Beta- The ‘White Noise’ SEOS15 – constant directivity horn adventures

!!!under construction!!!

White Noise Seos15 –  Constant directivity horn adventures in DIY sound reproduction

  • Some technical considerations

The idea of such a solution for a such loudspeaker solutiuon was inspired by Mr. Earl Geddes works [1] and [2],  concluded in his Summa speaker.
After searching for similar documents and theories, I find out a JBL white paper called ‘Improvements in Monitor Loudspeaker Systems’, written by
David L.Smith , D.B. Keele Jr. and John Eargle , published by J.AudioEng.Soc.,Vol.31,No.6 in June 1983.

So, what is constant directivity horn and how one can benefit from this techology, by using it’s principles in building constant directivity loudspeakers.

A horn is a tapered guide for the acoustic waves, designed to provide an acoustic impedance match between a sound source and the free air. The tapered shape of the horn allows the sound waves to gradually decompress and increase in displacement until they reach the mouth where they are of a low pressure but large displacement. This maximises the efficiency of the respective source in a way that a high pressure applied at the throat is converted to high volume velocity at the mouth. Depending on the mathematical ecuation describing the curve of the guide section, we have different horn shapes: conical, eliptical, hyperbolic, exponential or a combination of curves, like bi-radial horn.

The directivity of a horn is the propriety that describes the way the horn spreads the sound in space. Usualy, the way a horn disperse the sound in the air depends on the horn shape and varies with the frequency of the acoustic waves.

Directivity Control.
The directivity of a cone or dome diaphragm is largely uncontrolled, being
dictated by the dimensions of the diaphragm, and heavily dependent on frequency,
becoming sharper and sharper as frequency increases. You can solve this problem by using multiple driving units and digital signal processing, but a simpler and cheaper way to achieve predictable directivity control is to use a horn. The walls of the horn will restrict the spreading of the sound waves, so that sound can be focused into the areas where it is needed, and kept out of areas where it is not.

Despite the directivity control is said to be of high importance for sound reinforcement systems only, the concept gained attention from studio monitors and home theatre systems manufacturers, as being recognized that a controlled dispersed source excites less the environment, aka listening room or studio control room, making things easier (and cheaper) for the electrical room equalising or acoustic treatment.

As the time was passing, the trend in modern horn design had changed from loading to directivity control. Most modern horns offer directivity control at the expense of driver loading. An exponential horn can provide the driver with uniform loading, but at high frequencies, it starts to beam. It will therefore have a coverage angle that decreases with frequency, which is undesirable in many circumstances. Often you want the horn to radiate into a defined area, spilling as little sound energy as possible in other areas.
Many horn types have been designed to achieve this.
For the real picture of the directivity performance of a horn, you need the polar plot for a series of frequencies. But sometimes you also want to have an idea of how the coverage angle of the horn varies with frequency, or how much amplification a horn gives. This is the purpose of the directivity factor (Q) and the directivity index (DI).

Directivity Factor:
The directivity factor is the ratio of the intensity on a given axis (usually the axis of maximum radiation) of the horn to the intensity that would be produced at the same position by a point source radiating the same power as the horn.

Directivity Index:
The directivity index is defined as:
DI(f ) = 10 log10 Q(f ).
It indicates the number of dB increase in SPL at the observation point when the
horn is used compared to a point source. Because intensity is watts per square meter, it is inversely proportional to area, and you can use a simple ratio of areas. Consider a sound source radiating in all directions and observed at a distance r.  At this distance, the sound will fill a sphere of radius r. Its area is 4πr*2.  The ratio of the area to the area covered by a perfect point source is 1, and thus Q = 1.  If the sound source is radiating into a hemisphere,
the coverage area is cut in half, but the same sound power is radiated, so the sound power per square meter is doubled. Thus Q = 2. If the hemisphere is cut in half,
the area is 1/4 the area covered by a point source, and Q = 4. [ quote from ”Horn Theory:
An Introduction, Part 2” , By Bjørn Kolbrek,  Article prepared for].

Optimal horn parameters for a studio monitor use are as follows:
1) Constant coverage angle with consistent polar
patterns, both horizontally and vertically controlled
over the total operating range (1000Hz to 16000Hz minimum).
2) Coverage angles wide enough to mate at crossover
with a cone woofer (90°-100 ° square or a directivity
index [DI] of about 8 dB).
3) Faster flare than previously used, for lower second-harmonic distortion.
4) Shorter length to place woofer and horn in the
same acoustic plane. [JBL white paper –  Improvements in Monitor LoudspeakerSystems]

The Oblate Spheroid.
An oblate spheroid is a rotationally symmetric ellipsoid having a polar axis shorter than the diameter of the equatorial circle whose plane bisects it.

File:Ellipse axis.svg
Oblate spheroids are contracted along a line, whereas prolate spheroids are elongated.
The Oblate Spheroidal  Waveguide
This horn was first investigated by Freehafer [ J.E. Freehafer, “The Acoustical Impedance of an Infinite Hyperbolic Horn,” JASA vol. 11, April 1940], and later independently by Geddes [29. E.R. Geddes, “Acoustic Waveguide Theory Revisited,”  JAES Vol. 41, No. 6, June 1993], who wanted to develop a horn suitable for directivity control in which the sound field both inside and outside the horn could be accurately predicted. To do this, the horn needed to be a true 1Pi-horn. Geddes investigated several coordinate systems, and found the oblate spheroidal (OS) coordinate system to admit 1Pi waves. Putland, later showed that this was not strictly the case. More work by Geddes showed that the oblate spheroidal waveguide acts like a 1Pi horn for a restricted frequency range. Above a certain frequency dictated by throat radius and horn angle, there will be higher order modes that invalidate the 1Pi assumptions.

The OS waveguide does not have a sharp cutoff like the exponential or hyperbolic horns, but it is useful to be able to predict at what frequency the throat impedance of the waveguide becomes too low to be useful. If you set this frequency at the point where the throat resistance is 0.2 times its asymptotic value, so that the meaning of the cut-off frequency becomes similar to the meaning of the term as used with exponential horns, you get:
Fc= 0.2c/π x sinθo/rt    (where Fc is the cutoff frecquency, rt is the throat radius and rt and θo is half of the coverage angle ).

You see that the cutoff of the waveguide depends on both the angle and the throat radius. For a low cutoff, a larger throat and/or a smaller angle is required.
For example, for a 1″ driver and 60° included angle (θo = 30 degrees), the cutoff is about 862Hz. The advantages of the OS waveguide are that it offers improved loading over a conical horn of the same coverage angle, and has about the same directional properties. It also offers a very smooth transition from plane to spherical wave-fronts, which is a good thing, because most drivers produce plane wave-fronts.
The only disadvantage of the OS waveguide is that it is not suitable for low-frequency use.
To conclude, the OS waveguide provides excellent directivity control and good loading at frequencies above about 1kHz.

The Super-Elliptical Oblate Spheroid

The  superellipse, also known as a Lamé curve after Gabriel Lamé is a geometric figure defined in the Cartesian coordinate system as the set of all points (xy) with

\left|\frac{x}{a}\right|^n\! + \left|\frac{y}{b}\right|^n\! = 1

where n, a and b are positive numbers.

[ ]

Then, a super elliptical oblate spheroid  is a horn having a round entry throat and a mouth shaped as a  super ellipse. This is in theory. In practice looks quite simple 🙂

The Super Elliptical Oblate Spheroid made by Auto Tech from Poland has the following characteristics :


The measurement plots above were made  by AutoTech by using a B&C 250 DE compression driver coupled to the waveguide.

The horizontal response is illustrated bellow,

and the vertical response is showed here:

This fiber-glass waveguide has an entry throat that accomodate 1″ compression driver that opens to a horn mouth as large a s 15″ on horizontal axis, thus making it an almost perfect match for a 12” or  15” paper membrane driver.

The quality of craftsmanship for an Auto Tech made SEOS 15 , the fiber glass version, is quite  impressive for the cost.



White Noise building – choosing the drivers

  • 1 – High frequency driver wanted!

After purchasing the SEOS15 waveguide from Autotech – Poland, I was needed to pick the right driver for it. My initial plan was a three way – two ways plus a supertweeter – by using the Fountek Neo CD2 ribbon as super-tweeter. After checking for a local B&C dealer to acquire a D250 compression driver, I realize that the acquisition could  take ages ! Then, the Beyma dealer accepted to give me four of their 1” compression drivers to make a shootout test and to pick the one I like. Tanks for you kindness, Endre!

Beyma 1 inch drivers shootout web use

From left to right (upper picture), we have the following CD Beyma contenders: CD10Fe , CD10Nd, Cd10, CP380 and CP385Nd. Each compression driver was mounted at the throat of the SEOS 15, and measured ON Axis with a spectrum analyzer, as follows.

  – CD10 Fe, measured in free air, on axis:

Beyma CD10 Fe on axis Naked II web use

 – CD10Nd measured in free air, on axis:

Beyma CD10 Nd on axis Naked web use

 –  CP380 measured in free air, on axis:

Beyma CP380M on axis Naked 01 web use

CD385Nd measured in free air, on axis:

Beyma CP385Nd on axis Naked web use

Considering the measurements and the ratio quality/price, the winner was declared  the compression driver Beyma CD10Nd.

We just mounted the CD10Nd  into the SEOS15 mouth, and performed the second bunch of measurements, as pictured bellow:

CD10Nd mounted in SEOS15  waveguide, measured on- axis:

Beyma CD10 Nd in SEOS 15 Horn on axis web use

CD10Nd mounted in SEOS15  waveguide, measured at 15 degrees, horizontal:

Beyma CD10 Nd in SEOS 15 Horn 15 deg Horizontal web use

CD10Nd mounted in SEOS15  waveguide, measured at 30 degrees, horizontal:

Beyma CD10 Nd in SEOS 15 Horn 30 deg Horizontal web use

CD10Nd mounted in SEOS15  waveguide, measured at 45 degrees, horizontal:

Beyma CD10 Nd in SEOS 15 Horn 45 deg Horizontal web use

We finished with the off-axis measurements in vertical plane, as documented bellow:

CD10Nd mounted in SEOS15  waveguide, measured at 15 degrees, vertical:

Beyma CD10 Nd in SEOS 15 Horn 15 deg Vertival web

CD10Nd mounted in SEOS15  waveguide, measured at 30 degrees off-axis, vertical:

Beyma CD10 Nd in SEOS 15 Horn 30 deg Vertival web

CD10Nd mounted in SEOS15  waveguide, measured at 45 degrees off-axis, vertical:

Beyma CD10 Nd in SEOS 15 Horn 45 deg Vertical web

The measurements were done in my listening room, which is not anechoic at all, in these particular conditions :

– measurement were performed in my listening room

– equipment used to perform the measurement:
…..  Klark Teknik DN6000 Real Time Spectrum Analyzer
…..  Klark Teknik 6051 calibrated microphone

– all the measurements were performed with a sweep signal  generated by  the DN6000, in a range between 280 Hz and 31.500 Hz , with a spacing of 1/3 octave

– for the off-axis measurements the precision was +/_ 2 degrees

– for the off-axis measurements the reference was the interface plane between the driver and horn; while rotating the microphone, wee keep that distance constant.

– the signal level was 60 dB, and the measuring was done in absolute values.

-as reference amplifier was used an AA Craaft Sytems  PA solid state amplifier ( made in Germany)  with a power o 450 Watt/4 ohm per channel.

– drivers/ horn assembly were positioned at 1.20 meters high from the ground, and the calibrated microphone was positioned at 1 meter distance form the driver’s mouth exit.

And the winner is: CD10Nd by BEYMA

SEOS15 CD MATE  Beyma CD10Nd        Beyma CD10Nd

The upper pictures show (L-R) the back, side and throat view of the CD10Nd compression driver.

Key features:

• 1 in. (25mm) high frequency compression driver
• 111 dB, 2.83V@1m sensitivity
• Improved moving assembly mechanical coupling for excellent power handling capabilities
• PM-4 polymer diaphragm with higher surface tension energy
• Ultra lightweight edgewound aluminium ribbon voice coil
• Aluminum cover
• Neodymium magnet

Here we have the  frequency response +distortion graph         .               and here it is the impedance vs frequency plot

The physical dimensions and flange hole positions are here:

Beyma CD10Nd dimensions web use

Technical specifications:

Throat diameter……………..25 mm (1 inch)
Rated impedance……………..8 ohms
D.C. Resistance……………..4.3 ohms
Power capacity *…………….70 watt AES above 1.2 kHz
Program power……………….140 w above 1.2 kHz
Sensitivity** ………………..111 dB 2.83V @ 1m (when coupled to TD-164 prototype horn)
Frequency range……………..0.7 – 19 kHz
Recommended crossover………..1.2 kHz or higher (12 dB/oct. min.)
Voice coil diameter………….44.4 mm ( 1.75 inch)
Magnetic assembly weight……..1.1 kg (2.42 lb)
Flux density………………..2.2T
BL factor ………………….8.9 N/A

  • Choosing the bass/medium freqvency driver

I have chosen to build a two way controlled directivity loudspeaker, so the bass+midbass+low midrange  and  midrange frequencies  must to be reproduced by the same driver.  Picking the LF driver for or a two way monitor using a constant directivity waveguide is not an easy task, as the ideal unit should comply with lot of requests:
1) A smooth response curve within the required band to be reproduced
2) Controlled directional characteristics, that need to match with the HF waveguide at the crossover frequency, in both planes
3) High output at low distortion levels
4) Freedom from dynamic offset problems                                                                                                                                                         5) High enough sensitivity in order to be easily driven by my SET power amplifier

I will call this unit as ”woofer”,  despite the wider range that must be reproduced.

Having a good experience with 15” sized woofers from my previous project – Coaxial Mildness – I was narrowing the search field by looking for a high sensitivity ( > 96 dB ) 15 ” woofer, with paper cone, paper suspension, wider reproduced band (>1Khz)  and a decent directivity plot near 1 kHz.

That mean a perfect woofer for this task must have about 90 degrees dispersion pattern at around 1000 Hz, in our case.. Several high quality units from many manufacturers were studied:  JBL 2226h, B&C 15TBX100 (Geddes used this one in his Summa monitor), Faital Pro 15PR400, Eighteen Sound 15MB700, Beyma SM115K.

I really liked the JBL unit, as well as the B&C one, but they were quite expensive for my budget. I was looking for the 18 Sound also, but finally I got understanding from a  Beyma dealer here –  Prescom Audio. The final pick-up was the newly developed Beyma 15LX60V2, which it’s not so perfect, but it’s a really good quality unit for the money and fits my project at the limit 🙂 .

THIELE-SMALL parameters for Beyma 15LX60V2 woofer unit:
Resonant frequency, fs                              42 Hz             
D.C. Voice coil resistance, Re                   5.1 ohms
Mechanical Quality Factor, Qms             21.23
Electrical Quality Factor, Qes                   0.45
Total Quality Factor, Qts                           0.44
Equivalent Air Volume to Cms, Vas        105.53l
Mechanical Compliance, Cms                  92.4  µm / N
Mechanical Resistance, Rms                    1.9 kg / s
Efficiency,  ηo (%)                                       1.67
Effective Surface Area, Sd (m2)               0.091 m2
Maximum Displacement, Xmax*            9 mm
Displacement Volume, Vd                        812 cm3
Voice Coil Inductance, Le @ Zmin         2.1 mH


















The frequency response and free air impedance curve are presented below, as provided by the manufacturer:













I finally decided for this drive unit because of: good price/quality ratio, high sensitivity, low Vas (good for a compact design), powerful motor (9 kg magnetic assembly, BL factor=21.1) , decent low fs, smooth enough frequency characteristic, great power handling and lower thermal compression losses.

15LX60V2 thermal compression loss graph

Now, having the woofer, let’s simulate the ported box. I have using the Petoin Dominique website, as well as the free WIN ISD software for a cross-check of the results.

Here there are the cabinet calculations results made by using the Petoin Dominique method Online bassreflex enclosure calculation:

           – fB=  39.4 Hz;

           – cabinet volume =124.5 Liters ;

           – 2x vents with D=100mm, departed at 20cm each-other, having a length of 15.3 cm.

 We now could double check with the freeware simulator WINISD   obtaining:

attitube white noise SEOS15 SPL plot for beyma 15lx60v2 in bass reflex enclosure


A test cabinet was build, in order to check the simulations, with the physical dimensions established by the Petoin Dominique online software:

                             Volume de calcul de votre enceinte ……126.274 L
Epaisseur du bois …………………. 1.8 cm
Coeficient de Hauteur………………..1.405
Coeficient de Largeur………………..1.000
Coeficient de Profondeur …………… 1.202
Hauteur interne ……………………………..59.2 cm
Largeur interne ………………………………42.1 cm
Profondeur interne ………………………… 50.6 cm
Hauteur externe………………………………62.8 cm
Largeur externe ………………………………45.7 cm
Profondeur externe …………………………54.2 cm

The test cabinet looks like in these pictures (following the bold results for internal dimensions of the box):

Test cabinet view 0001Test cabinet for 15LX60V2 0002

Beyma 15LX60-V2 unit was measured being mounted on the test bass reflex enclosure

Test mid-bass cabinet for 15LX60V2 measured

as well as the bass reflex vent

Test cabinet 5LX60V2- bass refelx port measured

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grid (at ) attitube (dot com)
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