Design, Advanced Computer Modeling, Measurements and Discussion of a high efficiency tri-amplified speaker consisting of a low frequency vented enclosure (Bass Reflex), a hybrid conical/exponential midrange horn and a compression tweeter. The bass enclosure is modeled using BassBox Pro. The horn is 3D modeled using Hornresp. The measurements are made with SoundEasy with a full MLS (minimum length signal) implementation using the Ground Plane method and the Near-Field method.

3. HORN - INTRODUCTION
Horns have been used since the beginning of audio reproduction
technology.
PRO
Horn loudspeakers offer outstanding sensitivity (or efficiency)
RESULTING IN EXTRORDINARY DYNAMICS. For example:
AvantGarde Duo 104dB/W/1m
JBL CMCD-81 108dB/W/1m
Cerwin Vega EL36C 106dB/W/1m
Average 106dB/W/1m
A typical bookshelf speaker 79dB/W/1m
Difference 27dB/W/1m
Doubling the input power increases the sound pressure level (SPL)
by 3dB. Therefore, a typical bookshelf speaker will deliver 106dB
using 512WATTS OF ELECTRICAL POWER!
Note: 27/3=9
And 29= 512

4. HORN - INTRODUCTION
CON
• They are bulky
• They are expensive but require less power for
the same SPL
• Often exhibit an irregular radiation pattern
unless properly designed
• Have an uneven frequency response unless
PROPERLY designed

5. HORNS – EXAMPLES: COMMERCIAL SYSTEMS
Alura 100dB/W/1m $15,000/pair
AvantGarde Duo 106dB/W/1m $60,000/pair?
EXPENSIVE indeed!

6. EXPONENTIAL HORN PROJECT DESIGN (1)
The project consisted of designing and building three enclosures.
1. One vented enclosure for 30Hz to 200Hz (200Hz is the max
low-pass frequency for most subwoofer amplifiers) using a 15”
cone driver.
2. One exponential horn enclosure for 200Hz to 1800/2000Hz
using a 6” cone driver.
3. One enclosure for frequencies above 2,000Hz using one or
two 1” compression drivers/horns.

7. EXPONENTIAL HORN PROJECT DESIGN (2)
DRIVERS
• This was a project on a tight budget. The drivers were selected for their
specifications (Thiele/Small parameters) and affordability.
• Woofer: Dayton Audio PA380-8 $75.8 Excellent woofer for the price with
a low Qts of 0.24, a BL-product of 23.44Tm, a 3” voice coil and a sensitivity of
98.5 SPL/W/1m
• Woofer: Eminence Alpha-6A $44.99 Inexpensive midrange driver with a
large BL-product (8Tm), a low Mms (diaphragm mass=7gr) and a sensitivity of
93.6 SPL/W/1m
• Tweeter: Eminence 1” compression driver with horn (discontinued)

8. EXPONENTIAL HORN PROJECT DESIGN (3)
Cross-Over
• The speaker is tri-amplified using a Behringer Super-X PRO CX3400
stereo 3-way active crossover featuring Linkwitz-Riley 24dB/Octave filters.
Design Tools
• The 15” driver vented enclosure was designed using BASSBOX PRO, an
excellent commercial software package for designing sealed, vented and
bandpass enclosures.
• The exponential midrange was initially design in Excel, based on a
collection of white papers published by a horn “expert”.
• Later in the project, I discovered HornsRep, a free 3-dimensional finite-
difference wave propagation modeling software package. Free it is. Easy to
use, it is NOT, but proved to make excellent predictions!
-25
-20
-15
-10
-5
0
5
10
15
20
25
0 5 10 15 20 25 30 35 40
Scm2
L m
Area Expansion for Midrange Horn

9. EXPONENTIAL HORN PROJECT DESIGN (4)
Measurements
Without access to an anechoic chamber, measuring accurately the performance of a
loudspeaker is difficult as multipath reflections degrade the measured response. The state of the
art technique uses the MLS (Maximum Length Sequence) methodology. It is implemented in the
DRA LAB MLSSA analyzer and Audio Precision One analyzer. However, this equipment costs
between $5000 and $30000.
Nevertheless, similar results can be obtained using:
• A calibrated measuring condenser microphone $60
• A microphone preamp with phantom power $50
• A quality PC audio card (96kHz/24bit) $150
• SoundEasy software package $300
SoundEasy is many things but it is NOT EASY for sure. This being said, this is an incredible piece
of work with immense capabilities in terms of measurement and design. It uses a full MLS
implementation and calculate the impulse response of the measurement set-up eliminating
sources of errors associated with PC sound cards, amplifier, cabling and microphone preamp. A
true MARVEL!

10. EXPONENTIAL HORN PROJECT DESIGN (5)
Measurement Techniques
I used two techniques for measuring the frequency response of the speaker.
The Ground Plane Method
The speaker being evaluated is laid on its side on a flat surface away from any wall or other
sources of reflection, with the measuring microphone 2 to 3 meters away. This simulates a 2π
radiation environment*.
The Near-Field Method
A measurement is made with the measuring microphone 10mm away from the dust cap and
similar measurements are made for each port and/or additional driver. The data is then
summed digitally.
*I live in a cul-de-sac. It involves placing the speaker in my driveway 4 to 5m away from the garage door
with the microphone on a stand in the street…. Professional indeed, but with stacking enough
measurements to compensate for the birds, the dog barking, etc… It is possible to get good measurements.

11. LOUDSPEAKERS MEASUREMENTS (1)
I mentioned in earlier slides the difficulty in
measuring accurately the response of loudspeakers.
The biggest issue is reflections from the floor, ceiling
and walls. The best way to obtain valid
measurements is to locate the speaker in an
anechoic chamber. From the picture on the right, it
is clear that such chambers are EXPENSIVE.
Let’s look at how reflections affect the measured
(and HEARD) response of loudspeakers in the next
few slides and discuss methods of measurements
without using an anechoic chamber.
Loudspeaker setup in an anechoic chamber

12. LOUDSPEAKERS MEASUREMENTS (2)
Most often, the most powerful reflection is from the
ground floor. The plot on the right shows the direct and
reflected paths of the sound wave from the speaker to
the microphone.
d = distance from speaker to microphone
x = distance from speaker/microphone to reflection point
H = elevation of the speaker and microphone
𝒙 =
𝒅 𝟐
𝟒
+ 𝑯 𝟐
The difference in length between the reflected path and
the direct path is ∆𝒅 = 𝟐
𝒅 𝟐
𝟒
+ 𝑯 𝟐 − 𝒅
Geometry of measurement set-up

13. LOUDSPEAKERS MEASUREMENTS (3)
The amplitude of the direct wave is A. Assuming that
the sound pressure level attenuates with the square of
the distance, the amplitude of the reflected wave Ar is:
Ar = (d/2x)2A = KA with 𝐾 =
1
1+
𝐻2
4𝑑2
If the reflection coefficient of the floor is R, then
Ar = R(d/2x)2A = RKA Geometry of measurement set-up

14. LOUDSPEAKERS MEASUREMENTS (4)
c is the velocity of sound in air (c=331m/s). The
reflected wave is delayed by Td = Δd/c and:
𝑻𝒅 =
𝟐
𝒅 𝟐
𝟒
+ 𝑯 𝟐 − 𝒅
𝒄
For a given frequency f, the direct wave at the
microphone is:
W = A cos(2πft)
The reflected wave at the microphone is:
Wr = Ar cos(2πf(t+Td))= A K R cos(2πf(t+Td))
Geometry of measurement set-up

15. LOUDSPEAKERS MEASUREMENTS (5)
The measured signal at the microphone is the sum of
the direct and reflected wave. Therefore:
Wm = W + Wr or,
Wm = A (cos(2πft) + K R cos(2πf(t+Td))
And with T = 0 Wm becomes:
Wm = A (1+KRcos(2πfTd)) and
Wm/W= 1+KRcos(2πfTd))
Geometry of measurement set-up

16. LOUDSPEAKERS MEASUREMENTS (6)
Let’s assume that the reflection coefficient R is 0.8, d=2m and h=1m.
The plot below represents the ratio Wm/W. The combination of the
reflected waves and direct waves results in variation of +/-50% of the
measured signal at the microphone!
Wm/Wd=2m and h=1m

17. LOUDSPEAKERS MEASUREMENTS (7)
Same plot as earlier slide but presented in dB
Wm/Wd=2m and h=1m

18. LOUDSPEAKERS MEASUREMENTS (8)
Wm/Wd=5m and h=1m

19. LOUDSPEAKERS MEASUREMENTS (9)
Wm/Wd=10m and h=1m

20. LOUDSPEAKERS MEASUREMENTS (10)
As d/H increases, the measured response
becomes less and less affected by reflections.
This is the GROUND PLANE METHOD.
Wm/W
d=10m and h=0.2m

21. MITIGATIONS – THE GROUND PLANE METHOD
By placing the loudspeaker on its side on a large
hard surface such as concrete (R~1) and placing
the measuring microphone at a distance of 5m or
more, it is possible to obtain a good measurement
of the frequency response up to 3KHz or more.
This is the simulation of a 2π environment.
In this case, the actual amplitude is half of the
measured amplitude (or -3dB). This technique is
known as the ground plane method.
Wm/W
d=10m and h=0.2m
LOUDSPEAKERS MEASUREMENTS (11)
This technique could be used up to 20kHz by correcting the measured response, using the
data displayed in the graph in the upper left of the slide.

22. LOUDSPEAKERS MEASUREMENTS (12)
If the measuring microphone is placed very close to the driver (10mm from the dust cap) and the driver at least one
meter away from the floor . The amplitude of the reflected wave becomes negligible when compared to the direct
wave. The difficulty with this technique is in recombining the measurements from each driver and port into a single
measurement. This is the Near-Field Method. With care, this technique works very well.
Wm/W
MITIGATIONS – Near-Field Measurement

23. LOUDSPEAKERS MEASUREMENTS (13)
NOTE TO THE HI-FI NUTS
HI-FI NUT, Definition: A HIFI nut is an idiot with more money than
neurons happily buying the latest speaker cable at the modest cost of
$10,000 or spending with immense joy $3,000 on a… POWER CORD.
Yes, you read well. A $3,000 POWER CORD! Do you really think that
changing the 3 feet of copper wires from the socket to the amplifier
will make a difference? Then, what about the 100 feet of wires
connecting the socket to the breaker box? I can guarantee you that
these wires are made of the cheapest material the builder could get
away with. And what about the 100 miles of wires from the breaker
box to the power plant? You don’t believe me? Open, any HI-FI
magazine at Barnes and Nobles. Half the ads are for speaker wires and
other snake oil products. LOOK AT THE GRAPH AND SEE WHAT THE
FLOOR REFLECTION DO TO YOUR MEGABUCK TOWER SPEAKERS
seating 5m away from the speakers. The problem will certainly be
resolved with a new power cord….

24. Ports
Tweeter
Midrange
Woofer
SuperTweeter* EXPONENTIAL HORN
PROJECT DESIGN (6)
Note: You may notice a
strong resemblance with the
$15,000 Alura speakers.
However, I didn’t know the
existence of these speaker at
the time. GREAT MINDS
THINK ALIKE…

25. MEASUREMENTS - BASS ENCLOSURE
From a scanned hardcopy as all data (modeling/measurements, etc.) are lost
Ports 1,2,3
Near Field
Woofer
Summation
Port Reflections
Reflections from
Back of Enclosure
Flat Response (+/-3dB) from 35 to 300Hz

26. MEASUREMENTS - BASS ENCLOSURE
From a scanned hardcopy as all data (modeling/measurements, etc.) are lost
• Please note that the curves are plotted in relative amplitude as the measuring microphone is not calibrated for
ABSOLUTE SPL.
• The bass enclosure is build with ¾” MDF. Each panel is routed, glued and screwed for maximum rigidity. Bottom,
top panel as well as left and right panels are braced together to the back panel using ¾” MDF. The extensive
bracing prevent panel vibration and reduces internal reflections (not enough).
• The bass enclosure provides a smooth response
over the design frequency range (0 to 200Hz). The
sensitivity (computed from model) is 98dB/W.
• Note the notch in the near field woofer
measurement at the tuning frequency of the ports.
This is typical of vented boxes (or Bass Reflex)
• The internal reflections can be attenuated by filling
the box or padding the inside walls of the
enclosure.
• In any case, the port reflections are beyond the
design frequency range and 20dB below the
woofer output.
Minimum woofer motion
at port tuning frequency

27. EXPONENTIAL HORN MEASUREMENTS*
*Scanned from hardcopy
This is the only surviving hardcopy showing
the horn frequency response. Unfortunately,
it includes modeling of the horn enclosure
with other drivers and a modified horn
enclosure rendering the plot very confusing
3D Finite Modeling
using HornResp
(dashed black)
Measured Frequency
Response (solid black)

28. EXPONENTIAL HORN MEASUREMENTS*
This is the model and actual
frequency responses of the
horn. The data was recorded
using the ground plane
method.
*Scanned from hardcopy
3D Finite difference
Modeling using HornResp
(yellow)
Measured Frequency
Response (cyan)
Reflection from the back
of the enclosure

29. EXPONENTIAL HORN MEASUREMENTS*
Fabricating a horn is a time consuming, difficult and painstaking woodworking project. Such
poor result after so much work is very disappointing. However, ALL IS NOT LOST… … …
*Scanned from hardcopy
• The frequency response of the horn is
ABSOLUTELY, COMPLETELY, HORRIBLE!
• Surprisingly, it sounded quite good playing music
with the bass and tweeter enclosures. Not only to
me, but to anyone who listened to it...
• First observation: The finite difference modeling
from HornResp makes an excellent prediction of
the terrible horn response. Frankly this is quite
astonishing. I am indeed IMPRESSED!
• Second observation: This is a very poor design
• The deep notches above 1kHz are the result of
reflection off the back of the midrange enclosure.
(They look bad but are not heard normally.)
Notch

30. EXPONENTIAL HORN MEASUREMENTS*
However, when I compared the model prediction to the actual data, it became apparent
that the horn behaved EXACTLY as it should. The problem is that it is a VERY POOR DESIGN.
*Scanned from hardcopy
• This horn was based on a series of white
papers published by a “supposed” horn
expert. (I will not mention the name)
• I had not discovered HornResp yet. I began
experimenting with the modeling software
as the horn enclosure was almost complete
and I was puzzled by the model predicted
response.
• When I began taking measurements of the
horn, I was quite disappointed by the
results but was unsure as to the cause of
such poor data. Could it be a measurement
problem?

31. EXPONENTIAL HORN MEASUREMENTS*
BUT All IS NOT LOST… YET…
*Scanned from hardcopy
• LESSON#1: Horns behave in a very
complex manner. I don’t believe now that
there is a “Cookbook” approach that can
deliver an acceptable outcome.
• LESSON#2: Never (ever!) underestimate
the power of computer modeling. The
measured frequency response of my poorly
design horn is very complex. It is quite
astonishing that HornResp provides an
almost identical predicted response. This is
no accident!
• LESSON#3: It appears from these results
that my measurement techniques are
reliable. (This is good news as measuring
speakers is tricky business)
• LESSON#4: HornResp is a reliable
modeling software. (User friendly, it is not!)

32. EXPONENTIAL HORN MEASUREMENTS*
Horn Modification not done yet. Project is on standby
*Scanned from hardcopy
• ALL IS NOT LOST: The curved surfaces
make building a horn a difficult and time
consuming woodworking project.
• IT IS VERY DISAPOINTING to realize
that all this hard work results in such a poor
outcome.
• HOWEVER, it appears, from HornResp
modelling, that the horn enclosure can be
easily* modified to produce the RED response
using the same driver.
• NOTE: HornResp indicates that it may be
possible to design a horn with a 200Hz to
1.6kHz frequency response using an affordable
driver (Eminence Alpha-6A $50). The +/-3dB
ripples are perfectly acceptable.
Modified Horn
*i.e. a new horn section can be added to the throat of the
existing horn, resulting in a longer horn with a smaller throat and
higher compression ratio. A new driver enclosure needs to be
fabricated.
+/-3dB 103dB/W

33. EXPONENTIAL HORN MEASUREMENTS*
*Scanned from hardcopy
• The model indicates that the modified
horn will cover the 200 to 1.6kHz range. As
a rule of thumb, a mid-range horn works well
within a 3-octave range (200x23=1200Hz).
Therefore, a 1.6kHz frequency extension may be
optimistic and we may have to limit the horn to
1kHz or 1.2kHz. (pending measurements)
• A good quality 2” compression driver can
easily cover the 1kHz-20kHz frequency range.
The RADIAN 760PB (~$250) is a perfect example.
(111dB/W@1m) (Quite expensive though…) RADIAN 760PB OUSTANDING FREQUENCY RESPONSE

34. SPL AND POWER
Horn Modification not done yet. Project is on standby
• SPL and POWER… The midrange horn efficiency is 103dB/W@1m. When
compared to a typical bookshelf speaker of 79dB/W, this is 24dB more.
• To increase the Sound Pressure Level (SPL) by 3dB, the electrical power to
the speaker must be doubled.
• 24dB/3=8 and 28=256
• Therefore, 1W of power into the midrange horn produces the same SPL
as 256W into a bookshelf speaker! (or 32W into a good floor-standing speaker-
SPL=88dB/W)
Nothing equals the sheer dynamic range of a horn speaker!

35. HORNRESP MODELLING - EXAMPLE
FAITAL-PRO W6N8-120 6” Midrange Driver
Bl>10 - Strong Motor
for its class
Low cone mass
Low Le – Good for high
frequency
The combination of a strong Bl, low mmd and moderate
Le makes the W6N8 6” driver from FAITAL-PRO a good
candidate for horn loading ($129.00 at Part Express)

36. HORNRESP MODELLING - EXAMPLE
HORNRESP - INPUT PANEL HORNRESP - HORN DIMENSIONS
76CM

37. HORNRESP MODELLING - EXAMPLE
Cone displacement almost
reaches Xmax=5mm at
100Hz and 100W input
power. A second order high-
pass filter is recommended
below 200hz
125dB!
HORNRESP – SPL (100W input power) HORNRESP – Cone displacement (100W)

38. HORNRESP MODELLING - EXAMPLE
0
10
20
30
40
50
60
60
65
70
75
80
85
90
95
100
105
110
10 100 1000 10000
Impedance(Ohm)
SPL(dB)
Frequency (Hz)
SPL
Ze (Ohm)
Frequency Response (1W@1m) and Electrical Impedance in a hybrid (conical/exponential) horn
using the Faital-Pro W6N8-120 6” midrange driver