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) :
L=C/f,
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.
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 from “fast”
to “slow” end.
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 3 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
acoustically – wallpapers, 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:
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2. Combined response port + direct radiation:
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3. System impedance:
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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, as “slow”
sounding 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?
Reply:
1.
Simple case:
2.
Complicated case:
Conclusion
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.
