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IEE ELECTRONICS DIVISION: CHAIRMANS ADDRESS

The magic of marginal electronicsMuch of the excitement in both resea rch and practicalengineering lies in the exploration of the margins, orboundaries and limits, between what is just feasible andwhat is impossible. Electronics has a particular fascinationbecause, unlike other branches of engineering, its workingsare almost invisible, and its power to perform useful tasksis so great a s to be almost magical. A good understandingof the fundamental limits of the laws of science and of therules of thum b or design rules of current technology areneeded for the margins of engineering achievement to bepushed forward safely and effectively. The pape r contains apersonal selection of laws and rules and their application inthe fields of radio, control, digital electronics andspeculative future communications.

by Professor M.J. Underhill,MA, PhD, FEng, FIEE

1 On magic and marginsOne definition of magic s anextraordinary power o r influenceproducing results which defyexplanation. To many who havesuccumb ed to the fascination ofelectronics this definition wouldseem very appropriate.It is in the marginal area s of asubject that the principles andfundamentals assume the greatestimportance. For scientific researchit is the ultimate laws of scienc eand natu re that define theboundaries to be explored. Forengineering it is the limitingtradeoff between performance,safety, cost and timesca le thatbecomes t h e challenge.1,roiirirdo u~as ot ani~rigiriecr:FYW the middle sectioiil,corltIr-riocre11ted f h rM a c h i n a o f t h e Hock.\ aiidl i s iri all he i ~ d e r t o o kurircrerlcrl the originalc~otririiissioririd also, a si d . S 1 4 d , excecdirig the c o s ti r g i - r i d upoii RichardIiP l l der t ha 1

To meet this challe nge anexperienced and effective engineerELECTRONICS COMMUNICATION EN(

will have as a toolkit a number ofrules of thumb which describe thelimits of what is or is not easy (orcheap, o r quick) to achieve byengineering in current technology.This pap er is a personal, andtherefore selective and perhapssomewhat idi osyncratic, view oflaws, principles, rules of thumb,prejudices a nd useful tools whichhave served the auth or well as hismagical protective spells over 50years of involvement inelectronics.In additio n, in the final Sectionis a specula tion well a t the edge ofthe margins of possibility. I n thiscase the importa nce of suchprinciples is that they can be usedto test both the plausibility and, ifthis test is passed, the eventualrealisability of the spec ulation.2 On laws and engineeringEngineering an d science areimportant to eac h other, eventhough the motivationa l factors foreach a re arguably quit e different.Science is to a great degreecuriosity driven, where the goal isbetter understanding of the laws ofnature, whereas engineering hasas a goal the modification orcontrol of the environment (for thebetterment of the human conditionhopefully). Science (partic ularly inthe sh ape of Big Science)frequently calls for the ultimate inJEERING JOURNAL DECEMBER 1993

engineering achievement in orderto push forward the bounda ries ofunderstanding. Engineering needsscience because not allengineering can be based onexperience of what works inpractice. It remains true that anyengineering technoJogy willultimately only develop as far asthe limits allowed by the laws ofnature as discovered by scientificendeavour.Electronics has both its scienceand its engineering. For instance,Maxwells equations ar e a nexample of scientific lawswhichare unlikely to change much in theforeseeable future. In contrast thepower that digital electronicsprovides for the enginee r canreasonably confidently bepredicted to continu e to follow theempirical exponential lawofdoubling in processing spe ed everyyear an d doubling in availablememory capacity every 18 monthsfor the next ten or twenty years, asit has done for the last ten ortwenty years. (Admittedly thesecond ten years predi cted by thisrule of thumb is likely to requir esome new science, technology oralgorithmic paradigm shift as theprogress of current technologiesstarts to hit already predictedscientific an d physical limits.)In industry, engineers are alsoexposed to United Kingdomjudicial laws relating to contrac ts,sale of goods, safety and consumerprotection, and also to EuropeanCommunity (EC) laws, particularlyon electromagnetic compatibility(EMC). EMC is an intere sting are aof electronics wh ere the laws ofnatur e (i.e. he coupling ofunwanted electrical orelectromagnetic interference fromone piece of equipment to another)come up against man-made legalor judicial laws. Contract law ca nbe a dangero us legal minefield forthe unwary, over-enthusiasticenginee r who is too easilypersuaded by his colleagues in thecommercial department topromise in a contract to acustome r what t urns out to be onlyjust beyond the boundari es of thelaws of nature. The law ofcontracts would not appear toallow for the non-pe rforma nce of a

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contract owing to the limitations ofthc laws of nature. English lawsays: Impossibility does notgenerally excuse fromperformance.2Also force majeureis an event tha t ca n generally beneither anticipated nor reduced tocontrol. This certainly does notapp y to those laws of nature whichan engineer could be expected toknow, and so, claimingimpossibility, or force mujeure, inthese circumstances is just notallowable as a let out.

A good knowledge of principles,not only of engineering ru les ofthumb but also of the fundamentallimits of the laws of nature, is anessential (magical)protection(magical spells) to an engineerwho strives to push forward theboundari es. Too often the engineerfeels it is Murphys law (Ifi t can gowrong, it will) which rules his orher endeavours.3 On models and simulationThe creative side of science an dengineering is highly dependen t onthe conc ept of a model. A modelrepresents reality in an idealisedform. It can be empirical,theoretical, or computational. Forthe engineer the key issue iswhether a model is a sufficientlyaccurate representa tion of realityto be usable as a tool for effectiveengineering design.For engineering, utility isparamount . Often the theoreticalbasis of a model or modellingmethod is forgotten or ignored.For example, in electronicengineering the Laplacetranslo rm, which is based on somequite advanced mathematicalideas, manifests itself as theconcept of impedance. Impedanc eand its dependence on frequency isan absolutely essent ial concept forall but the simplest (DC or digital)electronic circuit design. Also,electronic filter designers andcontrol engineers happily use pole-zcro or root-locus diagrams asuseful design tools andconveniently ignore the originalmathematical basis of the Laplacetransformation.A nice examplc of utility at all360

cost taken to extremes is thenumerical method now muchemployed in the analysis of radioand radar antennas, namely themethod of moments. In thismethod the antenna model isdivided up into a large number ofpieces a nd the couplings andinteractions of all the piecescomputed in order to simulate heperformance c haracteris tics of theantenna (e.g. gain, directivity,sidelobes etc.). The problem withthe method is that, although itworks beautifully, it is actuallymathematically unsound . Themethod produces answers whicheventually diverge from the truth ifthe size of the pieces is made toosmall: and there is a mathematicalproof that this behaviour isinevitab le4 The correct size for thepieces has in practice to be chosenby trial and err or and experience.Computers have madesimulations (for example for themethod of moments above)basically very easy. However, theprecision and speed afforded bycomputers never guarantees that asimulation is actually an accuraterepresentation of the real world.The danger is that numericalprecision is mistaken forrepresentational accuracy. Inelectronic engineering, simulationis much used. For software designone may have few qualms aboutthis. The problem there isincreas ingly one of the control ofcomplexity and not one ofrepresentational accuracy.Simulation is still no substitute forhard-learned experience, althoughit increasingly becomes more andmore indispensable.For hardware designs, otherthan at the highest levels, even thebest simulations cann ot cover themyriad unknowns andunquantified aspects whichimpinge on design performance.Perhaps the most current exampleis electromagnetic compatibility(EMC) .Many a hardware circuitdesign at first fails to workproper ly, because of selfinterference or in terference from aswitched mode power supply, or itcann ot meet the new EC EMCregulations on radiation o rsusceptibility to electromagneticinterference. For RF circuitry suchas might be found in cellularradios several design iterations, forthis reason alone, are notunknown.A selection of good and usefulmodels a nd methods should be inthe toolkit of any engineer.Provided that these aredemonstr ably useful, theELECTRONICS COMMUNICATION EP

mathematical laws ehind suchmodels can safely be taken forgranted a t least for most, if not all,of the time.An appreciationof scaleOne attribute which could beconsidered to be an essentialelement in the armoury of a nengineer is an appreciation ofscale. Scale is taken here toencompass not only such conceptsas size, precision, accura cy andtolerances but also whethersomething is che ap or costly, orhard or easy to engineer andmanufacture, or dangerous or safe.It is well known that for theengineer too much precision canbe unnecessarily costly. Too littleprecision ca n lead to designswhich ar e not safe. So the questionof the right level of precision isnearly always important.The level of accuracy andprecision afforded even by thepocket cal culator is arguablyexcessive. The smallest lengthbelieved to have any physicalsignificance is the Planck leng th,( G h l Z n ~ ) ~ ,hich is aboutmetres X 1.61). The largest distancemeasure likely to be needed isprobably the diameter of theuniverse (taken to be twice thedistance travelled by radiation,such as light, since the big-bang,

estimated to be about 1.5 x I O years ago) and it is approximately0.3 X 10 metres. However, therange, o r scale, covered by most(scientific) pocket calculators isnow lo- to 10. So, it could besaid that even the design of thepocket ca lculator shows noappreciation of scale and is a nexample of over-design andengineering gold-plating by afactor of 10 (because2 X 99 -35-27 = 136).To such an extreme view theremust be a counterweight. I n thiscase it is cost: the marginal extracost of this overdesign ispractically zero nly a fewgrains of sand (silicon dioxide).The proposition is that at the end ofthe day the final manufacturingcost of any electronics isdetermined to a goodapproximat ion by its weight(which is a simple measure of theNEERING JOURNAL DECEMBER 1993



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amount of materials used), so thatcomplexity comes practically freeand the original creative efforts ofthe designer engineer unhappilybecome totally discounted.Engineers ar e already expectedto be numer ate, literate (includingcomputer literate) and articulate.To describe the attri bute of anappreciation of scale the wordmensurate or measurate) ouldperhaps be reintroduced.(Mensurate originated in 1653accor ding to the Concise OxlordDictionary and it also appears inRogets Thesaurus ). Mensuracy

should be regarded as an essentialattribute for any engineer.5 InvisibilityThe sad fact is that most of theprocesses of electronics areentirely invisible. In this respectelectronics differs from most othe rbranches of engineering. Electronsare too small to see; it is only by theeffects achieved that workings ofelectronics can be d educed.Computer modelling andsimulation often help in thevisualisation of the processestaking place. However, part of thefascination of electronics is theessential part that imagination hasto take because most of electronicsis invisible. What is really going onhas to be deduced an d imaginedfrom the evidence of indirectmeasurements.

In the days of the thermionicvalve the region where theelectrons flowed in the vacuumbetween the valve electrodes couldeasily be seen through thetranspare nt glass envelope. In fact,for a valve which was imperfectlyevacuated the passage of theelectrons would stimulate aninteresting faint blue glow, whichwas often visibly modulated inintensity by the electron curr entvariations.ELECTRONICS COMMUNICATION EN(

Microminiaturisation just makes:he problem of invisibility worse.Even the electrical wireszonnecting together the devices on3n integrated circuit will beIptically invisible in the nextgeneration of ICs. The electronmicroscope itself is already amajor tool for seeing ntegrated-zircuit structures. In the futu re, asdimensions are further reducedbelow the submicron level thescanning electron microscope(SEM) or perhaps the scanningtunnelling microscope (STM) willbecome the only way to see hecircuits at all. In fact, beams ofelectrons now provide the invisiblepencil o d raw the circuit anddevice patterns necessary to definethe functionality of an integrated-circuit chip in the first place.Free-space electromagneticradiation other than light iscompletely invisible but its manyapplications are easy to see. Someof these of parti cular interest willbe addressed later.6 From electricity to electronicsDefining electricity as the scienceor knowledge of how electronsflow and what this flow canachieve, immediately establisheselectrical engineering andelectronic engineering asessentially inseparable. There is aThe momertt rnaiz cast oflIi is age-long belief rz nzagic,Science bestowe d upoii iillthe blessiiigs o the ElectricCurrent Jean Giruudoux/Th e Eizchunted], 193.3)natural historical developmentfrom the former to the latter. Thefact that electricity has biological,and by implication hum an-biological, effects was establishedby Galvani in 1798 byexperimenting on frogs legs. Whatwas also established as afundamental tenet by thesubsequent experiments of othersis that a continuous electricalcircuit is required for a cur rent toflow unde r the action of a voltageor electromotive force.Furthermore the biologicaleffect of a curre nt flowing in ahuman being can be quitedrama tic, with death being a likelyoutcome of an arm-to-arm currentof only 50-1 50 mA. (Volts jol ts,mils kills,as the doggerel puts it).Thankfully, progressive advance in(IEE and BS) safety stand ards hasremoved much of the risk toJEERING JOURNAL DECEMBER 1993

human life and health that thepower of electricity brings as thedownside to its undoubtedbenefits.does not kill and can have little orno jolt. In the still somewhatsurp risin g demonstration of hairstanding on end under the actionof static electricity of severalkilovolts potential difference withlittle or no sensation to the ownerof the hair, this can easily beshown to be true. So even thesimplest laws relating to electricityand its safety have to be qualifiedby a better under standing of itsscience.From the areas of electronicsselected to be addressed in thefollowing Sections the thre adconnecting all electronics to itselectrical origins should hopefullybecome at least a little visible.However, it is worth pointing outthat electronics is a broad churchin that it contains large areaswhere the electron only takes partindirectly, e.g. electromagneticradiation, and areas where itsexistence is conveniently forgotten,e.g. computing and software.7 Radio is wireless and makeswavesElectromagnetic radiation, such asa radio wave, transfers energythrough Cree space without the useof wires. Radio is really wire-less

Volts without amps or milliamps

Suitable sensors can measure thevoltage or potential between anytwo points in space. But even i fthere is a voltage there must alsobe a current in orde r that powercan flow through space. Thcinnovative principle that Jame sClark Maxwell introduced in hisequations for electromagnetic(radio) waves was the concept ofdisplacement curren t; the rest ofhis equati ons he collected fromother so urces, e.g. Faradays andLenzs laws ol induction, Ampereslaw for magnetomotive force,Gausss divergence theorem, thelaws of continuity of cur rent and

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1Gauss,iv D(o r V D) = E E ~iv E = 0divB(orG.B)=ppiodivH=Ocurl E (or V x E ) = -313idt = -ppo aH/curl H (or P x H ) = -3Diat + j = so df id t )+ U

Faraday and LenzAmpereMaxwells displacementt current

With the continuity condition j = dp/3t directly implying the Lorentz conditiondiv A = -sopo / , these equations can be solved to give:Wave equationsV E = p p o ~ ~ o a 2 ~ i a t 2 ) Electric fieldP2H= pp0EEo d * H / W )GQ = p p o ~ ~ o ~ 2 A / W )piceo0 = p p o ~ ~ oa2A/a t2 ) ppoj

Magnetic fieldScalar potentialVector potential

Retarded potentials (are solutions of the potential wave equations)

cp = k ol where [p] = poexpp t- ric)4nmr rA = * ru r where[j]=jaexpp(t-r /c)and velocity c = E ~ ~ p p ~ ) - ~

I The displacement current in Maxwells equations an d the wave equationsasresulting solutionsconservation of charge, the law oflinear superposition, and Ohmslaw of conduction.The displace ment current is aninvisiblecurren t which can besaid to provide the means by whichpower and energy can flowthrough space withou t wires. It is awireless current. Fig. 1 shows thedisplacement current term inMaxwells equations an d thesolution of these to give theequations of waves propagatingwith finite velocity.Maxwells equations whensolved give equations of wavespropagating with the speed oflight. A direct consequence of thisis that the wavelength and thefrequency ar e inverselyproportional, with the speed oflight being the c onstant ofproportionality. This means thatthe principles involved in thedesign of the antenna whichradiates or receives radio energyscale precisely with wavelengthand inversely to the frequency ofinterest . This results in the antennaof the BBC long-wave transmitterat Droitwich transmi tting on198 kHz, approximately 1500 m inwavelength, being classified as asmall antenna: the height of theantenn a is 200 m, which is lessthan that of a full-size quart er-

wave vertical ant enna , whichwould be 375 m. (Actually it is aT ant enna with a flat top which isalso 200 m, but the smallnessargument still holds.)The gain, or ability, of a nantenn a to radiate power (orreceive power) in a given directionis almost the same for a very sinal1antenna (no matter how small it isas for its equivalent full-sizeantenna. (This is true for bothmonopoles and dipoles, where thefull-size versions are , respectively,a quart er-wave and a half-wave inlength). This is because theradiation patterns ar e almostidentical for the small and full-sizeversions. The gain is alsoproportional to the capture area ofthe ante nna. The capture areas offull-size and a small dipole, nomatter how small the dipole is inlength or wire thickness, are bothlittle over one tenth (0.12) of asquare wavelength. If the antennais made from a rod or wir e ofmoderate thickness, the physicalarea of even a full-length antennacan be as little as one fourhundredth of the capture area.There is however a catch: thebandwidth of a very small antenna(that is the band of frequenciesover which it works) is very small.There is a beautiful proof,

originated by L.J. Chu butarticulated in more practical termsby H.A. Wheeler , which showsthat the bandwidth as a frac tion ofthe frequency of interest cannotexceed a constant times the volumeof the sp here (expressed in units ofwavelength cubed) in which theantenn a can be contained, nomatter what shape the antenn a isor what material it is made from.The fractional bandwidth is thereciprocal of the quality factor, Q,which is the ratio of the energystored in the space around theantenna to the energy radiated orreceived during the time of onecycle of the waveform. Wheelersformula is in fact Q2 2m/L)-,where Y is the radius of the sphereand he wavelength at theFrequency of interest. Q is veryhigh for a small antenna and wefind that extremely strong electricand magnetic fields exist and sto reenergy in the spa ce immediatelysurround ing it when it is used fortransmitt ing even quite lowpowers (Fig. 2). In summary, ahigh value ofQ is the price paid forhaving a cap tur e area which ismuch bigger than the physical sizeof the anten na. On the other hand ahigh value of Q can expand theeffective capt ure are a to manytimes the size of a small antenn a.The ferrite rod ant enna used inradio receivers is an example of avery small anten na. For receivingBBC Radio 4 on 1500 metres a10 cm ferrite rod ante nna could becontained in a sphere which has aradius only 1130000of awavelength. If it was 100%efficient it could not have abandwidth greater than about198 kH~ (5000)~. uch a narrowbandwidth (about one millionth ofa hertz) would mean that only thecarri er frequency could bereccived. The sidebands whichcarry the programm e material (themodulation) would be totallyfiltered out an d nothing would beheard from the receiver.Fortunately H.W. Bode provedthat it is possible to trade efficiencyfor bandwidth. For the case of aresonant (high Q) circuit a tradeoffcan be made between thebandwidth and the power loss, sothat with quite a practical Q of 2or thereabouts the loss is about ahundred thousand times. Thissounds a lot but it is a loss which iseasily made good by the almostincredible sensitivity of any radioreceiver. A received signal ofwatt) is regarded a s a good signalat the receiver input.

watts (a million millionth ofa

For small transmitting antennas3 6 2 ELECTRONICS COMMUNICATION ENGIN EERING JOURNAL DECEMBER IYY



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there is Foster's' reaction theorem(based on a n energy conservationargument) , which is not very wellknown but which tells how tomatch a small antenna to atransmitte r with a minimum ofextra loss due to Q limitations. Italso allows maximum bandwidthto be retained when matching ananten na for several frequencies ofoperation. (The secret is tominimise the sto red energy bymaking all network reactances asfar as possible of the opposite signto the load reactances). Thistheorem was used in the design ofthe H F multicoupler in the beaconexpe rime nt in the first Universityof Sur rey satellite, the originalUOSAT."~Another property which varieswith the wavelength o r frequencyof radiation is what is called theskin depth. This is the depth thatthe radiation penetrate s a givenconducting material; it is inverselyproportional t o the square root ofthe frequency and of theconductivity of the mater ial. Theskin depth has a particularsignificance Cor hum an be ings. Itmeans that all the RF fields that wear e exposed to do not penetrate theskin sufficiently to give anysensation other tha n a heatingeffect simi lar to that of an electricfire, and then only when the powerdensity levels are similar, i.e. abouta kilowatt per square metre. Againsee Fig. 2 .Another nice theorem for radioanten nas and radi o transmission isthe 'principle ofreciprocity'. Itmeans that ifrcceiving andELECTRONICS COMMUNICATION EN(

transmitting antennas areinterchan ged there will be nocha nge in the received si gnal Cor agiven transmitt ed power (the pathloss is the same e ither wayprovided both anten nas are powermatched to their respectiveterminations). This is even true forthe earlie r example of the ferriterod antenna. For the fewmicroseconds that you could put400 kW into such an ante nna itwould be possible to receive asignal at the base of the BBC 200 mhigh antenn a at Droitwich equal tothat previously received by thereceiver with the ferrite antenn aTo obtain maximum radiatedpower an antenna must beresonated to the transmitlrequency and then matched inimpedance to the transmitte r.'Quiet' and 'silent' tuning","methods allo w this to be effectedprior to transmitting in anessentially undetectable way whichavoids any unnecessary spectr um'pollution'. The quiet tuningmethod is also a n application ofthe principle of reciprocity;interchangeof the position of adetector (sensitive radio receiver)and a test signal (very low powertransmitte r) in a match-sensingnetwork (standing-wave bridge)reduces th e radiated test signal bytwo order s of magnitude withoutaffecting the ability to determi nethe correct match conditions.8 The spectrum is a scarceresourceCurrently we use u p to about100GHz (10' megahertz) of theJEERING JOURNAL DECEMBER 1993

Fluorescenttubes detecting thestrongelectromagneticfields near a smalltransmittingantenna. Only 100watts weresupplied to a loopantenna typeA M A 3 from AA A)with a diameter ofone twenty-fifth ofa wavelength

electromagnetic spec trum for'wireless' transmission andcommunications. This can suppor tabout 30 million telephoneconversations or about 10millionlow-quality broadcast ch annels orabout 10 thousand televisionchannels, bu t obviously not all atthe sa me time. Cost considerationsmean that less than one tenth ofthe 100G H z spectrum is actuallywell utilised. It is useful tocompare 100G H z with thecapacity of one single optical fibre,which is about 2 4 000 GHz, or 240times as great. We are already inthe position that par ts of the radiospectrum are heavilyoversubscribed. There ar e twoconclusions to this. The first is thatthe EM spectrum should only beused when really needed for arequirement such as mobility;optical fibres should always beused wherever possible as analternative. The second reason isthat the spec trum should always beused as efficiently as possible,narrow-band modulation schemesand good frequency reuse beingthe major means for achieving this.

The spectrum bandwidth neededby a transmission depends o n theinformation or data rate of thematerial transmitted. Informationis taken to be that part of the datawhich is actually nee ded. Byremoving redundant data dramatic

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loop gain kept conslant

comparator attenuating voltagelow pass . controlledunwanted filter attenuated oscillator output= requency

digitaldivider

setfrequency

transmitter the oscillator noisespills over into the adjacen tchannels an d in t he case of areceiver signals in the adjacentchannels are allowed to corruptthe wanted signal by the processcalled reciprocal mixing. Ineither case the adjacent channelsbecome unusable.The frequency of an oscillator isdeter mined by a resonator tunedto the frequency of interest. Theability of a resonator to select onefrequency and not anoth er is givenby its Q, or quality, factor, which isthe same parameter as alreadyaddressed in the discussion on thebandwidth of an antenna.The phase noise of an oscillator,no matter how it is implemented,obeys a simple rule of thumboriginally put fo rward by LeesonI3(and subsequently both extendedand simplified by others i4). herule of thumb is that the timingjitterhoise which represents thephase noise in any oscillator isinversely proportional to thepower P of an oscil lator times thequality factor squared , Q2. Thus for

3 The principle of the high-gain phase comparator in a phase-lock -loop frequency synthesiser . The compensating attenuation al sotemperature can be made a lot lessthan the ambient temperaturewithout any real refrigeration. Theanalogy which can be made is thatof ground frost, where the groundtries to assume the noisetemperature of free space (4K)even though the air temperatureabove the ground is normal(provided there is no cloud cover ).This effect, for example, allowscur rent satellite TV dishes to be abit smaller than otherwise wouldbe the case: less gain, and henceless capture area, is needed for thesignal to overcome the noise. Therule of thumb when dealing withnoise is always to check the noisetempe ratu re to see if it is or is notin equilibrium with the ambienttemperature.9The theory of control is all abou tmaking things move as fast aspossible with minimum effort, and

Optimal control is the bestyou can do

To tvm action there

attenuates the sources of noisebandxvidth re duct ions can often bemade. For example, datacompr essio n by a factor of ten anda further three times bandwidthcompression (by multilevel coding)are to be in the new televisionstanda rds to bring the bandwidthoccupied by the digital signal backto that needed by the originalanalo gue signal Digitaltransmission does, however, bringother undoubted advantages, suchas better frequency reuse; this isbecause two digital signalsinterfere with each other less thantwo analogue signals. Shannons(well known) information theoremshows that such a tradeoff is onlypossible if eno ugh transmittingpower is used to give a largeenough received signal-to-noiseratio. In fact this is the way inwhich the spect rum occupied by asignal can be reduc ed below itsinformation bandwidth. The onlyproblem is that the power-bandwid th tradeoff follows alogarithmic law (logs to the base 2and then halved)so that anincrease of transmi tted power ofover 30 thousand times would beneeded to achieve a 30-to-bandwidth reduction by this meansalone.With a few rar e exceptions themeans by which one selects a givenchannel in the frequency spectrumis a stable frequency source whichis usually given the descriptivename oscillator.The frequency ofthe oscillator is changed to select adilk rent channel. I f the oscillatorused is itself noisy (having phasenoise), then in the case o ra

low phase noise in any oscillatorthe figure of meri t PQ shouldalways be as large as possible. Thisis also anoth er example of howbandwidth (whi ch is proportionalto Q - )can be traded with power P(but this time not in a logarithmicrashion).I t also turns out that the phasenoise of an oscillator can bereduced if its tempe ratur e isreduced (the noise is proportionalto temperature). In many cases inelectronics the effective noise

eqiactl arid opposite reactionNeuvtons Third La w)abou t reducing th e effects ordisturbances (or noise) on a systemto a minimum. Control can beapplied by electronics, but it canalso be applied to electronics toensure optimal performance.The two major techniques ofcontrol are feedforward, which ingeneral gives the fastest response

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times, and feedback, which is notso fast but allows noisedisturbances to be markedlyreduced. In both cases the veryuseful Laplace transform can beused to reduce t he system to becontrolled to an abstra ctmathematical model an d from thismodel the optimal control strategycan be designed. In the feedbackcase the techniqu e of the rootlocus (where the roots a re thepoles of the Laplac e transformcharacteristic equation of thesystem) has been used for manyyears. It allows near optimaldesigns to be reach ed using asimple, graphical, paper-and-pencil implementation, withoutovert recour se to any of theunderlying Laplace transformmathematics.Feedback control ca n be appliedto set the frequency of an oscillatorin a radio system in respon se to adigital command. Practically allcellular phones, car radios an d hi-fi tuners at present use a PLLfrequency synthesiser whichimplements the digital frequencycontro l using a phase-locked loop(PLL). The adva ntage of thisfeedback contro l system is that thelow phase noise that it is possibleto achieve with a st able fixedfrequency reference oscillator ca nin great part be transferred to thedigitally controlled variabl e-frequency oscillator.transfer function which describesthe path gain from an input pointto an out put point is given by theforwa rd path gain (FP) divided byone minus the loop path gain(Loop):ou tpu thpu t = FP/(l-Loop)This equation normally has a plusrather than a minus sign in thedenominator because negativefeedback is usually requi red tokeep the control system stable (a ndhence to prevent runawayoscillations of the output) . Thisquite general fact alloweddram atic improvements to bemade in reducing the phase noiseof PLL fr equency synthesisers. Theprinciple of the high-gain phasecompa rator is that, as the gain ofthe phase compar ator is increased,a compensating attenuation has tobe placed el sewhe re in thefeedback loop to keep the loop gainat its optimal value (Fig. 3).15 f it ispossible to place the attenuationclose to the output, most if not allsource s of noise within th efeedback loop become r educed ineffect by the value of theattenuation. In this way the output

For any single feedback loop the

ELECTRONICS COMMUNICATION EN1

(close to carri er) phase noise of thefrequency synthesiser ca n becomedramatically less (or it can betrade d off for a faster speed ofswitching from one frequency toanother). This principle wasoriginally designed into the Philipssynthesiser chip s HEF475014751in 1979 and subsequently into theSAA1057 and TSA6057 chips, thelatter of which provides thefrequency synthesiser in mostcurrent Philips car radios and hi-fituners.Optimal feedforward control isbased on a theorem of Pontryaginwhich employs somewhat abstrusemathematics (at least, abstruse toan engineer) to prove the commonsense proposition which, whenpar aph ras ed, is you will achieveyour objective in the shortestpossible time if you applymaximum possible effort duringtha t time . The basic complexity ofa control system is given by itsorder , which is always a positiveinteger (a nd is the number of rootsor poles in the denomina tor of thetransfer function or systemcharacteristic equation). Thesecond proposition of Pontryaginstheorem is that for time optimalcontro l you have to reverse thedirec tion of the applied effort frompositive to negative the sa menum ber of times as the orde r of thesystem. (Again commonsense c angive this answer without advancedmathematics; the number ofswitching instants, or degre es offreedom, in the control input, mustbe equal to the number of degreesof freedom, or order,of thesystems). The problem th enreduces to one of determining thetiming of the corre ct switchinginstants. The traditional method ofdetermining the switching instantshas been by dynamicprogramming, which needs acomputer to find the right answersessentially by trial and er ror.However, a recent advance hasbeen ma de which uses the Laplacetransform to derive somenonlinear simultaneous equationswhich, when solved, provide thecorrect answe rs for the switchinginstants. I n a useful number ofcases the equa tions can be solveddirectly, but for more complexsystems, unfortunately, a trial-and-error method has to be used to findthe answer, albeit in a mor e directand efficient way.A major achievement of controltheory is that it tells how aninitially unstable system c an bemade stable. An unstab le system ischaracterised by growingoscillations of its output or anJEERING JOURNAL DECEMBER 1993

output which accelerates towardseventual saturation or destruction.A prese nt day example is theEuropean Fighter Aircraft (EFA)which, if it was not stabi lised by afly-by-wirecomputer, would becompletely unflyable by a pilot. I nthis case th e instability isdeliberate because it makes theaircraft much more manoeuvrableand faster in response to controlcommands from the pilot. Otherexamples of unstable systems arcthe tight-rope walker and the platebalanc ed on a jugglers stick, thislatter being an exam ple of theinverted pendulum. It is generallythought th at you must havenegative feedback to stabilise allunstable systems and it is thereforerather surprising to rind that someunstable systems can actually bestabilised by oscillations if they areapplied from outside the system.The inverted pendulum is anexample of such a system. Ifvertical oscillations greater inamplitude than the downwardacceleration of the gravitationalforce are applied to the pivot, thependulum will swing of its ownaccord to a stable vertical position.The frequency of the oscillation isnot critical. I n fact this can also bedemonstrated to be true if thependulum is in several hingedsections (rods), and even if thehinges can bend in any direction asin a universal joint. The hingesmust, however, be rigid enough totransfer the applied accelerationfrom one rod to the next. Theconsequence of this is that,provided that you can accept arope made of a num ber of shorthinged rods, the I ndian Rope Trickshould no longer be considered amyth but ra ther a demonstrablereality (Fig. 4). (For those whodoubt the veracity of the above it isworth pointing out that theinverted pendul um is actually anonlinear system with respect tovertical motion of the pivot and sosimple linear control theory doesnot provide the correct theoreticalbasis for analysis of why theinverted pendulum can bestabilised by oscillation.)10 Fly-by-wire is only safeBecause digital systems such asdigital com puters ar e completelydeterministic and completelylogical they are considered sale touse in safety-critical real-timecontro l applications such a s fly-by-wire cont rol of civil and mili taryair cra ft. Any residual worries onthe sa& of such systems areusually direct ed at the software in

given time

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1 The Indian ropetrick threesection inverted[upside-down)pendulum stabilisedby vertical oscillationof the lowest pivotpoint

which store the true or falsestates (noughts and ones) of thebinary logic are given thedescriptive name of flip-flops.Areasonable analogy to a flip-flop isan inverted pendulum which isallowed to fall into a horizontalposition to the left to signify afalse,or 0, state or horizontally tothe right for a true, or 1 state.The maybestate thencorresponds to the metastablestate of the pendulum balancing inthe vertically uprigh t position.corresponding calculations on anassumed model o r a flip-flop showthat any flip-flop can sit in themetastable sta te for many timeslonger than it would normally taketo switch from one of its two stablestates to the other (that is undernormal switching conditions).Theoretically and practicallythere is always a finite and notinsignificant probability that aninpu t flip-flop of any real-timecomputer can be set into themetastable state. Furthermore t hemetastable state can propagat eseveral flip-flop stages into thecomputer, but fortunately withdecre asing probability. If thecomputer programme bases acritical real-time decision on theuncertain information of ametastable state a potentiallyunsafe computer e rro r will resultwith a finite probability.In a typical case the chanc es ofenter ing a metastable state lastinga time equal to the characteristictime constant T , of the flip-flopcould be as high as one in athousand . The characteristic time

Both investigations and

the tly-by-wire compu ters.Every effort is made to eliminatethe possibility of any software bugscreating unsafe conditions.Sophisticated matheniatical toolssuch as formal methods, theoremproving and code verification ar ebrought into play.However, there is one highlysuspect operation of the hardwareof the digital computer that ca nhave major safety implications.That is the process of arbitration,or deciding whether one event tookplace before or after another event.Inside the computer the need forarbitration c an be completelyavoided provided the computernever refers to the outside worldafter whatever programme it isexecuting has been started. Allactions and logical decisions thentake place synchronised with theinte rnal clock of the computer.Provided that the computer is welldesigned and not faulty there isthen a zero probability of aresulting err or o r deviation fromthe totally deterministic executionof the programme of the computer.The time when arbit ration isrequired is when a human beingpresses a key or butto n, or a real-time control system raises a flag, tointerrupt he computerprogramme so that new data canbe passed into the com puter . Theproblem is that the timing of theinterrupt request may coincidewith the co mputer clock, so thatthe input arbitra tion of yes herehas been a n interrupt or no herehas not been an interrupt becomesa totally indecisive maybe. Insidethe digital hardwar e the elements

const ant of the flip-flops in acontrol computer cap able of aclock rate of 8 or 16 MHz might beabout 10 ns o r longer. Theswitching time of the flip-flopwhen switching normally withlarge, decisive, input signals willbe considerably shorter and this iswhat is normally quoted in thedata sheets. Fig. 5 shows somemeasurements of metastability inbasic flip-flops.Very fortunately the probabilityP of the flip-flop staying in themetastable stat e decreasesexponentially with time Iaccording to t he formulaP = exp(-t/T,). This means that Coreach time constant T, of time theprobability decreases bye = 2.718.So the solution to the problem is towait long enough for the flip-flopto settle into a definite state with asnear as possible absolutecertainty. This would appear tobe the only solution to the problemsince no real-time system has (yet)been designed that avoids themetastable st ate ever beingenter ed. The general view is thatmetastability is inescapable,although there has been n o formalproof of this at the prese nt time.The question is how long is longenough for a flip-flop to settle withnear enough absolute certainty. Itcan be argued that an absolutelimit could be taken to be aprobability equal to the ra tio of thelargest length, the diame ter of theuniverse, to the Planck length. Thisratio is approximately lo6.Waiting a t ime of 143 timeconstants T , is enough to ensurethis level of (im)probability. For T ,

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equal to 10 ns, then in 1.43~s onecan be sur e that th e flip-flop in theabove example has really settled toa definite decision.The necessity to wait for a safedecision is treat ed in only a fewtext-books." So, unfortunately

there must be a finite probabilitythat som e safety-critical hardwaredesigns are not in fact safe at all. Ifthe real-time computer system isdesigned to wait for one cycle of acomputer with a 10 MHz cyclerate, th e probability of ametastable failure is only improvedby a factor of e , which is about22 000 With a fly-by-wirecomputer taking thousands of datareadings a second, this probabilityis decidedly unsafe.Good engineering ca n totally

avoid the likelihood of unsafe real-time computer failures due tometastability. Because of thedangers, it would be a wisepreca utio n if all safety-criticalsystems were audited t o check forcorrect design against metastableerro rs. This would be a relativelysimple measure to put i nto effectsince there is only one solution tometastability and th at is to waitlong enough.1 1 A marginal speculation:neutrino communications forthe invisib le fibreA good speculation can can have apowerful (almost magical ) effecton stimulating either evolutionaryo r revolutionary advances in bothscience and engineering. Goodspeculation has to be bothimaginative an d realistic. Thequality of a speculation can only be

Iffinally judged wi th hindsight an dhindsight ca n deal a cruel blow tothe overoptimistic or to thosewhose feet are not firmly on theground. The following is a'wouldn't it be nice if' type ofspeculation. The hope is that itslogical basis is at least reasonablyplausible, free from anyinsurmountable flaws and not inconflict with any 'laws of natu re'as they are now known.question, 'Wouldn 't it be nice ifthere was a free-space invisibleequivalent of the fibre-optic cable ?The proposition is that a highlyfocused beam of neutrinos couldbe a candidate mechanism for 'theinvisible fibre'. Neutrinos ar e ofcourse the fundamental particleswhich serve the function ofconveying a quant um of angularmomentum even though theneut rino mass is very small (stillthought to be zero accordi ng tosome neut rino theories).There are a number of appare ntflaws in this proposition. One isthat neutrinos barely interact withanything a t all. Onlya very tinyfraction of the neutr inos reachingthe eart h and originally emitted

The speculation arises from the

time

MOS 4011time

b

5basic flip-flop; b ) ircuit and successive time waveforms of half D-type flip-flopELECTRONICS COMMUNICATION ENGINEERI NG JOURNAL DECE MBER 1 Y Y 3

Metastability in any digital flip-plop takes several time constants to finally resolve: a) ircuit and successive time waveforms of

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from the nuclear reactions takingplace in the sun are actuallystopped by the mass of the earth;most pass straight through withouttrace. This transpa rency of allnormal materials is a greatadvantage provided that a beam ofneutrinos could be directed,modulated with intelligence orinformation, and then detectedefficiently by some mea ns a t adistant point. The informationwould be transmitted directly fromany one point to any other point onthe earth in a straight line.The question is then now couldneutrinos be detected moreefficiently than by the presentmethod, which relies on thestimulation of an atomic nuclearreaction with detectableradioactive decay o r fissionproducts."If it could be shown that theneutrino has a well defined andstable characteristic resonantfrequency then the process ofresonant in teraction could beengineered to increase the capturearea or captur e cross-section forthe neu trino by many times. Theprocess is analogous to the captur earea of a resonant radio antennabeing many times its physical ar ea.There have been numer ousexperiments measuring the 'beats'of interacting neutrinos.'" Theseare interpreted in (quantum-mechanical) wave function terms,but this does not rule out theproposition that a neutrino mayhave a characteristic frequencymore akin to that of anelectroma gnetic wave.(electron) neutrino mass is5 to 50 eV (5 eV is about onehundred thousandth of the mass ofan electron). If considered to be inthe form of pure electr omagneti cenergy (via the formula E = ku ,amass of 10 eV has a characteristicfrequency of about 2.4 x 1 l5H z , 012.4 x 10' G H z . (Ifnot in the form ofpure electromagnetic energy thecharacteri stic frequency would belower). This is not a very highfrequency, being only about sixtimes the frequency of visible light.Its wavelength (; l=c/u) is about0.1 pm or 1000 A, which is about200 atomic spacings i n a typicalcrystal lattice. Modern technologyallows layers of single-atomthickness to be created. It does nottake too much imagination tosuppose that a repetitive structureora tom s (pe rhap s in the form ofcavities) with a repetition distanceequal to the presumed neutrinowavelength could indeed be made.Such a structure could resonantly

The latest best estimate of the

ouple to a neutrino, travelling ast does at very nearly the velocity ofight, but only for a sharply definedlirection of incident neutrinos. Itnight have to have a spiral form to)e sensitive to the spin o r thetngular momentum that aieutrino has. Such a repetitive,tructure could act in the sameway as a high-gain multi -element)based-array radio antenna which,xc aus e of its high gain, wouldlave a very much enhanced:apture cross-section at therequency of the neutrino. Aurth er refinement which could bemagined is that the repetitive;tructu re is successively graded iniimension on the supposition that.he frequency of the neutrinoNould fall as it gave up energy to.he resonant repetitive structure.:A swept frequency receiver would.hen be needed.) This is the:onverse of the frequency sweepx-ocess used in thesynchrocyclotron to acceleratedec trons to higher energies. Thismethod of detection would be anighly directional absorptiveprocess, so that it could also beused to modulate the intensity of ax a m of 'transmitted' neutrinos byabsorption. The absorption couldbe varied by varying the angle ofincidence of the abso rbingresonant struct ure.Such a speculation is pretty far-Fetched and has a lot ofassumptions. If it transpires that alaw of physics has beencontravened then the speculationwill fail and not be fulfilled: but ifnot, then it would be an example ofhow a new piece of magic canappear in the margins. Even if thisparticular piece of magic neverhappens , then something elseequally magical almost certainlywill. So delving into the margins ofelectronics will continue to be anexciting and worthy challenge.

ReferencesI 'Longman concise Englishdictionarj ' (Longman, 1985). p.8352 CURZON, L.B.: 'Dict ionar yofla w'(Pitman, 1988,3rd edn.). p.2163 CURZON,L.B.:op.cir.,p.1874 COLLIN R.E.: 'Antennas andradiowave propagation' (McGraw-Hill,1985). pp.47-675 C H U , L.J.: 'Physical limitations of

xnni-directional antennas', J.App1. Phvs . ,kc em be r 1948, 19, pp.1163-1175j WHEELE R, H.A.: 'The radiansphe reiround a small antenna', Proc. I R E ,4ugust 1959,47, pp. 1325-1331.7 WHEELER, H.A.: 'Fundamentalimitations of small antennas'. Proc. I R E .December 19 47.35 , pp.1479-1484BODE, H.W.: 'Network analysis andeedba ck amplifier design' (VanVostrand. 19 45)FOSTER, R.M.: A reactance.heorern', E e l l S y s r . Tech.J . . April 1924.3p.259-2671 SMITHERS, C.R., andUNDERHILL, M.J.: 'The U 0 S A T h . l .Deacons experiment', R u d i o undElecrron. n g . , AugusliSeptember 1982,52. (8/9),pp.407-411I 1 LEWIS, P.A., and UNDERH ILL,M.J.: 'Quiet tuning an d matc hing ofantennas for radio silence operation',IEE Proc.-F., October 198 0, 127, 5).pp.361-36712 UNDERHILL, M.J. an d LEWIS,P.A.: 'Silent tuning of antennas'. IE ECon/: Pub .No 24.5, HF CommunicationSystems and Techniques, February 1 985,pp.94-9 813feedback oscillator noise spectrum ',Proc. IEEE, 1966, 54, (2) pp.329-33014 UNDERHILL, M.J.: 'Fundame ntalsof oscillator performanc e'. Eleclron.Commun. E n g . J . , August 1992,4 , (4),pp. 185-1 9315 UNDERHILL , M.J., an d CLARK,M.A.G.: British Patents I47 758 4 (1975)and 1519933(1977)16 CHANG. S.S.L.: 'Synthesis ofoptim um control syatems' (McGraw-Hill,1961).Chap. 9 . pp.216-25417 UNDERHILL , M.J., andCRAWFORD, M.J.: 'Simple derivation ofdead-beat bang-bang and stepped levelservocontrol', Eleclron. L e l f . ,2nd July1992.28, (14)pp.131I-l31318 VAN DER HEI DE. H.: 'Stabilisationby oscillation', Philips Tech. Rev . , 1974.pp.61-72, 34, (213). This article attr ibutc sthe discove ry of t he effect t o A.Stephenson according to a literaturesearch by B. van de r Pol in Phy.sicu 1925,5, 15719 WAKERLY, J.F.: 'D igital desig nprinciples and practices' (Prentice-Hall.1990),particularly Figs. 6-98 a nd 6-100in Chapter 620 BOEHM, F., and VOGEL. P . :'Physics of massive neutrinos'(Cambridge University Press. 1992, 2ndedn.)

LEESON. D.B.: A simple model of

EE: 1993

This Inaugur al Address was deliveredbefore the IE E Electronics Division atSavoy Place, London on 13th October1993.

Professor Underhill is Hcad ol th eDepartment of Electronic an d Electi-icalEngineering, University of Surrey.Guildford, Surrey GU2 SXH, UK.368 ELECTRONICS COMMUNICATION ENGINEERING JOURNAL DECEMBER Y Y

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