Loudspeaker Systems
Electroacoustics
Any transducer using a diaphragm or membrane to generate
sound is essentially a bidirectional radiator, since the air is excited
by both sides of the vibrating surface.
Since the driver dimensions are typically smaller than the
wavelength, sound will diffract around the driver forming an
aerodynamic short circuit.
The driver short circuit can be prevented using a baffle or some
enclosure to separate the sound from the two diaphragm sides.
The four most common designs are:
1. Closed back
Included in this group are closed-box (acoustic suspension) and
closed transmission line (anechoic termination) designs.
2. Parasite resonator
Included in this group are ported box (bass-reflex), distributed
port, and drone cone designs.
3. Acoustical filter
This type of enclosure is a closed-box design using a passive
acoustical filter controlling the front sound radiation.
4. Acoustic transformer
Included in this group are half- and quarter-wave resonators,
open transmission line, and various horn designs
Infinite Baffles
If the loudspeaker is mounted in a wall separating two large rooms,
the wall can be considered as an approximation to an infinite baffle.
Sometimes a closet or similar can be used as an approximation to a
second large room.
If the back room is large and suitably damped, the rear radiated
sound reflected back to the loudspeaker will be so weak that it will
not be heard through the loudspeaker.
It must also be remembered that the loudspeaker has poor sound
isolation. From the viewpoint of sound isolation, it is effectively a
hole in the wall.
Finite Baffles
The main purpose of the baffle is to prevent the
aerodynamic short circuit.
For a finite baffle to be effective, it must have dimensions
about as large as the wavelength at the lowest frequency
one wishes to reproduce.
The diffracted wave can be attenuated to some extent by
providing a sound absorptive layer on the rear side of the
baffle.
The baffle must have sufficient mass and rigidity so that it
is not excited by the loudspeaker. This requires baffles that
are quite heavy and braced.
Baffle resonance will lead to reduced sound insulation
between the front and rear side of the baffle.
An advantage of the baffle approach over a box enclosure is
the absence of internal acoustical resonance.
An example of the frequency response of a driver in square
baffle having sides 1.2 m is
Loudspeaker Cabinet
• The practical realization of an infinite baffle (the sealed
box) is rarely large enough to avoid significantly loading the
rear of the loudspeaker,
• The loudspeaker cabinet thus acts as a barrier between the
front and back of the speaker and its effect is mainly for
audio signals with low frequency.
• Sound pressure induced by vibrating membrane placed on
an infinite baffle at a distance a can be expressed as
SyM f 2
p
0,168a
• and the acoustic power is given by equation
P 0,168S 2 yM2 f 4
• where S is the surface of the baffle, yM is the maximum
effective size of the displacement, and f is the frequency of
sound waves.
Open-Rear Cabinet
Sound waves radiated from the l
rear of the speaker are of opposite
phase from those radiated from the
front and travel a longer distance
around sides of the cabinet to the
perception point P.
0
l
Open baffles are rarely used in
recording studio control rooms. P l0
They used in listening rooms and
domestic high-fidelity systems.
When mounted on the floor, the
solid surface below the open baffle
acts like an acoustic mirror.
Enclosed Cabinet
Rear side is closed to eliminate
the influence of sound from the
rear of the speaker and to
prevent lowering radiation
efficiency in low ranges. SMB
RMS: mechanical resistance MMS, SMS, RMS
RMB
of vibrating system,
MMA
RMB: mechanical resistance of RMA
cabinet,
RMA: radiation resistance.
Enclosed Cabinet
Enclosed space comes to present air stiffness, and the minimum
resonance frequency of the speaker system is determined according to
the volume.
The lowest resonance frequency of speaker system:
S MS S MB
f 0B 1
2
M MS M MA
MMS is mass of vibrating system, MMA is radiation mass, SMS is stiffness
of vibrating system, SMB is stiffness of cabinet.
a small sealed box must suffer from either poor system sensitivity or a
low frequency roll-off.
A cabinet which is 3 dB down with a given low frequency driver at 80
Hz would need to be 4 times larger if it were to be 3 dB down at 40 Hz
and 16 times larger to be 3 dB down at 20 Hz, so sealed box sizes do
tend to get larger very quickly if lower roll-of frequencies are required.
Phase-Inverting (bassreflex) Cabinet
Inverts phase of sound radiated
from the rear of the speaker in
order to widen a low-range
playback boundary.
MMP: radiation mass of port,
RMP: radiation resistance SMB
MMS, SMS, RMS
of port, RMB
MMAP: radiation mass MMA
of port,
RMA
RMAP: radiation resistance
of port.
RMAP, MMAP RMP, MMP
Phase-Inverting (bassreflex) Cabinet
The cabinet tuning frequency can be calculated
approximately as
where:
f = resonant frequency of box (Hz)
c = speed of sound in air
A = area of port in square meters
V = volume of box in cubic meters
Le = effective length of port in meters
Acoustic Labyrinth Cabinet
Partition panel is used within the cabinet to form an acoustic
pipe.
The pipe length is selected to produce a wavelength one-half of
the bass frequency to be reproduced – increasing the level.
In order to tame the strong resonant behavior exhibited by the
open pipe, absorbent material is introduced into the pipe to add
damping.
Some versions of ‘transmission lines’ are closed. In these
designs the line is made to be as absorbent as possible.
Acoustic Labyrinth Cabinet
Acoustic Labyrinth Cabinet
Acoustic Coupler
It employs a small speaker for drive and a large-aperture-
diameter diaphragm for radiation is provided in front of the
speaker – increase cabinet stiffness and lower playback
boundary.
Crossover
They are better described as frequency dividing networks.
It is difficult for one speaker unit to reproduce wide range of
audio frequencies.
No loudspeaker drive unit suitable for music monitoring can
provide a flat response over the entire musical frequency range.
That requires that the multiple drivers in a system need to be fed
by signals which are only appropriate to their designed
performance range.
A system of dividing the playback band and using special
speakers for high, middle, and low ranges has to be used.
Crossover is a dividing network divides and applies electric
input to each speaker.
Crossover
Passive crossover
the traditional approach where the network is
inserted between power
amplifier and loudspeakers. This is often
called a passive crossover although
the term low-impedance high-current
crossover would be more adequate.
Active crossover
the network is inserted ahead of the amplifiers, with each driver being fed power from
its own amplifier. Since separate amplifiers are used for each frequency range, these
systems are improperly called active filters,
Crossover
Reconstruction problems
Unfortunately, the division of the frequencies is not all that a
crossover must achieve.
They must divide the frequencies in a way that the individual
drive units can re-construct in the acoustic far-field of the
loudspeaker
due to the physical requirement of the radiation of the different
frequency bands, the sizes of the drive units give rise to a
displacement of the voice coils if the front faces of the drives
share a plane, common baffle.
If the displacement were to be 10 cm, then a frequency with a
wavelength of 20 cm would be received on the axis between the
two drivers with its polarity reversed from either driver with
respect to the other.
Therefore: f = 340/0.2 = 1700Hz
At 1700 Hz we would have cancellation on
axis
free-edged cone for high-frequency extension
However, this is not the only complication which arises in the
reconstruction.
All conventional filters exhibit the property of ‘group delay’. There is a
finite time necessary for the information in a signal waveform to pass
through a filter, which is a function of the slope of the filter and its cut-off
frequency.
As the frequency drops, the delay increases.
A filter of 24 dB/octave at 300 Hz would exhibit a group delay of around
one millisecond.
With a speed of sound of 340 m/s, one millisecond would represent
340/1000 m/s, or a 34 cm equivalent physical displacement.
The problem can be partially solved by the use of concentric loudspeakers,
but these concepts bring their own problems with them.
concentric drive units
Orders, slopes and shapes
Electrical filters are overwhelmingly the most common manner of
dividing the frequency bands.
An alternative approach to the inductor/capacitor (LC) design is a
resistor/capacitor (RC) method
First order crossovers are rarely used, because the low rate of
roll-off .
Second order crossovers, with their 12 dB/octave roll-offs, are
very popular with the manufacturers of small, two-way cabinet
loudspeakers.
They are relatively cheap to construct and the power losses
through the filters are quite small, but they will not reconstruct
the original waveform.
However, in general, a standard second order crossover yields
either a flat frequency response or a synchronous time response,
but cannot exhibit both properties at the same time.
Third order crossovers, with slopes of 18 dB/octave are popular in
more expensive passive loudspeaker systems
Typical 2-way, 18 dB/octave, 3rd order passive crossover
circuits
Active versus passive crossovers
For high quality loudspeaker applications, the consensus is almost
universally in favor of active crossovers. By virtue of their
feedback loops they can remain remarkably stable over very
many years, and complex filter shapes can be devised without any
loss of power efficiency.
Digital crossovers
As time passes, digital crossovers have become more
commonplace in professional loudspeaker systems,
although their use in domestic circumstances is still largely
restricted to home recording facilities.
They are particularly attractive because of the easy
implementation of almost any amplitude response, phase
response, signal delay.
