Bass reflex

Last updated January 19, 2024

RCA bass reflex shelf stereo speakers. RCA2ways.jpg — RCA bass reflex shelf stereo speakers.

A bass reflex system (also known as a ported, vented box or reflex port) is a type of loudspeaker enclosure that uses a port (hole) or vent cut into the cabinet and a section of tubing or pipe affixed to the port.^[1]^[2] This port enables the sound from the rear side of the diaphragm to increase the efficiency of the system at low frequencies as compared to a typical sealed- or closed-box loudspeaker or an infinite baffle mounting.

A reflex port is the distinctive feature of this popular enclosure type. The design approach enhances the reproduction of the lowest frequencies generated by the woofer or subwoofer. The port generally consists of one or more tubes or pipes mounted in the front (baffle) or rear face of the enclosure. Depending on the exact relationship between driver parameters, the enclosure volume (and filling if any), and the tube cross-section and length, the efficiency can be substantially improved over the performance of a similarly sized sealed-box enclosure.

Explanation

Unlike closed-box loudspeakers, which are nearly airtight, a bass reflex system has an opening called a port or vent cut into the cabinet, generally consisting of a pipe or duct (typically circular or rectangular cross section).^[3]^[4] The air mass in this opening resonates with the "springiness" of the air inside the enclosure in exactly the same fashion as the air in a bottle resonates when a current of air is directed across the opening. Another metaphor often used is to think of the air like a spring or rubber band. The frequency at which the box/port system resonates, known as the Helmholtz resonance, depends upon the effective length and cross sectional area of the duct, the internal volume of the enclosure, and the speed of sound in air. In the early years of ported speakers, speaker designers had to do extensive experimentation to determine the ideal diameter of the port and length of the port tube or pipe; however, more recently, there are numerous tables and computer programs that calculate, for a given size of cabinet, how large the port should be and how long the tube should be. Even with these programs, however, some experimentation with prototypes is still necessary to determine if the enclosure sounds good.

If this vent air mass/box air springiness resonance is so chosen as to lie lower in frequency than the natural resonance frequency of the bass driver, an interesting phenomenon happens: the backwave of the bass driver sound emission is inverted in polarity for the frequency range between the two resonances.^[3] Since the backwave is already in opposite polarity with the front wave, this inversion brings the two emissions in phase (although the vent emission is lagging by one wave period) and therefore they reinforce each other. This has the useful purpose of producing higher output (for any given driver excursion compared to a closed box) or, conversely, a similar output with a smaller excursion (which means less driver distortion). The penalty incurred for this reinforcement is time smearing: in essence the vent resonance augments main driver output by imposing a "resonant tail" on it. For frequencies above the natural resonance of the driver, the reflex alignment has no influence. For frequencies below the vent resonance, polarity inversion is not accomplished, and backwave cancellation occurs. Furthermore, the driver behaves as though suspended in free air, as box air springiness is absent.

When speakers are designed for home use or for high-volume live performance settings (e.g., with bass amplifier speaker cabinets and PA system speakers and subwoofers), manufacturers often consider the advantages of porting (increased bass response, lower bass response, improved efficiency) to outweigh the disadvantages (port noise, resonance problems). The design is popular among consumers and manufacturers (speakers cabinets can be smaller and lighter, for more or less equivalent performance) but the increase in bass output requires close matching of driver, the enclosure, and port. Poorly matched reflex designs can have unfortunate characteristics or drawbacks, sometimes making them unsuitable for settings requiring high accuracy and neutrality of sound, e.g. studio monitor speakers for use by audio engineers in monitoring facilities, recording studios etc. However it is possible to design a bass reflex system that mostly overcomes these drawbacks; and quality bass reflex designs are commonly found in demanding environments across the world.

Comparison with passive radiator

Passive radiators are similar in operation to ported bass reflex systems, and both methods are used for the same reason: to extend the system's low frequency response.^[5]^[6] A passive radiator is the use of one or more additional cones (diaphragms) in a cabinet instead of ports. These passive diaphragms do not have a magnet or voice coil and are not connected to a power amplifier. Acoustically, they behave largely the same around their tuning frequency as a port, as they also act as a Helmholtz resonator excited by the rear side of the bass driver's diaphragm. Passive radiators can be tuned independent of their dimensions by adding or removing mass from the diaphragm of the passive radiator. This makes them useful for smaller enclosures with the same box tuning where an equivalently tuned port would be impractical. They also sidestep the midrange pipe resonances that can be an issue on ported enclosures in full range systems.^[7] However, to be effective, they require a much greater surface area on the cabinet exterior than a port. They are also considerably more expensive than a port tube, as they are effectively a speaker driver minus its voice coil and motor magnet.

History

The effect of the various speaker parameters, enclosure sizes and port (and duct) dimensions on the performance of bass reflex systems was not well understood until the early 1960s. Subsequently, pioneering analyses by A.N. Thiele,^[8]^[9]^[10] J.E. Benson^[11]^[12] and Richard H. Small ^[4]^[13]^[14]^[15] presented the theoretical foundations for the synthesis of bass reflex loudspeaker systems to meet specified low-frequency performance criteria were developed into a series of "alignments" (sets of the relevant speaker parameters) that allowed designers to produce useful, predictable responses. Keele^[16] extended the design options by presenting a new set of 6th-order vented-box loudspeaker system alignments. All of these results made it possible for speaker manufacturers to design bass reflex loudspeakers to match various sizes of enclosures, and to match enclosures to given speakers with great predictability. Due to the physical electromechanical constraints, it is not possible to have a small speaker in a small enclosure producing extended bass response at high efficiencies (i.e., requiring only a low-powered amplifier). It is possible to have two of these attributes, but not all; this has been termed Hofmann's Iron Law after J. Anton Hofmann of KLH's summary (with Henry Kloss) of Edgar Villchur work years earlier. The sound pressure produced depends upon the efficiency of the speaker, the mechanical or thermal power handling of the driver, the power input and the size of the driver.

Bass reflex vent. Bassreflexrohr.jpg — Bass reflex vent.

Advantages

Novak^[2] concluded that a bass reflex enclosure can have greater acoustic output for a given amount of distortion, lower total harmonic intermodulation, and transient distortion than a completely closed-box of similar size. Such a resonant system augments the bass response of the driver and, if designed properly, can extend the frequency response of the driver/enclosure combination to below the range the driver would reproduce in a similarly sized sealed box. The enclosure resonance has a secondary benefit in that it limits cone movement in a band of frequencies centered around the tuning frequency, reducing distortion in that frequency range. Ported cabinet systems are cheaper than a passive radiator speaker with the same performance; whereas a passive radiator system requires one or two "drone cone" speakers, a ported system requires only a hole or port and a length of tubing.

Limitations

Step responses of various high-pass filter functions, each with a -3 dB cut-off frequency equal to 50 Hz. The step response of a standard B4 vented-box low-frequency alignment is depicted in (a), while that of a standard B2 (Q = 0.7071) closed-box low-frequency alignment is depicted in (b). MultiStepResponse.png — Step responses of various high-pass filter functions, each with a −3 dB cut-off frequency equal to 50 Hz. The step response of a standard B4 vented-box low-frequency alignment is depicted in (a), while that of a standard B2 (Q = 0.7071) closed-box low-frequency alignment is depicted in (b).

Compared to closed-box loudspeakers, bass reflex cabinets have poorer transient response, resulting in longer decay times associated with the bass notes.^[4] Some example step responses for various high-pass filter functions are shown in the relevant figure, where each filter has an identical −3 dB cut-off frequency of 50 Hz. In that figure, (a) represents the step response of a conventional B4 vented box alignment, while (b) represents the step response of a B2 closed-box alignment with Q = 0.7071. The transient response of a vented-box loudspeaker can be improved by choosing a QB3 alignment similar to (c), which results in a more well damped transient response than that produced by the B4 alignment. However, a C4 vented-box alignment similar to (e) results in a less well damped transient response.

In order to achieve their bass output, ported loudspeaker enclosures stagger two resonances: one from the driver and the boxed air, and another from the boxed air and the port. At the vent tuning frequency, the output from the port is the primary source of sound output, as the displacement of the woofer is at a minimum. This comprises a more complex, higher-order system than an equivalent closed-box loudspeaker enclosure. The interaction between the two resonances results in a system that possesses less damping and increased time delay (increased group delay). Due to the latter, a flat steady-state bass response does not occur at the same time as the rest of the sonic output at higher frequencies in the operating region. Instead, it starts later (lags) and the lag increases, accumulating over time as a longish resonant "tail" arriving behind the main "body" of the acoustic signal. As a result of their electrodynamic characteristics, ported enclosures, which are well approximated as 4th-order high-pass filter systems, generally result in poorer transient response at low frequencies than do closed-box loudspeaker systems, which are 2nd-order high-pass filter systems.

Another trade-off for this augmentation is that, at frequencies below the vent tuning frequency, the port unloads the cone and allows it to move with very large displacements. This means the speaker can be driven past its safe mechanical operating limits at frequencies below the tuning frequency with much less power than in an equivalently-sized sealed enclosure. For this reason, high-powered systems using a bass reflex design are often protected by a high-pass filter that removes signals below the vent tuning frequency. Unfortunately, electrical filtering adds further frequency-dependent group delay. Even if such filtering can be adjusted not to remove musical content, it may interfere with sonic information connected with the size and ambiance of the recording location or venue, information that often exists in the low bass spectrum.^[17]^[18]

Whether or not the effects of these in a properly designed system are audible remains a matter of debate. A poorly designed bass reflex system, generally one whose vent is incorrectly tuned too high or too low in frequency, tends to produce excessive output at the tuning frequency relative to the rest of the pass-band of the loudspeaker system. This behaviour can add a "booming" one-note quality to the reproduction of the bass frequencies. Although some may consider that this is due to the port resonance imposing its characteristics to the note being played, it is simply the result of a non-maximally flat frequency response function. If such a peak in the bass response of a bass reflex enclosure coincides with one of the resonant modes of the room, a not unusual occurrence, the effects will be further exacerbated. In general, the lower in frequency a port is tuned, the less objectionable these problems are likely to be.

Ports often are placed on the front baffle, and may thus allow transmission of unwanted midrange frequencies reflected from within the box into the listening environment. If it is undersized, a port may also generate "wind noise" or "chuffing" sounds, due to the turbulence around the port openings at high air speeds.^[19] Enclosures with a rear-facing port mask these effects to some extent, but they cannot be placed directly against a wall without causing audible problems. They require some free space around the port so they can perform as intended. Some manufacturers incorporate a floor-facing port within the speaker stand or base, offering predictable and repeatable port performance within the design constraints.

Port compression

Port compression is a reduction in port effectiveness as sound pressure levels increase. As a ported system plays louder, the efficiency of the port reduces, and distortion emitted by the port increases. This can be reduced by port design, but not totally eliminated. Asymmetrical loading of the driver cone during high level usage can be reduced by placing a baffle at the inside end of the port tube. This baffle can also serve as a stiffening structural element of the enclosure.

Applications

Subwoofer cabinets used in home cinema and sound reinforcement systems are often fitted with ports or vents. Bass amp speaker cabinets and keyboard amp speaker cabinets, which have to reproduce low-frequency sounds down to 41 Hz or below, are often built with ports or vents, which are typically on the front of the cabinet (though they are also placed on the rear). Even some expensive hi-fi speakers have carefully designed ports.

Related Research Articles

A subwoofer is a loudspeaker designed to reproduce low-pitched audio frequencies, known as bass and sub-bass, that are lower in frequency than those which can be (optimally) generated by a woofer. The typical frequency range that is covered by a subwoofer is about 20–200 Hz for consumer products, below 100 Hz for professional live sound, and below 80 Hz in THX-certified systems. Thus, one or more subwoofers are important for high-quality sound reproduction as they are responsible for the lowest two to three octaves of the ten octaves that are audible. This very low-frequency (VLF) range reproduces the natural fundamental tones of the bass drum, electric bass, double bass, grand piano, contrabassoon, tuba, in addition to thunder, gunshots, explosions, etc.

<span class="mw-page-title-main">Loudspeaker</span> Converts an electrical audio signal into a corresponding sound

A loudspeaker is an electroacoustic transducer that converts an electrical audio signal into a corresponding sound. A speaker system, also often simply referred to as a speaker or loudspeaker, comprises one or more such speaker drivers, an enclosure, and electrical connections possibly including a crossover network. The speaker driver can be viewed as a linear motor attached to a diaphragm which couples that motor's movement to motion of air, that is, sound. An audio signal, typically from a microphone, recording, or radio broadcast, is amplified electronically to a power level capable of driving that motor in order to reproduce the sound corresponding to the original unamplified electronic signal. This is thus the opposite function to the microphone; indeed the dynamic speaker driver, by far the most common type, is a linear motor in the same basic configuration as the dynamic microphone which uses such a motor in reverse, as a generator.

Audio crossovers are a type of electronic filter circuitry that splits an audio signal into two or more frequency ranges, so that the signals can be sent to loudspeaker drivers that are designed to operate within different frequency ranges. The crossover filters can be either active or passive. They are often described as two-way or three-way, which indicate, respectively, that the crossover splits a given signal into two frequency ranges or three frequency ranges. Crossovers are used in loudspeaker cabinets, power amplifiers in consumer electronics and pro audio and musical instrument amplifier products. For the latter two markets, crossovers are used in bass amplifiers, keyboard amplifiers, bass and keyboard speaker enclosures and sound reinforcement system equipment.

<span class="mw-page-title-main">Tweeter</span> Type of loudspeaker

A tweeter or treble speaker is a special type of loudspeaker that is designed to produce high audio frequencies, typically deliver high frequencies up to 100 kHz. The name is derived from the high pitched sounds made by some birds (tweets), especially in contrast to the low woofs made by many dogs, after which low-frequency drivers are named (woofers).

A woofer or bass speaker is a technical term for a loudspeaker driver designed to produce low frequency sounds, typically from 20 Hz up to a few hundred Hz. A subwoofer can take the lower part of this range, normally up to 80 Hz. The name is from the onomatopoeic English word for a dog's deep bark, "woof". The most common design for a woofer is the electrodynamic driver, which typically uses a stiff paper cone, driven by a voice coil surrounded by a magnetic field.

<span class="mw-page-title-main">Electrostatic loudspeaker</span> Sound playback device

An electrostatic loudspeaker (ESL) is a loudspeaker design in which sound is generated by the force exerted on a membrane suspended in an electrostatic field.

<span class="mw-page-title-main">Horn loudspeaker</span> Loudspeaker using an acoustic horn

A horn loudspeaker is a loudspeaker or loudspeaker element which uses an acoustic horn to increase the overall efficiency of the driving element(s). A common form (right) consists of a compression driver which produces sound waves with a small metal diaphragm vibrated by an electromagnet, attached to a horn, a flaring duct to conduct the sound waves to the open air. Another type is a woofer driver mounted in a loudspeaker enclosure which is divided by internal partitions to form a zigzag flaring duct which functions as a horn; this type is called a folded horn speaker. The horn serves to improve the coupling efficiency between the speaker driver and the air. The horn can be thought of as an "acoustic transformer" that provides impedance matching between the relatively dense diaphragm material and the less-dense air. The result is greater acoustic output power from a given driver.

Thiele/Small parameters are a set of electromechanical parameters that define the specified low frequency performance of a loudspeaker driver. These parameters are published in specification sheets by driver manufacturers so that designers have a guide in selecting off-the-shelf drivers for loudspeaker designs. Using these parameters, a loudspeaker designer may simulate the position, velocity and acceleration of the diaphragm, the input impedance and the sound output of a system comprising a loudspeaker and enclosure. Many of the parameters are strictly defined only at the resonant frequency, but the approach is generally applicable in the frequency range where the diaphragm motion is largely pistonic, i.e., when the entire cone moves in and out as a unit without cone breakup.

<span class="mw-page-title-main">Full-range speaker</span> Type of loudspeaker

A full-range loudspeaker drive unit is defined as a driver which reproduces as much of the audible frequency range as possible, within the limitations imposed by the physical constraints of a specific design. The frequency range of these drivers is maximized through the use of a whizzer cone and other means. Most single driver systems, such as those in radios, or small computer speaker designs, cannot reproduce all of the audible frequencies or the entire audible audio range.

<span class="mw-page-title-main">Loudspeaker enclosure</span> Acoustical component

A loudspeaker enclosure or loudspeaker cabinet is an enclosure in which speaker drivers and associated electronic hardware, such as crossover circuits and, in some cases, power amplifiers, are mounted. Enclosures may range in design from simple, homemade DIY rectangular particleboard boxes to very complex, expensive computer-designed hi-fi cabinets that incorporate composite materials, internal baffles, horns, bass reflex ports and acoustic insulation. Loudspeaker enclosures range in size from small "bookshelf" speaker cabinets with 4-inch (10 cm) woofers and small tweeters designed for listening to music with a hi-fi system in a private home to huge, heavy subwoofer enclosures with multiple 18-inch (46 cm) or even 21-inch (53 cm) speakers in huge enclosures which are designed for use in stadium concert sound reinforcement systems for rock music concerts.

Loudspeaker measurement is the practice of determining the behaviour of loudspeakers by measuring various aspects of performance. This measurement is especially important because loudspeakers, being transducers, have a higher level of distortion than other audio system components used in playback or sound reinforcement.

The Isobaric loudspeaker configuration was first introduced by Harry F. Olson in the early 1950s, and refers to systems in which two or more identical woofers operate simultaneously, with a common body of enclosed air adjoining one side of each diaphragm. In practical applications, they are most often used to improve low-end frequency response without increasing cabinet size, though at the expense of cost and weight.

A speaker enclosure using a passive radiator (PR) usually contains an "active loudspeaker", and a passive radiator. The active loudspeaker is a normal driver, and the passive radiator is of similar construction, but without a voice coil and magnet assembly. It is not attached to a voice coil or wired to an electrical circuit or power amplifier. Small and Hurlburt have published the results of research into the analysis and design of passive-radiator loudspeaker systems. The passive-radiator principle was identified as being particularly useful in compact systems where vent realization is difficult or impossible, but it can also be applied satisfactorily to larger systems.

A guitar speaker is a loudspeaker – specifically the driver (transducer) part – designed for use in a combination guitar amplifier of an electric guitar, or for use in a guitar speaker cabinet. Typically these drivers produce only the frequency range relevant to electric guitars, which is similar to a regular woofer type driver, which is approximately 75 Hz — 5 kHz, or for electric bass speakers, down to 41 Hz for regular four-string basses or down to about 30 Hz for five-string instruments.

An acoustic transmission line is the use of a long duct, which acts as an acoustic waveguide and is used to produce or transmit sound in an undistorted manner. Technically it is the acoustic analog of the electrical transmission line, typically conceived as a rigid-walled duct or tube, that is long and thin relative to the wavelength of sound present in it.

<span class="mw-page-title-main">Acoustic suspension</span> Loudspeaker cabinet design

Acoustic suspension is a method of loudspeaker cabinet design and utilizations that uses one or more loudspeaker drivers mounted in a sealed box or cabinet. Acoustic suspension systems reduce bass distortion that can be caused by stiff motor suspensions in conventional loudspeakers.

wOOx Technology is a brand created by Philips to identify loudspeaker systems that employ passive radiator technology along with active equalisation to maximize the output of the passive diaphragm. wOOx Technology optimizes the active bass driver, the passive bass radiator, and the active equalisation curve to obtain maximum low-frequency reproduction in a relatively compact configuration.

<span class="mw-page-title-main">Electrodynamic speaker driver</span> Individual transducer that converts an electrical audio signal to sound waves

An electrodynamic speaker driver, often called simply a speaker driver when the type is implicit, is an individual transducer that converts an electrical audio signal to sound waves. While the term is sometimes used interchangeably with the term speaker (loudspeaker), it is usually applied to specialized transducers which reproduce only a portion of the audible frequency range. For high fidelity reproduction of sound, multiple loudspeakers are often mounted in the same enclosure, each reproducing a different part of the audible frequency range. In this case the individual speakers are referred to as drivers and the entire unit is called a loudspeaker. Drivers made for reproducing high audio frequencies are called tweeters, those for middle frequencies are called mid-range drivers, and those for low frequencies are called woofers, while those for very low bass range are subwoofers. Less common types of drivers are supertweeters and rotary woofers.

Veritone Minimum Phase Speakers, or VMPS, was a loudspeaker manufacturer founded in 1977 by speaker designer Brian Cheney. Many VMPS speakers received favorable reviews from audio critics, such as the RM40, which was awarded Best of CES in the High-End Audio category in 2002. VMPS was in operation for over 35 years, from January 1977 to December 2012, when it closed soon after the death of company owner Brian Cheney on December 7, 2012.

A transmission line loudspeaker is a loudspeaker enclosure design which uses the topology of an acoustic transmission line within the cabinet, compared to the simpler enclosures used by sealed (closed) or ported designs. Instead of reverberating in a fairly simple damped enclosure, sound from the back of the bass speaker is directed into a long damped pathway within the speaker enclosure, which allows far greater control and use of speaker energy and the resulting sound.

References

↑ de Boer, E. (1959). "Acoustic Interaction in Vented Loudspeaker Enclosures". The Journal of the Acoustical Society of America. 31 (2): 246–247. Bibcode:1959ASAJ...31..246D. doi:10.1121/1.1907703.
1 2 Novak, J. (1959). "Performance of enclosures for low-resonance high-compliance loudspeakers". IRE Transactions on Audio. AU-7 (1): 5–13. doi:10.1109/TAU.1959.1166180.
1 2 Thuras, A. L. (1932). "Sound Translating Device" (PDF). U.S. Patent No. 1,869,178, Application Aug. 15 1930, Patented July 26, 1932. Retrieved 2022-07-02.
1 2 3 Small, R. H. (1973). "Vented-Box Loudspeaker Systems–Part 1: Small-Signal Analysis". Journal of the Audio Engineering Society. 21 (June): 363–372.
↑ "The Subwoofer DIY Page - Passive Radiator Systems". www.diysubwoofers.org. Retrieved 2023-01-02.
↑ McGowan, Paul (April 30, 2013). "Passively radiating". psaudio.com. Archived from the original on 2016-11-27. Retrieved 2019-11-20.
↑ "Passive Radiator Technology" . Retrieved 2023-01-02.
↑ Thiele, A. N. (1961). "Loudspeakers in Vented Boxes". Proceedings of the Institution of Radio Engineers Australia. 22 (8): 487–508.
↑ Thiele, A. N. (1971). "Loudspeakers in Vented Boxes: Part 1". Journal of the Audio Engineering Society. 19 (May): 382–392.
↑ Thiele, A. N. (1971). "Loudspeakers in Vented Boxes: Part 2". Journal of the Audio Engineering Society. 19 (June): 471–483.
↑ Benson, J. E. (1972). "Theory and Design of Loudspeaker Enclosures, Part 3—Introduction to Synthesis of Vented Systems". A.W.A. Technical Review. 14 (4): 369–484.
↑ Benson, J. E. (1993). Theory and Design of Loudspeaker Enclosures. Synergetic Audio Concepts. ISBN 0-9638929-0-8.
↑ Small, R. H. (1973). "Vented-Box Loudspeaker Systems–Part 2: Large-Signal Analysis". Journal of the Audio Engineering Society. 21 (July/August): 438–444.
↑ Small, R. H. (1973). "Vented-Box Loudspeaker Systems–Part 3: Synthesis". Journal of the Audio Engineering Society. 21 (September): 549–554.
↑ Small, R. H. (1973). "Vented-Box Loudspeaker Systems–Part 4: Appendices". Journal of the Audio Engineering Society. 21 (October): 635–639.
↑ Keele, D. B. Jr. (1975). "A New Set of Sixth-Order Vented-Box Loudspeaker System Alignments". Journal of the Audio Engineering Society. 23 (5): 354–360.
↑ Holman, T. (1997). Sound for film and television. Boston, MA: Focal Press.
↑ Chattopadhyay, Budhaditya (2017). "Reconstructing atmospheres: Ambient sound in film and media production". Communication and the Public. 2 (4): 352–364. doi: 10.1177/2057047317742171 .
↑ Bezzola, Andri; Devantier, Allan; McMullin, Elisabeth (October 2019). "Loudspeaker Port Design for Optimal Performance and Listening Experience". 147th AES Convention (Paper Number 10311, Open Access). Retrieved 2021-05-15.

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[DeBoer1959-1] Boer, E. (1959). "Acoustic Interaction in Vented Loudspeaker Enclosures". The Journal of the Acoustical Society of America. 31 (2): 246–247. Bibcode:1959ASAJ...31..246D. doi:10.1121/1.1907703.

[Novak1959-2] 1 2 Novak, J. (1959). "Performance of enclosures for low-resonance high-compliance loudspeakers". IRE Transactions on Audio. AU-7 (1): 5–13. doi:10.1109/TAU.1959.1166180.

[Thuras1932-3] 1 2 Thuras, A. L. (1932). "Sound Translating Device" (PDF). U.S. Patent No. 1,869,178, Application Aug. 15 1930, Patented July 26, 1932. Retrieved 2022-07-02.

[Small_VBPt1-4] 1 2 3 Small, R. H. (1973). "Vented-Box Loudspeaker Systems–Part 1: Small-Signal Analysis". Journal of the Audio Engineering Society. 21 (June): 363–372.

[PR_Systems-5] "The Subwoofer DIY Page - Passive Radiator Systems". www.diysubwoofers.org. Retrieved 2023-01-02.

[McGowan2013-6] McGowan, Paul (April 30, 2013). "Passively radiating". psaudio.com. Archived from the original on 2016-11-27. Retrieved 2019-11-20.

[Accuton-7] "Passive Radiator Technology" . Retrieved 2023-01-02.

[Thiele1961-8] Thiele, A. N. (1961). "Loudspeakers in Vented Boxes". Proceedings of the Institution of Radio Engineers Australia. 22 (8): 487–508.

[Thiele_VBPt1-9] Thiele, A. N. (1971). "Loudspeakers in Vented Boxes: Part 1". Journal of the Audio Engineering Society. 19 (May): 382–392.

[Thiele_VBPt2-10] Thiele, A. N. (1971). "Loudspeakers in Vented Boxes: Part 2". Journal of the Audio Engineering Society. 19 (June): 471–483.

[BensonTDLEPt3-11] Benson, J. E. (1972). "Theory and Design of Loudspeaker Enclosures, Part 3—Introduction to Synthesis of Vented Systems". A.W.A. Technical Review. 14 (4): 369–484.

[Benson1993-12] Benson, J. E. (1993). Theory and Design of Loudspeaker Enclosures. Synergetic Audio Concepts. ISBN 0-9638929-0-8.

[Small_VBPt2-13] Small, R. H. (1973). "Vented-Box Loudspeaker Systems–Part 2: Large-Signal Analysis". Journal of the Audio Engineering Society. 21 (July/August): 438–444.

[Small_VBPt3-14] Small, R. H. (1973). "Vented-Box Loudspeaker Systems–Part 3: Synthesis". Journal of the Audio Engineering Society. 21 (September): 549–554.

[Small_VBPt4-15] Small, R. H. (1973). "Vented-Box Loudspeaker Systems–Part 4: Appendices". Journal of the Audio Engineering Society. 21 (October): 635–639.

[Keele1975-16] Keele, D. B. Jr. (1975). "A New Set of Sixth-Order Vented-Box Loudspeaker System Alignments". Journal of the Audio Engineering Society. 23 (5): 354–360.

[Holman1997-17] Holman, T. (1997). Sound for film and television. Boston, MA: Focal Press.

[Chattopadhyay2017-18] Chattopadhyay, Budhaditya (2017). "Reconstructing atmospheres: Ambient sound in film and media production". Communication and the Public. 2 (4): 352–364. doi: 10.1177/2057047317742171 .

[Bezzola2019-19] Bezzola, Andri; Devantier, Allan; McMullin, Elisabeth (October 2019). "Loudspeaker Port Design for Optimal Performance and Listening Experience". 147th AES Convention (Paper Number 10311, Open Access). Retrieved 2021-05-15.

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