Sound Systems: Design and Optimization. Modern Techniques and Tools for Sound System Design and Alignment

549 Pages·2010·113.86 MB·English

by  Bob McCarthy (Auth.)

1
CHAPTER
Transmission
transmissionn.trans-
mittingorbeingtrans-
TRANSMISSION GOALS
mitted;broadcast
program
Transmissionistheconveyanceofawaveformfromoneplacetoanother.Transmission
transmitv.t.1.passon,
qualityisjudgedbyhowfaithfullythearrivingsignaltrackstheoriginalwaveform.We
handon,transfer,com-
capturetheoriginalacousticorelectronicwaveform,withtheintentofeventually municate.2.allowto
reconstitutingitintoanacousticwaveformfordeliverytoourears.Theoddsareagainstus. passthrough,bea
Infactthereisabsolutelyzeroprobabilityofsuccess.Thebestwecanhopeforisto mediumfor,serveto
minimizethedistortionofthewaveform,i.e.,damagecontrol.Thisistheprimarygoalofall communicate(heat,
effortsdescribedinthisbook.Thismaysounddispiriting,butitisbesttobeginwitha light,sound,electricity,
emotion,signal,news)
realisticassessmentofthepossibilities.Ourultimategoalisonethatcanbeapproached,
ConciseOxford
butneverreached.Therewillbelargenumbersofdecisionsahead,andtheywillhinge
Dictionary
primarilyonwhichdirectionprovidestheleastdamagetothewaveform.Thereareprecious
fewavenuesthatwillprovidenone,andoftenthedecisionwillbeaveryfineline.
3
Our mainstudy ofthe transmission path willlook at threemodes oftransmission: line
level electronic, speaker levelelectronic, and acoustic. Ifanylink inthe transmission chain
fails, ourmission fails. Byfarthemost vulnerable link inthechain is thefinal acoustical
journey fromthe speaker tothelistener. Thispath is fraught withpowerful adversaries in
the formofcopies ofouroriginal signal (namelyreflections and arrivalsfrom theother
speakers inour system),which willdistort ourwaveform unless they areexactcopies and
exactly intime.Wewillbegin withadiscussionof theproperties oftransmission thatare
commonto allpartsofthe signalpath (Fig.1.1).
AUDIO TRANSMISSION DEFINED
Anaudio signalundergoes constant change, withthe motion ofmolecules and electrons
transferring energy awayfromavibrating source.When theaudio signalstopschanging, it
ceases toexistas audio. Asaudio signals propagateoutwards, themolecules and electrons
are displaced forwardand backbut never actuallygo anywhere,always returning totheir
FIGURE 1.1
Transmissionflowfromthesignalsourcetothelistener.
SoundSystems:DesignandOptimization
r2010BobMcCarthy.PublishedbyElsevierLtd.Allrightsreserved.
SECTION 1
Sound Systems
point oforigin.The parameter thatdescribes theextentof thechangeis theamplitude,
also referredtoas magnitude. Asingle round trip fromorigin and backisacycle.The
round trip takes time.That lengthoftime is theperiod and isgivenin seconds, orfor
practicalreasons in milliseconds(ms).The reciprocalof theperiod isfrequency,the
number ofcycles completedpersecond, giveninhertz(Hz). The round trip is continuous
withno designated beginningor end. The tripcan beginanywhere onthe cycleand is
completed upon ourreturn tothesame position. The radialnature oftheround trip
requires ustofind ameansofexpressingour location aroundthe circle.Thisparameter is
termedthe phaseofthe signal.The valuesareexpressed indegrees, ranging from01
(point oforigin) to3601 (acomplete round trip). The half-cyclepointin thephase
journey, 1801, willbe ofparticular interest tousas wemove forward.
Alltransmission requiresamedium,i.e., theentity through which theaudio signal passes
frompoint topoint, made ofmolecules or electrons.In ourcase,theprimary media are
wire (electronic) and air(acoustic),but there areinterim media aswellsuch asmagnetic
and mechanical. The processoftransferring theaudio energybetween media isknown as
transduction. The physicaldistancerequiredto complete acycleinaparticular medium is
the wavelength and isexpressed insome formoflength, typicallymeters orfeet.The size
ofthe wavelength foragivenfrequency is proportional tothe transmission speed ofour
medium.
The physical nature of the waveform’s amplitude component is medium-dependent. In
our acoustical case, the medium is air and the vibrations are expressed as a change in
pressure. The half of the cycle with higher than the ambient pressure is termed
pressurization, while the low-pressure side is termedrarefaction. A loudspeaker’s
forward motion into the air creates pressurization and its rearward movement creates
4 rarefaction.
The movements ofspeaker cones donot push airacross theroom inthe manner ofafan.
Ifaroom is hot,it isunlikely thatloud music willcoolthings down. Instead airismoved
forward and thenit is pulledback toitsoriginal position. The transmission passesthrough
the medium,whichis animportant distinction. Multiple transmissions canpass through
the medium simultaneously even fromdifferent directions.
Electricalpressurechangeisexpressedaspositiveandnegativevoltage.Thismovementis
alsotermedalternatingcurrent(AC)sinceitfluctuatesaboveandbelowtheambient
voltage.Avoltagethatmaintainsaconstantvalueovertimeistermeddirectcurrent(DC).
Our designand optimization strategiesrequire athorough understanding of the
relationships between frequency,period, and wavelength.
Time and frequency
Let’s startwithasimple tone, asinewave, andthe relationship offrequency (F)and
period (T):
T ¼1=F and F ¼1=T
whereT is thetime period ofasingle cycle insecondsandFis thenumber of cyclesper
second (Hz).
To illustratethis point, wewill useaconvenient frequency and delayfor clarity:1000Hz
(or1kHz) and 1/1000th ofasecond (or1ms).
Ifweknow thefrequency, wecansolve for time.Ifweknow time, wecansolve for
frequency. Therefore
CHAPTER 1
Transmission
F ¼1=T 1000Hz31=1000s
1000Hz30:001s
1000Hz31ms
T ¼1=F 0:001s31=1000Hz
1ms31=1000Hz
For mostof this text,weabbreviate thetime period tothe term“time”toconnote the
cycle duration ofaparticular frequency (Fig. 1.2).
Frequency is thebest-known parametersince it iscloselyrelated tothe musicalterm
“pitch.” Most audio engineersrelate firstinmusical termssince fewofusgot into this
business because ofalifelong fascination withacoustical physics.Wemust gobeyond
frequency/pitch, however, sinceourjob is to“tune”the sound system,nottunethe
musical instruments. Optimization strategies require anever-present three-waylink
between frequency,period,and wavelength. The frequency 1kHz existsonlywithits
reciprocal sister 1ms. Thisis notmedium-dependent, nor temperature-dependent, nor
waiting upon astandards committeeruling.This isoneof audio’s fewundisputed
absolutes. Iftheaudio istraveling inawire,those twoparameters willbe largely sufficient
for ourdiscussions. Once intheair,we willneed toaddthe third dimension:wavelength.
A 1kHz signal onlyexistsinair asawavelength about as longasthe distancefromour
elbow toour fist.Allbehaviorsat 1kHz are governed by thephysicalrealityofthe signal’s
time period and itswavelength.The first ruleofoptimization is tonever think ofan
acoustical signalwithout consideration ofall threeparameters.
5
Wavelength
Wavelength isproportional to themedium’s unique transmission speed.A givenfrequency
will haveadifferentwavelength in itselectronicform (over500,000 (cid:2)larger) thanits
FIGURE 1.2
Amplitudevs.timeconvertedtoamplitudevs.frequency.
SECTION 1
Sound Systems
Table 1.1 Speedofsoundreference
Plainlanguage Imperial/American Metricmeasurement
measurement
Speedofsoundinairat01 1052ft/s 331.4m/s
+Adjustmentforambientair +(1.1(cid:2)T) +(0.607(cid:2)T)
temperature TemperatureTin1F TemperatureTin1C
= Speedofsoundatambient =cfeet/second = cmeters/second
airtemperature
acoustic version.Ifthe medium is changed,its
transmission speed and all thewavelengths change
withit.
The wavelength formula is
L¼c=F
whereL isthe wavelength inmeters, cis the
transmission speed of themedium, and Fis the
frequency (Hz).
6
Transmission speed through airis amongthe slowest.
Wateris afarsuperiormedium interms ofspeed and
high-frequency (HF)response; however, thehazards of
electrocution and drowning make thisan unpopular
sound reinforcement medium (synchronized
swimming aside).Wewillstickwith air.
The formulas forthe speedof sound inairare as
shown inTable 1.1.
Forexample, at 221C:
c¼ð331:4þ0:607(cid:2)22Þm=s
c¼344:75m=s
The audible frequencyrange giveninmost books is
FIGURE 1.3
20Hz to20kHz. Fewloudspeakers are ableto
Chartoffrequency,period,andwavelength(atroomtemperature)forstandard reproduce the20Hzor 20kHz extremesat apower
one-thirdoctavefrequencies.
levelsufficient toplay asignificant role.Itis more
usefulto limitthe discussionto those frequencies we
are likelytoencounter in thewild: 31Hz(the low Bnoteon afive-string bass)upto
18kHz.The wavelengths withinthis band fallinto asizerange ofbetween the widthof a
fingerand astandard intermodal shipping container. The largestwavelengths areabout
600times largerthanthe smallest
(Figs 1.3–1.5).
Whyit is thatweshould be concerned about wavelength?Afterall,there areno acoustical
analyzers thatshowthis on their display.Thereare no signal-processing devices that
CHAPTER 1
Transmission
depend onthis for adjustment. In practice,thereare
some applicationswhere wecanbe blissfully
ignorant ofwavelength, for example:when we usea
single loudspeaker inareflection-free environment.
For allotherapplications, wavelength isnot simply
relevant: it isdecisive.Wavelength isthe critical
parameter inacoustic summation.The combination
of signalsat agiven frequencyis governed by the
number of wavelengthsthatseparate them. Thereis
alot atstake here,as evidencedby thefact that
Chapter 2 isdedicated exclusively tothis subject:
summation. Combinations ofwavelengths canrange
from maximum addition tomaximum cancellation.
Since weare planning on doing lotsofcombining, (a)
we had bestbecome conscious ofwavelength.
TEMPERATURE EFFECTS
As wesaw previously,the speedof sound inairis
slightly temperature-dependent. As theambient
temperature rises, sound speedincreasesand
therefore thewavelengths expand.This behaviormay
slightly affecttheresponse of oursystems overthe
duration ofaperformance, since thetemperature is
subject tochange eveninthe mostcontrolled
environments. However, although it is often given
7
substantial attention, this israrelyamajor factor in
the big picture.A poorlydesigned systemis not
likely tofind itselfrescued by weatherchanges. Nor
is it practicaltoprovide ongoing environmental
analysis overthe widespread areasofan audience to
compensate for draftsinthe room.For our
discussion, unless otherwisespecified, wewill
consider the speed ofsound tobe fixed
approximately at room temperature.
The relationship between temperature and sound
speed can beapproximated as follows: a1%change
in thespeed ofsound occurs witheither a51C or
101F changeintemperature. (b)
FIGURE 1.4
Handyreferenceforshortwavelengths.
Waveform
There isno limit tothe complexity ofthe audio signal.Waves atmultiple frequencies may
be simultaneously combined to makeanew and unique signalthatis amixtureofthe
contributing signals. Thiscomposite signal isthe waveform,containing anunlimited
combination ofaudio frequencies withvariableamplitude and phaserelationships. The
waveform’s complex shapedepends upon thecomponents thatmakeit upand varies
constantly as they do.A keyparameter ishow the frequencycontent ofthe contributing
signals affectsthe combined waveform (Figs1.6–1.8).When signalsat different
frequencies are added, the combined waveform will carrythe shapeofbothcomponents
independently. The higherfrequency is addedtothe shapeofthe lower-frequency
waveform. The phaseofthe individual frequencies willaffectthe overall shapebut the
SECTION 1
Sound Systems
different frequencies maintain theirseparate identities.These signals canbe separatedlater
by afilter(asinyour ear)and heardas separate sounds. When twosignalsof thesame
frequency arecombined, anewand unique signal iscreated thatcannot be filtered apart.
In thiscase,the phaserelationship hasadecisiveeffect upon thenature ofthe combined
waveform.
Analogwaveform typesinclude electronic, magnetic,
mechanical, optical, and acoustical. Digital audio
signalsare typicallyelectronic, magnetic, oroptical, but
the mechanicsof thedigitaldata transfer arenot critical
here.Itcould be punch cards aslongas wecan move
themfast enoughto readthedata. Eachmedium
tracksthe waveform indifferent forms ofenergy,
suitable forthe particulars ofthattransmission mode,
complete withits own vulnerabilities and limitations.
Digital audio is most easilyunderstood when viewed as
amathematical rendering ofthewaveform.For these
discussions, this is nodifferent fromanalog,whichin
any ofitsresident energy forms canbe quantified
mathematically.
The audio signal canbe visualized inthreedifferent
forms as shown inFig.1.9. Asingle cycleisbrokeninto
fourquadrantsof901each.Thismotionformillustrates
themovementofthesignalfromapointofrestto
maximumamplitudeinbothdirectionsandfinally
8 returningtotheorigin.Thisisrepresentativeofthe
particlemotioninairwhenenergizedbyasoundsource
suchasaspeaker.Italsohelpsillustratethepointthat
themotionisbackandforthratherthangoingoutward
fromthespeaker.Aspeakershouldnotbeconfused
FIGURE 1.5 withablower.Themaximumdisplacementisfoundat
Chartofspeedofsound,period,andwavelengthatdifferenttemperatures. the901and2701pointsinthecycle.Astheamplitude
FIGURE 1.6
Referencechartofsomeofthecommontermsusedtodescribeandquantifyanaudiowaveform.
CHAPTER 1
Transmission
FIGURE 1.7
Combinationofwaveformsofthesamefrequencyatthesamelevelwithdifferentphaserelationships:(a)01relativephasecombinesto +6dBamplitude,
(b)901relativephasecombinesto +3dBamplitude,(c)1201relativephasecombinesto +0dB,(d)1801relativephasecancels.
9
FIGURE 1.8
Combinationofwaveformsofdifferentfrequencieswithdifferentlevelsandphaserelationships.(a)Secondfrequencyis5(cid:2)higherand12dBdowninlevel
fromthefirst.Phaserelationshipis01.Notethatbothfrequenciescanbeseeninthecombinedwaveform.(b)Sameas(a)butwithrelativephaserelationship
at1801.Notethatthereisnocancellationinthecombinedwaveform.TheorientationoftheHFtracehasmovedbuttheLForientationisunchanged.
(c)Combinedwaveformof(a)withthirdfrequencyadded.Thethirdfrequencyis25(cid:2)thelowestfrequencyand18dBdowninlevel.Thephaserelationship
ismatchedforallfrequencies.Notethatallthreefrequenciescanbedistinguishedinthewaveform.
SECTION 1
Sound Systems
FIGURE 1.9
Threerepresentationsoftheaudiowaveform.
increases,thedisplacementfromtheequilibriumpointbecomeslarger.Asthefrequency
rises,thetimeelapsedtocompletethecycledecreases.
The radialformrepresents the signalas spinning inacircle.The waveform origin point
corresponds to thestartingpoint phasevalue,which could be anypoint onthe circle.A
cycle iscompleted when wehavereturned tothe phasevalueof thepoint oforigin.This
representation shows therole thatphasewillplay. Thedifference inrelative positionson
10 this radialchart ofanytwo soundsources willdetermine how the systems willreactwhen
combined.
The sinusoidal waveform representation isthe most familiartoaudio engineers and can
be seen on anyoscilloscope. The amplitude value istracked overtime and tracesthe
waveform inthe order inwhich thesignal passesthrough. Thisisrepresentative ofthe
motion over time oftransducers and changingelectrical valuesofvoltage overtime.
Analog-to-digital (A/D) converterscapture this waveform and createamathematical
valuation of theamplitude vs.time waveform.
Perspectives:Ihavetried
tobringlogic,reasoning,
andphysicstomyaudio
TRANSMISSION QUANTIFIED
problemapplications.
WhatIhavefoundis Decibels
that,whenthecauseof
Transmission amplitudes, alsoknown as levels,are most commonly expressed indecibels
aneventisattributedto
(dB),aunit thatdescribes aratio between twomeasures. The decibelis alogarithmic
“magic,”whatthisreally
meansisthatwedonot scaling systemusedto describeratioswithaverylargerangeof values.Using the decibel
haveallthedataneces- hasthe addedbenefit ofcloselymatching ourperception ofsound levels,which is
sarytounderstandthe generallylogarithmic. There are variousdB scalesthatapply totransmission. Because
problem,orwedonot decibels are basedon ratios,they are alwaysarelativescale.The question is:relativeto
haveanunderstanding
what? Insome cases,wecompare toafixed standard. Because audio isin constant
oftheforcesinvolvedin
change, it isalso usefulto haveapurely relativescalethatcompares twounknown
producingtheobserved
signals. Anexample ofthe lattertype is theratio ofoutput to inputlevel.Thisratio, the
phenomena.
gain ofthe device,can be quantified eventhough adrivesignal suchas music is
DaveRevel
constantly changing.If thesame voltageappears at theoutput and input, theratio is 1,
also knownas unity gain,or0dB.Ifthe voltageat the output isgreater,the gainvalue
exceeds1,andexpressedindB,ispositive.Iftheinputisgreater,thegainratioislessthan
1andexpressedindBisanegativenumber,signifyinganetloss.Theactualvalueatthe
CHAPTER 1
Transmission
inputoroutputisunimportant.Itisthechangeinlevel
betweenthemthatisreflectedbythedBgainvalue.
There aretwo typesof log formulasapplicable inaudio:
Level
RelativelevelðdBÞ¼20(cid:2)log 1
10Level
2
Power
RelativepowerðdBÞ¼10(cid:2)log 1
10Power
2
Power-related equations usethe 10 logversion, while
pressure- (SPL) and voltage-relatedequations usethe 20
log version.Itis important thatthe proper formula be
used sinceadoubling ofvoltageis achangeof6dB
while adoubling ofpower isachange of3dB. Forthe
most part,we willbe using the20 log versionsince
acoustic pressure (dBSPL) and voltageare theprimary
drivers ofourdecision-making. Figure1.10 providesa
reference charttorelate theratiosof valuestotheir
decibel equivalents.
FIGURE 1.10
HereisahandytipforMicrosoftExcelusers.Figure1.11
showstheformulaformatforlettingExceldothelog TheratioofoutputtoinputcanbeconvertedtodBwiththiseasyreferencechart.
Tocompareagivenleveltoastandardone,Level isthegivenlevelandLevel
calculationsforus. 1 2
isthestandard.Toderivethegainofadevice,Level istheoutputleveland
1
Level istheinputlevel.Likewisethepowergaincanbefoundinthesameman- 11
2
nerbysubstitutingthepowerparameters.
THE ELECTRONIC DECIBEL: dBV AND dBu
Electronic transmission utilizesthe decibelscaleto
characterize thevoltage levels. Thedecibel scaleis
preferred by operatorsover thelinear scaleforits
relative ease ofexpression.Expressed linearly,wewould
find ourselves referring tothe signalin microvolts,
millivolts, and voltswithvarious setsofnumbervalues
and ranges. Such scalingmakesit difficult to tracka
variablesignal suchas music. Ifwewantedto double
the signallevel,we would havetofirstknow the (a)
voltage ofthe original signaland then compute its
doubling. Withdynamicallychanging signalssuch as
music, the levelat anymoment isinflux, making such
calculations impractical. The decibelscale providesa
relative changevalue independent of theabsolute
value. Hencethedesire todouble the levelcanbe (b)
FIGURE 1.11
achieved byachange of6dB, regardless oftheoriginal
value. Wecanalso relatethedecibel toafixed MicrosoftExcellogformulareference.
standard, whichwe designate as“0dB.” Levels are
indicated bytheir relative valueabove (+dB)or below
((cid:3)dB)this standard. This would be simplest,of course,
if therewereasingle standard, but tradition inour industryis topickseveral.dBV and
dBu arethe mostcommoncurrently. These are referenced todifferent valuesof1.0 and
0.775V(1mWacross a600Ωload) respectively.The differencebetween theseis afixed
amount of2.21dB.Note:For ease ofuse,wewill usedBV as thestandard inthis text.
Those whoprefer the dBustandard should apply +2.21dB tothegiven dBVvalues.
SECTION 1
Sound Systems
Level
LevelðdBVÞ¼20(cid:2)log 1
10 1V
Level
LevelðdBuÞ¼20(cid:2)log 1
100:775V
The voltage-relateddB scalesservetheimportant purpose ofguidance towardthe optimal
operating rangeofthe electronicdevices.The upperand lower limitsofan electronic
device are absolute,not relative values. Thenoise floor hasasteady averagelevel and the
clip pointis afixedvalue. These areexpressed indBV. The absolute levelofour signalwill
need topass between these twolimits inorder toprevent excess noise or distortion. The
areaenclosedby these limitsis thelinearoperating area oftheelectronic device.Our
designs willneed to ensurethatthe operatinglevelsof electronicdevicesare appropriately
scaledfor thesignal levelspassingthrough.
Once wehavecapturedthe audio waveform inits electronicform, it willbe passed
through the systemas avoltage levelwithnegligible current and thereforeminimal power
dissipation.Low-impedance output sections, coupled
withhigh-impedance inputs, give usthe luxuryof
notconsidering thepower levelsuntil we have
reachedtheamplifier output terminals.Power
amplifiers canthen be seen asvoltage-driven input
deviceswithpower stageoutputs todrive the
speakers.The amplifiergives ahugecurrent boost
and additional voltagecapability as well.Figure1.12
providesareferencechart showing the standard
12
operatingvoltage levelsforallstages of thesystem
signalflow.The goal is totransmit thesignal
through thesystemin thelinear operatingvoltage
rangeofallof thedevices,without fallinginto the
noise floorat thebottom.
Thereis stillanother set ofletter appendices thatcan
be addedon tothe dBvoltage formulas.These
designate whetherthe voltagemeasured is ashort-
termpeakor theaverage value.AC signalsaremore
complex tocharacterizethan DC signals. DC signals
areagivennumber ofvolts above orbelow the
referencecommon. ACsignals, by nature,goboth up
anddown. Ifanaverage weretakenovertime, we
would conclude thatthepositive and negativetravels
oftheAC signalaverage out to0 V.Placing our
fingersacrossthe ACmains will quickly alertusto
thefact thataveraging out to0 Vover time doesnot
meanthereis zero energythere. Kids, don’t trythis
athome.
TheAC waveform risestoamaximum, returnsto
zero,falls toaminimum, and then returnsagain to
zero.The voltagebetween thepeak and thezero
point, eitherpositive ornegative, isthe peakvoltage
FIGURE 1.12 (V ).Thevoltage between the positiveand negative
pk
Referencechartforthetypicaloperationalvoltageandwattagelevelsatvarious peaksis thepeak-to-peak voltage(Vp–p)and is
stagesoftheaudiotransmission.AllvoltagesareRMS. naturallydouble thatofthepeak value.The