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Rogozhin Labyrinth Loudspeaker Enclosure

Article is addressed to audio DIY people and contains short but complete instructions how to calculate and make labyrinth loudspeaker with method of design developed by myself.  
I want to represent simple and convenient loudspeaker “Folded labyrinth” enclosure principle of own design. Labyrinth in general is also known as: constant cross section quarter wave resonator, organ pipe resonator, constant cross section transmission line.
Practically confirmed advantages of this design are simplicity of calculating and making, high enclosure rigidity, fast and articulated upper and lower bass reproduction, absence of ”single note”  effect common to bass reflex enclosures based on classic Helmholtz resonators.  BR resonators are resonating based on elastic pulsation of the air pressure inside of enclosure, while labyrinth is quarter wave resonator. Further advantages of labyrinth over classic bass reflex are laminarity of the air flow at the port and low air velocity in the channel, bigger radiation surface.  All abovementioned insure full absence of turbulence tones at any volume level and better integration in the listening rooms having there own acoustic modes linked to room geometrical dimensions.
Another interesting feature is low Q-factor of the resonator that makes such labyrinth less sensitive to the speaker driver parameters deviations. Low Q-factor also make it possible to tune sound characteristics even without having possibility to change the geometry of final construction. This can be done by tuning resonator Q-factor with varying the type, quantity and location of damping material in the channel.
So, loudspeaker enclosure principle looks like at following picture:

Main tuning frequency depends of the channel length.  For channel with constant cross section area (no tapered neither expanded flare) :


where L – sound wave length, C=343 m/sec sound velocity in the air, f – frequency.
Tuning frequency (F) accordingly is expressed like:

F =L/4=343/f/4.

Labyrinth resonance is composite function with a plenty of nonlinear parameters. It was impossible to change all parameters with small steps on real models and thus to find out all relations to the final tuning and sound.  This obstacle was keeping away labyrinth enclosure from being popular. It was randomly done in semi “blind” way by enthusiastic personalities and by companies who could afford some extensive and cost consuming research.  Some of them achieved good match of all parameters and such designs became legendary ones.
I offer simple and convenient calculation methodology based on PC simulations with free software Hornresp (David McBean is an author).
Last versions of the soft got option to calculate not just horns but also constant cross section area and tapered quarter wave.
 Mr. McBean`s page offers free download: www.hornresp.net.ms.
So pipe has not one resonance but some harmonic sequence of them – 1F, 3F, 5F  etc.

Main resonance mode 1F is one that used to provide bass extension for the speaker with targeted final frequency, other modes are not welcome at all for us and we should take some actions for decreasing them. The biggest amplitude belongs to the mode 3F. It is decreased by moving speaker driver position to 1/3 of total channel length. Thus we create extra mode in the channel which is out of phase with mode 3F. Q-factor of both modes are almost the same so they compensate each other and at the response of labyrinth speaker  with 1/3  driver dislocation one can observe small and narrow 1-2dB dip instead of 3F mode peaking.

5F mode level is much less and usually is almost eliminated by filling channel with damping material. It can be detected only with microphone (not by listening test), or to hear it in case if channel filling with damper was not sufficient.  Higher modes are eliminated totally with proper damping material inside of the labyrinth. Filling with damping material is needed in case of using labyrinth for driver used not just for bass but also for midrange diapason. Damping is not an obligation at all if labyrinth is used like an enclosure for subwoofer with proper electronic filtering.  Subwoofer labyrinth without filling performs with higher efficiency. Empirically we got optimal quantity of damper filling: fluffed up polyester (or similar) evenly distributed in four upper turns of the enclosure. Two lower turns are free from filling. All channel should be covered (glued) with felt up to 5 mm thickness. Felt thickness should be taken into account when designing the channel cross section.  It should be increased against simulated with Hornresp for cross section area occupied with felt. Lowest turn can be free from felt, especially if one does not plan grill to cover the port.
Channel cross section shape (proportions) one should try to make according to golden ratio: 1 x 1.6
Internal modes between parallel walls of such channel will compensate each other.  (S.A.M.: we eliminated those modes by developing TCSL – triangular cross section labyrinth with certain specific proportions of triangle walls )

Triangular channel should eliminate potential problems with internal modes but results in more complex designing approach that basic design of this article. One should know that triangular shape is not a guarantee for parasitic modes absence because at some certain proportions of the walls can possibly create modes. So felt should be used at least. Still in majority of cases triangular cross section labyrinth works perfectly and putting felt on just two walls is enough. Perfect way to set turns of triangular cross section labyrinth was developed by Volodymyr Saburov, S.A.M., Ukraine.  His Sonido drivers based loudspeakers established a reputation of unique both by design idea and sound.

Golden ratio or TCSL labyrinth is an approach that achieves goals which are in principle unachievable for simplified labyrinth speakers with tapered channel, so called transmission lines.

In spite of producers claiming that such loudspeakers are free from parasitic modes due to one wall being angled, that is not the case in real world because other two walls stay parallel for all length of the channel. Modes of parallel walls are compensated here only with damping material. Such type of loudspeakers is usually made to achieve lowest possible cut off frequency with smallest enclosure volume: tapering permit to get lower tuning than supposed by channel and also such speakers are heavily stuffed with damper.  All those factors make it possible to surprise customer with lowered cut off but such approach decreases quality of bass in terms of dynamics, as speed of sound lowered significantly in such channel and impulse signal transmission is negatively effected. Subjectively bass moves fromfasttoslowend.
If speaker is designed like subwoofer, golden ration or triangular cross section can be ignored to certain stage but if there is any opportunity to apply those rules, one should do it.

 One should pay attention also to geometrical dimensions of the dedicated room and placement of the speakers during designing stage to get best of the labyrinth loudspeaker.
In Hornresp one should use 2Pi option if speaker is planned to be used close to walls, on some shelf, port is close to floor etc. 
If speaker is going to be put on stand or to be placed few meters away from walls one should design using 4Pi option of the soft.
Best case scenario if real measured frequency response graph can be used to balance out simulated bass response on proper level in relation to its mid-high output.  Sometimes, to get correct tonal balance final tuning frequency can differs from calculated based on driver Thiele-Small parameters.
To avoid hum at main room mode between front and back wall, one should take it into account when developing frequency response of future labyrinth.  Measure distance from wall behind the listener and behind the speakers and make calculation:

Froom mode = 343/Lbetween walls/2.

Example: small room х 4 meters. Speaker is planned to be put along short wall, listener will be close to opposite wall. Find main room mode:

F=343/4/2=42,875 Hz.

If room is medium damped acousticallywallpapers, minimum of furniture and carpets, one should design labyrinth speaker with frequency -10dB at 43 Hz.
In real life this figure depends a lot from room staff, placement of the speakers and listener. Average is 10

Some tips to pick up speaker driver

For constant cross section labyrinth we usually want driver Qts:

·                                 < 5” – 0,5 and higher;
·                                 6-8” – 0,4-0,5;
·                                 10-12” – 0,4;
·                                 15-18” – 0,3-0,4.

When making choice of tuning frequency we should also pay attention to the volume displacement of the driver.  We cam model perfect response from 30hz with 6” driver but… it will go out of its linear excursion at 1-2 watts already.  It will be perfect speaker on the paper but one can not listen it loud enough and dynamics will be damaged also.
Also should be noted, that resonant frequency of the driver is decreased in labyrinth due to joint air mass in the channel. Sometimes it can be 1,5 times.
Based on experience following advise can be given, what limit of driver resonance should be picked according to its size

·                                 < 5” – 60 Hz and higher;
·                                 6-8” – 40-60 Hz;
·                                 10-12” – 25-35 Hz;
·                                 15-18” – 20-30 Hz.

Of course drivers with other figures can be used, but normally speaker efficiency will be lowered in this case.

VAS and Mmd/Mms are directly linked to Qts and Fs. Basic parameters for making choice of labyrinth driver should be Fs and Qts, but if Vas is too big, driver with soft surround can be forced out of linear excursion more easily. Usually this is the case for too low Fs drivers if to compare with their diameter and having low Mms at the same time. That would be great for sealed box or bass reflex, as they higher up the Fs.

Some tips for modeling labyrinth with «Hornresp»

1.       Target is to match cross section and length of the channel keeping driver position 1/3 and to get graphs roughly like these:
1. Port response:

2. Combined response port + direct radiation:

3. System impedance:

2.       Such shape graphs confirm optimal  Qt and tuning frequency of resonator for given speaker driver. They show response of empty, unstaffed channel and are suitable for designing subs and bass sections which are supposed not to be staffed after, or staffed with damping material taking into account further system Q lowering (because of damper).

3.       Graphs like below reflect cross section less than optimal:

4.       Some cross section area reduction (less than optimal) provide us with better group delay and impulse parameters, lowering total speaker volume but by cost of lowering efficiency.
Sometimes that can be used to tune cut off higher than main room mode, It`s not recommended to make cross section area less than half Sd.
5.       Graphs below shows cross section area more than optimal, system Q is higher than optimal

6.       Systems with slightly higher Q than optimal can be designed if further staffing with damping material will be used to lower it and to get proper response shape (in case if soft shows optimal response graph one should understand that staffing will reduce the efficiency in real life). Usually 1-3 dB peak can be compensated by damping material. Not advised to design systems with cross sectional area more than double Sd.
7.       Accuracy of tuning to the driver Fs can be controlled with impedance graph, symmetry of width and height of the peaks is an indication of labyrinth tuning frequency to be the same like driver Fs in empty unfilled channel. Filling channel with damper not just lower system Q but also reduce sound velocity inside of enclosure. This also lower final tuning frequency. Real impedance graph can vary till full peaks smoothing and obtaining one gradual boost around tuning frequency. It depends on damping material properties and its quantity.
8.       One should target group delay not to exceed 15 ms. Maximum 20 ms. Optimal 10-12 ms. Also group delay below cut off does not impact final sound a lot, so below cut off it can be more than optimal. The only limit – group daly rise should be below 40 Hz, asslowsounding around 40 Hz is especially unpleasant for human ears, it is linked with psychoacoustics.
9.       One should control with Hornresp not to get out from Xmax during design stage, but real excursion of the driver in damper filled labyrinth will be less than predicted by soft in empty channel.

Speaker plan design

Common materials like plywood, fiber board, etc. can be used. Enclosure of such type has good rigidity due to construction features.
Usually 16-20 mm thickness is enough for 12” driver.
Important point is to make turns in proper way. One should apply diagonal boards in the turns corners (see picture). This will prevent unwanted increase of cross section area on the turns.  Distance between edge of horizontal partition and diagonal turn board should be equal to the height of channel on its straight sections.
Total axial length of the channel is an total of all internal distances between front and back baffles in all sections. 

The most frequent question is:
-          I calculated perfect labyrinth but my driver does not fit in it becaurse of dimensions. What should I do?


1. Simple case:

 2.       Complicated case:


Loudspeaker principle described in this article is simple way to get good sounding, predictable and repeatable result, it permits to get well balanced system of loudspeaker plus room that is usually problematic when purchasing industrially produced sealed and bass reflex speakers, does not matter of how expensive they are.
Helmholtz resonator is popular because of being simple, cheap and compact solution, while quarter wave resonators show better performance and in room integration. Home sealed or bass reflex speakers easily achieve low cut off in compact boxes, but  at the expense of narrow dynamic diapason and intensive room modes exiting.  Properly designed labyrinth is intermediate solution between compact bass reflex or sealed home loudspeakers and bass horns, which can give perfect sound characteristics but being huge and not practical with dimensions.  Labyrinth permits to get almost any cut off frequency, even below Fs of the driver, is less sensitive to the room modes than bass reflex, and is simpler in designing/making than bass horns.

Ukraine, 2011
Cut version, translated by Volodymyr Saburov, S.A.M. http://www.facebook.com/SaburovAudioManufacture