Bass reflex housing

Bass reflex housing of a typical two-way speaker with a pipe opening (below)

Vented enclosures are a special form of speaker enclosures for bass speakers and subwoofer . In such a box, the housing is not closed, but rather has an opening - the bass reflex channel. The sound component radiated backwards from the loudspeaker is used to "amplify" the bass reproduction. The channel acts as a resonator in cooperation with the internal volume and increases the efficiency of the box in the area of ​​the built-in resonance frequency of the loudspeaker.

Goal setting

As is the case with transmission lines or backloaded horn loudspeaker housings, the rearwardly emitted sound component of a loudspeaker - usually referred to as the chassis in this context - is used to increase the reproduction in the low-frequency range relevant to the human ear. To put it more simply, a box of this type offers "more bass". In fact, it increases the sound pressure at the chassis resonance frequency at the expense of frequencies far below; it therefore depends on the parameters of the loudspeaker in question to what extent such a use makes sense.

Resonance voting

The resonance is matched by the length or the cross-sectional area of ​​the duct (the compressible air in the duct transfers the loudspeaker vibrations to the air mass in the housing, which together with the elasticity of the air in the duct forms a resonator).

Mostly by changing the length of the bass reflex tube, an adjustment to the so-called Thiele-Small parameters of the loudspeaker and to the volume of the housing can be made.

The coordination can be done through experiments , mathematical approximation formulas (coordination according to William John Joseph Hoge) or with the help of computer simulations . So-called equivalent circuit diagrams are used in the simulation . The aim is as linear a frequency response as possible down to the lower limit frequency and a reduction in the diaphragm excursion at low frequencies.

The use of bass reflex enclosures (BR enclosures for short) makes it possible to use loudspeakers (also called chassis or drivers) with electrodynamic drives that are relatively strong in relation to the size of their baffle opening. Loudspeakers of this type have a low level of efficiency in closed systems at low frequencies in the range of the built-in resonance frequency .

The so-called tuning frequency determined by the BR housing and the channel compensates for the low level of efficiency in the lower frequency range - the loudspeaker generates a higher sound intensity with the same deflection of the membrane. This enables systems with a higher degree of efficiency with a lower cut-off frequency than with closed housings of the same size.

Single ventilated bass reflex housing

Diaphragm stroke of closed (blue) and single ventilated housing (violet) with constant free field sound pressure

Maximum sound pressure of a closed (blue) and a single ventilated housing with constant diaphragm deflection: The supported working area (peak outside the graphic) and the steep drop in the ventilated system below it can be clearly seen

The effective range of the resonator is in the range of about 0.75 * fb ... 2 * fb, in this range the maximum sound pressure level is improved by at least 2.5 dB.

In the range between 0.75 * fb and 0.9 * fb, the diaphragm stroke is reduced, but it is still very high there, so that frequencies above 0.9 * fb can be regarded as the optimal working range.

Asymptotic behavior : 12 dB / oct below the resonance frequency, 12 dB / oct below the tunnel resonance frequency, 24 dB / oct if both apply.

Calculation of the reflex channel

The general formula for calculating Helmholtz resonator channels with a circular cross-section with an assumed inner diameter d of the pipe is for its length l (each in cm):

${\displaystyle l={\frac {23400\ {\cdot }\ d^{2}}{f^{2}\ {\cdot }\ V_{\text{B}}}}-0{,}8{\cdot }d}$

f stands for the desired tuning frequency (in Hertz ), and V _B for the effective net internal volume of the housing (in liters). The factor −0.8 xd is the so-called muzzle correction.

For BR boxes, a housing quality of Q _tc = 0.707 is normally aimed for ( Butterworth characteristic: optimal balance between frequency response and step response ). The corresponding internal volume results from the overall quality Q _{ts of} the chassis used and its equivalent volume V _as (in liters):

${\displaystyle V_{\text{B}}=11\ {\cdot }\ V_{\text{as}}\ {\cdot }\ {Q_{\text{ts}}}^{2{,}87}}$

The channel length l (in cm) is determined here with an assumed cross-sectional area A _f (in cm²) also via the resonance frequency f _{s of} the chassis:

${\displaystyle l={\frac {{Q_{\text{ts}}}^{1{,}8}\ {\cdot }\ A_{\text{f}}\ {\cdot }\ 168939}{{f_{\text{s}}}^{2}\ {\cdot }\ V_{\text{B}}}}-{\bigl (}0{,}88{\cdot }{\sqrt {A_{\text{f}}}}{\bigr )}}$

However, the type of control of the loudspeaker box influences the result, as Q _ts results from the electrical quality Q _es and the mechanical quality Q _{ms of} the chassis:

${\displaystyle Q_{\text{ts}}={\frac {1}{{\frac {1}{Q_{\text{es}}}}+{\frac {1}{Q_{\text{ms}}}}}}}$

When using a passive speaker crossover z. B. their internal resistance and the chassis resistance R _e add up to R _Sum (each in ohms ), whereby Q _es changes as follows:

${\displaystyle Q_{\text{es*}}={\frac {{Q_{\text{es}}}\ {\cdot }\ {R_{\text{Sum}}}}{R_{\text{e}}}}}$

Which means for the above BR channel length calculation that Q _{ts has to be} replaced by Q _{ts *} ; summarized by:

${\displaystyle Q_{\text{ts*}}={\frac {{Q_{\text{es}}}\ {\cdot }\ {Q_{\text{ms}}}\ {\cdot }\ {R_{\text{Sum}}}}{{Q_{\text{es}}}{\cdot }{R_{\text{Sum}}}\ +\ {Q_{\text{ms}}}{\cdot }{R_{\text{e}}}}}}$

This correction applies primarily to passive loudspeakers. With active control (= no further components between amplifier output stage and chassis), only the output resistance of the amplifier acts here, which has little influence on common transistor output stages - in contrast to tube amplifiers .

In principle, BR channels can have any cross-sectional shapes (as long as they remain the same over the entire length) and can also be curved, kinked, etc. Too small or too narrow channels, however, cause air turbulence (whistling noises), while channels that are too large and the like. a. for higher frequencies radiated from the membrane back of the chassis are audibly "transparent". Several channels can also be used. As long as they have identical dimensions, the above BR channel formula also applies to their respective length: Only the variable d then has to be replaced by d ∙ √ n , where n stands for the number of channels. A speed of the air oscillating in the duct of up to Mach 0.16 is not considered critical, which is why the cross-section of the duct should not be too small in relation to the loudspeaker diameter and stroke (roughly: pipe diameter = 1/3 of the loudspeaker diameter to duct cross-section = 1/5 the membrane area).

It should be noted that V _B (as mentioned at the beginning of this section) denotes the effective net internal volume of the housing. This means, on the one hand, that the volume of embedded crossovers and protruding chassis magnets must be added when dimensioning the housing size, as well as that of the BR channel itself. On the other hand, the inserted damping material causes a virtual increase in V _B by around 10 , depending on the quantity and nature up to 30%.

Structure of the box

It is beneficial to keep the area around the mouths of the bass reflex ducts free of damping material in order to allow the air to circulate freely in the ducts. Also, the pipe mouth should therefore at least by the amount of the inside diameter of obstacles, such. B. the rear wall, be removed.

Experience has shown that it is generally beneficial to place the outer opening of the BR channel as far away as possible from the woofer (roughly as shown in the picture). In the case of attachment to the rear wall of the housing, etc., the influence of the wall on which the box is located must be taken into account when installing it close to the wall.

advantages

• Significantly higher sound pressure level (up to 13.5 dB) possible in the area of ​​the lowest octave , or
• Expansion of the power bandwidth by 1.1 octaves (factor 2.2)
• Stronger bass reproduction with chassis with more powerful drives, whose frequency response would otherwise drop prematurely due to mutual induction due to large deflection.
• different tuning options (Hoge, Thiele / Small, Novak, Bullock, ...); Frequency response and housing size can be designed in a variety of ways with the given chassis and space.
• Significantly lower deflection of the membrane with the same sound level.

disadvantage

• Greater group delay or poorer impulse fidelity
• Steeper drop in the transfer function below the lower limit frequency
• If the chassis transmits frequencies with a wavelength in the range of the tunnel (bass reflex tube), tunnel resonances occur. This problem occurs with practically all bass reflex boxes that also reproduce medium frequencies with the same loudspeaker. Disruptive internal resonances in the case can also penetrate the outside through the bass reflex tube.
• If the tunnel is insufficiently dimensioned, the high speeds of the air in the tunnel lead to disruptive flow noises, and due to the friction of the air on the tunnel walls and turbulence, the effectiveness of the bass reflex duct decreases.
• When sound is emitted below the resonance frequency of the overall system, the lack of spring stiffness of the air cushion leads to excessive membrane deflections and simultaneous cancellation of sound from the loudspeaker and tunnel side (acoustic short circuit). The large deflection leads to non-linear distortion and intermodulation , and if the voice coil hits the magnet, it can even damage the loudspeaker.

• With active speakers:
  • The tunnel resonance frequency defines the power frequency response; if the lower power bandwidth is defined, this is added to . ${\displaystyle 1{,}1\cdot f_{\min }}$
  • Active speakers are usually built smaller than passive speakers and then electronically equalize the frequency response afterwards.

This electronic equalization practically always includes a 2nd to 4th order protective filter against frequencies below . Such filter steepnesses can hardly be achieved with passive filters (loudspeaker crossovers in passive boxes) or are too material-intensive. ${\displaystyle f_{\min }}$

The reduction in the housing volume is limited by the higher electrical power required in the low frequency range - it must also be ensured that the mechanical overdrive occurs before the electrical overload. Furthermore, the resonator tunnel must not be too long (reference value ~ 1 / Vs).

literature

• Götz Schwamkrug: Loudspeaker boxes: assembly - replica - conversion . 2nd edition, Elektor-Verlag, Aachen, 1989, ISBN 3-921608-83-X
• Berndt Stark: Loudspeaker manual: Theory and practice of speaker building . 7th edition, Richard Pflaum Verlag, Munich, 1999, ISBN 3-7905-0807-1
• Friedemann Hausdorf: Handbook of loudspeaker technology, 3rd, revised. Ed., Verlag Peter Schukat, Haan, 1990

Individual evidence

1. ↑ WinISD. Retrieved April 25, 2019 (UK English). 
2. ^ Friedemann Hausdorf: Handbook of Loudspeaker Technology, 3rd, revised. Ed., Verlag Peter Schukat, Haan, 1990

Web links

Commons : Bass Reflex Enclosure  - Collection of images, videos, and audio files

• Loudspeaker: Hole in the box, now what? The bass reflex cabinet, for beginners
• Loudspeaker: Relationship between efficiency, below the cutoff frequency and housing volume