific description of the relation between sourcecharges and electromagnetic fields, due to the 20th

century American physicist, Richard P. Feynman.In Feynmans equations, the interaction betweenthe source charge, the destination charge and the

electric field is explicit, not indirect. Also, inparticular, the action of a radio transmitting

antenna to produce electromagnetic waves isdescribed directly rather than indirectly.

Feynmans method shows the electromagneticforce acting at a distance, but it also allows thecalculation of the traditional electric and magnetic

fields, denoted by symbols E and B, that are widelyused historically in electromagnetic theory as well.

Feynmans Equation

About 1950, R.P.Feynman2 wrote a single niftyequation that describes the electric field E (andthus the force) produced by an electric source

charge q0

acting on another (destination orreceiving) electric charge. Electric charge is a

fundamental property of some (but not all) types ofelementary particles such as electrons and protons.Feynman also uses one supplementary equation to

define the magnetic field B used in the traditionaldescription of magnetic interactions. The electric

field and the force related to it are vectorfields (aconcept explained later), indicated by the use ofbold-face type like this: E .

Here is Feynmans equation:

note terms:

+

+= r

rr uuu

E2

2

2220

1

dt

d

crdt

d

c

r

rqK Eq. 1

2Feynman did not publish this formula until 1963 in the

Feynman Lectures (see bibliography) , although he informed

many people about it verbally.

This supplementary equation, from Feynman,defines the so-called magnetic field B, as follows:

c/EuB r = Eq. 2

When we know the value of E and B, the force Facting on a known destination electric charge q1,can be calculated. When there is no B field, theforce is merely F=q1E. When the destination

charge q1 is moving with a vector velocity v, thecomplete force is given by the so-called Lorentz

force formula (historically known many decadesbefore the Feynman formulas):

( ))(1 BvEF += q Eq. 3

Fig. 1. (next page) This figure is intended to helpthe reader visualize some of the terms in

Feynmans equation (Eq. l). Two small circlesrepresent the electric charges that are the source

(q0) and the receiver or destination (q1) of theelectric field respectively. They are eachrepresented by a convenient size small circle in the

figure. The circle is actually nota good pictorialrepresentation of the ideal point charge that Eq. 1describes. Charge q1 is included in Fig. 1 only to

indicate the place where the E field acts; q1 is not

actually mentioned in Eq. 1. This figure representsa case in which the two charges are notmovingrelative to each other, so the line between them,labeled r, is both the present line and the retarded

line discussed later in this document. Because thereis no relative motion3, the unit radial vector ur is

parallel to the line r, and also to the electric fieldvector E. The unit vector ur was drawn to appear inblue (or gray) color on your display. Color is used

to set the unit vector apart from the line r. In thisparticular case, there is no B field, because there is

no relative motion of the charges. We draw r, urand E on the same diagram only to show that theyare all parallel to each other in this case. Their

relative lengths should not be compared using this

3For the moment we will put aside a discussion of how the

two electric charges can have no relative motion when there

is a force acting on each one. Just assume that some other

thing (for example, foam-plastic tweezers!?!) that does not

have any interaction with the electric field holds the electric

charges in place at this time.


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figure because they each have different physical units.

q0 ur

rq1

E

The unit vector ur has no physical units! It does notrepresent a physical length in meters for exa mple.

It is only used to define a direction in space. Theline rhas a length measured in meters. The electricfield E has units of newton/(amperesecond) or

N/(As); that is, its physical unit is the ratio of forceto electric charge. When E and q1 are multipliedtogether, the product is the force vector, F, which

is notshown in this figure. F is parallel to E in thisparticular example.

There is also a reciprocal force and electric fieldproduced by charge q1 acting back onto charge q0

as well, which can be computed by means of theFeynman equations, and in a few cases it is useful

to calculate this other force as well. In these noteswe seldom do that.

If you need more background informationregarding the mathematical symbols used in these

equations, you will benefit from reading anexplanation of the symbols and operations in theseformulas in Appendix 2.

We have identified the three additive terms inFeynmans equation by means of numbers on thetext line above Eq. 1. Each term can be identifiedwith one of the three types of fields (or forces),

namely 1. electric, 2. magnetic, and 3.electromagnetic (radiation) fields and forces

respectively:

1. The first term involves only the (retarded)

distancerbetween the source and destinationelectric charges, and does not have any dependence

on the motion (if any) of the charges. The direction

of the force is parallel to the (retarded) linebetween the two charges. In contrast to the

stationary situation shown here, when the twoelectric charges are in relative motion (notshownin this figure), the force is parallel to the line

between the two charges at thepasttimecorresponding to the time for a light wave to travelthe full length of the connecting line. This is called

the retardeddistance. Here the word retardedrefers to the position of the line at a previous time

(and not to the level of intelligence of the line!).For a case where there is no relative motion of thetwo charges, the direction of the unit radial vector

ur and the electric field, and resulting force, are allparallel to thepresentdirection of the line.

We identify the force associated with term 1 as thewell-known electrostatic force, or the related

electric field due to an electrically charged object.If term 2 and term 3 are both zero, the simplified

equation corresponds to what is historically4 calledCoulombs law indicating that the magnitude ofthe electric field E is proportional to the source

charge q0 and inversely proportional to the square

of the distance r. To observe an example of thisforce, you can rub a drinking glass briskly with acloth (preferably on a winter day when the air is

4Named for Charles Coulomb, a 19

thcentury French

physicist. The unit of electric charge, the amperesecond

(abbreviated As), is also called a coulomb in his honor. You

may also notice that Newtons law of gravity is also

similar. It also involves a force that is inversely proportional

to the square of the distance between two interacting masses,

but proportional to the product of the two masses (rather than

the product of the two electric charges).


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dry low humidity), and the glass and the clothwill then pick up and hold (at least temporarily)

small objects like a loose hair, or particles of dust,or a piece of paper about the size of your

fingernail. This force is due to the non-zero electric

charge produced by the removal of electrons fromone object and their excess presence on the other

object. The force or field described by term 1 isstill present if the two charges have some non-zero

relative velocity and acceleration (which wouldproduce some additional force(s) described by theterms 2 and 3). In many real situations, the

electrostatic force between large objects is zero orvery small (particularly compared to the force of

gravity, for example) because these large objectsare electrically neutral that is they have no net

electric charge. They containequal

numbers ofelectrons and protons. An electron has the sameamount of electric charge as a proton, but the

charge is of the opposite sign or polarity (negativevs. positive). An example of an electrically neutralobject is the drinking glass before you rub it with

the cloth. In contrast to the situation of largeobjects, for very small objects, like atoms, the

electrostatic force between the so-calledelementary particles5, such as the electrons andprotons, is the largestforce present in the atom

much larger than the force of gravity between theelectrons and the protons.

2. The second term involves both the distancebetween the two electric charges, and also the

relative velocity of the two charges. When the twocharges have zero relative velocity, this term is

zero. When the electric charges are in relativemotion, there is a force, related to term 2, inaddition to the electrostatic force (related to term

1). We use the word magnetism to describe thissecond force. In the classic treatment of

5The wordparticle is used for electrons (and other

elementary particles) for historical reasons. Unfortunately

this word gives the impression that an electron is a little

sphere or speck, sort of like a ping-pong ball. In fact it is

incorrect to characterize an electron as a particle similar to a

macroscopic particle in general, because its interaction with

other things is best described by means of a wave equation. In

a few cases, we get the right answer by treating an electron as

a point object, but not in all cases. Some authors describe an

electron as a wavicle. We will describe more about this in

later documents.

magnetism, and in most published material aboutmagnetism, we define an auxiliary vector field

called the magnetic field, usually described by thesymbol B. Feynman gives an auxiliary formula,

Eq. 2, that describes the magnetic field. The

formula shows that the derived B field is zero whenthe total electric field (due to all three terms) is

parallel to the retarded line between the source anddestination charge. More information about

magnetic interactions will be given in anotherdocument.

3. The third term involves the relativeacceleration between6 the two electric charges.

When the two charges are in a state of non-zerorelative acceleration, there is a force on the

destination electric charge that is parallel to thedirection of the retarded acceleration vector of thesource charge. Acceleration describes the time rate

of change of the velocity, and velocity describesthe time rate of change of the position. This thirdterm in the Feynman equation describes the

electromagnetic radiation of an antenna in a verydirect way. More information about radiation will

be given in another document.

Electrons and Protons; Conductors and

Insulators. The electric charges and currents ofinterest in telecommunications are almost all due to

the presence and motion of electrons. An electronis a tiny elementary7 atomic particle. All electronshave the same amount of (negative8) electric

charge. All electrons also have the same mass,9.1095 10-31 kg. There are also elementary atomic

6Acceleration is the rate of change of magnitude or direction

of velocity with time. An object going in a straight line at a

constant speed is notaccelerating. An object that is in the

midst of slowing down or speeding up is accelerating. An

object that moves in a curved path is accelerating because itis changing the direction of its velocity (vector), even if it is

not changing the magnitude of the velocity.7

Since about 1950 physicists have agreed that electrons and

protons can be divided into even more fundamental particles,

such as quarks and the like. However, these processes are not

of interest for telecommunications, and thus we continue to

describe electrons and protons as elementary, implying that

they cannot be further divided into smaller particles.8

Electric charge occurs in two opposite forms, called

respectively positive and negative. This is in contrast to other

properties of matter such as mass (or weight) that occurs in

only one form (excluding so-called anti-matter).


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particles called protons, having the same amount ofelectric charge but the opposite polarity or sign,

namely positive. Protons have much more massthan electrons (proton mass is 1.67210-27 kg , equal to

1787.1 times the mass of an electron). Individual

atoms, and molecules of gasses, of liquids and ofsolids cling together because of the mutual

attraction between electrons and protons. Protonsare generally confined to the nucleus or center of

each atom, and do not move about in any way thatis significant for telecommunications. Electrons inmany materials, called electrical conductors, are

able to move about within the material, thusproducing an electric current. Most metals, like

copper or iron, are conductors. In another class ofmaterials, called electrical insulators, electrons

cannot easily move about within the insulator (forreasons to be explained in a later document), andwe say that electric current cannot flow through

insulators9. Glass, most synthetic plastics, andmany natural materials such as stone, dried plantfibers, etc. etc. are examples of electrical

insulators. The availability of both conductors andinsulators conveniently allows us to construct wires

with insulating coating to carry current where wewant it, and to prevent current from going wherewe do notwant it.

Semiconductors . Some materials have similar

physical properties to insulators, but they do permitan amount of electric current to flow that is muchlarger than current flow through an insulator, but

not as large a current as some conductors. Thecurrent in samples of such materials also increases

at higher temperature, which is a behavior contraryto conductors. These materials are called semi-conductors. Some examples of semiconductors are

the elements silicon, selenium and germanium, andthe transparent diamond crystal form of the

element carbon, and certain alloys such as galliumarsenide, an alloy of the two elements gallium andarsenic. (A different crystal form of carbon, a black

substance called graphite, occurs in coal and pencil

9When ordinary voltage is applied across a sample of a

typical insulator, there is typically an almost un-measurably

small electric current flow, so no insulator is perfectly

insulating. Some of this tiny current flow is typically due to

surface contamination of the insulator due to water

molecules and other substances.

lead, but is a conductor.) Integrated circuits,transistors and diodes are made using

semiconductors. More information aboutsemiconductors will be given in another document.

Static Electricity. In ordinary circumstances, anatom and a molecule contain an equal number of

electrons and protons (and also, in the nucleus,some number of electrically neutral elementary

particles called neutrons). It is possible by variousmethods to temporarily add or remove one or moreelectrons to or from a molecule to produce a non-

neutral atom or molecule that has a net electriccharge. This is called an ion. In an object of

ordinary human size (called a macroscopicobject) there are ordinarily the same number of

electrons and protons, and thus the object as awhole is electrically neutral. There may also be atemporary situation in which the object as a whole

has a net positive electric charge because someelectrons have been removed by rubbing the objectwith another material, or the object temporarily has

a net negative electric charge because someelectrons have been temporarily removed from

another object that was used to rub it, and theseextra electrons are temporarily deposited on theobject that now has a negative total electric charge.

This process of producing a net electric charge on amacroscopic size object is called static electricity,

frictional electricity or tribo-electricity.

Superposition of Total Field from many source

charges. When we deal with macroscopic sizeobjects, we typically cannot accurately treat the

source (or destination) object as a tiny point orspeck. Such objects typically have non-zerodimensions and have a definite shape. For example,

a charged object may be a large sphere, or a cube,or a cylinder. An extreme case of a cylinder is a

very long cylinder with a very small diameter,which we call a wire (particularly when it is madeof metal). When the amount of electric charge is

distributed over the surface10 of the object in aknown way, or when the amount of electric charge

10Static electric charge is typically confined to the surface of

electrically conducting objects, and does not stay in the

interior of the conductor, for reasons we will discuss in a later

document.


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is distributed among all the parts of the interior11 ina known way, we can find the total distant electric

field produced by this distributed electric charge byconceptually and mathematically dividing the total

charge into many small pieces. The many pieces

are small patches or parts of the surface for asurface electric charge, or many small cubes for an

interior electric charge. Each piece is then used asthe source charge for the purpose of computing the

electric field it causes at a distant point, eachsource piece standing at a specific and usuallydifferent distance rfrom the destination or

receiving charge location. In order to use Eq. 1accurately, each little piece must be small enough

so that its largest dimension (height, width orlength) is much smaller than the retarded length r

appropriate for that particular source piece. Ingeneral this mathematical process of combining theelectric field from all the little pieces is facilitated

by means of the mathematical method12 ofintegralcalculus. For source charge objects of certainsymmetrical shapes (for example a sphere or a

cylinder), a simple formula can typically be foundfor the electric field caused by such a symmetrical

shaped electric source charge. For objects that donot have a highly symmetrical shape, the electricfield can be calculated to a high degree of

numerical accuracy using a computer to add theparts of the total electric field due to each piece

of the source charge object. Similar methods ofintegral calculus can be used to find the totalmagnetic field caused by a current-carrying wire

having an intricate convoluted shape.

In general, this method of computing the totalelectric field (or any other total electrical quantity)by adding together pieces of the electric field

caused by pieces of the source charge(s) is calledthe principle of superposition. Looking ahead to

the topic of electric circuits, we will find that avery similar process can be used in electric circuitsas well, to find any output item that is caused by

the simultaneous action of two or more sources.For example, we may need to compute the total

electric current in a particular place or in a

11Electric charge can stay at a fixed position(s) in the interior

of an insulator.12

You do notneed to know the details of integral calculus for

this course.

particular component in the circuit, due to thesimultaneous effect of two separate electric power

sources (sources of current or voltage that generatepower) acting together. In many instances, the

direct calculation is somewhat complicated and

tedious. We can simplify the solution process byfirst calculating the first desired partial current due

to source number 1 acting alone, while sourcenumber 2 is turned off. Then we can find the

second desired partial current due to source number2 acting alone while source number 1 is turned off.The total current caused by both sources turned on

simultaneously is then the sum of the first desiredpartial current added to the second desired partial

current.

The principle of superposition is valid for multiplesources in any electrical system that has twonecessary properties:

1. The relationship of each of the individualsource parameter(s) to the desired (output) result

must be linear. A simplified example to aid inunderstanding of the term linearis this: Suppose

that we find that input voltage of 1 volt at locationA in a certain circuit produces an output current of3 amperes at location B. If doubling the input

voltage to 2 volts correspondingly doubles theoutput current to 6 amperes, and in general,

increasing the input voltage by a factor M alsoincreases the output current by the same factor M,then the relationship between the input voltage and

the output current is linear. A more detailedexplanation of the term linear will be given in a

later document.

2. The use of more than one source

simultaneously must not change the operation oreffect of any of the other sources on the destination

quantity. For example, consider a situation inwhich we want to measure (or compute) the totalelectric field due to the simultaneous presence of

two separate source electric charges. We canconceptually temporarily remove (or turn off that

is, conceptually set the charge value to zero) onesource charge at a time and find the electric field atthe destination point due to each source charge

acting alone. When we put backboth sourceelectric charges in their respective places


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simultaneously we are faced with an importantfact: each source charge exerts a force on the other

source charge, as well as exerting a force on thedestination charge. In some cases13, if we do not do

something special to hold the two source charges

stationary, the presence of one source charge willpush the other one away from its original location.

This changes the distance rfrom the source to thedestination charge for each charge, so we cant use

the principle of superposition in such a situation.We have not yet discussed how to hold an electriccharge stationary. You might conceptually think of

holding it in place with a clamp or a pair oftweezers. However, it is not good to do this by

using a conductive metal object, or by using mostinsulators, because that would change the electric

field compared to field produced by the sourceelectric charge just magically staying in place withno other objects nearby, for reasons that we will

discuss in a later document. The most nearlypractical method (but not guaranteed!) to hold anelectric charge in place is this: hold it by using a

very porous insulating material, such as a foamplastic (like the white styro-foam used to make

disposable coffee cups), since it is mostly air (ormostly vacuum if we do the experiment in outerspace). Some textbooks use another theoretical

conceptual method to define the total electric fieldwithout having one source charge disturb the

position of the other source charges. Theyconceptually use very small electric charges in thelocation of each source charge, so that the very

small charge does not in theory affect the positionof any of the other source charges. The very small

source charge in theory produces a very small butappropriately distributed electric field. Afterfinding the very small electric field, we then scale

up the destination field value to the valueappropriate to a large correct-size source charge.

Electron spin and permanent magnets.Incidentally, aside from their role as the

13In some cases, the source charge is stuck at one place on

the surface or in the interior of an insulator, so we do not

need to be concerned that it will move due to the force

produced by another charge. However, when an insulator is

present somewhere between the charges, we need to know

how to properly account for the presence of the insulator in

the calculation of the electric field, which is a topic we have

not yet discussed in these notes.

fundamental quantum of electric charge,individual electrons also have an internal source of

magnetic effects that we attribute to internalmechanical rotation or spin of the charged

material that comprises the electron. In many

practical cases, we can ignore the magnetic effectsof electrons and treat each electron as just a simple

electric charge. This is justified in many situationsinvolving a large quantity of electrons because the

spin directions from many different electrons in amacroscopic piece of material are pointing indifferent randomly chosen directions. The external

magnetic effects of such a randomly oriented groupof electron spins is zero, since equal quantities of

electrons with spin orientation in oppositedirections cancel out each others magnetic effects.

Therefore most materials are not normallymagnetic. However, in certain materials, many ofthe electrons in an object are aligned in the same

direction in space, so that the magnetic effects ofthe electron spins all add together. We will notdescribe the detailed reasons at this time. A piece

of the element iron, or certain alloys of iron withsome other materials, can be made to produce

external magnetism in this way, and such an objectis known as apermanent magnet. Permanentmagnets can be made from a piece of initially non-

magnetized iron or other suitable alloy, bytemporarily placing the iron inside a coil of wire

carrying a large constant current. The magneticeffect of the electric current aligns the spindirection of the relevant electrons in that piece so

that their spins are almost all parallel and pointingin the same direction in space, and they mutually

help to hold other internal electron spins in thesame direction. Conversely, heating ormechanically shaking a permanent magnet can

cause re-orientation of the space direction of theindividual electron spins, and this can reduce or

destroy the permanent magnetism.

Electron Velocity. The movement of electrons

produces magnetic forces described by the secondterm in the Feynman formula. We will describe

two categories of electron motion. Electrons maymove through (almost) empty space, as they doinside the picture tube of a television set or a

computer monitor. In a picture tube, a structure atthe back of the tube called an electron gun uses a


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porous metal electrode with a high positive voltage(to be explained) that pulls electrons from a red-hot

wire filament. This wire is heated by a largeelectric current (like the hot filament in an

incandescent light bulb). The electron gun

attracts the electron but most of these electronspass trough holes in the electrode, and then these

electrons continue moving toward the screen of thepicture tube. After being acted on by the electron

gun, individual electrons move substantially in astraight line at a substantially constant speed insidethe picture tube. Because these electrons are

moving through an almost perfect vacuum, theywill typically go a long distance14 before they hit,

collide with, or otherwise interact with a moleculeor another electron. (There is also some apparatus

in the picture tube to make the electron move to thedesired place on the screen, which we will notdescribe just now.) The moving electrons therefore

produce a magnetic effect due to their velocity, andtheir ordinary physical velocity is what we use interm 2 of Eq. 1. If the electron is changing

direction, the unit vector ur is rotating, and if thedistance ris changing that also affects term 2.

These electrons moving at constant velocity do notproduce radiation (term 3) since they are notaccelerating. Although individual electrons move

at a constant velocity, there are typically severaldifferent electrons in flight at the same time. The

velocity of each individual electron typicallydiffers from that of other electrons, and the totalnumber of electrons in flight varies from one

moment to the next. The total current produced bythis group of moving electrons therefore varies

slightly from moment to moment, and we attributethis to the random variations in individual electronvelocity caused by random thermal motion

(discussed more in the following paragraphs).Individual electrons also move at constant velocity

over long distances in other near-vacuumsituations, such as in outer space or in the upperatmosphere of the earth.

Electrons can also move inside a conductor, such

as a metal wire. However, here they do not move instraight lines at a constant speed for very long. Buttheir average overall velocity is used for term 2.

14We say that these electrons have a very long average (or

mean) free path in a good vacuum.

When a large number of electrons simultaneouslymove in substantially the same direction, they

produce a large total electric current. At the sametime each individual electron in a solid or liquid

conductor is also moving simultaneously in a

multi-segment path due to its own random thermalmotion15 and collisions with other objects. When

this composite motion is analyzed, we cancalculate the velocity of the electrons (for the

purpose of calculating magnetic interactions andother purposes) by using the net velocity due to theorganized directed movement of the electrons,

together with a small random unpredictablevariations due to the thermal motion of the

electrons.

For many situations in which there is a very largecomposite electric current compared to the smallshort term thermal motion variations, we can

completely ignore all the random thermal motionsfor many design and analysis purposes. This istypically the way we analyze and design equipment

for high electric currents, as in electric motors andgenerators. In contrast16 to the high current in an

electric motor, the opposite case of a very smallelectric current occurs in, for example, a radioreceiving antenna. In a radio receiver, it is very

important that the desired electric current isstronger than the random variation of the current

due to thermal motion of electrons, or we will not

15Here we give examples of random thermal variation in total

current due to the motion of a large number of electrons.

Thermal voltage variations occur as well as thermal current

variations, although we dont give examples here. At

temperatures close to absolute zero (different

superconducting transition temperatures apply to different

materials), the random thermal motion ceases and the

electron (described as a point particle as we have done here)

moves in a straight line without experiencing any collisions.

This is called a super-conducting state. Under theseconditions, the conductor appears to have no electrical

resistance.16

Some people divide the field of electrical engineering into

two categories this way: One category is called power

engineering and uses high electric currents while justifiably

ignoring the minute thermal variations in current. The other

category encompasses telecommunications such as telephone

and radio, where designers must take care to avoid problems

occurring when the desired small signal current is not much

larger than the thermal variation in current. In the German

language, the two corresponding terms are strong current

(starkstrom) and weak current (weichstrom) engineering.


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be able to accurately receive radio signals, forexample. As we will describe later, this random

variation of electric current sets a minimum levelon the detectable received radio signal power, and

thus affects the maximum distance between a

transmitting radio antenna and a receiving radioantenna.

When the electrons in an electrical conductor areeach moving in random unrelated directions and

notall moving in substantially the same direction,there is no net total electric current despite their

random motion. For example, at room temperature,

electrons in a conductor are all engaged in randommotion even when there is no electrical connection.

a

1 1

b

2 2

33

4 4

5

56

6

E

F

This is called random thermal motion orBrownian17 motion. In this situation, electronsmove in each segment of their path for a relatively

short distance in a substantially straight line at asubstantially constant speed. Then the electron

collides with another object inside the conductor,such as another electron, or the nucleus of one ofthe atoms (the nucleus comprises protons and

neutrons). After the collision, the electron typicallywill rebound in a different direction. After a

collision, an electron may rebound with eithermore or less energy than it had before the collision.The energy exchanged in these collisions is

typically conserved (energy is neither gained norlost; a so-called elastic collision). In general, if

the collided electron gains energy, the thing (theother electron or the proton) it collided with loosesenergy. If the electron looses energy, the thing it

collided with gains energy.

Figure 2. (above) a) Example of the path of oneelectron in random thermal motion inside aconductor. It follows the path in the order shown

by the numbered corners, and experiences 4

17Named for Robert Brown, a 19

thcentury British scientist

who first observed under a microscope the random motion of

small specks of dust in water, later explained by Einstein in

1908, and others, as a result of thermal motion of atoms. You

can see Brownian motion in specks of dust when illuminated

by a bright l ight in the air of a mostly darkened room.

collisions at points labeled 2, 3, 4 and 5. When it

reaches point 6 we see that there is no netdisplacement from the electrons initial position atpoint 1 in this particular example. b) This

illustrates the corresponding travel of the sameelectron in a conductor, where it now experiences a

combination of both random thermal motion andacceleration to the left, due to an electric field Edirected to the right and consequently a force F

directed to the left (because the negative charge ofan electron produces a force on the electron

opposite in polarity to the electric field E). Theelectric field E is caused by source charges that arenot shown here and that are outside of the region

illustrated in this figure. Note that the segments ofthe path are now curvedbecause the force F causes

an acceleration of the electron, in contrast to theconstant velocity in Fig. 2 a). The overall motion ofthe electron in part b) is similar to its random

thermal motion without the electric field, but there

is a net displacement in part b) due to the effect ofthe electric field. This displacement is the distancebetween point 1 and 6. The net speed of theelectron in part b), used for calculating the total or

net current for magnetic interactions and otherpurposes, is given by the ratio of this net

displacement to the time consumed to move frompoint 1 to point 6. The amount of displacement isexaggerated in part b) compared to a typical

electron path for ordinary current and roomtemperature, so it can be seen more easily.


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We can illustrate this for visualization by

describing the moving electron in a conductor as apoint object. We can do this because in some

purposes, like this one, we know in advance that an

electron can be treated as a point object for analysisof its motion, and the results are known to be

accurate. In other situations, we know that it is notaccurate to treat an electron as a point object, but

instead it is necessary to analyze the motion of theelectron based on the movement of a waveformthrough space. An example of the latter situation

occurs when we try to analyze the motion of anelectron around the nucleus of a single atom.

Fig. 2 compares the path history, over a short time

interval, of a room temperature electron havingpure thermal motion (a) with the hypothetical caseof showing the motion of the same electron moving

through the same time interval of history, but withan electric field present in the conductor (b). Wesee in part (b) of the figure that there is a small

amount of net directed motion due to the electricfield. The random thermal motion, as we will

discuss in a later document, causes continualrandom variations in the total electric current andthis thermal fluctuation is a limiting factor when

we attempt to measure very small electric currents.

Electron Acceleration. Electrons accelerate inmicroscopic or in large-scale accelerations.Microscopic accelerations occur, for example,

when an electron in an atom oscillates andtherefore accelerates. This can occur, for example,

when the electron is in the midst of a quantummechanical change from a higher to a loweramount of energy. This can occur because the atom

is part of a material that is given a higher energylevel by means of heating, as for example the

incandescent filament of a light bulb, or by meansof a collision with other electrons, as in the glow ofthe phosphorescent coating on the inside front

surface of a television screen or cathode ray tube.The phosphorescent material on the display screen

is struck by high-energy electrons coming from aso-called electron gun inside the picture tube.This will be discussed more in later documents.

Large scale acceleration of electrons can occur, forexample, for electrons in a radio transmitting

antenna. The electric current in that antenna isintentionally reversed in direction in an oscillatory

manner, like a ball attached to the end of a spring

and engaged in a mechanical oscillation. Electronscan engage in large-scale acceleration when

flowing in a conductor as a part of a rapidlychanging electric current. For example, when we

want to intentionally transmit electromagneticradiation from a radio-transmitting antenna, we usea radio frequency (rf) amplifier to deliver an

oscillating electric current to the transmittingantenna. To transmit in the original North

American cellular frequency band this rfalternating or oscillating current goes through a

complete cycle about 850,000,000 oscillations orcycles per second (850 megahertz). During eachcycle, the current flows in one direction for half the

cycle time and in the opposite direction for theother half of the cycle. During most of the cycletime the antenna current is changing in magnitude

(but not in direction) at a high rate. Since thecurrent is the first time derivative of the charge

displacement, the rate of change of the current isthe acceleration or second time derivative of themotion of the electric charges in the antenna.

Comparison of electromagnetic Power at a

Large Distance. We find an interesting conclusionwhen we compare the power conveyed from asource charge to a distant destination or

receiving charge by means of the three differentterms of Feynmans equation. We find that of the

three: electrostatic force (term 1), the magneticforce (term 2), or electromagnetic radiation (term3); the electromagnetic radiation conveys more

power to a distant electric charge than either of theother two. This is the reason that electromagnetic

waves, either guided via a wire or cable, or flowingthrough open space (in the form of radio waves)are the primary means of electrical communication.

The power conveyed by the forces associated witheach of these three terms will be described in a

later document in more detail.

There are some cases where the force related to

terms 1 or 2, or the power conveyed via the actiondescribed by terms 1 or 2, is greater than the force


11/24


or power from term 3. This may occur in a regionnearthe source, in contrast to a large distance.

These situations are not usually of practical interestfor long distance telecommunication.

E and B vs. Voltage and Current, Distributedand Lumped Components

In some situations we need to know the value of

the electric field E and the magnetic field B atalmost every location in space, so that we cancompute the force acting on a destination electric

charge at these locations (using the Lorentzformula Eq. 3). In these cases the electric or

magnetic field is not contained within a device orcomponent, but has important effects far from the

source. For example, this detailed field informationis needed to find the effect of radio waves thattravel to several radio-receiving antennas at

different locations.

In contrast, there are also many situations in which

the electric or magnetic field related to an electricalcomponent is almost completely contained within

that component. Many electrical components areintentionally designed so that there is little or noelectric or magnetic field outside of the component

itself. We will give more details in a later

document, but there are three simple and widelyused electrical components typically designed with

this objective: an electrical resistor, a capacitor,and an inductor (or the related family of inductor-

like devices called transformers). In an electrical

resistor, the electric field of interest is mostlycontained inside a resistive material in the interior

of the resistor device in normal use, and the electricfield outside the device is much smaller in

magnitude. In an electrical capacitor, there is astrong electric field inside the component duringnormal use, but very little electric field outside of

it. In an electrical inductor, an electric field occursinternally inside the component during part of the

time, and at that time there is little external electricfield. (In fact, many inductors and transformers are

made by winding insulated wire around a coreshaped like a toroid or doughnut, just to minimizethe amount of external magnetic field.) For these

components, particularly when used with electriccurrents that do not alternate at an extremely highfrequency, the internal electric field is typically

uniform in various physical parts of the componentat any one time. Of course in such components, the

internal field changes from moment to moment intime, but not so much from place to place.

a) External viewb) Cross SectionView

Electron flow direction(opposite conventionalcurrent)

White arrows represent

internal electric fielddirection in resistor.

Fig. 3. Electric Field Inside a Resistor. Portions ofthe complete electrical circuit outside the resistorare not shown.

A simplified illustration to help you visualize the

electric field inside a typical electrical resistor isgiven in Fig. 3. Part a) of Fig. 3 is an external view

of a typical composition resistor18

. The resistorhas a cylindrical shape, composed of an electricallyinsulating plastic material on the outside. Typicallythe exterior of the cylinder is marked with lettering

or with colored paint stripes to indicate itsresistance value. The cylinder is typically less than

10 mm diameter (for low power resistors used intypical electronic applications) and its length is

18Other types of resistors are made from metal wire or other

highly resistive materials also, but are not illustrated.


12/24


about 20 mm to 50 mm. It has two axial metalconducting wires at the two ends, that act as the

terminals for electric current flow. A cross-sectional view b) illustrates that an approximately

cylindrical interior part of the resistor is made of

so-called carbon composition material. Thisinterior material uses a conductive adhesive to hold

together particles of black graphite carbon,manufactured by grinding anthracite hard coal

into a powder. The adhesive hardens duringmanufacture.

When activated by an electric power source in theelectrical circuit external to the resistor, a current

flows from one terminal to the other via the carboninterior of the resistor. The electric current is

composed of moving electrons. In part b) of thefigure, a black arrow pointing to the left is used toindicate the direction of electron flow via one of

the wire terminals at a particular instant. Forhistorical reasons, conventional electric current isdescribed as the flow of positive electric charges.

Electric current in solids is in fact composed of themotion of electrons, each of which has a negative

electric charge 19. Consequently

Accompanying the electron flow illustrated here is

an electric field inside the carbon core of theresistor. The electric field is a vector quantity,

having a direction substant ially parallel to the axisof the resistor. Two white arrows are shown in partb) of the figure to indicate the direction of the

internal electric field. The electric field points inthe opposite direction from the electron flow, but in

the same direction as conventional current flow.The electric field and the electron motion gotogether. You may view one as the cause and the

other as the result. A better statement is that boththe electric field and the current are caused by parts

of t he electric circuit that are external to theresistor and not illustrated in the figure. If one of

19This was not known until the electron was identif ied about

1890. Some books and training manuals written for

technicians (in contrast to engineers and scientists) use the

opposite direction for conventional current flow so that

electron motion is the direction of current flow. The majority

of documents on science and engineering still use the

convention that positive current flow is opposite to electron

flow.

them is reversed in direction, the other one is alsoreversed.

In practice it is much more convenient to deal with

the energy difference per unit of electric charge

that occurs in the resistor, instead of using theinternal electric field. This can be found in a very

simple manner for most resistors that have a simplesymmetrical shape. For example, consider a case

where we establish, by means of measurement ortheoretical analysis, that the internal electric field Eis uniform everywhere inside the resistor core, and

has the value 10 volts/meter. Consider that thelength of the carbon composition interior of this

resistor is 20 mm (that is 0.020 meters). Theenergy difference per unit of charge that travels

through this resistor is then the product of theelectric field value and the length, namely 100.020or 0.2 volts.

It is usually much more convenient to analyze ormeasure the voltage than it is to analyze or measure

the internal electric field of a resistor. For manyelectrical components the relationship between

voltage and current is (lucky for us) described bymeans of a relatively simple formula. This allowselectrical engineers and scientists to accurately

analyze or design electric circuits.

An electrical resistor, for example, has aparticularly simple relationship between voltageand current. Over a wide range of voltage and

current, the operation of a resistor can be describedvery simply by means of a number, called the

resistance of the resistor. This is the ratio of thevoltage divided by the current, described by thefollowing equation. The equation is called20 Ohms

law.

R=V/I Eq. 4

WhereR is the resistance of the resistor, measured

in ohms. Vis the terminal voltage difference of theresistor, andIis the current. Various sizes

(different values of resistance) of resistors can bemanufactured having the same length and diameter.To make a higher resistance resistor, the internal

20Named for Georg S.Ohm, the 19

thc. German scientist who

discovered that most resistive materials follow this law.


13/24


carbon core is intentionally made longer and/orthinner in diameter. The total resistance of a

resistor is the sum of the resistance of the internalcore and the two metal wire electrodes. For most

resistors, the resistance of the two metal terminal

wires is very small indeed compared to the internalcore.

Most resistors are labeled with a maximum power

rating as well as being marked to indicate theirresistance. The power P (measured in watts orjoules/second) dissipated, or converted into heat,

by an electrical resistor is the product of thevoltage and current, but it can also be described via

either of two alternative formulas:

P=VI=V2/R=RI2

Eq. 5

If the power dissipated in a resistor exceeds the

rated power, the resistor will typically get so hotthat it will be damaged. For example, it may burnup! A designer first determines the correct

resistance of a resistor for a particular application(for example, to limit or control the amount of

electric current flowing from a voltage source).Then at the mechanical embodiment design stage,the designer determines via analysis the maximum

power level that resistor must dissipate, andchooses a physical resistor with the appropriate

power rating. Manufactuers of resistors increasethe maximum power rating by making the resistorphysically larger, by adding heat exchange fins or

using other shapes that increae the flow of coolingair around the resistor.

In electrical jargon, item 2) is called the voltage,and it is measured in volts (abbreviated V). One

volt corresponds21 to an energy change of one joule(abbreviated J) per amperesecond of electric

charge. A volt can also be described alternativelyas the product of a uniform electric field and thedistance an electric charge moves through that

electric field. The unit of measurement of an

21Named for Alessandro Volta, a 19

thcentury Italian

scientist. If you have not already noticed this, all metric

system scientific unit terms that are named for individuals are

capitalized when abbreviated (example: V), but are not

capitalized when written in full (example: volt). Terms not

named for individuals (meter, gram, etc.) are not capitalized.

electric field is newton/(amperesecond) or,equivalently22, volt/meter. The product of

volt/meter with a length in meters has the unit ofvolts.

In most situations where the electric or magneticfield associated with a component exists mainly

inside that component, it is not necessary for adesigner or end user of that component to know the

details of the internal electric or magnetic field 23.In many situations, a designer or other user of sucha component only needs to know the relationship

between the voltage and current (volts and amps) atthe terminals of the component. The relationship

may involve the current and voltage directly. Thevoltage and current may be related by a formula, or

the relationship can be described by means of agraph or a list of volt-amp value pairs. For somecomponents, like the inductor, the relationship

involves the voltage and the time derivative of thecurrent. In contrast, for a capacitor, the relationshipinvolves the current and the time derivative of the

voltage. This will be described in more detail in alater document.

Regarding the other two simple electricalcomponents: An ideal inductor is described by the

formula v=L(di/dt), where L is the inductance ofthe component (unit: henry, abbreviated H) and

di/dt is the time derivative or time rate of change ofthe current (unit of currrent: ampere/second; unit ofdi/dt is ampere/second2).

Jargon Issues. In some older documents, voltage

was sometimes described as electromotive force.That is misleading, because voltage is not a forcein the mechanical sense of that word. In older

English language documents, and today in someforeign languages, the word tension is or was

used as a synonym for voltage. Today, in theEnglish language, the word tension is used only to

22The details of these two equivalent but different-appearing

units are explained in a later document.23

Certain types of inductors or transformers in particular

have a higher external magnetic field than is desirable, and

they consequently interact in an undesirable way with other

nearby inductors and transformers by means of their magnetic

fields. In such a case, it then is necessary to place these

components with care to avoid undesired magnetic field

interactions.


14/24


describe mechanical tension (internal pulling forceper unit area inside a solid material).

Categories of Electrical Components. In many

situations, electrical and electronic designers

assemble various electrical components to performa particular process on an electrical signal. The

designer can usually characterize each componentwith adequate accuracy for design purposes merely

by knowing the relationship between the voltageand current at the terminals of the component.

Electrical components are sometimes categorized

according to the following types.

Table 1. Types of Electrical Components

Category of Component(s) Definition or Description: Examples:

Passive vs. Active Passive: Converts electric

power into heat or mechanicalpower, or stores electric powertemporarily but ultimately

returns it to the circuit.Active: Obtains electric power

from a source (for example, a

power supply) and puts thatpower into the circuit.

Passive: Resistor, Inductor.

Active: Transistor used inconjunction with a battery orpower supply device (see

more details in laterdocument); photoelectric cell,

electric generator (battery or

rotating generator).

Linear vs. Non-Linear Linear: An output variablesuch as current is proportionalto an input variable such as

voltage.Non-Linear: Output variable isnotproportional to input

variable.

Linear: Resistor, Inductor.Non-Linear: Diode, Transistor(see more details in later

document)

Lumped vs. Distributed Lumped: Described accuratelyby stating a relationship

between voltage and current atthe terminals of the device.

Distributed: Proper analysisrequires description of fields(or voltage and current) at

different places within thecomponent.

Lumped: Resistor, Inductor.Distributed: long length of

transmission line or cable,Antenna.

Some Active (power generating) devices:

Electric circuits do many interesting things

because, in addition to passive components, theyalso contain active components. Activecomponents get power via some mechanism from

an external source of power (sometimes called aprime mover) and produce electric power in theelectric circuit. At the interface between the active

device and the rest of the circuit, the active devicemay appear to produce a specified electric current

(called a current generator or current source) oralternatively it may appear to produce a specifiedvoltage (called a voltage generator or voltage

source). We also use active sources theoretically asan equivalent circuit or substitute for the analysis

of a device like a transistor. See further commentsbelow and in later documents. It is instructive to

list a variety of active components and describe theessential facts about what they do and how they doit:

Electro-chemical cell or battery. Strictly speaking,a battery is an electrical series combination of

several individual cells, but in everyday use theterms cell and battery are almost synonymous. An

electrochemical cell uses two conductive electrodes(typically two different metals or metal alloys, suchas copper and zinc) that are both immersed in an


15/24


electrolyte, which is an acid or basic (alkaline)chemical solution. An example of an acid

electrolyte is sulfuric acid (H2SO4) in water, and anexample of an alkaline electrolyte is sodium

hydroxide (NaOH) in water. When an external

conductive path is connected between the twoelectrodes, electric current will flow. In the

external circuit, the current flow is generallycomposed of moving electrons. In the elecdtrolyte,

part of the current flow may be due to moving ions non-neutral atoms having either extra or absentelectrons. In the internal path through the

electrolyte, the current is generally comprised ofelectrons moving in one direction and positive ions

moving in the opposite direction. Anelectrochemical cell appears to the electric circuit

as a constant voltage source. A somewhat moreaccurate model is a constant voltage source inseries with a small electrical resistance to represent

the internal electrical resistance of the cellelectrodes and ionic/electron path through theelectrolyte.

When metals are immersed in an electrolyte, some

electrons are removed from the metal atoms. Thenet voltage of the cell is equal to the differencebetween two voltages, each of which is

characteristic of one of the electrode materials.These voltages are called the ionization potential

or ionization voltage of that electrode material.Each ionization voltage is the voltage (energy perunit of electric charge) required to remove an

electron from its position in an atom of thatmaterial to the outside world. (An electron can be

removed from a metal and the energy required todo this can be measured in different ways asidefrom the chemical reactions in the electrolyte.

Another method, for example, is to give theelectron more energy by shining ultra-violet light

of a suitable frequency or wavelength on thesurface of the metal.) For most combinations ofcommonly available metals, the difference between

the ionization voltages for two electrodes is in therange of 1.5 to 2.2 volts. The voltage of a cell is not

affected by the type of electrolyte used, but thechoice of electrolyte does affect the useful life ofthe cell, its internal resistance, its ability to operate

at low temperatures, and other importantproperties.

When the electrical resistance of the circuit

connected to an electrochemical cell is constantover time, the amount of current flow is constant as

well. The substantially constant current produced

by an electrochemical cell is typically calleddirect current (dc), although a more logical name

would be constant or uni-directional current.

Dry cells. For safety and convenience, most cellsmade for consumer use do not use loose sloshingliquid electrolyte, but instead have the electrolyte

solution absorbed in a sponge- like material. This iscalled a dry cell, since the liquid will not pour out

of it.

Primary vs. Secondary (Storage) Cells:Electrochemical cells can also be divided into two

classes regarding their capability to be electrically

recharged and reused. Primary cells are designed tobe used once and then discarded. Primary cellsexhaust their available energy as the electrodes

undergo chemical reactions that are not feasible ornot economical to reverse. For example, in normal

use the zinc electrode in a typical primaryflashlight24 battery is converted into zinc sulfate,which is not sufficiently soluble to permit reversal

of the chemical reaction to recharge the cell andreuse it. Part of the decline in power output is due

to the formation of gas bubbles on the surface ofsome electrodes. Subjecting the primary cell to asmall reverse dc current can cause partial re-

absorption of these gasses and thus extend theuseful life of such primary cells, but many people

in the industry do not rank this process ofdepolarization as it is called, very highly on aneconomic basis.

In contrast, secondary cells are rechargeable. The

chemical reaction that occurs in the cell to produceelectric current can be reversed by running anelectric current through the cell in a direction

opposite the directioin of discharge, from anexternal dc source. The result of this intentional

reverse current is to restore the chemicalcomposition of the electrodes and the electrolyte totheir original composition so the cell can be used to

24The word flashlight is the North American term for the

British words electric torch.


16/24


store and deliver electric energy repeatedly.Secondary cells are typically called storage

batteries.

Secondary cells of various types are widely used in

telecommunications. So-called Lead-Acid cells,using metallic lead as one electrode and lead oxide

paste held in a grid of metallic lead as the otherelectrode, with a sulfuric acid electrolyte, are used

extensively for automobile electrical systems andfor the main working local power source in bothwired and wireless telephone switching and

transmission systems. The lead-acid cells used fortelecommunications applications are made with

highly refined and purified lead electrodes and aredesigned to last for twenty years of use or more. In

contrast, automotive lead-acid cells are made fromrather impure lead and are only designed with athree-year useful life expectancy.

A fully charged lead-acid cell has a voltage ofapproximately 2 volts (compared to typically 2.2

volts for open circuit test conditions when nocurrent is flowing). The original telephone step-by-

step switching equipment and the subscriber-loopcentral office power voltage have traditionally beensupplied by a series battery of 24 cells of

approximately 2 volts per cell, giving a supplyvoltage of approximately 48 volts in all telephone

central and transmission offices up to the presentday. (In the past certain long loop servicesutilized up to 96 volts, but these are seldom used

today since remote switching concentrators permita wired telephone installation to always use less

than 8 km of subscriber loop wire and thusstandard 48 volt battery power.) In some PBXequipment and radio equipment a 24 volt (or other

less-than-48 volt) battery assembly is occasionallyused.

In telephone outside plant wiring, and in mostinternal telephone industry wiring using 48 volt

batteries, the positive terminal is grounded(connected to the earth via a large copper spike

sunk into moistened and good electrical conductingearth). This minimizes the most serious type ofelectrolytic corrosion of outdoor wire. Some

corrosion does still occur, but the result of usingpositive ground dc power is that a less offensive

surface corrosion (copper oxide and/or coppercarbonate) forms on top of copper wire, for

example. This surface corrosion does not consumethe copper wire or make it thinner. In contrast to

the positive ground used in the telephone industry,

most other types of automotive and electrical andelectronic equipment is designed with the earth or

the frame or housing of the electronic equipmentconnected to the negative terminal of the low-

voltage dc power source. There are also someconflicting uses of insulation color codes on wiresin the telephone industry vis--vis other electrical

and electronic industries. This is described in otherdocuments later in this course.

Other secondary storage cells: Lead-acid cells are

typically too heavy for portable device use. Avariety of other electrode metal or alloy pairs arewidely used for portable electronic and

telecommunications equipment. Notable storagebattery electrode materials are nickel-cadmium(NiCd), lithium-hydride (LiH) and nickel-metal-

hydride (NiMH).

One of the challenges of storage cell technology isto get the maximum output from a storage cell for agiven amount of cubic volume, weight (mass), and

input energy. Lithium batteries are very light inweight for a given power output. Lithium and

NiMH cells are claimed to have very good outputof stored energy, in contrast to NiCd cells whichsuffer from the problem called storage cell

memory. NiCd and certain other storage cells,when rercharged without first being fully

discharged, tend to deplete their output after onlypart of the input energy has been extracted. Forsuch memory storage cells, a complicated and

overall energy-wasting regimen of artificialdischarge (typically into a resistor) is required

before each recharge session, to ensure that all thestored energy in the cell can be utilized.

Current Sources:

Several active devices produce a specified currentoutput, in contrast to the specified voltage outputproduced by electrochemical batteries and rotating

machines. The most widely used current sourcesare photo-electric cells, both the older vacuum-tube


17/24


electric eye devices and the more modernsemiconductor photoelectric cells used for solar

electric power and the like. Vacuum tubephotoemission cells typically produce only

microamperes of current, but modern solar cells

can produce hundreds of amperes. Theoreticalcurrent sources are also used for the design and

analysis of junction transistor circuits.

Rotating machine generator. Most of the electricenergy generated in the world comes to the enduser via rotating machinery. The basic mechanism

of generating power in a rotating generator followsfrom Eq. 3. Conductive wires are moved through a

region of magnetic field B with velocity v toproduce a force F on the electrons in those moving

wires, thus causing a current. In most installations,the conductive wires are stationary in the outerframe of the generator. Current-carrying wires

mounted on a rotating structure (the armature) andturned by a mechanical prime mover, are drivenby an exciter current source to produce the B

field. In some installations, permanent magnets areused to produce the B field. The moving coils or

magnets induce a voltage in the various coils onthe stationary frame. The prime mover is typicallya turbine driven by falling water, or by steam

produced from burning a fossil fuel (oil or coal, forexample) or steam produced from the heat of a

nuclear reactor.

Various other types of rotating machine generators

are similar in principle but different in details ofconstruction and size from the generator described

above. They are called by various historical namessuch as a magneto (used historically to producetelephone ringing current) or an alternator

(typically used in conjunction with a rectifier explained in later documents in an automotive

electric power system).

All public power-generating systems today produce

alternating current (ac). Alternating Current issometimes considered to be the antonym of direct

current (dc). The two letter name is used forcurrent or voltage; we say ac voltage. In publicelectric power systems, ac has a repetition

frequency of 60 Hz in North America and Japan,and 50 Hz in most other parts of the world. The

spatial pattern of the B field used in the rotatinggenerator is designed so that the ac power voltage

waveform is a sinusoid or sine wave. A sine wavehas the special property that all the currents and

voltages in all the components used in an electric

power network will have sinusoidal voltage andcurrent waveforms of the same frequency, provided

that all the electrical components used in the powernetwork are mathematically linearin their

relationship of voltage and current. (Please reviewthe brief description regarding linear passivecomponents on p. 7, 8 and 16.) The current and

voltage in various devices in a linear powernetwork thus may differ in individual amplitude

and in individual phase (time delay of the sinewave in comparison to a standard timing or clock

sine wave). Therefore, the power network isrelatively easy to regulate and control because thecombination of any two sine wave currents having

the same frequency but different phase and/oramplitude is a sine wave of the same frequency.The power generating system is not required to

sometimes generate square or triangular waveformsin order to meet varying demand. It only needs to

generate sine wave power, with the amplitude ofthe current appropriately adjusted to meet presentpower demand at any time of day or night!

When sinusoidal alternating current power was

first used in the late 19th century, all thecomponents in the power network were linear.Most of the components used in the public power

network were incandescent light bulbs, and a fewelectric motors both electrically linear devices (at

least approximately linear). Today, several kinds ofnon-linear devices are indeed used in the publicpower network, such as fluorescent lights for

example. However, the vast majority of electricalcomponents used in the public power network,

such as electric heating devices, all types of motorsused in homes and factories, the power suppliesused in consumer electronics and data processing

systems, and most other electrical devices appearto the electric power network to be mathematically

linear.

Why is ac used for public electric power

systems?


18/24


The original Edison public electric power system inthe 1880s used 110 volts dc. Edisons competitors,

particularly George Westinghouse and NikolaTesla, developed ac electric power generating and

distribution systems that were more efficient and

therefore less expensive to use. There was a verybitter public relations battle fought over several

years, and eventually won by the ac proponents.The improved efficiency of the ac power system is

the result of using power transformers (explainedin a later document in this course) to converttransmitted power from low voltage and high

current (for example, 110 volts at 10 amperes) intoa waveform of high voltage and low current (for

example, 440 volts at 2.5 amperes) at the generatorend of the power transmission wires, and then to

use another transformer at the consumer end to re-convert the waveform back into low voltage (forexample, 110 volts at 10 amperes once again).

Most of the loss of power (the inefficiency) inelectrical power transmission wires is due to thepower converted into heat by the current flow and

the series or longitudinal resistance of the wires25.In fact, this loss is proportional to the square of the

current, so reducing the current from 10 A to 2.5 Acuts the power losses by a factor of 16, and not justby a factor of 4. It was not necessary to carry a

possibly unsafe high voltage all the way to theconsumers premises, since the power could be

converted back into a low voltage with highcurrent, which is safer for the end users.

Unfortunately, although all public electric power

systems in the world use ac, there are twonominally incompatible frequency and voltage

standards.

Power Supply. Most electronic devices that get

their electric power from an ac power outlet

include a so-called power supply. A better andmore logical name would be a power converter,but that is historically a jargon term used for aspecial kind of power supply. A power supply

utilizes relatively high voltage alternating current(example: 110 volts, 60 Hz alternating current in

North America) available from a power outlet in abuilding, and produces a low voltage direct current

25This is true for both telecommunications transmission

wires and power transmission wires as well.

for electronic equipment. The low voltage may be,for example, 1.5 volts, 3 volts, 5 volts, 9 volts, 12

volts, 24 volts, or certain other less-used lowvoltage levels. Some power supply designs produce

more than one low voltage dc output. Without

going into circuit designs, a power supply typicallydoes the following things to 110 volt ac power:

1. Converts the alternating current into

unidirectional pulsating current by means ofa diode circuit that only permits currentflow in one direction. (Diodes are described

more in a later document.)2. Stores energy (typically in a capacitor)

during the parts of each original ac cyclewhen the current is large.

3. Draws on that stored energy to fill incurrent flow during the portions of theoriginal ac cycle when the ac wall outlet

delivers little or no current.4. Regulates (filters) the internal dc voltage

so it is free from undesired small variations

due to the original alternating currentsource or due to changes from moment to

moment in the amount of current drawn bythe power consuming devices (for example,by the computer hardware).

5. Multi-voltage option: Some power supplies,particularly those made for portable

equipment, can operate properly regardlessof whether plugged into 110 volts at 60 Hzor 220 volts at 50 Hz. Very convenient for

international travelers.


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____________________________________Appendix 1: What is a Vector? What is a

Field?

Vector and Scalar

In general, a field in electromagnetism or

physics is a mathematical quantity that has adefinite value at each point in space. Both vector

and scalar fields are used in mathematics andphysics. Wind velocity in the atmosphere is anexample of a vector field. At each point in space,

the wind has a magnitude (measured in km/hvelocity units) and a direction (described by

giving the angle between the direction of thewind and some reference like east, north, etc.).

As we will describe, three quantities or valuesare needed to specify a vector in a three-dimensional space. Two quantities or values are

needed to specify a vector in a two-dimensionalspace.

Temperature in the atmosphere is an example ofa scalar field. It has a magnitude but no direction.

Only one number is required to state the value oftemperature at a location.

Remark: In abstract mathematics the term fieldis also used in a special way that is different

from its meaning in connection withelectromagnetic fields. This special meaning isnot relevant to this document but is stated here to

make the difference clear. It has some relevanceto error detecting or correcting codes, but not to

electromagnetism. A field in abstract algebra is aset of quantities (such as integers or realnumbers, or other similar abstract entities) and

operations including the operataions of addition,subtraction, multiplication and division, or other

abstract operations that are analogous to theseoperations. You may ignore this paragraph forthe purposes of this document.

Vector Notation Basics

Vector notation allows us to write a singlesymbolic equation on paper that represents three

separate equations (in the case of vectors in athree-dimensional space). A vector is a

mathematical quantity having both a magnitudeand a direction in space26. A vector is often

pictured on paper as a symbolic arrow or adirected line segment. A mathematical vector

typically represents a physical line segment, or

some other physical phenomenon having amagnitude and a direction, such as a wind in the

atmosphere. A real physical arrow, made ofwood and used by an archer, is aphysical

directed line segment. It is a physical objectsubstantially in the form of a straight line or aslender cylinder. We can describe its magnitude

as its physical length measured in meters.Arrows made of different lengths of wood have

different magnitudes. When we hold an arrow indifferent orientations (for example, straight up or

pointing east and so on) it assumes differentvector values, all having the same magnitude.Other types of vectors have a magnitude that

symbolically represents other physical quantitiessuch as velocity, acceleration, movement ordisplacement of an object, and so forth.

Consider a three dimensional space in which thelocation of any point is given by means of three

numbers representing the distance measuredalong one of three perpendicular lines or axesrespectively (distance measured in meters). A

vector in a three dimensional space can bedescribed by three numbers. Two numbers, or

one number are/is not enough to specify thevector correctly and unambiguously. Onecategory of methods for describing a vector is to

specify a magnitude and a direction. A vector oran arrow has a direction relative to its

environment in three-dimensional space27, which

26 In medical science, the word vector represents the thing

or mechanism by which an infection is transmitted from

one patient to another. For example, the vector of yellow

fever is a mosquito that carries the virus from one patientto another. This specialized medical meaning has only a

remote relationship to the mathematical meaning.27

In these simple examples we consider a three-

dimensional rectangular co-ordinate system in space in

which one axis (called the x axis) is oriented in the east-

west direction, with east taken as the positive direction.

The second axis (called the y axis) is oriented in the north-

south direction, with north as the positive direction. The

third axis is oriented in the vertical or up-down direction,

(called the z axis) with up as the positive direction. For our

examples, we will assume that the earth is a very, very

large sphere (or we only study small regions of space) so


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can be described by either of the followingmethods, both of which involve two items of

data:a) the angle (measured in degrees or other

units of angle measurement) between the

arrow and a line (axis) oriented in thenorth-south direction, and a second angle

between the arrow and an axis oriented inthe vertical direction (up-down relative to

the local ground level), orb) the ratio of the length of a shadow or

projection of the arrow to the true

physical length of the arrow, for twodirections of projecting the shadow. In

one direction the shadow or projection iscast onto a horizontal plane (like a large

flat sheet of paper) from a light directlyoverhead, and for the second direction thelight source shines due west onto a piece

of paper oriented perpendicular to thatlight beam.

We see that in both method a) and b), there are

two items of data in addition to the length(magnitude) of the arrow. Three items of data are

needed altogether because we are describing thevector in a three-dimensional space.

There is also another method (lets call it methodc) to describe the vector in three-dimensional

space by giving three shadows or projections ofthe arrow onto three perpendicular planes. Inmethod c we do not need to give the length of

the arrow as an independent item of data. In fact,the true physical length of the arrow can be

calculated from the three projections using theso-called 3-dimensional Pythagorean rule thatthe square of the length of a major diagonal of a

right-angle rectangular solid (a rectangularprism) is equal to the sum of the squares of the

lengths of the three rectangular edges. Each oneof the three projections or shadows is equal inlength to one of the edges of a rectangular prism

enclosing the arrow as a main diagonal.

This method we call c is, in fact, the most widelyused method for describing three-dimensionalvectors in general. However, all the methods for

that its surface is substantially flat and the z axis is always

parallel to itself at all locations in the x,y plane.

describing the magnitude and direction areequally valid and data from one method can be

used to derive or calculate the three items of dataused in an alternative method.

Using method c, we can write a single symbolicequation that states that one vector A is equal to

another vector B, but this is merely a symbolicway to represent three separate equations

regarding the projections on the threeperpendicular axes of three-dimensional spacerespectively. Notice the use of bold face type to

represent a vector on paper. (Of course, bold facetype is also used for other purposes not involving

vectors as well.) We typically use the lettersymbolsx, y andz to denote quantities associated

with the three perpendicular axes in a threedimensional space. The projections onto therespective axes of a vector A are denoted

respectively as Ax, Ay and Az, called the threecomponents of the vector A. Note that the threecomponents are not individually vectors. Each of

the components along one of the axes is anordinary real number (also sometimes called a

scalar to distinguish it from a vector). Forexampl

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