Keele (1981-05 AES Preprint) - Direct LF Driver Synthesis

7/24/2019 Keele (1981-05 AES Preprint) - Direct LF Driver Synthesis

1/33

DIRECT LOW-FREQUENCY DRIVER SYNTHESIS 1797(E-6)

FROM SYSTEM SPECIFICATIONS

D. B. (Don) Keele, Jr.

James B. Lansing Sound, Inc.

Northridge, CA

Presentedat

the 69thConvention

[^_/_11

1981May12 15 _,Hi/

L o s A ng e le s

Thispreprinthas been reproducedfrom theauthor'sadvance

manu

s

cript,without editing, correctionsor considerationby

theR

e

vi

e

w Board

.

TheAES tak

e

s no responsibilityfor the

contents

.

Additionalprepr

i

ntsmay beobtainedby sending reque

s

t

and remittance to theAudioEngineeringSociety, 60 East

42ndStreet,New York,New York10165USA.

Allrights reser

v

ed

.

Reproductionof thispreprint

, o

rany

portion thereof,is notpermitted without directpermission

from theJournalof th

e

AudioEngin

e

eringSociety

.

AN AUDIOENGINEERINGSOCIETYPREPRINT


2/33

DIRECT LOW-FREQUENCY DRIVER SYNTHESIS FROM SYSTEM SPECIFICATIONS

B Y

D.B . (Don)Keele, Jr.

James B, Lansing So

u

ndl Inc.

Northridge, CA 9]32

9

The usual procedure for direct-radiator Iow-fr

e

quenc

y

loud

s

peaker

system design leads to calculation of the drlver_s fundamental electro-

mechanical parameters by an intermediate specification of the Thiele/

5,nail parameters. A reformulation of the s

y

nthe

s

is procedure to eliminate

the intermediate Thiele

/

Small calculation lead

s

to a set of equations

that yield the drlver's electromechanical parameters directly from the

system specifications.

These equations reveal some moderatel

y

surprising relationships when

the different system types (closed-box, fourth-order vented-box,

sixth-order vented-box) are compared. For example, for a specified

LF cutoff (f3)_ mldband effi

c

ienc

y

and driver slzej the fourth-order

vented-box driver is found to be roughly three times more expensive

(judged on the amount of magnet energy required) than the closed-box

driver.

C

onversel

y

for a given f3, enclosure volume (VB), maximum

diaphragm excursion (Xmax) and acousti

c

power output (PAR) the

fourth-order vented-box driver is some five times cheaper than the

closed-box driver

It is also found that for direct-radiator systems in general, a specified

f3, VB, Xmax, and PAR leads to the total moving mass (MMs) depending

inversely on the sixth power of the cutoff frequency i.e. a one-thkd-

octave reduction in f3 results in a four fold increase in massl Further-

more_ the same conditions reveal that the sixth-order vented-box

driver moving mass is some 42 times lighter than the closed-box driver

providing the same mldband acoustic output and f3 i If cone area and

efficiency are held constant_ the direct-radiator system driver actually

gets less expensive as the Iow-frequency limit is extended.

GLOSSARY OF SYMBOLS

B magnetic flux density in driver air gap

c velocity of sound in air (= 345 m/s)

CMS compliance of driver diaphragm suspension

f frequenc

y

(Hz)

fB resonance frequency of vented enclosure

fC resonance frequency of closed-box system

-i-


3/33

f5 resonance freq uency of unenclosed driver

f3 Iow -end cu toff (ha lf-pow er or -3 dB ) frequency of sys tem

h systemtuning ratio (= lB/tS)

kp pow er ra ting c ons ta nt

k3 frequency ratio constant for system(= tS

/

f3)

kTL effic iency constant (assum es 2_oin % )

I length of volce-coll conductor in magnetic gap

MMS

t

otal moving massof driver including air loads

P A R dlsplacement-lJmited acoustic power output rating (used in this paper

in a more general sense to indicate the mldb and max imum acoustic output

of a system_ drivers designed from the equations in this paper will reach

their displacement and thermally limited input limits at the _ame continuous

power levels in the system passb and (P ER -- P E(max ) )

P E R displacement-lim ited electrical power rating

P E (max) thermally-lim ited max imum input power

Q B tota l enclosure Q at fB resulting from all enclosure and vent losses

Q L enclosure Q at fB resu lting from lea ka ge losses

Q T tota l Q of driver at fS resu lting from all system resistances

Q E S Q of driver at fS considering electrom agnetic dam ping only

Q M S Q of driver at fS considering m echanica l losses only

Q TC tota l Q of closed-b ox system at fC including all system resistances

QTS ttal Q f driver at fs cnslderJngall driver resistances

(

= QESQMS /

\ QMsJ

RE dc resis tance of d river voice coil

RME electromagnetic dampingfactor of driver (= (BI)2

/

RE)

SD effective surface area of driver d iaphragm

V A S volum e of a ir having sam e acoustic com pliance as driver suspension

(com pliance equivalent volum e)

V B net interna l volum e of enclosure

V D peak d isp lacem ent volum e of driver d iaphragm (= SD X m ax )

Xm ax peak linear d isplacem ent of driver d iaphragm

04. systemcompliance ratio (= VA s/VB)

'

_a reference efficiency of systemin % (half-space acoustic load)

density of air (= 1.21 kg/m3)

O J ra d ian Frequ ency (= 2 'il' f)

-2 -


4/33

1 . IN TR ODU C TION : Traditionally (pre 1 9 7 0 ) the design of direct-radiator loudspeaker

systemshas

b

eenmostly an empirical proce

s

s. Quoting R.H.

S

mall in his introduction to

his monumentalseries of paperson dlrect-radJator loudspeaker systemdesign

/

'[-3

7

..

T h e d e s ig n o f a lo u d s p e a k e r s y s t e m is t r a d i t io n a l ly a t r ia l - a n d - e r r o r

process guided by experience: a likely driver is chosen and various

en

c

losuredesignsare trled until the s

y

stemperformanceis found to

be satisfactory. In sharpcontrast to this empirical designprocessis

the synthesisof man

y

other englneerJngsystems.

T

his beginswrth the

desired systemperformancespecifications and leadsdire

c

tly to specifi-

cation of systemcomponents. Thls lat

t

er approach requiresthe

englneer to have precise knowledge of the relationships between system

performanceand componentspecificatlons."

Small's synthesistechniques for closed-box

/

_

/

and vented-box

Z

_.

/

tsystemdesign

start from the desired systemspecifications suchas midband reference efficiency (97o),

net internal enclosure volume (VB), Iow frequency cutoff point (f3), mldband maximum

acoustic output power (PA R ) and leads to specification of the required driver in terms of

the basic design parameterscalled the Thlele/Small parametersts, VA S' QES, QMS,

Oo_, VD and PF(ma_l'..... TheseThiele/Small driver parametersare then usedwith a

selected driver cha_t_ragmarea (SD)or maximumdiaphragm excursion value (x a ), and

d e s i r e d v o ic e - c o i l r e s is t a n c e (R E } t o c o m p u te t h e d r iv e r s f u n d a m e n ta l e le c t r o m m e c _ a n lc a l

parameters: total moving mass(MMs), suspensioncompliance (CMS), BI product, and

electromagnetic damping factor (I_j_E) which being roughly proportional to magnet

assemblyweight is also proportional to magnet cost .

Eventhough the concept of the Thiele/Small dr[ver parametershascontributed greatly

to the analysis, synthesis, design, and measurementof dJrect-radlator loudspeakersystems,

the Jntermedlatecalculation of these parameterssomewhatdr

s

gulsesthe important relation-

ships between the driver's mechanical parametersand the target systemspecifications. In

this paper, equations are developed which yield the driver's fundamentalelectromechanical

parametersdirectly from the desired systemspecifications. Important relationshipsare

derived which show how the driver's electromagnetic dam

p

ingfactor (and hence magnet

cost) depend

s

on systemtype (closed-box vs vented-box vs equalized vented-box) and

s p e c J f i c a t l o n s .

2. DRIVERDESIGN VIA INTERMEDIATE

T

HIELE

/

SMALL PAR

A

METERS

Small's design techniquesfor direct-radiator loudspeakersystemsstart froma specifi-

cation of the desired performance required which includes:

f3 Iow-frequency half-power (-3 db) cutoff point,

V B net in terna l v olu m e of enc los u re ,

'_o midbandreference efficienc

y

(half-space load),

Responseshape: i.e. systemtypeand alignment information, and

PAR maximummldband acou

st

ic output power

-3 -


5/33

(note that only two of the three specifications f3, VB, and 7o

can be selected, the third dependso%the first two through

the efficiency equation: To-- kl_

r3 VB)'

Once the systemtype (closed, vented or vented plus EQ, etc.)and frequency

responseshapehave been selected, values for the systemparametersk3 (= ts

/

f3),

C:_(= VA s

/

V_), QT, h (= fB

/

fS), and kpare fixed and can be determined by a

numberof dlf_'erentmeans(Smallz'_,3_, ThJeleZ'2[.._,and Keelez_..,7. Knowledge of

the systemsarge-signal target specifications a long with the systemparametersallows

calculaHon of the drivers Thlele

/

Small basic designparameterstS, QES' QMS, QTS'

V

A

S' VD' and PE(max)as follows:

fs =k3f3 (1)

VAS --c_VB (2)

QTS=QT (3)

QMS = Selected,

QES = QMS QTS

/

(QMs- QTS)' and (4)

7_0 -- k/j f33 VB. (5)

Small's relationship for the displacement limited acoustic output powerZ_, eq. 40

7

:

PAR= kp f34 VD2 (6)

can be solved for VD yielding:

i P_A R, and (7)

v0=

-

7

PER= PAR/To (8)

The ph

y

sical specification of the driver ma

y

now be comple

t

ed b

y

selecting ar

b

itraril

y

the driver cone area Sgand voice call resistance RE,and then calculating the

drJverls

electromechanical parametersas outlined

Jn

L_,

sec,

JO00_,The required value of peak

displacement volume (VD) for the d

r

iver must

b

e divid

e

d into accepta

b

le valu

e

s of S

D

and x_.v (St, ma

y

be ar

b

itrarily selected ormay be computedknowing the desired value

of Xma'"x'J.e.'"SD = VD/Xmax).

T

he driver's electromechanical parametersare given by Z'_, eqs. 61 - 65

7

:

v

CMS _:o_-S-S_ (9)

MMS i i0

(2_'fS_'zCMS

-4-


6/33

_/2_ fsP_MMs I1

I

i)

V

Q E S

RME= (BI)

2/

RE= 2_'fs MMS (12)

Q E S

3. DIRECTDRIVERSY

N

THESIS

Method

The designmethod outlined in the previous section can be streamlined by eliminating

the intermediate calculation of ThJele

/

Small parametersand proceedingdirectly from the

systemspecifications to the driver's mechanical parameters. In general, substitutions

are made in eqs. (9) - (12) for the Thlele

/

Small parametersin termsof the systemspecJfi-

cations and a set of equaH ons are derived yielding the desired driver mechanical parameters.

SystemSpecifications Required

The derived equations can be organized ;n several different ways depending on which

of the _ndependentsystem

s

pecifications are chosen. I have chosen to derive three complete

sets of equations each using as variab les two of the three parameters of the efficiency-volume-

cutoff set (_o, VB, f3)' Within each of the three setsa further division is madeon roughly

small-signaI/large-slgnal considerations. In the first small-slgnal category, SD is chosen

arbitrarily and appears explicitly in the equations while Xma x is allowed to float so that V D

is satisfied. In the secondcategory, the values for PAR, Xmax, and kp appear explicitly

with the cone area SD allowed to float.

D e r iv a t io n E xa m p le

To illustrate the derivations of the equations, one exa

m

ple will beworked out for

one pair of speclficattons (f3, V B) to yield the equations for the total moving mass M M S .

Froma knowledge of the systemparametersk3, CK, QT, H, k

yL

, and kp derived

from knowing the desired systemtype and responsefunction (seeSec. 2) the following

derivation can b e worked out. From the knowledge that

VAS = 0

/

. VB (13)

eqo (9) can be transformed into:

CM= cx vB (14)

c2 SD2

This value of C M S along with

fs

k33 (15)

-5-


7/33

when sub

s

titutedinto eq. (10) yields: 2

MMS= _ c2 SI) (16)

4 _2 k320_ f32 VB

which is the desired result with mostly small-signal specifications evident and SD

a pp ea rin g e xp lic it ly .

To convert to the large-signal format, SmalP s relationship for the displacement limited

acoustic output power eq. (6) must b e used along with

VD--SDXma (17)

to

y

ield a value for SD in termsof mostly large-signal specifications:

PAR 18

SD-

X m ax2 J_p f34

Thisvalue for SD can Jnturnbe usedwith eq. (16) to give MMS in termsof mostly large-

s ig na l s y ste m s pe cif ic a t io ns :

C PAR (19)

MMS = 4-'_32_kp Xma x f36VB

This equation illustrates the very strong dependence of M M S on f3 (inversely on the

six th power of f3 ) for a specified P A R ' x max ' and V B, O_servations on the whole set of

derived equations will be deferred until after all the equations are shown.

4. DIR EC T S Y N TH E S IS E Q U A TIO N S

Following the procedure as outlined Jn Sec. 3, the equations can be derived for all

the drlver_s mechanical parameters. These equaH ons are shown Jn the following listing.

F ro m S m a l l - J g n a l S p e c if ic a tJ o n s

C o m b i n a t i o n s

Total M oving M ass

SD (20)

3&_o MMS= _6

f3 & Vi5 = _ c2 SD2 (21)

4 _.2 k3

2

f32 VB

'_0 & VB = _ c2 *n '_' SD (22)

4'

/r

2 k

3

20( '_J

o

2

/

3 VB

/

3

-6-


8/33

From Small- Signal Specifications (continued)

CombJnations

Sus p en sio n C o m p lia nc e

f &_, = C_ _, (23)

3 CMS

c k_ sg-_3

= O( VB (24)

f3&VB _ SD2

= (X VB (25)

'_0 & VB _ '

/_o c SD

B I P ro d u c t

Bi = /_ C2k7_ ('1_ E '

f3 & _* _

o

J_ _e [(3l)_ SD f3 _a (26)

J_ 7 ' SD t f3VBI: (27)

3 & VB = /J_-_-_ES k3m

/ 2 I/3 r

//

_o c' k_ _ RE (28)

)_e & VB = _J21},QEsk3 C_ ' sD

01

/

3

B2

/

3

E le c tro -m ag n e tic D a m pin g

_ SD

2 k_ . f32 (29)

f3 & _'0 RME 2,11.,QESk3C>( 7'_,

2

f3&VB

= _

c_

SD (30)

2 1T Q E s k3IX f3 V B

?_, & VB - c2 k)_1/3 SD2 (31)

2'11'QES k3 y- 2]01/3 VB2/3

-7 -


9/33

From Large-SignalSpecifications

CombTnafions

T o ta l M o v in g M a s s

Poc2k_ . PAR (32)

f3 & To MMS -

4_ '2 k32_( kp Xmax2 f337_o

2

f3&VB _ c . PAR (33)

= ' 2 f36 V1TZ k3_ kp Xmax B

c

2k_

vBPAR

(34)

_o & VB =

4"

/

t'z 1


10/33

From La rge- Signal Specifi cations (conti nued)

C o m b i n a t i o n s

B I P rod uc t (c ontinu ed )

f3&vB _- ,

//

_ c2 ]

/

PARRE I391

V

2

'

1'

F

QESk3_, kP Xmax V f3_BVB

o,v, : ,

r

,

[

PAR RE VB2

//

3 ' (40)

Xmox

E lectromagnetic Damping

c2 k

/I,

.

PAR

(41)

f3 _ RME =

2 '1 7 'Q E S k3_ kp f32 Xm ax 2'_ '

c2 PAR (42)

f3&VD =

2 I'/'QEs k3_ kp f35 Xmax2 V8

c2 kT_5/3 . PARVB2/3 (43)

'

)

7, &V B =

2

2 11-QEsk3_ kp _,,.(05/3Xmax

5. SELECTIONOF SYSTEMTYPEAND RESPONSESHAPES

Threedifferent types of direct-radiator loudspeakersystemswere cho

s

ento illustrate

t h e u s e ' o f t h e d e r iv e d e q u a t io n s :

1. C2ND: Closed-box, second-order high-passresponse_

2. V4TH: Vented-box, fourth-order hlgh-passresponse_and

3. V6TH : Vented-box , six th-order high-pass response.

The third systemtype (V6TH)requires the useof an external second-order high-pass

filter/equalizer which provides sub-sonic energy rejection andmodestboostequalization

(+6 db)in the lowest octave of operation (seeZ'_, Alignment 157, _.,7, _6j7,and Z_,7.

All three systemtypes have been analyzed extensively and enjoy popularity in the market-

place z

/

'l-8J. Maxlmally-flat (Butterworth) or near maxlmally-flat responsecurveswere

chosen for each othe three systems(0.4 db ripple or less).

-9-


11/33

Thesystemparametersof the three typeswere selected from information contained

in Z_-3_ 5

/

7. Reasonablesystemlosseswere assumedwith realistic attainable efficiency

constants(k_). The systemparameterswere juggled sothat an exact ratio of efficiency

constantsbetween the systemtypeswas maintalned_ i.e. a ratio of 1:2:5 (0, +3 dB_+7 dB)

for the closed-box, vented-box fourth-order, and vented-box sixth-order systemtypes

respectively. Theseefficiency ratios are very close to the ratios attained by the theoretical

lo s s - f re e s y s te m s

All parameterswere derived assumingthe systemsare operated from amplifiers having

negligible output resistance. Theclosed-box type is further assumedto obtain mostof it's

total damping from electromagnetic coupling and mechanical driver loss

e

s

,

and the effects

of any filling materials were neglected 4

'

_, Sec. 9

7

.

T

hevented-box systemis assumed

to have a leakage lossQ of (QB = QL = 7)Z_, Sec

.

11

,7

. Theselected systempar

a

meters

are shownin Table 1. Table 2 showsthe Thlele

/

Small driver design data and equations

usingthe systemparametersfrom Table I and the relationships of eqs. (1) - (8). Fig. 1

showsthe small-slgnal responsecurves of the three chosensystemtypes normalized to their

midbandefficiency levels.

6. DIRECTSYNTHESISEQUATIONS WITH EVALUATEDCONSTANTS

The systeminformation in Tables ] and 2 was usedto evaluate the constant factors

in eqs. (20) - (43) for the three systemtypes. The resultant equationsare shownin

Tables3 - 5.

7, EQUATION OBSERVATIONS

A numberof moderately surprising observationscan be madeabout the direct synthesis

equationsshown in Tables 3 - 5. Somerather interesting relationshipsare indicated when

the different systemtypesare compared. A numberof these relationships have been observed

before but it helpsto repeat them here as an aid to the systemdesigner for ga_nlng insight

into systemdesign factors and tradeoffsz_ - 8_7. Referto Tables3 - 5 when reading the

following outlined observations.

General Observations

Thefollowing commentsapply to all the analyzed systemtypes.

A. Small-Signal

1. The total driver moving mass(MMS) and RME(cost) are proportional

to the squareof the cone area (SD)or cone diameter to the fourth

power (a strong dependencel). Large conesmean lots of massto

movearound and lots of magnet to move themI If possible, it would

be moreeconomical to reduce MMsand RMEby trading SDfor Xmax

sothat VD is maintained (VD = SD Xmax).

2. BI is directl

y

proportional SD

2 4

3. Suspensioncompliance (C S goesas ]/S D or 1/dla Largecones

imply not only high massbut also require high stiffness for control.

- 10-


12/33

B

.

Large-signal

1. MMKa _ RM_(cost) are proportional to PARand inversely proportional

to x'_ax% 'rK'Tsshowsthe magnetcost rising in direct proportion to the

de

s

ired acoustic output power and decreasingwith the squareof the drivers

excursion capabilities

.

You will pay for high power outputl

A

ny

allowab le increase in Xmax, wJll pay for itself in decreased driver cost.

2. Compliance goesas 1/P^o. High driver suspensionstiffnessgoesalong with

high powerdrivers

.

Mo_t%igh-power musical instrumentand professional

loudspeakershave suspensionswhich are quite stiff.

3. BI goesas I/Xmax and the squareroot of PAR.

Specific ObservaHons

Theseobservationsapply only to the specific systemtypesand particular parameters

specified.

A. For Specified Cutoff Frequencyand Efficiency (Table 3)

1. If you are forced into usinga particular driver slze, the closed-box system

is cheaperl This i s becauseMMS _shigher for the vented systemsat the

sametime the box size is smaller. The following table showsthe approximate

ratios if SD is held constant.

Type MMS& BI RME(cost)

C2ND x 1 x 1

V4TH x 1.8 x 3. I

V6TH x 2.2 x 4

.9

2

,

The vented-

b

ox s

y

stemis cost effective onl

y

if the driver size can be

allowed to decrease. The table showsapproximate costbreak-even

points for driver size specifications.

ype reaRatio iameterRatio

C2ND I 1

V4TH 0.56 0,75

V6TH 0,45 0,67

Thismeansthat a sixth-order vented systemdriver mustbe two-thirds

the diameter of the closed-box systemor smaller to be cost effective.

3.

S

mall-Signal (specified f3' _o, and

S

D)

a. MMsand BI are proportional to f3' Thi

s

is true for a fixed SD

arfd'_e becauseas f3 goes up the-box size grows smaller.

-I1-


13/33

varie

s

as f3 ' In thi

s

ca

s

ethe driver actuall

y

gets

. R

M

E(cost) 2

cneaper as the system'sresponseis extended lower (normally it's

the other way around if the box size ismaintained constantlg see

Sec

.

B.3.

d

further on for behavior under specified f3 and VB).

Thisis due to the box size getting larger as f3 i

s

decrea

s

e

d

.-

c. MMSand RME(cost)varies as 1/_o . High efficiency costslesst

4. Large-Signal (specified f3, rio , PAR, andXmax (SDfioat))

a. Fora specified Xmax and PARthe vented-box drivers are cheaper

becausethe cone

s

ize i

s

smaller.

Type RME(cost) Ratio

C

2ND 1

V4TH 0.39 (1

/

2.6)

V6TH 0.26 (1

/

3,8

b, Vented-box drivers are lighter.

Type MMSRatio

C

2ND 1

V4TH 0.22 (I/4.6)

V6TH 0.12 (.1/8.5)

B

.

For Specified Cutoff Frequenc

y

and Box Volume (Table4)

I MMS and RME(cost) proportlonal to i/V B, Drivers for small boxes

are more expensive 1

2. Small-Signal (specified f3, V_, and SD)

a

.

For the

s

ameSD_the

c

lo_d-box and sixth-order vented-box

drivers are nearl

y

the same

c

o

s

twith the Fourth-orderven

t

ed-box

driver moreexpens;ve.

Typ

e RME

(cost) Ratio

C2ND i

V4TH i,57

V6TH 0.98

b , Vented-b ox conesare lighter,

Type MMsRatio

C2ND .1

V4TH 0.88 (1/I. 13)

V6T

H

0.44 (i

/

2.3)

- 12-


14/33

3 Large-slgnal (specified f3, V- p., and x )

_ _; ma

a. For the same ex cursion capab lhtles (Xmax _the vented-b ox cones

are very much lighter This is due to'f_e much larger diaphragm sizes

F o r th e lo w e r - o r d e r s y s t e m ty p e s .

Type MMSRatio

C2ND 1

V4TH 0.11 (9times lighter l)

V 6 T H 0 0 2 4 (42 tim es llgh ter l)

b M oving mass varies inversely as the six th power of the cutoff frequency l

Driver moving mass increases quite dramatically For decreases in f3

becausethe cone size increasesalso. For each 1/3rd octave extension

of bass response the mass goes up by a factor of four

c. V ented-b ox drivers are much cheaper (b ecause the cone siz es are much

smaller For a specified Xmax)


C2ND

V4TH 0.19 (5 times cheaperl)

V6TH 0052 (19 times cheaper )

1 5

d. RA_ (cost) varies as /lq You pay dearly to extend the Iow-frequency

res'_nse of the system "For each 1/3rd octave decreasein f3, cost rises

by 3.2 1 Contrast this with the activity in Sec. A .3.b mentioned

p r e v io u s ly F o r s p e c i f i e d f3 a n d '_ o .

C For Specified E fficiency and Box Volume (Tab le 5)

1. MMS and RME(cost)are proportional to 1/'_ where x ranges from 1/3 to 2

For different parameters and conditions. H igh'er efficiency is cheaper This

i s d u e to c u t o f f r is in g w i t h in c r e a s e s in e f f ic ie n c y .

2. Small-Signal (specified 7Zo_VBr and SD)

a. Vented-b ox drivers are more expensive i driver slze is fixed (see

S ecs. A .4.a and B.3.c).

Type RMEcost) Ratio

C2ND 1

V4TH 2.0

V6TH 1.7

- 1 3-


15/33

b. Vented-b ox drivers are heavier if cone size is fixed.

Type MMSRatio

C2ND 1

V4TH 1,4

V6TH i .3

c. RME(cost) is proportional to 1/VB(2/3), Big box driversare cheaper

ifs D and 9 7 _ are fixed.

i

3. Large-S igna l (specified _o_ V R P ^_ and x )

a. Vented-box drivers are levi ex_nsive liraD is allowed to float (xmax

constanb contrast this with Sec.D.2.a above).


C2ND 1

V4TH 0.61

V6TH 0.76

b. Vented-box drivers are lighter if SD is allowed to float (Xmax constantt

contrast this with Sec. C .2.b ab ove).

Type MMSRatio

C2ND 1

V4TH 0.44

V6TH 0.59

c. RMFgoesas VB(2/3). Big box drivers are more expensive if Xmax,

No ' and PARare fixed (contrastwith Sec. C.2.e above).

- 1 4-


16/33

8. EXAMPLESOF SYSTEMDESIGN

Threesetsof exampleswill beworked out for the three combinationsof independent

s

y

sfemspecificatlons- I f &

T

_

a

_2 f &V _and3 _

e

&V B, Foreach

s

etof 3 ' 3 B '

combinations, the three types of systemswill be synthesizedfor comparisonpurposes.

Only brief info

r

mation will

b

e contained here, pl

e

aserefer to

/

V,

Z

_, Secs.

9

- 1000_,

/_, Secs. l I - 1_7and/_.7 for more complete design information. Foreach example,

graphswill be

s

hownplotting the

s

mall-signal frequenc

y

re

s

ponse(efficienc

y

vsfrequenc

y

),

maximum continuousacoustic output power and maximumcontinuouselectrical input power.

AA:IxlmumAcoustic Output Power

The cuwes for output power indicate, at each frequency_ the maximumcontinuous

acoustic power output and soundpressu,{eevels J_SPLe 201uP)generatedin the reverberant

field of a reference environment (85mv (3000ffv) roomwith 200 sablnsof absorption)

before 1

.

the driver burns itself up (driver

t

h

e

rmal limit) or 2. dis

t

or

t

ion

b

ecome

s

too

high (driver displacement limit), whichever occurs firstZ_, Appendix 1,7 The Iow frequency

maximumpower ou

t

put of a driver dependshighl

y

on the t

y

p

e

of enclo

s

ure it is usedin.

Frequencyresponseequalization (if used)_of course_hasno effect on maximumacoustic

o u t p u t .

Ideall

y

, a

sys

temshould be thermall

y

limited over its full operating frequenc

y

range.

Displacement limiting implies that the system"sinput electrical power mustbe decreased

belo

w

the driver*

s t

hermall

y

Jimlted maximumin

p

ut power P_

,

_ or dJ

s

tortlonwill

c_

,

max

]

becometoo high, Thecomputer simulations used in this paper assumeshat the drJvers

cone displacement is linear up to + x_ .. (distortion accep

t

able) and non-linear

b

e

y

ond

(distortion unacceptable). Thesyster_sdisplacement Jim,tedmax,mumoutput is the power

the s

y

stemcan generate when the cone excursion is _+

X

max.

/

Vb

x

JmumElectrical Input Power

Th

e

curve

s

fo

r

input power indicate_ at each frequenc

y

, the maximumcontinuou

s

elect

r

ical input power

b

efore 1. the driver

b

ums itself up (driver

t

hermal limit P in =

PE(max))or 2. driver displacement equals + x max (driver displacement limit)_ whichever

oc

c

ursfi

r

st.

D

isplacement limited input p_wer is indicated b

y

inpu

t

powersle

s

s

th

an the

thermal limit (Pin


17/33

The following

s

pecifications mustbe met:

f3 20Hz

Re

s

pon

s

e: Nea

r

maximall

y

flat acceptable

_o 0

.7

(= PAR

/

Ri

S

D

O. 1134m2 (176 in2)

PE(max)' PER 100W

PAR 0.7W

Thesmall-signal equations in Table 3 may be usedto computeMMS, CMS, BI,

and RMEas follows

(closed-

b

ox s

y

stemt

y

pe (C2ND), RE= 6.

5

ohms):

S D 2 f3

MMS =0.45 , = 0.45 (0.1134)220 = 0,17kgl

Fo 0.7

CMS =0.297. S_

'

_f_ =

0

.2

97 (0

.7) = 2.0x 10-3 m

/

N ,0.1134)2 (20)3

u o

BI =1.93 SDf3 R_ = 1.93(0.1J34)(20)

6_5

7

6.5 = 13.3Tm and

RME =3.71 , SD f3 = 3,71 (0

.1

134)2 (20)2 = 27

.

3 N

s/

m.

?7 0.7

The drivermspeak displacement volume (VD) is computedu

s

ing

t

he equation from

Table 2:

VD = 1.08. P_AR= 1.08 (V"_ = 2.26 x 10-3m 3(2260cm3).

f7

(20) 2

Likewise Xmax is calculated:

Xmax= VD/S D = 2.26 x 10'3/0. ] 134= 2.0 x 10-2 m (20mm).

In the samemanner the parametersfor the other systemtypes including the Thiele/S_all

paramete

r

sma

y

be computedfrom the information contained in Tablet - 3. Thecomputed

information is shownin tabular format in Fig. 2. Fig. 5 showsplots of the small-signal

frequenc

y

response,maximum continuousacoustic outputt and maximumc

o

ntinuous

electrical input power of the three aha lyzed systemtypes.

-

16-


18/33

Comments

H olding cutoff frequency and efficiency constant in this ex ample m eans that the

h igher effic iency constant (k w ) of the vented -b ox system s shows u jo in F]g._ as a

d ecrea se of b ox volu m e (V B ). The b _x volu rys ra nge from 0 .7 5 m (26 .4 ft ) for the

c losed-b ox system (C 2N D) to 0 . ]S m v (5 .3 ft ) for th e vented-b ox system (V 6 T H ), a

5 to ] range

A nalys is of the data in Fig. 2 for m oving m ass (M M s) and electrom a gnetic dam p ing

(R M i:) clearly shows the tetldency of the vented-b ox drivers to b e heavier and m ore costly

thar_the closed-box driver if cutoff frequency, efficiency, and driver size are specified,

The increased cost for the vented-b ox drivers is due to the sm aller enclosure siz e (V B )

tha t these driver's m ust opera te in. If a sm aller 30 0 m m (1 2 in) drivers could have b een

used (with increased ex cursion capab ility) for the vented s ix th-order system (V 6TH ), its

cost would have b een com parab le to the closed-b ox driver.

E x am ination of the graph for m ax im um input pow er Fig. 5c revea ls the com m on prob lem

of all vented-box systems of Iow power handling capacity below box resonance (fB). The

c losed-b ox system can handle up to 6 6 w atts a t very Iow frequenc ies while the vented-b ox

systems taper off to roughly 5 watts in the same range. These input powers are based on not

ex ceeding the linear ex cursTon lim its of the drivers. M ost drivers however can normally

ex ceed their X m a x ratings b y som e tw o to three tim es b efore b eing dam aged w hich m eans

that their very-low frequency maximum [nput power ratings before damage (safe operaHng

range) are significantly higher than that shown, ApproprTate high-pass filtering should be

used with a ll vented-b ox system s if apprec iab le b elow b and energy in the program m ateria l

is expected.

The vented-box sixth-order system (V6TH) has a good combination of Iow-frequency

performance_ small box siz

e

, and high-pass filtering which is inherent in its design. If

m odera tely reduced m ax im um outpu t in the low est octave of opera ffon (Fig. 5b ) is

allowable (the maximum system output curve should match the spectral content of the

program material), the sixth-order vented system would be a good choice.

Example 2. Specify f3, VB' PAR and Xmax.

A "bookshelf" loudspeaker system is to be designed with strong response to 30 Hz

and capable of 0.2 acoustic watt midband (107 dB SPL reverberent field, R = 200).

Diaphragm excursion is to be limited to a moderate value to limit doppler/FM distortion.

Power amplifier and driver size are not important.

The following specifications must be met:

f3 30Hz

R esp onse: N ea r m a x lm a llv fla t a c cepta b le

VB 0.057m3 (2 ft 3)

PAR 0.2W

x 6,25 mm (0.25 in)

max

- 1 7 -


19/33

Thesystemand driver design data which result from these specifications are shown in

Fig. 3. Fig. 6

s

howsthe plots of respon

s

e,maximumoutput, and maximuminput power.

Comments

Specifying cutoff frequency and box volume leaves systemefficiency free to float

depending on the value of k_t . This is reflected in Fig. 3 in the efficiency (_o) row

asa range of values of 0.18% for the closed-box system(C2ND) up to 0.9% for the

vented system (V6TH ). Fig. 6a clearly shows the efficiency differences as a function

o f f r e q u e n c y .

In thJs example, a specific max imum acoustic output power P Ar of 0 .2 watt was

specified (see Fig. 6b ). This means that the different efficiencies of the three types of

systems require different input powers to attain the same output. This is indicated in

Fig. 6c where the closed-box system(C2ND) requires 112watts to generate the same

acoustic output that the slxth-order vented-box system(V6TH)can do on 22.4 watts.

A further specification of this example is a specific value of maximumexcursion

to limit distortion. This allows the cone size to vary to maintain the required value of

VD which dependson the power rating constant (kp), which is higher for the vented systems.

In this example, the specifications were met by a 380 mm(15 in) driver for the closed-box

(C 2N D), a 25 0 m m (1 0 in) for the vented -b ox fou rth-ord er (V 4TH ), and a 20 0 m m (8 in)

for the slxth-order vented-box system(V6TH).

Examinationof the MMsand RMErows in Fig. 3 indicate an extremely large range

of values with the closed-box (C2ND) values on the very-high side and the vented-box

sixth-order (V6TH)s

y

stemvalues on the ver

y

-low side (42:1 ratio of MMSI, 19:1 ratio

of RMEI). The closed-box (C2ND) RMEvalue of 134 N s

/

m is larger than the largest

magnetassemblyJBL makes (about 120N's

/

m) and is bordering on the high-end of

realizability In contrast, the vented sixth-order (V6TH) systemMMS of 12.9 g and

RMEof 7 N.s

/

m borderson the Iow end of realizabillty

_rketing Considerations

The biggest problemwith the sixth-_ordervented system(V6TH) is the rather anemic

looking 200 mm (8 in) driver in the 2 fi-box (the marketing department wonff like it I).

Butnow lets look at that 380 mm (15 in) driver in the closed-box system(Wow1, we can

really sell that one l). Well, maybewe can put a 300mm(1

2

in) or 380 mm (15 in)

passiveradiator with that 200 mm (8 in) driver in the vented sixth-order systemand come

upwith a sellable package (this systemis quite close to the Electro-Voice Inc. system

described by Newman in Z'6.,7).

Example3. Specify _o' VB, PE(max)' and Xmax

A "sub-mini" compact loudspeaker systemis to be designed containing a buiIt-in

Iow-power 20 watt amplifier. Thesystemmust beable to generate continuous levels

of 10_dB (about 0.1 acoustic watt) in the reverberent field of a typical living room

(85m and R= 200 sabins). Coneexcursion is to be limited to 5 mmpeak to peak

- 1 8-


20/33

a

nd

dri

v

er size

is n

ot i

mp

orta

n

t.

L

ow-e

n

d cuto

ff

fre

qu

e

n

cy

i

s for

th

e

mo

stpart

u

n

imp

or

t

a

n

t

b

ut mu

s

tbe

l

ower than

10

0

H

z. Theserequire

m

e

n

ts lead to specif

i

catio

n

s o

f

:

f

3

4 1

00

Hz

R

esp

o

nse

:

Ne

a

r ma

x

imall

y

f_

t

a

cce

p

t

ab

le

VB

0

.

01

42 m_ (

0.

5 f

t

v)

9

_

0

0

.

5

%

(

=

0

. i/

20 x

1

00

%

)

PE

(

max)tP

E

R 2

0 W

PAR OlW

Th

e syste

m

a

nd dri

ve

r

de

sign

data resu

lt

i

ng

fr

om th

ese

sp

e

cif

i

c

a

ti

o

n

s a

r

e s

h

o

wnJn

F

i

g. 4.

Pl

otsof frequencyre

s

po

n

se ma

xi

mumoutput

_

and ma

xi

mu

m

input are shown

i

n

F

i

g

.

7.

Comm

e

n

ts

Sp

e

cif

y

ing

eff

i

c

i

enc

y

an

d box volum

e

in thi

s exa

mpl

e a

ll

o

w

s f3 t

o float so

t

h

a

t th

e

ef

f

ic

i

e

n

cy e

q

ua

ti

o

n

eq

. (5) is

sat

i

sfied. C

u

to

ff

fre

q

uenc

i

e

s r

an

g

efrom

67 H

z

F

o

r

t

h

e

closed-box

s

y

st

emdown to 39 Hz for

six

t

h

-o

r

de

r

ven

t

ed syste

m(

F

i

g. 7a

), E

vent

h

ou

gh

t

h

e

vented s

yst

e

m

shave

l

ower response

tha

n t

h

e clo

se

d

-b

ox

sy

ste

m

the

i

r mov

i

n

g

massan

d

magnet requ

i

remen

t

sare

l

ess

(

F

i

g.

4)

. Due to the speci

fi

ed X

m

ax value the

cl

osed-box

s

ys

te

m

u

se

sa 2

5

0

mm (10 t

n

)

d

ri

ver w

hi

le t

h

e vented-

sys

te

m

sre

q

u

i

re a

s

ma

l

ler2

00 mm

(

8

i

n

)

dr

i

ver

.

T

h

e lower box resonancefrequencie

s

of t

h

e vented syste

m

spush

t

he

i

r d

l

spla

c

e

m

e

nt

l

imi

t frequenc

i

e

s

down a

l

so. F

ig

. 7c

i

n

di

cate

s

that

t

he

s

y

s

te

m

scan hand

l

e fu

ji

ra

t

ed

th

er

m

a

l i

nput power

o

f 2

0

watts down to: 6

7

Hz,

4

8

H

z, and 3

4

Hz for t

h

e C2

N

D

t V4

T

H

,

a

n

d

V

6TH

sy

ste

ms

respec

ti

ve

ly

. Thevented s

i

x

th

-or

d

e

r sy

ste

m

can ha

n

d

l

e fu

ll

ra

t

ed powe

r

a fu

ll

octave be

l

ow t

h

e c

l

o

se

d bo

x

system

,

9. C

ON

C

L

US

ION

Equat

i

o

n

s

ha

ve been

p

resentedthat al

l

ow co

m

pula

H

ono

f

t

h

e d

i

rect-rad

i

a

t

o

r l

ou

d-

spea

k

er

drlv

e

r_

se

l

ectro

m

ec

hani

cal

pa

ra

m

ete

r

sd

i

re

ctly f

ro

m sy

ste

m

spec

ifi

cat

i

ons. T

h

e

se

e

quat

i

ons

s

peedu

p

t

h

e de

sl

gnprocesso

f

d

ri

ver

s

for c

l

osed-

b

ox and ven

t

ed-

b

o

x

loud

s

pea

k

er

sy

ste

m

san

d

g

i

ve t

h

e

d

e

slg

ner new

J

n

slg

hf

i

nto

s

y

s

tema

n

d d

ri

ver

r

e

J

a

tro

ns

hl

psand trade

offs. T

h

eder

i

ved re

l

at

J

onsh

lpsin

d

i

cate

t

hat

t

he ve

n

te

d

-

b

o

x sy

s

t

e

mi

s extre

m

ely eco

n

om

i

ca

l

when co

mpa

red

t

o

th

e clo

s

ed-

b

o

x

s

yst

e

m

w

h

e

n th

e sy

s

te

ms

are spec

i

f

i

ed

f

or a part

i

cular

I

ow-frequency cutof

fj

e

n

c

l

o

s

urevo

l

u

m

e

f

m

a

x

i

mu

m

acou

s

t

i

c output, a

n

d dr

i

ver e

x

cur

si

on.

- 1

9

-


21/33

REFEREN

C

ES

z"lJ R

.H.

Small

,

"Dr

rect

-Radla

t

o

r

Loudspeake

r

SystemAnalysis

,

" J., Audio

Eng. Soc

.

,

v

ol.

2

0,

p

.

3

8

3

(

J

une

1

97

2).

/_J R.H. Sma

ll

, "C

l

os

e

d-B

o

x L

ou

d

s

p

ea

k

er

Sys

tem

s

,

"J. A

udio Eng.

SO

c

.,

vol.

2

0

,

p. 798

(D

ec. 19

7

2

)

,

and

v

ol

.

2

1,

p

. 11

(Jan

./Fe

b

.

1

9

7

3

)

.

_

.,7

R

.H.

Sm

all,

"

Vented-

B

ox

L

oudspea

k

erSys

t

e

m

s

_"

J. Audio Eng.

SO

c., vo

l

. 2

]

,

p

. 363

(

June

197

3

)

, p.

4

38

(

Jul

y/A

ug

.

1

9

73

)

, p

.

5

49 (S

ept

. 19

;

_3

),a

n

d

p

. 63

5 (O

ct

. 19

73).

_4

,7 A.

N

. Thlele,

"L

oudspea

k

ers

i

n

V

ented

B

oxes

_"

J. Audio Eng.

SO

c._vo

l

. 19,

p 382 (

May

1

97

1

)

, and p.

471 (

June

19

71

)

.

Z'

_J

D.

B. K

eele, Jr.,

"

A

N

ew Set of S

i

x

th-O

r

d

er

V

ented-

B

o

x L

ou

dsp

ea

k

erSy

s

tem

Al

l

gn

m

ents,

"

J. Audio Eng. Soc., vol. 23, p. 35

4 (

June 1975

)

.

Z'

_J R

.J.

N

ew

m

an,

"

A

L

oud

speak

erSystemDes

i

gn Util

l

zlng A S

ix

t

h

-

O

r

d

er

B

u

f

terw

o

rt

h

R

e

s

ponseC

h

a

r

acter

i

st

i

c,

"

J. Audio

Eng

. Soc., vo

l

.

2

1, p.

4

5

0 (J

ul

y/

Au

g

.

1

973

)

.

z

"

T

J

D.

B

.

K

eele, Jr.,

i

'Sens

J

fivi

t

Y of T

h

iele's

V

ente

d L

oud

sp

ea

k

er

E

nclosureAlignments

to Pa

r

a

m

e

t

er

V

ar

i

a

ti

on

s

,

" J

. Audio Eng.

S

oc., vol

2

1

,

p. 2

4

6

(May 19

73

)

.

Z'

_

A.

N

. T

hi

ele,

"L

oud

s

pea

k

ers,Enclo

su

re

s

and

Eq

u

a

lisers,

" P

roc. of the IREE(Australia),

vol. 3

4

,

p

.

4

25

(N

ov. 1

97

3

)

o

-

2

0

-


22/33

TABLE 1.

SELECTED SYSTEM PARAMETERS

System

System Type

Closed-Box Vented-Box Vented-Box

Parameter

C2ND V4TH V6TH

k3 (=fs

/

f3) 0.433 1.O 1.0

(=VAs

/

V B) 5 1.06 2.12

QT 0.308 0.40 0.30

QTC 0.754 ........

H (=fB/fS) O 1.0 1.0

k 1.17xlO4 2.34x104 5.85x104

kp 0.85 6.9 _6

Responseype: C2 B4 C6

Note. 1. All units SI

2. Efficiency constant kq computed for noln %.

3. The vent ed-box 6th-orde r (V6th) s y s t e m t y pe r equire s the us e of an ext e rnal

2nd-order high-pass filter/equalizer wlth a Q of 2 (+ 6 dB lift) at a corner

frequency equal to box resonance fB (mfs = f3 for this alignment) [4 - 6 , 8].

-21-


23/33

TABLE 2.

THIELE

SM LL P R METER DRIVER DESIGN D T

Small Signal

fs V4TH f3

v v

VAS = .06 V4THI VB

L ,12 V6T __

: I-_ _ l

Qvs L 3 v6T_

QMS = 5.0

V4THI

17_ V6TH__]

F. 334 C2ND----

= I0.435 V4THJ

QE Io.348 _6T_

K. 17xl0-4 C2ND-_

n

(%) J 2.34x10 -4

V4THJ

, VB f33

L. 85xI0-4 V6TH _

Large Signal

Notes: 1. Al

l

units are Si, o (efficiency) in %.

2. Bracket s enclose const ant multipliers which depend on sy s t em t ype

where: C2ND, V4TH_ and V6TH indicate types: Closed-box 2nd-

order, vented-box 4th-order, and vented-box 6th-order respectively.

- 22-


24/33

TA BLE 3

DIR E C T S

YNTHES IS EQU TIONS

FO R S PE CIF IE D C U TO FF FR EQ UE NC Y N D E FF IC IE NC Y

Small- Signal Large- Signal

_._5 c2N_ r3 _536 c2_

=io.8o5 V4TH

SD2 =

IO.117 V4TH

.

PAR

MMS 11.007 V6THI _o J0.063 V6THJ Xmax233t/o

_.297 c2N_

1

_252 c2_ X

m_3_o

: 10.031 V4THJ , _10 = 10.217 V4THJ ,

CMS J0.025 V6TH__J SD---_ J0.403 VSTHJ PAR

BI :J3.41 V4TH I SDf3 = Jl.30 V4THI . I

J4.26 V6TH__J '/7o Jl.07 V6THJ m-'_-_ V ']Jo

_._, c_N'b-I IZ._ c_

RME J18.17 V6THJ _o JI,14 V6THJ Xm_2r32_o

=J11.63 V4THJ , SD2f32 = J1.69_ V4THJ , PAR

Note: Referto noteson Table2 and commentsn Sec,7: SpecificobservationsSec.A,

- 23-


25/33

TA BLE 4

DIR E CT S YN TH E SIS E Q UA TION S

FO R S PE CIFIE D C U T O FF FR E QUE NC Y A ND B C X VOL UM E

Small - Signal Large - Signal

J-_89J C2ND--- ['_578 C2ND--'] P

. =13442 V4TH I , SD2 =J499 V4TH-Jo _ 'AR

MMS L.]721 V6THJ f3'--_VB J'108 V6THJ X_axf3VB

J_'.47x 10.5 C2ND----J [-_.95x 10.5 C2N'DJ Xmax2f34VB

=J0.74x 10-5 V4TH J , VB =J5.08 10-3 V4THJ,

CMS Jl.47x 10~5 V6TH J S J23.55 I0 '5 V6THJ PAR

_3_T_B C2ND P R

BI =J223 V4TH J SD = 84.9

J__6 V6TH__J L_.I V6TI-IJXmax V f3VB

17 x 104 C2ND--- J'_7.29 x 103 C2ND---J PAR

=J4.97x 104 V4TH J SD2 =J 7.20x 103 V4THJ,

RME J3.11 x 104 V6TH__J _ L_1.94x 103 V6TH__JXmaxZf35VB

Note: Refer to notes on Table 2 and commentsin Sec. 7: Specific observations Sec. B.

- 24 -


26/33

TA BLE 5

D IR .E C T S Y N TH E S IS E QUA T _C NS

FOR S PE C IF IE D E FFIC IE NC Y A ND BOX VOL UM E

Small - Signal Large - Signal

F9.31 C2ND'D- J6-.27x 10-5 C2N"DJ

MMS J13.07 V4THJ SD2 = J2.73 10-5 V4THJ VBPAR

= . x .-z-:_

12.04 V6THJ _y3VB 1/3 J3.68x 70-b V6TH.J Xmax

f_.47xO-_2N_v_ F16 c2N__ _/3

= i0.74x 10-

b

V4THI = J3.5

2

V

4

THI . Xrnax

CMS L].47xlO -5 V6TH__J S-_ J4.81 V6TH.,_J VBI

/

3 PAR

= =J0.080 V4THJ..-L--J

BI JslJ55'

4

,0 V6THjV4THJSD

/

3V'B

2/

3 0L0_:089 V6TH_ Xrnax 1

T

_o5

/

3

ff_50 c2N_ SD_ _.4_103 C2N_1

= ]3063 V4THJ

I I

_1

7

3 2/3 = J 6.40x 10-3 V4THI VB2/3 PAR

RME J2598 V6TH__J '

/

o VB max

7.95 x 10-3 V6THJ 'x 2 ,_/3

N ote: R efer to notes on Tab Je 2 and com m ents in S ection 7 : S pecific Ob servations S ection C .

- 25_


27/33

_10

C2flO

L6

Y

E

L

__

- 4B_

d

/

lo-- --- C'

L

OS_LO-

/

_x (a)

SECOND-

_ _ _7_

-2

0

-- _ Ot

c

=

0

.759, _=

o

._,3z_

,

-2o--I '1 I--H I III. . I I I H-HF

V4TH

O

--

LE

VE

L -.S4B

/

---

d_ -- ,VEzvz-,z'z3-Box

40 FOP_T-O_Z_ER

__/ __ ____ (b)

20 _ =/.Oeo,

-_o I I I I I I I IH+

0.1

0.2

0,

3

O

.

E

__ 'd ,_ I0

+

/

0

-ID---- w,,-,

'

VE

_T

ED

-_

O

a

(c)

_ S txr, - O[eDEe

/ /1_ _=_ O,-=o.o

-

_

o, / ,

,

1 = 7

-so /I IJ,/l{lll -- I I ,,

k

o.I O.;Z 0.3 t_,_

2

3 5' lo

Fig. 1. Small-slgnalfrequencyresponseurvesof the three chosensystemypeswhoseparametersare

shownin Table 1. Thecurveshavebeennormalizedto the systemcutoff frequency(f3)andto their

midbandefficiency levels. Thesystemypesare: a.) closed-boxsecond-order(C2ND), b.) vented-

boxfourth-order (V4TH),and c

.

)vented-box sNth-order(V6TH). Referto Sec.5 for moreinformation.

- 26 -


28/33

EXAMPLE

I.

PARAMETER

Specified f3' %' PAR' & SD

System TTpe m

Closed-Box Vented

-

Box Vented

-

B

o

x

Parameter C2ND V4TH V6TH

t))f) _ 20 Hz

_)VB 0.75 m 3 (26.4 ft31 0.37 m3 (13.2 ft31 0.15 m3 (5.3 ft31

'_ 0.7_

_-

n

o

FB 20 Hz 20 Hz

PAR --_ 0.7 w _

._

--"

fs 8.7 Hz 20 Hz 20 Hz

- VAS 3.74 m3 (132 ft 31 0.4 m3 (14.0 ft 31 0.32 m3 (11.2 ft 31

_JqTs 0.31 0.40 0.30

(/)1

O.33 O.44 o.35

JVO 2260 cm3 (138 In31 795 cm3 (48.5 In31 523 cm3 (31.9 In31

MMS O.17 kg 0.30 kg 0.37 kg

CMS 2.Oxi0 '3 m

/

M 2.1xi0 '4 m

/

N 1.7 x lO'4m

/

N

BI 13.3 T.m 23.6 T.m 29.4 T.m

RE --dF- 6.5_

RME (_ cost 27.3 N's/m 85.5 N.s/m 133.5 N.s/m

SO _-_ O.113 m2 (176 in 21 _-_

Effective Dia. 380 mm (15.0 In)

Xmax 20 mm (0.78 In) 7.0 mm (O.28 In) 4.6 mm (O.18 in

PER

PE(max) _ 1OO w ,

Fig. 2. System and driver parameters for the three system types oF example 1: A sub-

woofer system designed to use a 460 mm (18 In) driver with specified cutoff fre-

quency and efficiency. Note that the vented-box drivers have more moving mass

and magnet requirements than the closed-box drivers[ Note also the wide box

volume range for essentlalty the same performance.

- 27-


29/33

E XA M PL E 2 . P A R A M E T E R S

Speclfled f3' VB' PAR

'

$ Xmax

. Sys

t

em T

y

pe

C1osed- Box Vented- Box Ven

t

ed-Box

Parameter C2N0 V4TH V6TH

J Jr3 _ 30Hz

J J,mV_ _ 5.66x10'2 m 3 (2 ft31

EE _ i;

41 4_

.J,,I, o.i8 o.36, o.9o

>- _o 30 30

_fB

j n..j PAR _ O. 2W _--

Ifs 13.0 Hz

30

Hz

30 Hz

AS 0.28 m3 (10 ft31 0.060 m3 (2.12 ft31 0.12 m3 (4.24 ft31

0.31 0.40 0.30

QTS

QMS 3.9 5.0 2.2

O.ES 0.33

0.44

0.35

VD 539 cm3 (32.9 In 31 189 cm3 (1],5 In 31 124 cm3 (7.6 In 31

MMS 550 g 60 g 12.9 g

CMS 2.7x10 '4 m/N 4.7x10 '4 m/N 2.2xlO'3m/N

B1 29.6 T.m 13.0 T.m 6.7 T.m

RE _ 6.5a

RME (4 cost) 13.4.4 N's/m 26.0 N.s/m 7.0 N.s/m

8.5x10 '2 m2 3.0x10 '2 m2 2.0xlO '2 m2

SD

)Effective Dia. 0.33 m (12.9 In) 0.20 m (7.7 In) 0.16 m (6.2 in)

Xmax _ 6.35 mm (0.25 in)

PER' PE(max) 112 w 56 w 22.4 w

Flg. 3. System and driver parameters for the three system types of ex

a

mple 2: A book-

shelf system designed for specific enclosure size, low-end llmlt,

a

coustic

power output, and diaphragm excursion. Note the very wlde differences In

driver size, input power, moving mass, and magnet requirements with the vented-

box drivers on the low side. If driver slze can be allowed to decrease (as In

this example) the vented-box drlvers can be extremely cost effective.

- 28-


30/33

EXAMPLE 3. PARAMETER

Specified no, VB, PE(max) and Xmax

System Type

Closed-Box Vented-Box Vented-Box

Parameter C2ND V4TH V6TH

E _ VB _ 1.42x102m3 0.5ft3)

_no C 0.5

fB 53.2Hz 39.2Hz

PAR -_ O.1w

fs 29.0Hz 53.2Hz 39.2Hz

II

o7'

l

x

l2'5 ft3) l'5xlO-2m3 (O'53 ft3) 3'OxlO-2m3 (1'06t3)3.9 O.445'00'40 O.352'20'30

-VD 76cm3 4.6In3) 43cm3 2.6in3) 51cm3 3.1in3)

MMS 56.8g 24.7g 33.4g

CMS 5.3x10-4 m/N 3.6x10-4 m/N 4.9xlo -4 m/N

B1 14.2 11.1 12.4

RE _-- 6.5_2 _:_

RME (m cost) 31.O N,s/m 19.0 N.s/m 23.7 N.s/m

SD 3.04xlo2m2 1.7OxlO2m2 2.06xlo2m2

EffectiveDla. 0.20m (7.7in) O.15m (5.8 In) O.16m (6.4 in)

Xma _ 2.5mm O.1in)

PER PE max) 20w 20w 20w

Flg. 4. System and driver parameters for the three system types of example 3: A sub-mini

compact system for use with a low power amplifier targeted for a specific ef-

ficiency, box volume, and cone excursion. Note the extension of low-frequency

cutoff for the vented-box systems. Even though the vented systems go lower in

frequency their drivers still have less mass and magnet requirements (the vented

systems use a 200 mm (8 in) driver while the closed-box uses a 250 mm [10 in])

- 29-


31/33

--

EX

Am

PLe

',

I o.7_

E

_r

lC/

E

N

ct

'

./_'

o,,,,

-

/I

' F_'

aUENCF

0

.

01 i,

_

V

4

T

V

(//_,-_,,ca

-'-.l:,-v,T,_Wm,_)

o.

oo

r

/

I I I I I III I I I I I III

120 -

_ O

-- ,7_,)z_dr_

Io_

/

,'

1

' M _

x/_uA4

--o,o

+

(b)

/ /

,

dB _

t

_-

-v

4

v

_

/

_C

OUSTIO Wnr

rs

90

5

. O

UTPUT

- ).

0

0

+

(_v,,',_'. //

FiELg -- ,-7

//

I I I I I Ifl I I I I I III

o

.

oo

o

,r

1o

2

0 30 15_1 1o_ 20111301[I

6

00 1ol211_

1

oo

-

2

_ c2Ns PE'


32/33

- - Exa_

e

LE

2.

/ V

_

E

F

n

ct_'Nn

/ K

v_.

;:' ,X-

c

-

o.oJ, /,i _;:_ vs

u

,_

u

I I I I I I [I

lib 28 Sg 5g 1l]0 2e8 311g 508 111021

120

,

f.O

/

I10 (o._w)/07Wi, OA

MhXlMUM COUS'TIC,

PL -

- C2ND / ,,

"' )o

wE

_

,oo /,,._.;W


33/33

/0 .............

'_- EXAMPLE _.

FR

C

lEI

_

_ .__,'_?_? _ a_._

V_TH /

*t

'.'

.,

'

,'"''F}

,y?

_"a

Erm

c

/E

N

cr

l

o.-- ._,,,,,,...

_

(o)

A __ // , _

_

.> V

_

0

,

01 /

_

/

_''

1/

'%'v4H,..

,, /

_R

E' a U

E

/

V

O Y

/,

//

........

,0

0

1 /

_

'

_

I

I I IIII I I t I IIII10 28 8B 150 181B 288 3511 WSIB ION

120

...... f,O

rio - E_MpLE_. --O+

M

a

x _u_ I

Ac

_

u

s'

n

c

PL

-- v4r_-.____.

,. t)._.,

Ho,

_

uuPi

-^,

i

oo

./:

'*'"

?//"/ IVIAXlM LIbS -_uu_

B -

-

WT_

I

_C

O

U

STI

6 Mr

rs

(b)

.o__x T7 -

REwR_,

18 28 _J8 EO 188 2l_8 3g(I EO8 1098

I0O ' '

EXAMPLE3

.

7

5

,

__ M

Ar/_4UA4

E

L EeT, q/CAL

(c)

EO

M,mM

u

M .

JNPU.7-

NPUT -

--

POW

E_

Po W ER

W,4T _ 1_*t, Y4;TH-_/'?_r. .'

P.,.,,.;;2ot

ia ;e

_

. 8e

_

ee ;ee

s

ee see

_

eee

FREQUENCY .Hz

Fig. 7. Curves of systemresponsedata f_r example 3: c "_b-mMi" compact systemwith specified

efficienc

y

(0

,5

%) and box size 0.0142 mv (0.5 ft _) for use with a 20 watt amplifier. Refer to Fig. 4

for data, and to Sec. 8: example 2 for more details. Graphs indicate a.) Efficiency vs frequency,

b,) maximum continuous acoustic output, and c,) maximum electrlcaJ input power.

-

32 -

Keele (1981-05 AES Preprint) - Direct LF Driver Synthesis

Documents

Transcript of Keele (1981-05 AES Preprint) - Direct LF Driver Synthesis