Audio Engineering Society

Convention Paper
Presented at the 142nd Convention
2017 May 20–23 Berlin, Germany
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the Audio Engineering Society.

The Acoustic Design of Minimum Diffraction Coaxial
Loudspeakers with Integrated Waveguides
Aki Mäkivirta, Jussi Väisänen, Ilpo Martikainen, Thomas Lund, Siamäk Naghian
Genelec Oy, Iisalmi, Finland
Correspondence should be addressed to Aki Mäkivirta (aki.makivirta@genelec.com)

ABSTRACT
Complementary to precision microphones, creating an ideal point source monitoring speaker has long been
considered the holy grail of loudspeaker design. Coaxial transducers unfortunately typically come with several
design compromises, such as adding intermodulation distortion, giving rise to various sources of diffraction, andresulting in somewhat restricted maximum output performance or frequency response. In this paper, we review
the history of coaxial transducer design, considerations for an ideal point source loudspeaker, discuss theperformance of a minimum diffraction coaxial loudspeaker and describe novel designs where the bottlenecks ofconventional coaxial transducers have been eliminated. In these, the coaxial element also forms an integral partof a compact, continuous waveguide, thereby further facilitating smooth off-axis dispersion.

1 Introduction
Positioning of microphones can determine theoutcome of a recording, and small microphone
location changes can make the difference between
the resulting sound being good or sublime.
Microphone placement is based on listening, which
in turn requires an equal amount of accuracy.
Mixing and mastering are other critical phases where
trust in what the engineer hears is essential for
setting levels, pan, equalization, effects, andevaluating the sound stage width and otherfundamental aspects of the presentation quality.
Reliable monitoring affects how well a track or aprogram translates to other rooms and playback
conditions.
Traditional loudspeaker designs place individualtransducers on the front baffle of the enclosure.
Typically, transducers are stacked vertically to avoid
time-of-arrival differences when the listener moves

to off-axis locations on the horizontal plane as this is
the more typical movement in the monitoring room.
For vertically stacked transducers, movement in the
up-down direction changes the timing between thetransducers, and this can generate audible tonalchanges at the crossover frequencies. Such crossovercoloration makes subjective evaluation unreliable indirections where the geometry between thetransducers changes with listener location or head
movement. Head movements are a stabilizing factor
used by listeners when evaluating and controllingsound stage and imaging [11]. Coloration can be a
confounding factor with loudspeakers used forresearch also.
Coaxial designs, where several transducers are on
the same acoustical axis, do not suffer from thesound colour change problem, and have long been
regarded as a potent solution to improve the qualityof the loudspeaker as a sound radiator. The
fundamental benefit of a coaxial design is that thegeometry of the transducer distances to the listening

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location remains the same when the listener moves
off-axis to any direction. Because the relative timing
does not change or changes minimally, themagnitude response at the crossover transition
remains flat also for the off-axis positions.
Another benefit of coaxial designs is that they canhave stable frequency response also when thelistener is close to the loudspeaker. This improves
near field monitoring as the sound colour created by
the loudspeaker remains stable with the changing
distance to the loudspeaker.
Near field monitoring can reduce the influence ofthe room acoustics and improve the maximal SPL ofthe loudspeaker without evoking nonlinearities intransducers typically occurring at high excursions.
However, current coaxial transducers suffer fromproblems such as sound-colouring diffraction due todiscontinuities between the coaxially located drivers.
Particularly two-way coaxial designs can haveproblems with Doppler distortion, having to operateeach transducer over a wide frequency band.
Although a two-way active loudspeaker is theubiquitous reliable work horse of the industry, athree-way design offers the potential for improving
performance in several ways including extended
frequency range, better control of directivity, higher
output capacity and lower distortion. Particularly forcoaxial designs, a three-way construction can alsosignificantly reduce the issue of Doppler distortionin the coaxial transducers.
A three-way design allows better optimization oftransducer characteristics (for example sensitivity,
linearity, output capacity, directivity, materials andconstruction methods used) than a two-way design
because of the narrower frequency range for eachtransducer. More optimal crossover frequencies canbe chosen to circumvent acoustical constraints intransducers and enclosure characteristics. Physicallylarger loudspeakers have the surface area needed fora waveguide to enhance directivity control, andachieve a better performance in challenging room
acoustics.
While a three-way construction has its strong points,
implementing it in a compact enclosure suitable forsmaller rooms, is a challenge. Coaxial transducer isused in order to create the surface area needed for a
waveguide.
The present paper discusses briefly the history of
coaxial transducers before describing the designprinciples for implementing an acoustically coaxial
three-way loudspeaker with a large directivity
waveguide. Three design case examples of such aloudspeaker are implemented and tested for
performance.
Typically, a coaxial transducer uses two magnet
motors – one for the tweeter, the other for the
midrange. We describe a coaxial transducer using asingle magnet motor with two air gaps, one for thetweeter, one for the woofer. To minimize diffraction,
the gap between the tweeter dome and the midrange
cone, as well as the midrange cone and the enclosure
surface, are bridged with elastic material, creating an
acoustically continuous surface shaped to minimize
diffraction. The elastic members in the designs may
be glued in place, and can introduce acousticallysignificant steps in the surface of the midrange cone.
Finally, the paper presents the concept of
acoustically concealing multiple woofers under the
waveguide, enabling the creation of a large
continuous front baffle surface for mid and highfrequencies. The two woofers spaced to the ends ofthe enclosure lay under the waveguide andacoustically combine to create controlled directivity
in bass frequencies. The proposed woofer systemenables physically compact enclosures wherehorizontal and vertical radiation characteristics canbe made similar. The enclosure can be manufactured
using different casting technologies, such as in die
casting or injection molding.

2 Acoustic benefits of coaxial design
The coaxial transducer arrangement has acoustic
benefits. A multiway loudspeaker has twotransducers reproducing sound simultaneously
across the crossover range of frequencies.
Conventional multiway designs have transducer
locations distributed across the front baffle. The
summation of the outputs from any two transducers
is usually designed to be in phase in the primarylistening direction (acoustical axis). When the two
outputs are in the phase the system output remains

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Design of MDC Loudspeakers with Integrated Waveguides

flat. For off-axis locations, the two transducers are
not in phase because the distances to the transducers
have changed from the design geometry (Figure 1).
This can produce audio coloration which changes
when the listener moves further off-axis. Placing
transducers coaxially can reduce or eliminate suchcoloration.
Crossover performance is further improved by timealigning the two coaxially constructed transducers at
the crossover frequency, with the benefit ofmaintaining the time domain waveforms. This isparticularly important for those transducer
constructions where the physical height of thetweeter and midrange transducers are significantly
different.

Figure 2: Altec Lansing 601 coaxial transducer,
showing a fixed multicell tweeter horn in the apex of
the woofer cone.

Figure 3: Example of a coaxial transducer with thewoofer cone forming the waveguide surface for thetweeter dome; also here the tweeter is surrounded bya fixed edge and there is a gap (opening) between
the tweeter and the woofer cone inner edge.

Figure 1: Avoiding off-axis coloration in coaxial
system design (bottom) over the conventionalvertical stacking (top).

Figure 4: Example of a coaxial transducer with atweeter in a fixed horn structure installed in the apex
of a woofer.

3 Evolution of the coaxial transducer
The idea of implementing a multiway transducer
system coaxially is not new. Already in the 1940s,
Altec Lansing launched the ‘601’ coaxial transducer[1] with a section horn tweeter coaxially located in a
12 in woofer. This was followed closely by the
Tannoy Dual Concentric design [2,3]. By the 1970s,
with the introduction of UREI 813, the three-way
coaxial loudspeaker became popular in audio
monitoring [4].

When the woofer works down to bass frequencies(two-way systems) the woofer cone displacement
becomes large and this can generate a Doppler shift
in the audio radiated by the tweeter. As the woofer
cone is making a harmonic movement, this Doppler
shift varies harmonically. This leads to a system
where low frequencies tend to modulate highfrequencies, causing relatively large intermodulation
distortion.

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When the woofer cone surface forms the waveguidefor the high frequency radiator (concentric
transducer, Fig. 3), inter-modulation distortion tends
to be larger than for constructions with a fixed horn
located in the apex of the woofer (Fig. 4). Theintermodulation can be reduced by directing low
frequencies to a separate woofer transducer, using
the coaxial transducer as a midrange-tweeter
radiator. The intermodulation distortion problems
typical for these designs can be significantly reducedwith a physically displaced woofer in a three-way
arrangement [5].
The fixed horn tweeter coaxial designs suffer fromdiffraction of sound around the mouth of the horn.
The sound diffracting around the horn mouth travels
to the woofer cone, then reflects backwards andsums with the direct sound with a fixed delay andfrequency specific level, creating sound coloration.

4 Elements of a novel coaxial design
There are four primary types of compact three-way
loudspeakers.
The first type is the conventional non-coaxial
transducer
arrangement,
where
individualtransducers are arranged in the front baffle of theloudspeaker enclosure, displaced from one another.
When three transducers are placed on the front
baffle area, there is little surface area left for
directivity control particularly in the midrange andwoofer frequencies. Crossover coloration problems
are typical at the two crossover frequencies in theoff-axis directions.
The second type is the approximately coaxial
arrangement. This places an island containing atweeter and midrange transducer on top of a woofer.
Some approximately coaxial systems stack all threetransducers while the transducer axes are notcoaxial. Approximately coaxial designs reduce theloudspeaker front baffle needed for transducers. The
transducer height differences and the delayed
contribution of diffracted audio creates colorations.
Directivity matching is problematic and contributes
to coloration in off-axis directions.
Two coaxial transducer technologies are used inthree-way arrangements. These are the concentric

tweeter-midrange arrangement and the horn-loaded
tweeter system.
Certain concentric transducers apply mechanicacoustic fitting between the tweeter and the
midrange to minimize the effect of the acoustic
discontinuity and hence the diffraction-related
colouring between the tweeter and midrange [12].
The concentric arrangement can show a tendency forintermodulation distortions. It is difficult to optimize
the midrange cone shape sufficiently to make themidrange work as a high-performance waveguidefor the tweeter. Seating of the midrange cone to thetransducer chassis and the joint or gap between thetweeter and midrange can create acoustic
diffractions.
The horn-loaded tweeter in a coaxial transducer
reduces intermodulation but can add other problems.
Some frequency-dependent amount of sound isdiffracted around the horn mouth edges. The soundinterferes with the direct radiation of the tweeter
horn. This creates direction and frequencydependent variations in the sound pressure level,
making it difficult to achieve flat frequency
response. The delayed addition of diffracted audio
affects the system impulse response. The horn cansustain resonances that in some designs have beenaddressed using digital signal processing, but it ischallenging to completely remove these artefacts.
4.1
Minimized diffraction design
The concentric transducer arrangement is acandidate for reducing the diffraction problems
typical in coaxial transducers. To minimize acoustic
diffraction in the coaxial three-way design,
improvements are needed in order tocreate a coaxial midrange-tweeter transducer with minimized acoustic diffraction

create an acoustically continuous surface
for the tweeter and midrange transducer
radiationminimize the acoustic impact of having
woofer in the enclosure
To avoid acoustic diffractions, the enclosure surface
starting from the tweeter is made smoothly shaped,

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Design of MDC Loudspeakers with Integrated Waveguides

without large edges or openings. The midrange coneis shaped as a part of this form.

midrange are optimized for the frequency range andthe output capacity needed.

4.2
Waveguide design
The waveguide shape is designed using optimization
in a physical model (FEM modelling) to enable
controlled directivity radiation for the tweeter aswell as midrange frequencies.
The waveguide is extended to the ends of theenclosure to minimize the acoustic diffraction at theedges of the waveguide. The enclosure sides are also
close to the ending of the waveguide and this further
contributes to minimization of the acoustic
diffraction at the edges. The edge diffraction wascomputer optimized using FEM modelling.

Figure 5: Crosscut view of the concentric transducer
arrangement (acoustical axis facing up). Also seen
are the radiation cavities for dual woofers with thedirectivity waveguide extending to cover thewoofers.
4.3
Coaxial transducer design
The coaxial transducer contains tweeter andmidrange transducers. The midrange cone forms apart of the front baffle waveguide shape. The
midrange movement is enabled by elastic sections in
the midrange cone. The capacity for movement is
optimized by the dimensions of the elastic sections.

Figure 6: Crosscut view of the concentric transducer
showing the magnet motor shared by the tweeter andmidrange transducers and the elastic sections of themidrange cone enabling the midrange to be shaped
into a part of the directivity waveguide (acousticalaxis facing up).
4.4
Woofer cavity design
Two oval (racetrack-shaped) woofers are locatedunder the front baffle shaped as a waveguide (seeFig. 5 and 7). Woofer radiation happens throughopenings, one for each woofer.
The front baffle creates a cavity over the fronts ofthe two woofers (see Fig. 9). This cavity has natural
resonance frequencies that depend on its volume andshape. The resonances store energy and create
colorations and changes in the time domain responseof the system.

The joint from the tweeter to the midrange is createdwith a ring. The ring surface shape is optimized tominimize diffraction near the tweeter transducer.
The tweeter and midrange share the magnet motor.
The motor has two air gaps. The air gap locations
and sizes are optimized using modelling to minimize
one transducer from affecting functioning of theother due to magnetic field modulation or saturation
effects. The back cavity for the tweeter as well as the

Figure 7: Acoustically concealed woofers radiate
low frequency through acoustically optimized
openings in the ends of the front baffle; this enables
the whole front baffle to be used as a waveguide.

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4.5
Composite dual-woofer design
Two spaced woofers are built into the front baffle ofthe enclosure (see Fig. 10 for the principle). They
are recessed in cavities, allowing the enclosure front
to extend as an acoustically continuous surface (seeFig. 9).

Figure 8: Principle of the woofer cavity and thejoined volume filled with absorbent for resonancecontrol (dark grey shaded areas) under the surface ofthe directivity waveguide; one oval woofer space
shown.

Because the two woofers are spaced at a certain
distance from each other, they create increased
acoustic directivity along the axis of displacement.
The woofers are fed with the same audio signal. The
distance between the woofers has been selected suchthat the directivity of the woofer system matches the
directivity of the coaxial tweeter-midrange system at
the midrange-to-woofer crossover frequency.
The two woofers have oval racetrack shape. The
longer dimension of the woofer transducer isselected so that this creates a matching directivity
along the smaller dimension of the front baffle, on
the axis orthogonal to the woofer displacement axis
(see Fig 10). The directivity control waveguide isdesigned to match the directivities of the dualwoofer system at the crossover frequency.

Figure 9: Crosscut detail of the woofer transducer
under the surface of the directivity waveguide(acoustical axis facing up).
The cavity resonances in the operational range canbe avoided by designing the cavity dimensions
suitably. The resonances can also be damped
acoustically using absorbing material placed injoined volumes with the cavities for the cases wheresome resonant tendency remains (see Fig. 8).
The size and shape of the opening of the front cavity
has a strong influence on the nature of the cavity
resonance. The opening is optimized to minimize theresonance and at the same time to minimize theacoustic diffraction at higher frequencies that the
opening may cause.

Figure 10: Dual woofer system creating an
acoustically coaxial woofer transducer in relation to
the tweeter-midrange coaxial transducer.
In the largest of the designs (design C), the distance
between the centres of the two woofers is 268 mm.
The total woofer diaphragm area is close to that of around 255 mm (10 inch) woofer. The woofers areloaded by a bass reflex enclosure having a reflex
port opening to the back of the enclosure. The two
openings for the woofers are spaced at a distance of
380 mm. This corresponds to 0.56 wavelengths at
the woofer-to-midrange crossover frequency (490Hz) and gets even smaller in wavelengths when thefrequency decreases. As this distance in wavelengths

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Design of MDC Loudspeakers with Integrated Waveguides

is small, lobing in the radiation pattern due to using
two woofers does not occur [7].
The directivity characteristics of the dual-woofer
arrangement is in this case similar to a round woofer
with a diameter 457 mm (18 inches) along the axisof displacement. Along the perpendicular axis, thewoofer directivity is determined by the size of the
opening for woofer radiation.

5 Three consolidated designs
Three different sized systems have been designed
using the principle of a minimum diffraction coaxial
in a waveguide. The main parameters of the three
types A, B and C are given in Table 1.

System types A and B share the single magnet motor
design with two air gaps, while the system type C isof a more conventional design with two separate
coaxial magnet motors.
type
parameter

A

B

C

299
189
212

350
237
243

433
312
278

Enclosure dimensions
height
width
depth

mm

Tweeter diameter

mm

19

19

19

Midrange diameter

mm

90

90

127

Woofer dimensionsmm

130x65170x90200x90

Table 1: Overview of the three system types

6 Results

Figure 11: The principle of construction for thesystem types A-C. The front shows woofer openings
at top and bottom of the enclosure and a centeredcoaxial tweeter-midrange transducer (left); the rearside shows the bass reflex port opening (right).
The main differentiating features are differences in
the woofer design and in coaxial tweeter-midrange
transducer design. System types A and B use a paper
cone woofer while type C uses a honeycomb woofer
design with stiff planar diaphragm.
System types A and B have a midrange cone design
with separate elastic members in the inner and outeredges of the aluminium cone. System type C uses analuminium cone covered by an elastic surface, also
extending across the inner and outer edges of thecone to allow the elastic joint needed for midrange
cone movement.

6.1
Directivity control
The low diffraction coaxial transducer seating in the
directivity control waveguide of the enclosure front
creates a continuous acoustic surface for highfrequencies radiated by the tweeter and midrange.
The coaxial transducer design has minimal acoustic
discontinuity. The large waveguide enables control
of directivity across the operating frequency range ofthe tweeter-midrange system. The waveguide
geometry minimizes sound colouring diffractions.
The compact three-way design presents a waveguidesurface area equal to that found in large size threeway main studio loudspeakers. In the case of type C,
the directivity control (see Fig. 14) exists down to
300 Hz in the larger axis dimension and down to 700
Hz in the smaller dimension.
6.2
Temporal alignment
While it is known that the human auditory system
has a frequency-dependent resolution limit to narrow
band temporal changes in an audio signal,
maintaining accurate temporal relationships isbeneficial, when doing so does not cause thesmearing of the temporal detail in the signal.
Applying filters on the audio signal amounts to

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convolving the signal with the impulse response
describing the filter functions. Convolution tends toincrease the total length of the system impulse
response.
If the system impulse response becomes excessively
long, some early parts of the impulse response canbecome audible as separate auditory events [8, 9].
In principle, if the relative timing of the audio output
remains constant, i.e. if the loudspeaker presents a
constant delay to all frequencies, waveforms may be
accurately reproduced. While, ideally, the phaserelationship between different frequencies should
not change during reproduction, the human auditory
system is more sensitive to local variation in thesystem delay at mid frequencies rather than at very
low or very high frequencies.
High resolution time-frequency analysis (Figure 13)
can be used to study the relative timing of the soundoutput as well as to understand the length of thesystem response in time.

6.3
Multitone distortion
The performance of the proposed design was
evaluated against the typical performance of theestablished implementations of compact three-way
loudspeakers in the case of the system type C.
A multitone measurement signal was used.
Multitone measurements can give relatively realistic
measurements of the overall linearity because thesignal is a complex multifrequency signal containing
a wide bandwidth and presenting in that sense a load
similar to a realistic wideband audio signal. The test
signal contained 30 tones distributed evenly on a log
frequency scale across the audible range, from 21 Hz
to 20 kHz.
The case examples of the different technologies
include the typical technologies currently applied incompact three-way loudspeaker designs.

In the plots of time-frequency analysis, the system
input-to-output delay has been removed and thesmallest delay is shown at zero. When signal
processing is used to align the time response of thesystem, the input-to-output latency is sacrificed,
especially when aligning the loudspeaker delay
down to lower frequencies.
System types A and B use signal processing torealign the mid and high frequencies. For thesetypes, the delay starts growing at bass frequencies
where the electro-mechanical delay of the high passnature of the design is displayed as an increase in the
delay. System type C displays the natural minimum
phase character of the electro-acoustic design.
The delay for all system types starts growing close
to the low corner frequency, mainly due to the
combined effect of the woofer mechanicalresonance, bass reflex enclosure resonance characterand the associated signal processing containingsome band limiting filters to control the woofertransducer excursion below the Helmholtz resonancefrequencies.

Figure 11: Multitone signal-to-distortion for caseexamples of the different technologies: (A)concentric, (B) conventional non-coaxial, (C)approximately coaxial, (D) fixed tweeter horn
coaxial, and (E) proposed technology.
The technologies were represented by case example
products of the concentric type tweeter-midrange
system (A), conventional separate transducer
arrangement (B), approximately coaxial approachwith the tweeter located on an island suspended over
the tweeter and a displaced woofer (C), fixed horntype tweeter coaxial with the midrange transducer(D), and the proposed acoustically coaxial minimum
diffraction transducer system (E). It is worth noting

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Design of MDC Loudspeakers with Integrated Waveguides

that in this case study, technologies A and D were infact two-way systems, and this may affect the
distortion figures for these two cases.
The multitone distortion to audio signal ratio wasmeasured for each of the case examples and the
distortion within the frequency range 100 Hz to 10
kHz was considered (Fig. 12). It is worth noting thatwhen the frequency range was limited to 500 Hz to
10 kHz, the results remained relatively the same.
The signal level for cases B to E was 89 dB SPL,
and for case A 84 dB SPL.
The classic concentric technology is showing
tendency for intermodulation distortion and low
signal-to-distortion ratio. This may be due to theindividual characteristics of the transducer and may
not reflect a universal principle.
The conventional separate transducer three-way
system did not show a clear advantage in terms of
the intermodulation distortion although it has
theoretically an advantage over coaxial systems [6].
6.4
Subjective evaluation
To evaluate potential angle-continuous off-axis
radiation differences between the three-way monitor
technologies labelled as B and E (previous
paragraph), a subjective evaluation test was devised.
The DUT is placed in an anechoic room, adjusted
for flat frequency response on the acoustical axis.
The DUT is rotated using a turntable, while playing
an audio signal. The output is recorded using acalibrated microphone. Figure 12 shows the test
setup.

Recordings are started with the DUT at -90 degrees
relative to the microphone direction, and stopped
when the DUT is pointing +10 degrees. The rotation
rate is 1.5 degrees per second, and various types ofstimuli were applied.
The resulting audio recordings are loudnessnormalized per ITU-R BS.1770 [10] and listened tousing headphones to eliminate secondary room
acoustic influence. Our ears are generally superior to
the eyes in recognizing a temporal pattern, so clues
to possible differences in performance might befound this way.
Using broadband noise as stimulus, patterns can bereadily heard with high quality traditional DUTs
(technology B) compared to the coaxial design(technology E), even when the former are oriented
as intended. Technology E device produces anartefact-free listening result regardless if they are
oriented vertically or horizontally. Both technologies
show the systematic change in the frequency balanceof the sound due to the higher directivity of radiationin high frequencies. The traditional technology B
also exhibits mid frequency range tonal balancevariation related to the frequency response changes
that are happening because of the time-of-flightchanges from multiple drivers when the loudspeakerrotates. Subjects describe the technology B artefacts
as "phasing" at the recording distance w = 1.60 m,i.e. not in the nearfield. Consequently, differences
may also be audible when loudspeakers are used forsound quality evaluation. The particular loudspeakerrepresenting technology B used in the study is acompact three-way with the tweeter, midrange andwoofer not only vertically displaced but also
horizontally. This may explain largely the audibilityof the midrange tonal balance variation.
The subjective evaluation suggests that a coaxial
technology can reduce the complexity of evaluating
the sound character by making the loudspeaker morewell-behaved and, in that sense, more predictable asa monitoring tool, particularly in compact three-way
constructions, where the small baffle area precludes
vertical stacking of drivers.

Figure 12: Listening-based test of DUT rotating at a
microphone distance of w

More subjective evaluation studies of multitransducer loudspeaker designs are being planned.

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Design of MDC Loudspeakers with Integrated Waveguides

7 Conclusions
We have presented the concept of designing threeway loudspeakers combining compact enclosure size
to coaxial tweeter-midrange transducers having
minimized acoustic diffraction, seating the coaxial
transducer as a part of the directivity control
waveguide, and a dual-woofer system. Seating thewoofers under the waveguide enables a large
continuous, low diffraction front baffle surface forthe mid and high frequencies. The two spaced
woofers acoustically combine to extend the
directivity control to bass frequencies.
These concepts have been applied in the designs of
three different sizes of loudspeakers. The
performance data confirming the design objectives
has been presented. Comparisons with othercompact three-way design technologies currently
used, including other techniques for implementing
coaxial transducers for three-way designs andtraditional implementations of high performance
three-way loudspeakers, have been reported.

Directivity Dual Concentric Transducer,”
Proc. 92th AES Convention, preprint 3257,
Vienna (1992).
[4]

Borwick, Loudspeaker and headphonehandbook (3rd ed.), Focal Press, 474–476(2001).

[5]

Klipsch, “A note on modulation distortion:
coaxialandspacedtweeter-woofer
loudspeaker systems,” Journal AES, vol. 24,
no. 3, pp. 186 – 187 (1976).

[6]

Dupont,Lipshitz,“Modelingtheintermodulation distortion of a coaxial
loudspeaker,” Journal AES, vol. 58, no. 9, pp.
699 – 707 (2010).

[7]

Kinsler,
Frey,
Coppens,
Sanders,
Fundamentals of Acoustics (3rd ed.), John
Wiley and Sons, pp. 176 – 185 (1982).

[8]

Moller, Minnaar, Olesen, Christensen,
Plogsties, “On the Audibility of All-Pass
PhaseinElectroacoustical
Transfer
Functions,” J. Audio Eng. Soc., Vol. 55, No.
3, pp. 115 – 134 (2007).

[9]

Karjalainen, Piirilä, Järvinen, Huopaniemi,“Comparison of Loudspeaker Equalization
Methods Based on DSP Technique,” J. Audio
Eng. Soc., Vol.47, No.1/2 (1999).

[10]

Recommendation, ITU-R BS.1770-3: Algorithms to measure audio programme loudness
and true-peak audio level, ITU-R, Geneva,
Switzerland (2012).

[11]

McNally, Martin, “Sound localization withhead movement: implications for 3-d audio
displays,” Frontiers in Neuroscience,
Lausanne, Switzerland (2014).

[12]

Dodd, Oclee-Brown, “Design of a
Coincident-Source Driver Array with Radial
Channel Phase-Plug and Novel Rigid Body
Diaphragms,” Proc. 127th AES Convention,
NYC (2009).

8 Acknowledgments
We thank our colleagues at Genelec and abroad forhelping us overcome numerous obstacles, some ofwhich have been described here.
We thank Harri Koskinen for brave, functional andfatigue-free attention to the industrial design.
We are very deeply indebted and grateful to thegiants lost, but living in our memories, for idealism,
inspiration and skills, during the decade-longdevelopment process of these coaxial concepts: Ari
Varla and Ilpo Martikainen.

9 References[1]

Altec Lancing, Duplex Loudspeaker System,
http://alteclansingunofficial.nlenet.net/Duple
x.html, read at 24 Sept 2014.

[2]

Dual Concentric Loudspeaker Drive Units,
http://www.44bx.com/tannoy/, read 24 Sept
2014.

[3]

Dodd,

“A

Wide

Dispersion

Constant

AES 142nd Convention, Berlin, Germany, 2017 May 20–23
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Mäkivirta, Väisänen, Martikainen, Lund, Naghian

Design A

Design of MDC Loudspeakers with Integrated Waveguides

Design B

Design C

Figure 13: The temporal performance of design types A-C. Impulse response, centered at maximum energy (toprow); group delay variation (second row); high resolution (wavelet) time-frequency analysis (third row) and azoom-in to the first 1.6 ms of the system impulse response (bottom row). Frequency scale extends to 48 kHz.
Color indicates sound level in dB, see the right column for the color key.

AES 142nd Convention, Berlin, Germany, 2017 May 20–23
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Mäkivirta, Väisänen, Martikainen, Lund, Naghian

Design A

Design of MDC Loudspeakers with Integrated Waveguides

Design B

Design C

Figure 14: The performance of system designs A-C. Graphics from top to bottom, magnitude responses on the
acoustical axis (bold) and in 15, 30, 45 and 60 degrees off axis on the horizontal plane (top); ultrasonic extensionof the on-axis response (second down); directivity on the plane with the longer axis, in 3 dB increment from -180
degrees to 180 degrees around the system (third down); directivity on the plane with the shorter axis, similar
scaling as in the previous (fourth down).

AES 142nd Convention, Berlin, Germany, 2017 May 20–23
Page 12 of 12