PREPRINT

WHAT'SSO

SACREDABOUTEXPONENTIAL

NO.

1038

(F-3)

HORNS?

BY
D. B. KEELE,JR.
ELECTRO-VOICE,INC.
BUCHANAN,MICHIGANPRESENTED

AT

51sf

CONVENTION

MAY

13-16,

THE

197S?i _i!i_A_T
A_D_O_._TG_TEERI_Ta
SOOI_TY
PR_RINTDThis preprint has been reproduced from the author's
advancemanuscript, without
editing,
correctionsorreview by the Editorial
Board.
For this reason there
may be changes should this paper be publishedin theAudio Engineering
Society Journal.
Additional
preprints
may be obtainedby sending
request and remittanceto the Audio Engineering
Society
Room 449, 60 East 42nd Street, New York, N.Y. 10017.
f:

Copyright

1975 byAll

therightsAudio

Engineeringreserved

SocietyWHA,T,S
SO SACREDABOUT,,EXPONENTIAL
HORNS?

D. B. Keele_ Jr,
Electro-Voice_Inc.
Buchanant Michigan _g107

The malntenance of constant directlvity
withfrequency In hlgh-frequency
exponential
horns
is quite dlfflcult.
Two main sound industry
solutions
are the multtcell
and radlal/sectoral
horns.
While the multicell
exhibits
fairlyconstant directlvlty_
both designs suffer from mid/high-frequency
polar Ioblng and mldrange narrowlng t and the radialshows continually
decreasing verticalbe&mwidth as frequency Increases.
A new series of horns which optimallyjolnsamodlfled conicalhorn with an exponentlal
throatsection corrects
these problems_ whlle offering
very well behaved polar patterns
and constantdlrectlvlty
up to 16 kHz.

INTRODUCTION:
Horns are used in sound systems primarily
for two reasons:(I) high
efficiency(and the resultant
hlgh acoustic output with low distortion)end(2) pattern/coveragecontrol.
The Ideal horn should have constant dlrectivlty
and coverage angle and provide a constant acoustic
load to the driverat allfrequencies
In the designed operating
range of the horn.
Up to nOw_ thesegoals were for the most part met by designs based on exponential
horn theory.
The exponential
horn was found to be particularly
effective
In providing
good
response right down to horn cutoff_ especiallyfor the hyperbolic-exponential
designs [I,7.
Unfortunately
the exponential
horn in its purist
form Is not conducive
to control of beamwldth and directlvlty.
The dlrectione)
character)sticsofthe exponentlal
horn are found to be highly dependent on the flare
rate _2_
p. _.
To get around this problem two main horn designs have surfaced:-1-(1) the multlcellularhorn and (2) the radlal/sectoral
horn.
Both thesedeslgns in one way or the other attempt to simulate an acoustic
sourcewhlch Is the analog of a portion of a pulsating
sphere.
This is a resultof acoustic
theory which states /_ p. 5Q7:'_ portion of a sphericalsurface large compared towavelength and vibrating
radlally_emits uniform soundradiationover a solid angle subtended by the surface
at the center of curvature.
To obtain uniform sounddistribution
over · certaln
solid angle_ the radial
air motion must have the same phase and amplitude overthe sphericalsurface Interceptedby the angle having
its center of curvature et the vertex and the dimensionsof the surface must be large compared to wavelength.
When these conditions
are satisfied
for all frequencles_
the response will
be independent of the position
withinthe solid angle. _The perfect pulsating
sphere segment provides quite good constant beamwidth high frequency (dimensions much larger than wavelength) polers but Is
found to suffer from a couple of defects of its own. in the frequency range
where the wavelength ls comparable to segment slze_ the polar pattern getsquite narrow and sometimes collapses
to some qO to 50%of the high frequency
beamwldth Z_r_ p. 40-b,2, p. 5_7.
In addition,
above this frequency_ thesphere segment radiation
exhibits
moderate loblng and fingeringin the polar
response.
The multlcell
end radialhorn designs are only moderately successfulinsimulating
the radiallyvibratingsphere surface.
As a result_
their dlrectlonal
characteristics
exhibitsome of the defects of the sphere radiation
along wlth some defects of their Own.
On first
examination
the conical horn appears to have excellent
potential
in simulating
the sphere segment because of Its Inherent constant solid angle
conflguration_
but unfortunately
its poor low frequency performance has kept
designers
from using It.
This paper describes the design of a new class ofloudspeaker horns based on an optimal joiningof modified
conical and exponential
flares.
Thishorn design exhibits
the excellent
pattern controlofthe conical_ but without
the mldrange narrowing and HF Iobing_ and the good
low frequency response of the exponential.

THE IDEAL HORN:
As stated In the introductio%
the Ideal horn should have constant dlrectlvity
and beamwldth as a functionof frequency and provide a constantacousticload to the driver.
A real world horn, being of finite
size_ offers
dlrectivlty
control
only down to that frequenCy where the wavelength is comparable to horn mouth size.
Below this frequency_ the beamwidth increases-2-monotonically(roughly
doubling
for each halfing
of frequency
up to 360 °where the horn then becomes an omnldirectionalsource_8ean_vidth
is defined)n thls
paper as the total
includedangle
betweenthe directionsatwhich
the sound pressurelevel(SPL) Is down 6 dB from the on axls
reference direction.
Fig.
1 illustrates
a hypotheticalideal

the beamwldthvs.
horn providing
a piefrequency(in one plane
only)
for
slice
polar
responsewithcoverage

angle-_l.l
Note thatthe beamwldth
ls constantdown to fl- and then roughly
doublesfor each octave
decrease
In frequency.
The interEept
frequencyfi
is the point
where
the asymtote
to the beamwidth
curve
for Iow frequencies(f_fT)
crossesthe ratedbeamwldth
angle,
fi
is roughly
thatfrequency
where Eom slze
is comparable
to wavelength.
Fig,
2 likewiseshows the beamwidth
for a hypothetical
ideal
rectangularcoveragehorn radiating
into asolid
cone of space with
angles_H by-e v _p. 112_'.
Physicalsize
constraintss
discussed
laterin thls
paper,
governthe orderingof the intercept

frequenciesl,e.

if-(_t_-t

_

then

fA-V_

fiH.

Fig.
3 shows the dlrectivity
index D I _p. I0__7 vs. frequency
for thesame hypothetical
rectangularcoveragehorn.
Above the upperintercept
frequency flv
the dtrectivtty
is constant,
For Iow frequencies(f _fTX)
the
directlvlty
increases
at a rate of up to 6 db per octave.
Between _-l_H and
fir
the dlrectlvtty
rises
at 3 db per octave.

EXISTING DESIGN PROBLEHS:
RadialHorn:
A conventionalradial/sectoral
horn design
is shown pictoriallyin Fig.
4.
The exponential
flare
is createdby straightsides on two boundaries
andcurvedsides
on the othertwo boundaries_
p. 5__.
Typicalpolar
patternsfor
thishorn are shown in Fig. 5.
Typlcalbeamwldth
and dlrectivlty
curvesare shown respectively
In Figs.
6 and 7.
An examinationof Figs.
5_ 6 and 7 reveals
severalperformance
problems
withthe radlal
design.
Note the mldrange
horizontal
beamwidth
narrowingaround1.25 kHz.
Observe the continual
decrease
In verticalbeamwidthwithincreasing
frequency.
The effects
of polarloblngon beamwidth
are indicatedin Fig.
6 by the non constanthorizontal
bean_vldth
between2 kHz and 10 kHz.
The relatively
large
throatdimension(X-X In Fig. 4) makes itself
evident
inthe eventual
decreaseof horizontal
high frequency
beamwidth
and the continuallyrisingdtrectivlty(Figs.
6 and 7).

IThe pie slice
or wedge shape certainly
is not the ideal
polar
pattern
for aliapplications.
For a source
elevated
above a flat
plane,
asource whose vertlcal
strengthvariesInverselyas the sin of the offaxis
angle would
compensate
precisely
for the inverse
level
with
distance
law.

-

3 -

de,

IDEAl_[_EANll4/IDTH q_;

HOR_

BE_Mw_rM

LOG

Va

FREaUEIVCY

f --_'

Fig. I.
Bearnwldth versus frequency for a hypothetical
ideal horn.
The beamwidth is constant at e, above f_ and roughly doubles for each octave decrease In
frequency below f_T:' For very Iow frequencies_
the beamwldth attains
360° where thehorn radiates
omn_[directlonally.
\,,/OE_L cwxo'v _0_'N%'

BE_KIWIDT-H

''2'

V$

FI_EQLIEIVCY\\

BEAt4WtDTtt
Lo_

_

_'H

\

',,
_

_
_,

HOR.

"_ _,...

VE_'T;\

Loc_,_c.__.
Fig. 2. Bearnwidth versus frequency for an ideal
provldes a _H (hor.) by 1_/ (reft.)radiation
pattern.

rectangularcoveragehorn thatIDEAL

NOR'IV DIR'EC TI V /TY
V/

RATEDD_lV__.,j

DIF?ECTIV ITYiNDEXDz
_

dB

0

LO_

_' _

3. Dlrectlvity(= I0 2.log RO) as a function
ideal Fig.
rectangularcoverage index
horn oD_Fig.

offrequency

for

the

F?ADI/L. HOR'Nx

HOR.
SECTI0_
V'ER'/T
5ECTION

Fig. q.
Sketch of a typical
60° horizontal
coverage angle exponential
radial/se_toralhorn.
The horlzontal
sectlon expands with strelght
sidewalls
angled at
60 _ while the exponential
taper is provided by the curved verticalboundaries.
The following
experimental
measurements shown In Figs. 5 to 7 were mede on a 60°
redlalhorn with overall dimensions of 20.3 cm(8 In.) mouth height,
61.3 cm(24.1 in.)mouth width and 50.8 cm(20 In.) length.

'

5 '

HOR.

VE R'IT

o'

o'

o'

FgEQ g[_/£ Y

o'

/_/

5'00 H;'
330'

xx
5

-

\

I kFtz\ X _/¢_--..x4Jo"

5 g/-/z

o"

'__

o'

SCALE
Fig.
from
mouth)
horizontal

5.

Some

measured
beamwldthse]ected

one-third

on
at

the
60 ° radial
1 kHz andtheoctaveIS 5 DECIBELS

bandwidthhorn
discribed
horizontal
Ioblng-

6 -PER DIVISION

polar

responses

(3

in

4.
kHz.

the

Fig.
at
5

'

o'

Note

metersnarrow

/+2 °

,.

_3

I

X I i_1", I _FF_I
I
FREQUENCYINHERTZ

Fig. 6.
Beamwldth (-6 dB) plottedagalnst frequency for the 60° radialhorn
discribed
in Fig, 4. The angular coverage of this horn is rated at 60° x 40° by
the manufacturer.
These measurements were taken from a complete set of one-thlrd
octave polar curves measured in EV's anechoic chamber, Observe the horizontal
narrowing around 1.25 kHz and the steadily
falling
verticalbeamwldth with frequency.

+20

Il[Il

rl

I

I

I IIl(III]_0 ° RADIAL

I o dD,B

I !lIlFP_QU_NCY
iNHERTZ

Fig. 7. Oirectlvlty index DT vs. frequency for the 60° radlal horn of Fi . 4.
Notice the steady rise as frequency
increases.
The Ideal rectangular
60 x 408
coverage angle horn, with wedge shaped polar patterns_ would have a DI of +12.6 dB.

-7-

Hultlcellular

Horn:

The multicell
is depicted
in Fig. 8 _p. 5_[7.
Thishorn consistsofa largenumber of small
exponential
horns withaxls
passing
througha common point.
This assemblage
In the low and mid frequencies
effectively
simulates
a sphericalsurfaceof uniform
phase and amplitude
at the mouths ofthe horns.
At higher
frequencies
above 6 kHzj however_ each horn Independently
radiatesa narrower
beam.
This
gives
rise
to severeripplesIn the
HF polar
response
as one goes on and off
axis of each individual
horn.
FIg.s
9 to 11 illustratesome typicalmeasurementson thistype of horn
(an Electro-Voice
H253 2 x 5 cell).
Note thatthe multicell
exhibitsthemtdrange
narrowing
effectin both horizontal
and verticalplanes.
Beranekp. 10_87 dlsplays
some beamwldth
versusfrequency
curvesfor the multicell
whichshow the midband
narrowing
effectIn more detail.

WHAT TO DO?
Assuming
the designer
wants
to simulate
the pulsating
spheresectionmore closely_is thereanothertype of horn flareotherthan exponential
which would
work better?
The answer
is yes and that flareturns
out to be
the conical
(Fig.
12).
Unfortunatel%the Iow frequency
responseof theconicalhorn is quitepoor.
In comparison
to an exponential
horn of thesame overall
dimensions_the conicalhorn has much less output
In the firsttwo octavesof operation.
Fig.
13 compares
the efficiencyof the two horn
types
when each is driven
by a matched acoustic
source(see appendix
I).
Disregarding
the low frequency
efficiency
problem_the conicalhorn
is found to be very conducive
to designs
thatrequireuniform
coveragein a speclflc
solld
angle.
The constant
solid
angle
configurationof theconicalhorn precisely
flts
the requirements
notedin the paragraphquotedin the Introductionof thispaper.
In additlon_
the conicalhorn can bemade large
withoutlimit
and not incur
destructive
mouth reflections
back
into
the horn as is exhibitedby the exponential
horn _.
This
lattercharacteristicof the conicalhorn allows
the designer
to optlmise
coverage versus
frequency
by increasing
the hornJs
lengthand size_
withoutfear
of degrading
response.

A SOLUTION:
Researchdone for a previous
paper ff-_7, which dealt
withselectionofan optimum exponential
horn mouth sizefor radiation
intofractional
solid
angle
spaces(q_21_
suggested
to the author
an optimum way to joinanexponential
flare
and conicalflare
togetherin the same horn (see appendix
2) .2

2The author
is indebted
to his former
boss at Electro-Voice_Gilllom_for first
recognizing
that
this
combination
would
and for constructionof a working
model.

-8-John
be useful

2 x5

MULTICE

LL

Flg, 8. Sketch of · typicalmulticellularexponentialhorn.
This unit Is the 2 x 5 cell
Electro-Voicemodel 14253with overall
dimensions of b_.5 cm(17.5 in.) mouth helght,
92.7
cm(36.5 In.) mouth width and 53.8 cm(21.2 in.)length.

HOE.

VERT.

o'
330'

F fi E r_U_;IVC Y_

o'
_0'

330°

_/__

2 kH,
/

l0 kHzSCALEIS 5 DECIBELSPERDIVISION
Fig. 9. Selected one-thirdcell of Fig. 8. Note the Iobing
row verticalcurve at 2 kHz,octave polarend fingering'

9~

measurements on the 2 x 5 multiin all the polars and the nar-

30'

J60

21_

N_LT'I_
i
i

i

i

12S

I_EAMt'YIDTt. I

Ioo

IN

_o3

DEGEEF__

50

80

eo
FREQUENCY
IN HERTZ

8.
in

Flg.
10.
Bean_idthversusfrequencyforthe 2 x 5 multicell
discribed
The manufacturer
rates
this
horn as covering
120 ° x 60 °.
Observethebeamwidth
at 630 Hz (hot.)and 2 kHz (vert.)

in Fig.
decrease

ill/il/L/I
i0

FREQUENCY
IN HERTZ

Fig.
cell

Fig.
11.
Dlrectivlty
Index OI against
frequency
for the 2 x 5 multicellof8.
The typicallyuniform
directivlty
above 800 Hz explains
why the multihas seen such wide usage in sound systems
over the years.
-

10-CO_/ICAL

HORN
0

_IDE

VIEW

FRONT

VIWW

Fig.
12.
A 60 ° circularcrossection
conicalhorn (otherwise
knOWn as a
megaphone).
The conicaltaper
is the only one which provides
a constant
solid
angle
to wavefronts
traveling
through
the horn.

lllll

,o,,.

o
dB

i ,

, 1I J

EX_NENT'_"I I I

V JJ4d"l'"-1' 4"t"///
I

, i

-2o

_V
i/ I %Q, I-30j_-_0 _ _ __ •F Xz ---_ _ _ _Fig.
13.
Effic'ency
comparison
between an exponential
and conicalhorn withthe same overall
dimensions
when driven
by the matched acousticalsource(see
appendix|).
Observe the poor conicalresponse
between I00 and 500 Hz.
The exponentlat
has a cutoff
frequencyof 100 Hz end an optimum size mouth (kca H = 0.93,
see Lq_)forradiation
into the half-space
load.
The radiation
impedance forthehalf-spaceenvironment
is modeled by a piston(same diameteras hornls
mouth)
inan Infinite
flat
plane.
- II-

This composite flare horn would be an exponential
In the firstportion andconicalthereafter(Fig. lb).
This new combination exhlbits
the good Iow
frequency response of the exponential
and the excellent
coverage control of
the conical.
Fig. 15 shows response comparisons between different
sized exponential
and composite conical-exponential
horns (hereafter
called the CE horn) allwith the same cutoff
frequency and throat diameter.
In comparison withan exponential
horn of the same mouth/throat
size and equivalent
low frequency performance,
the CE horn is found to be roughly 10 to hO% longer(length depends on selected coverage angle)=

MIDRANGENARROWING:
The newly designed CE horn is not without
its own problems, however.
The polar narrowing effect,when the horn mouth Is roughly comparable towavelength,
still
exists.
Also_ the polar Ioblng and fingeringcharacteristicof the sphere segment radiationis also exhibited.
An Imperlcallyderivedsolutionto these problems was found In a secondary rapid flaring
near themouth of the CE horn (FIg. 16).
The secondary flaring_in addition
to solving the narrowing problem, was found also to considerably
reduce the Ioblng
and fingeringin the polar response.
Good results
were obtained when roughly the last third of the conicalhorn sldewall was displaced outward so as to double the included angle (FIg.
16).
On first
thought,
this Increase In physicalmouth size would seem tohave the effect of narrowing the beamwldth even further.
However, measurements of amplitude across the horn mouth show that the effective
acoustic
source size actually
decreases, because the amplitude
Is much highTr In thecenter of the horn than on the outside edges (these comments only apply tothe frequency range where the wavelength is comparable to mouth size, at
higher frequencies
the amplitudeis again roughly constant over the hornmouth).

ANGLE-SIZE-FREQUENCYTRADEOFFS:
For a specificdesired coverage angle and intercept
frequency,
how large
must the horn be? An lmperlcelly
derived relationshipwes found to hold forthese variables(Fig. 17, also see Fig. I):
X =K

where,X=

horn mouth width,- 12 -

CE HORN

MGUT_

EXF'ONENTlaL"_--- ---s,- CONICAL
Fig. lq.
boundary pointreflections,

A multiflare
horn combining exponentlel
and conicalflares.
The
between the two flaresshould be selected to minlmlze junction

-13-

I
I
I
i

//
,/

L _JJ:- ,0.22'1T St'
Re = 10.3': .....

ff.
--,.Tsff........
-_-[
20 iN, -....

Fig. 15. Efficiency
versus frequency comparisons of several different
sizedexponential
and composite
conical-exponential
horns (CE horn) using the matchedacoustic
source(appendix
I).
All of these horns are developed
from the sm
circularcrossectlon
hyperbollc-exponential
prototypehorn wlth cutoff fc = 360 Hz,
T = 0.6 and throat dlameter of 0.98 inch (a).
The sol Id angle _ of the added conlcai section
is equal to that provided
by a perfect
60 ° x /40° coverage angle horn.
The optimum transition
from exponential
to conical flares
occurs et !1 Inches fromthe start of the horn.
Three different
sized exponential
prototypehorns are considered which are
centered about the optimum size Lq_. Houth diameter ratiosof one-helf
optimum(_)(kca H = 0.5), optlmum(_(kca H = I) end twice optimum (_(kca H = 2) are
analyzed.
For each of these prototype exponentials_
two conical-exponential
horns are generated:
I · CE horn which has J_he same length as the exponential
prototypebut with a smaller mouth slze and 2(_) a CE horn whlch has the same
mouth diameter but Is longer than It_scorr_esponding
exp_entlal
prototy___.
These
horns ere designatedrespect lvely___,_._ _f_._the _prototype,C(_} _Dfor the (_) prototype
and _C_
for the _prototype.
These nine horns are depictedin (a) with all relevant
dimensions shown.
Only the sidewall
contouris shown; the complete horn is developed by rotation
this curve about the center line.
- lb-

of

?_..-Soy. ----_ 0

_/_L

(b)

L_ ._OUTflLEVEi.

-.0_o__O,,.__..ol.I ll.I
I }1I ..:,fl'q
-TV

{[_-.

PIxm

I /
m

_o=_o,,-,-oF
IIIllU_J
L_I[ ,-/fT_-_l(d)-_^*_.
,,o_....
_ .....

t L.,,:.z /**/,Y ' I'_°I..."71
__o
7

1
/
/

FREQUENCy
IN HERTZ
The efficiency

comparisons

for

the

three

cases

are

shown

In

(b),

(c)

and

(d).

In general,
the CE horn provides more output below cutoff and somewhat more passband
ripplethan its exponentlal
prototype.
The added response deviations
are negligible
for

most

practical

cases.

-15

-

CE

FtORN

MOUTH

F'LARI

N6'_ADD_'D

F/..,,,RR E

Fig. 16.
Illustrationof added flaring
on mouth of conlcal-exponentlal
hornwhich corrects mldrange polar narrowing and polar loblng/fingering.
Effectivecorrection
resulted when approximately
the last third of the conicalsection was
moved outward to roughly double the Included angle.

Fig. 17. Depictionof a generalized
horn (In one plane only)
coverage angle _ and maximum mouth dimension X.

- 16-

which provldes_)" =

coverage angle of horn (assumed to be the same as theincluded angle between the horn's sidewalls),

frintercept frequency down to which coverage angle ismei ntai ned, and"K m a constant(=2.5 x JOb' m-deg-Hz_ or
I x I0 ° In.-deg-Hz).

Eq. (|) applies to a broad class of horns which simulate
sphere sections or arcs, including the multicell,radialage only) and the new CE horn.

radially vibrating(horizontal
cover-

Flg. 18 graphicallydisplays eq. (I).
Note the large mouth sizes required for narrOw coverage angle horns which operate down to relatlvely
lowfrequencies.
For example, a horn of 20° coverage angle required to operate
down to 500 Hz must be about 2.5 meters (100 in.) wide.

_en

For rectangular coverage area horns, a further relationshipholds betthe coverage angles, sizes and intercept frequencies.
Analysis yields

A ",

XH m
Xv

sln_-_r
sln _1/(2)where A is the horn mouth height-width
aspect ratio.
to a maximum of 120° eq. (2) is approximately

If _H and _/A _ "QH

are limited(3)ev
Eq. (3) indicates that the mouth aspect ratio Is fixed once the coverage angles
are selected,
i.e. a b,O° x 20° horn would have a 2:1 mouth ratio etc.
Substituting
f_v/f1jt yields

eq.

(I)

for XH and XV Into eq.

fIv _,_
fIH(3) and solvingfor

the ratio(4)-

Eq. (4) governs the ordering and ratio of the Intercept
frequencies once thecoverage angles are selected.
For the 40° x 20° horn example, this meansthat upper Intercept frequency will be four times higher than the lower frequency.

PRODUCTAPPLICATION:

three

The CE horn theory dlscrlbed In this paper was applied to the design ofhigh frequency (400 to 16,000 Hz) rectangular coverage horns.
Nominal

-17-

I0 _

_°°
·

_/0o

HORNMOUTU
J xt,
WIDTH

o._

16o

',1 x

"

_o

,

--

, ' R?,_x'"· ,',%.', ',

\

2sooo

x-e _:-· "I\X ,_

I0"J IWCI.JS,,' _X

o.o,
--

25'

,_,b? "I

00,,

_-'q

0.G3

0o,

lll'_ o,FREQUENCYIN HERTZ

Fig. 18. Graph showing relationship between horn mouth width (or height)
X, coverage angle O and intercept frequency fT' For a specific combinatlon of G
and X the horn provides beamwl,lth controJ onl_ down to fi(see Fig. I).

- 18-

coverage
angleswere chosen
to match existingsoundindustr_radialand multicell
horns.
Coverage
comblnatiens
targetsof 90 ° x 40°_ 60
x 40 ° and 40 ° x
20 ° were selected(_H x_/_
horizontal
by verticalrespectively).
In everycase_ maintenanceof verticaland horizontal
beamwidthtobeamwldth
down to about
500 Hz was desired.

2 kHz

(f_V

'

1.6

kHz)

Computermodel studies
shouldbe of the hyperbolic
The initialthroatdiameter
Voice
H.F. driver.

indicatedthat
the exponential
portionof the horn
type with
T = 0.6 and cutoff
frequencyof 360 Hz.
of 1.3 inches
was chosen
to match e new Electro-

The desired
rectangularcoverage
was developedby a combinationof horizontal
and verticalflaringwhich
is very similar
to the radial
design.
A
shortinitialthroatsectionof 0.5 inch provides
a transition
regionwhere
the crossectlonchangesfrom circular
to rectangular.
From thispointonthe horizontal
flaring
Is wedge shaped withstraight
sides
angledat the desired
horizontal
coverage
angle(except
for mouth flaring).
The verticaldimensionvariesso as to maintainthe overall
hyperbolic-exponential
flare
in the first
partof the horn.
For the chosen angles
and cutoff
frequencies_
the change
from exponential
to conicalflareoccursat about 5 to 11 inchesfrom the startof the horn_
Beyond thiscoupling
region_the verticalexpansion
is a straightsided wedge
shape with
Included
angle
equal
to the chosen vertical
coverage
angle.
Fig.
19 shows horizontal
and verticalcrossectlonsof each of the threehorn designs.
Flg.
20displaysmeasured
beamwldth,
directlvity
factor(R_)_ and off-axis
response
curvesfor each design.
These measurements
were derived
from onethirdoctavehorizontal/verticalpolar
responses
run in EVes anechoic
chamber.
The polar
curvesfor each horn are displayed
In appendix
3.
ROwas computedby a method dlscrlbed
by Davis
Lr_ and Wilson
Z-_7.
All
off-axls
response
curvesare referenced
to the on-axis
level.
Note the constantdirectivity
and beamwidthabove
1.6 kHz for these
designs.
Constant
dlrectlvity
in a horn implies
thatan axial
frequency
responsewitha particulardrivershouldbe in close
correspondence
to thatdriverts
power response.
This was checkedon the 90 ° design
by equalizing
flat
thepower responseof a driver(from
200 Hz to 15 kHz) and then usingthat
driverwith
EQ and runninga 3 mater
on-axishorn response
curve.
The_ results
of
these
tests
are shown in Fig. 21.
Flg. 2la shows the equalized
power responseof the driveras measured
on a 6.1 meter
terminatedtube.
The axial
responseof the 90° horn wlth
thisdriverattached(same EQ as in Fig. 21a)is shown in Fig.
21b.
The
horn'sdtrectivity
Index
is also plotted_
withthe same scale_for reference purposesin Fig. 21c.
Comparisonof Figs.
21b and c indicatesgoodcorrespondence.

-19-_0°×20 ° CE HOI_I_

'_o
°

HOR.

,_2_

(,, ,,,.)

VERT. (_,~.)

Fig. 19a. Horizontal
and verticalcontour sketchs of the 40 ° x 20° coverage
long-throw conical-exponential(CE) horn (EV model HR4020). The transition
fromexponential(fc = 360 Hz, T = 0.6) to conical occurs at 12.7 cm (5 In.) from thestart of the horn.

- 20 -

_0'×_0 ° CE HOR:N

60' HO_'.

a_'__

/

j

_o'

l

VERT. _.2 _Fig. 19b. Sketches of horizontal
and verticalcontours of the 60° x 40°
medium-throw CE horn (EV model HR6040). The switch from exponential
to conicaloccurs at 23.6 cm (9.3 in.) from the start of the horn.

-21-

DO°XL/O' CE HOrN

I_,._ ,~._/-.,

s_,,,(22,,,,.)_...1_3.2 cm

Fig. 19c.
model HRg040).

Contour sketches of wide angle 90° x 40° coverage CE horn (EVChange to conical occurs at 16.5 cm (6.5 in.) from horn start.

- 22 -

_O°_O° //OR/V

BEA/_W'IDTN_o° x vo° //aRm

,.,.,

,", E

"'il

"

vER,.

i,.

-vE_T:."':i ,---n('-Gae) _LOG_,O'xvo° /-/oR_

_ -,

,
.....
i,,

VER T."_,'

,

:_i

_

_ _

_

,SCALEj

T I ,

"'i"

_

_._

, I_,,'_1
_ _

_

,i_

|

_ _

I:/
_ _._

_

i

" i_i
i .... ,:,,, ,,=. ....
_,,__,,,, ,_l Ill0 _'[i_ii ]ii;

I%

o,

1

(_)

Directivity Factor R e (Q)48.7 (+104,-12.6)

Directivity
Factor Re (Q)17.7 (+6.3,
6.6)(average 1.25 kHz to 16 kHz)

FIg.
on

the

2Oa.

three

{10 Log Re, average 800 Hz(10 Log Re average 800 Hz

to 16 kHz)to 16 kHz)

shown

of

bearnwidth
in

Fig.

19.

and

directivity

Note

both

the

factor/index
well

directivityof thesedesigns(cOmparewlthderivedfromthe measured
one-third
octave

on

which

horns

16 kHz)Directivity Index D i
10.4 dB (+.9, -.6 dB)

to 16 kHz)theuniform
curveswere
the(average 800 Hz

Directivity
Index Di
12.5 dB (+1.3,
1.7 dB)(10 Log Re, average 1 25 kHz

Displayhorns

Directivity Factor Re (Q)10.9 (+2.5,-1.5)(average 800 Hz to 16 kHz)

Directivity
Index Di
16.9 dB (+.8-1
3 dB)

o

are

shown

in

appendix3.

behaved
Figs.
polar

measurements
beamwidth

2 and _).
responses

and

These
taken

LtO°xFO° HdRIV'
0=st ±:_.lL;ikl

LGO°X VO° HORn,_iod:' i, :1_.,_=.L_=__

90°x qo° /./o_/v_ _,........
o° 1_-_-_iI; = [,1" " 1 ,o.%_°l-L_q_l!l-I.-I I=1 J:

HOIYlZONTAL

•l

_l !

OFF-FI.XI5

[

:1

I

,l

, I

_

, I
_

_1 1_= :1+_oo .J_l°: : ::'

"'

"

'

"

'

'

! I

..-,,._,.1.,,o.°_s,°T'iLl,_il,,li"
i i",1,I111_1

It+"_°.:[_

±30
°

r

_1__

_,_

'

_ _

"3°°.,I_T!I

I '' I,!il+s°° _,_11lll,!_lllll;,I

lj

+40°

-s_,

.,:1_1=:iI+-6o° ._= JI r _ilrl"1

i 'T'_k-"

i

i

l

_I I

.........
I_._--_,:i ,1.4-4 ,o,e:.....hT-4_--.T
FF-VT-r-:.T:'_io,,,°;°°ii
iiiii ,,i

VEI_TICAL+5o,t,L,,o--

OFF-AXI3-s

F?ES_ONSE

i

+_1oo
-:i

i I _=

--

I

+-1_
° "
'

:

-,

r

±aoo _o!_-_+.,oocl l__lll
I

,],=

T _

-m

I I

,-_._=,=m I1=.,[_"___o ° ,JI

-F
Fig.
three

20b.

horns

derivedon-axis

of

one

time

spectrum

relatively
the

Fig.

19

of

one-third

taken

at

from
the polars
showninlevel.
The curves
shown

sponseof

Display

would
good

uniform

getat

anaIyzer_if

octaveselected

frequency
off-axis

appendix3.
here
indicate

response
angles.

Eachtheoff-axls

angTeswith

thehorn/driver

wereequalized

off-axis

response
naturecurves
of

the

on
polar

these

on

curves

the
were

curve
is referenced
todlcect-fleld
frequency

various

non-lobing

curves

These

a

horns

responses.

one-third-octave
flat
is

a

on

direct

the
re-

real-

axls.

II l
T'

II

The

result

=II

I

_

ii

:l

,-'1
i

'_

'

I -"-1"_'1

, I

I

!

l;'i

!!1._I.__.,_,_,
M___.o_..,,o_.,.,.....,_SO
Ja...,,,,.,AN,r_L..,u. F,.. I0_.,

Ob _

'

__--p
----

''

z;.

"''_

.

i-I

'

Y"

'iLl: ,

-1-',''_E,'_--._:''' : j :_;'w, s....2aQ_/._ ..p.,s,..,lO_../.._

. .

I'

.

i';

':_:

_ ;

:_

i,:

._ .

".'

] ;

i -'_:'_" _'!'
_....

B_aol
& K_r
M
ObJ

_

P ............

Range'__d'--L _'"_

Re,briC,_, , _,w_t'I--o;-d_

L .......

· _ :-_v_,,]v..... _t ,C,_r_F_,' :..[__ti',_ '_-_'.'tzt-:!
;b'r:L_t_!
_hi'__:

W, S=.ed

T

?--

__.

'.._ t;_,'.,'

Freq

_

HZ

_O_mmf_c

",per

Spee,

_

.......

__,'_i_:: _-:-_-:._J _,.,'[',:L;,U-_'b -__t-_-I.... L: :.-m-,...............
Lx*'°[':rl.ij_!i__:.i:-'__'-.
,,:_'.
, ,__.
._

Fig, 21.
Results of experimental
measurements on 90° x 40° horn to determine trensmlssion
characterlstlcs
when used with driverwhich has a flat
power output response curve.
(a) shows the driver's
power frequency response
as measured on a 6.1 meter anechoic pipe and equalized with a one-thlrd
octaveequallzer(1/8 inch Bruel and Kjaer mic).
The HRgOb,
O_s axial
frequency response
taken et 3 meters with the equalized
response driverattached Is shown in (b).
For comparison, the dlrectivlty
index vs. frequency of the HRgOb,
O_ plottedonthe same scale,
Is shown in (c).

- 25 -

It should
be noted
that the designs
bear a resemblance,
exceptformouth flaring
and absenceof Internal
baffles,
to a horn design
patentedsome thirty
years
ago by K) Ipsch E77.
The rectangularcoverage
implementationof the CE horn is similar
to Klipsch_s
designin thata form of wavefront"astlgmatlsm"
is generated.
Thls arises
becausethe vertical
wavefront
radiusof curvature
is different
from the horlzontal
radius.
Froma practicalstandpoint,
thisastigmatism
appears
to be of no consequencewhatsoever.

CONCLUSION:
A new classof horns which exhibit
very
constantdJrectivity
and beamwldth
have been d/scrlbed,
These horns optimallyjoin
a modified
conicalflare
withan exponential
flarethroatsection.
The good low frequency
response of the exponential
horn is retained
while
the conlcal
flare
providesexcellentpatterncontrol.
The angularradiation
characteristics
are foundto be much better
than the exponential
multicellularhorn but withoutthecomplex
Internal
cell/baffle
arrangement.
The new classof horns provide
a very wlde design
marginin selectionof designed
horizontal
and vertical
coverage
angles.

-26 ~REFERENCES

V.
p.

Salmon,"A New Family
212 {January
19461.

[_7

H. F. Olson,
York,1960).

C_u7

L.

Z[L7

D. B.
Audio

L. Beranek,

Acoustics

Keele,
Jr.,"OptimumEn 9. Soc. Convention,

D. Davis,
So.o.c_._c.
vol.
Zr_7

Acoustlca]"On Standardizing
2]_ pp. 730-731

G. L. Wilson,"Directivity
and Measurement
Methods,"ofHorns,"J.

Englneerinq

P. W. Klipsch,(January
19511"Loudspeaker{Application

Soc.

_D. Van

Nostrand[McGraw-Hill,

New York,

Am.,

vol.

Co.,

17,

New

1954).

Horn Mouth Size_"
presented
at thePreprint
No. 933 (B-71(September
the Measurement(November1973).
Factor"J. Audio

Q or
En9,

{December19731.
CZ7

Aco.ust..

of

-

J.

Audio

En9.

R_)? Standard
Terminology
Soc.,
vol.
21, pp. 828-833

Hor%"
United.States
date June'19451.

- 27

q,"

46th_..
19731.

Patent,No.

2,537,

14!

APPENDIX

1

THE MATCHED ACOUSTIC

SOURCEA relatively
easy way of comparing
differenthorn
to efficiency
and frequency
response,uses the conceptticsource.
The matched acoustic
sourceis an acoustic
sourceconductance(volume velocity/pressure)
of
GS

=

S

GS

=

sourceconductance,

densityofflares,withrespectof the matched acousgenerator
with
a

(5)

where

Po

When thissame area

c

=

speed

S

=

crossectlonaJ

of

air

sound

generator
is used toS, a power available=(=1.21kg/m 3)

in

air

(=343

area

of

acousticm/s),source.

and

drive
an
efficiency

acoustic
can beload
impedance
deflnedYL withthe

2 GS GL

(Cs;

2

(6)

where

No

=

power

available

efficiency,G$=source

GL

=

real

BL

=

complexYL=

GL + JBL = acoustic

conductancepart(=S/{PoC)),of acoustic
part

of

load

acoustic

admittance,
load

load

admittanceandadmittance

Note thatthe power available
efficiency
assumes a value of 0.5
the load is an infinite
pipe of area S (characteristic
admittance
The transformation
betweenacoustic
impedance Z a and admittanceor

50%whenof S/_eoc)),
Ya is Ya =1/Z a .
The matchedsourcecan be thoughtof as simulating
an ideal
driverofzero mOving mass end infinite
suspension
compliance.
The simulated
driverls
BI product,coll
resistanceand diaphragmarea are chosen so as to yield5_
efficiency(motlonal
impedance one-halfof input
impedance)
when itdrivesan Infinite
tube of the same diameteras the horns throat.

- 28

-

APPENDIX 2
OPTIHUHFLARE JOINING
The conical and exponential
flares were joined together
in a mannerv_tch minimizes
Internal
reflections
at the junction
point between thetwo flares.
This was accomplished by selecting
the junction
point tominimize the junction
reflection
coefficient
over a selected band of
frequencies.
This specificcase was analyzed is some detailin a previous
paper L_7.
For a circularcrossection
exponential
horn of cutoff
frequency fc'
feeding into a conlcal horn of solid angle UrJ, the following
radius at
the junction
point was found to minimize internalreflections
over therange fc to lO fc:
aj

-

0._

sin_kc

(7)

where
aj

=

radiusat ]unction

_

half

kc

=

2 q-T/_

fc=

exponentialc=speed of sound.

point,

angle of cone withsolid

angle_'

C = _-r'Tfc/C,_orn cutoff

frequency,

andOnce the ]unction
radius is computed by eq. (7), it is a simple matterto compute the ]unction
distance from the start of the exponential
horn bythe use of the exponential
horn equation.
APPENOIX 3
HORNPOLARCURVES
The directional
characteristics
of each of the three horn designs (withdriverattached)
were measured by running a set of horizontal/verticalpolar
responses,
in EV's large anechoic chamber, at each one-thirdoctave center
frequency.
The test signal was one-thirdoctave bandwidth limited
pseudorandom pink noise (! Hz rep rate) centered at the indicatedfrequencies.
The measurement microphone was placed 3.5m (11.5 ft)(4.5m for the HR4020)
from the horn mouth, whlle rotation
was about the horn rear driver
flange.
The horn was suspended freely wlth no baffle.

- 29 -

The

followingpolarspseudo-random

noise

with
polar.

angle.
At

The
each

superimposed.
markedcurve

polar.

The

show
are

the

beamwidth

The

the

curvesthehorizontal

shown

anglesfrequency,

toresults

clearlymay

beamwidth
beamwldth_/O'x20° Ho_'u

and

of

these

In

the

centerhorizontalbenumberis?ot.,q_¢:c:::Z
HORIZONTAL

SCALEIS 5 DECIBELSVERTICALPER DIVISION

z

-

by

numbers

30

o

The

vertical

level

are

noted

on

polars

have

each
in

on

of
of

comparlng

printedlistedeffectsvariations

frequencies
andseparated

angle

tests.
cyclicthetop_r_eoNs_

each

been

beamwidth
center

in

the

every

of
case.

each

_0 ° X ilo° HOF_!

POLAR

/

-31

-

RE_PO_S£

9O°X qO° HOI_N......

PDLA_

I......

- 32 -_E'SPONSEs,'P'