Acoustic transmission line

This image is actually an inverted folded horn. You can tell as the throat is larger than near the port opening. A true Transmission Line enclosure is the same width 'vent' throughout. .

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.

Examples of transmission line related technologies include the (mostly obsolete) speaking tube, which transmitted sound to a different location with minimal loss and distortion, wind instruments such as the pipe organ, woodwind and brass which can be modeled in part as transmission lines (although their design also involves generating sound, controlling its timbre, and coupling it efficiently to the open air), and transmission line based loudspeakers which use the same principle to produce accurate extended low bass frequencies and avoid distortion. The comparison between an acoustic duct and an electrical transmission line is useful in "lumped-element" modeling of acoustical systems, in which acoustic elements like volumes, tubes, pistons, and screens can be modeled as single elements in a circuit. With the substitution of pressure for voltage, and volume particle velocity for current, the equations are essentially the same. Electrical transmission lines can be used to describe acoustic tubes and ducts, provided the frequency of the waves in the tube is below the critical frequency, such that they are purely planar.

The body of this article covers the general principles of acoustic transmission lines, and in particular their use in loudspeaker enclosure desighn (topology), in which sound from the back of the bass speaker chassis passes along a long (generally convoluted) path within the speaker enclosure. The path is often covered with varying types and depths of absorbent material, may vary in size or taper, and may be open or closed. In such a design, the aim is that undesired resonances and energy produced by the speaker which would otherwise cause undesirable auditory effects, is instead selectively absorbed or reduced ("damped") due to the effects of the duct, or alternatively only emerges from the open end in phase with the sound radiated from the front of the driver, enhancing the output level at low frequencies. Transmission line loudspeakers designs are complex to implement, but their high fidelity frequency response can begin far below that of a typical speaker or subwoofer, into the infrasonic (7 - 20Hz models were commercially produced by British company TDL) without needing a separate enclosure or driver.

Purpose and design overview

A transmission line is used in loudspeaker design, to reduce time, phase and resonance related distortions, and in many designs to gain exceptional bass extension to the lower end of human hearing, and in some cases the near-infrasonic (below 20 Hz). TDL's reference speaker range contained models with frequency ranges of 20 Hz upwards, down to 7 Hz upwards, without needing a separate subwoofer. Irving M. Fried, an advocate of TL design, stated that:

"I believe that speakers should preserve the integrity of the signal waveform and the Audio Perfectionist Journal has presented a great deal of information about the importance of time domain performance in loudspeakers. I’m not the only one who appreciates time- and phase-accurate speakers but I have been virtually the only advocate to speak out in print in recent years. There’s a reason for that."

"It is difficult and costly to design and manufacture a time- and phase-accurate speaker system. Few of today’s high-end loudspeakers are time- and phase-accurate designs. The audio magazines need to appeal to a broad spectrum of advertisers including many who make speaker systems which are time incoherent. The magazines, and the reviewers who write for them, have ignored or downplayed the issue of time- and phase-accuracy in order to maximize advertising revenue. I am not alone in recognizing this situation".

The transmission line (TL) is the theoretical ideal (and one of the most complex) construction with which to load a moving coil drive unit. The most common and practical implementation is to fit a drive unit to the end of a long duct that is usually open at the far end. In practice, the duct is folded inside a conventional shaped cabinet, so that the open end of the duct appears as a vent on the speaker cabinet. There are many ways in which the duct can be folded and the line is often tapered in crossection to avoid parallel internal surfaces that encourage standing waves. Depending upon the drive unit and quantity – and various physical properties – of absorbent material, the amount of taper will be adjusted during the design process to tune the duct to remove irregularities in its response. The internal partitioning provides substantial bracing for the entire structure, reducing cabinet flexing and colouration. The inside faces of the duct or line, are treated with an absorbent material to provide the correct termination with frequency to load the drive unit as a TL. A theoretically perfect TL would absorb all frequencies entering the line from the rear of the drive unit but remains theoretical, as it would have to be infinitely long. The physical constraints of the real world, demand that the length of the line must often be less than 4 meters before the cabinet becomes too large for any practical applications, so not all the rear energy can be absorbed by the line. In a realized TL, only the upper bass is TL loaded in the true sense of the term (i.e. fully absorbed); the low bass is allowed to freely radiate from the vent in the cabinet. The line therefore effectively works as a low pass filter, another crossover point in fact, achieved acoustically by the line and its absorbent filling. Below this “crossover point” the low bass is loaded by the column of air formed by the length of the line. The length is specified to reverse the phase of the rear output of the drive unit as it exits the vent. This energy combines with the output of the bass unit, extending its response and effectively creating a second driver.

Essentially, the goal of the transmission line is to minimize acoustical or mechanical impedance at frequencies corresponding to the driver's fundamental free air resonance. This simultaneously reduces stored energy in the driver's motion, reduces distortion, and critically damps the driver by maximizing acoustic output (maximal acoustical loading or coupling) at the terminus. This also minimizes the negative effects of acoustic energy that would otherwise (as with a sealed enclosure) be reflected back to the driver in a sealed cavity.

Transmission line loudspeakers employ this tube-like resonant cavity, with the length set between 1/6 and 1/2 the wavelength of the fundamental resonant frequency of the loudspeaker driver being used. The cross-sectional area of the tube is typically comparable to the cross-sectional area of the driver's radiating surface area. This cross section is typically tapered down to approximately 1/4 of the starting area at the terminus or open end of the line. While not all lines use a taper, the standard classical transmission line employs a taper from 1/3 to 1/4 area (ratio of terminus area to starting area directly behind driver). This taper serves to dampen the buildup of standing waves within the line, which can create sharp nulls in response at the terminus output at even multiples of the driver's Fs.

In a transmission line speaker, the transmission line itself can be open ("vented") or closed at the far end. Closed designs typically have negligible acoustic output from the enclosure except from the driver, while open ended designs exploit the low-pass filter effect of the line, and the resultant low bass energy emerges to reinforce the output from the driver at low frequencies. Well designed transmission line enclosures have smooth impedance curves, possibly from a lack of frequency-specific resonances, but can also have low efficiency if poorly designed.

One key advantage of transmission lines is their ability to conduct the back wave behind the transducer more effectively away from it - reducing the chance for reflected energy permeating back through the diaphragm out of phase with the primary signal. Not all transmission lines designs do this effectively. Most offset transmission line speakers place a reflective wall fairly close behind the transducer within the enclosure - posing a problem for internal reflections emanating back through the transducer diaphragm. Older descriptions explained the design in terms of "impedance mismatch", or pressure waves "reflected" back into the enclosure; these descriptions are now considered outdated and inaccurate as technically the transmission line works through selective production of standing waves and constructive and destructive interference (see below).

A transmission line speaker employs essentially, two distinct forms of bass loading, which historically and confusingly have been amalgamated in the TL description. Separating the upper and lower bass analysis reveals why such designs have so many potential advantages over reflex and infinite baffle designs. The upper bass is completely absorbed by the line allowing a clean and neutral response. The lower bass is extended effortlessly and distortion is lowered by the line’s control over the drive unit’s excursion. One of the exclusive benefits of a TL design is its ability to produce very low frequencies even at low monitoring levels - TL speakers can routinely produce full range sound usually requiring a subwoofer, and do so to very high levels of accuracy. The main disadvantage of the design is that it is more labor-intensive to create and tune a high quality and consistent transmission line, compared to building a simple enclosure.

History of transmission line loudspeakers

Invention and early use

The concept was termed "acoustical labyrinth" by Stromberg-Carlson Co. when used in their console radios beginning in 1936.http://www.radiomuseum.org/r/stromberg_acoustical_labyrinth_837.html This type of loudspeaker enclosure was proposed in October 1965 by Dr A.R. Bailey and A.H. Radford in Wireless World (p483-486) magazine. The article postulated that energy from the rear of a driver unit could be essentially absorbed, without damping the cone's motion or superimposing internal reflections and resonance, so Bailey and Radford reasoned that the rear wave could be channeled down a long pipe. If the acoustic energy was absorbed, it would not be available to excite resonances. A pipe of sufficient length could be tapered, and stuffed so that the energy loss was almost complete, minimizing output from the open end. No broad consensus on the ideal taper (expanding, uniform cross-section, or contracting) has been established.

Modern Transmission Lines

Source for much of this section: Loudspeakers: for music recording and reproduction (Newell & Holland, 2007) 

The birth of the modern Transmission Line speaker design came about in 1965 with the publication of A R Bailey’s article in Wireless World, “A Non-resonant Loudspeaker Enclosure Design”, detailing a working Transmission Line. Radford Audio took up this innovative design and briefly manufactured the first commercial Transmission Line loudspeaker. Although acknowledged as the father of the Transmission Line, Bailey’s work drew on the work on labyrinth design, dating back as early as the 1930s. His design, however, differed significantly in the way in which he filled the cabinet with absorbent materials. Bailey hit upon the idea of absorbing all the energy generated by the bass unit inside the cabinet, providing an inert platform for the drive unit to work from; unchecked, this energy produces spurious resonances in the cabinet and its structure, adding distortion to the original signal.

Shortly thereafter the design entered mainstream Hi-Fi, through the works of Irving M. "Bud" Fried in the United States, and a British trio: John Hayes, John Wright, and David Brown.

Fried was exposed during his time at Harvard University to high fidelity audio reproduction, and later became an importer of audiophile items. Under the trademark "IMF" (his initials), from 1961, he eventually became involved with many advancements in audiophile equipment: cartridges (IMF – London, IMF – Goldring), tone arms (SME, Gould, Audio and Design), amplifiers (Quad, Custom Series), loudspeakers (Lowther, Quad, Celestion, Bowers and Wilkins, Barker, etc). In 1968 he met John Hayes and John Wright, who had already designed an award winning tone arm in the UK and had brought along a transmission line speaker designed by John Wright - described by Hayes as "fanatical regarding quality"  - in order to promote and demonstrate the tone arm at a New York hifi show. Irving unexpectedly received a number of orders for the unnamed speaker, which he dubbed the "IMF". The British pair, along with Hayes' colleague David Brown, agreed to form a UK company to design and manufacture speakers which would be sold by Irving in the United States. John Hayes later wrote that:

Of course, Bud, had called it the IMF, and therefore, perhaps mistakenly we registered IMF and formed an IMF company... At no time did Bud Freed have any input on the designs. We sold him speakers and he was the US Distributor...  [...] Bud Freed was never a Director or shareholder of IMF Electronics. IMF electronics were the only company manufacturing the transmission line speakers. The name IMF was adopted because Bud Freed had demonstrated the first prototype speakers at the New York hi fi show, and because of the publicity and the fact that he had used his name on the then unnamed speakers, we stuck with the name which was a mistake on our part. It was never his company. After our lawsuit he called his speakers Freed.

The relationship broke down acrimoniously when Irving began to make his own, poorer quality speakers, also marketed as "IMF", and refused to cease until a court agreed that the UK business had the right to the trademark IMF for loudspeakers. Following the split, Irving in the USA (under the brandname "Freed") and the three founders of IMF Electronics in the UK (via a joint venture with driver manufacturer Elac under the name TDL), both became well known in audiophile circles for many years as major advocates of transmission line speaker design. TDL closed after John Wright's gradual failing of health and death in 1999 from cancer. He was described in his 1999 obituary as "one of the most important figures on the British hi-fi scene since the mid-1960s... best remembered for his transmission-line loudspeaker designs". The brand was acquired by Audio Partnerships (part of retailer group Richer Sounds).

Design principles

Fig. 1 - relationship between TL length and wavelength

Fig. 2 - Frequency response (magnitude) measurement of Drive unit & TL outputs

Phase inversion is achieved by selecting a length of line that is equal to the quarter wavelength of the target lowest frequency. The effect is illustrated in Fig. 1, which shows a hard boundary at one end (the speaker) and the open-ended line vent at the other. The phase relationship between the bass driver and vent is in phase in the pass band until the frequency approaches the quarter wavelength, when the relationship reaches 90 degrees as shown. However by this time the vent is producing most of the output (Fig. 2). Because the line is operating over several octaves with the drive unit, cone excursion is reduced, providing higher SPL’s and lower distortion levels, compared with reflex and infinite baffle designs.

The calculation of the length of the line required for a certain bass extension appears to be straightforward, based on a simple formula:

λ = 344/4 × f

where:

• f is the quarter wavelength frequency
• 344 m/s is the speed of sound in air at 20 degrees C
• λ is the length of the transmission line

The complex loading of the bass drive unit demands specific Thiele/Small driver parameters to realise the full benefits of a TL design. Most drive units in the marketplace are developed for the more common reflex and infinite baffle designs and are usually not suitable for TL loading. High efficiency bass drivers with extended low frequency ability, are usually designed to be extremely light and flexible, having very compliant suspensions. Whilst performing well in a reflex design, these characteristics do not match the demands of a TL design. The drive unit is effectively coupled to a long column of air which has mass. This lowers the resonant frequency of the drive unit, negating the need for a highly compliant device. Furthermore, the column of air provides greater force on the driver itself than a driver opening onto a large volume of air (in simple terms it provides more resistance to the driver's attempt to move it), so to control the movement of air requires an extremely rigid cone, to avoid deformation and consequent distortion.

The introduction of the absorption materials reduces the velocity of sound through the line, as discovered by Bailey in his original work. L Bradbury published his extensive tests to determine this effect in an AES Journal in 1976 and his results agreed that heavily damped lines could reduce the velocity of sound by as much as 50%, although 35% is typical in medium damped lines. Bradbury’s tests were carried out using fibrous materials, typically longhaired wool and glass fibre. These kinds of materials however produce highly variable effects that are not consistently repeatable for production purposes. They are also liable to produce inconsistencies due to movement, climatic factors and effects over time. High specification acoustic foams, developed by manufacturers such as PMC, with similar characteristics to longhaired wool, provide repeatable results for consistent production. The density of the polymer, the diameter of the pores and the sculptured profiling are all specified to provide the correct absorption for each speaker model. Quantity and position of the foam is critical to engineer a low pass acoustic filter that provides adequate attenuation of the upper bass frequencies, whilst allowing an unimpeded path for the low bass frequencies.

Older descriptions

Older acoustical models discussed transmission lines in terms of "impedance mismatch" or pressure waves "reflected" off the terminus opening back into the cavity. In fact, there is no "reflection". The driver mounted in a resonant cavity exhibits behavior akin to "cavitation" in which a series of gas pressurizations and rarefactions oscillate back and forth in a captive state. As the driver propagates this alternating train of weak adjacent pressure and vacuum pulses down the transmission line - waves that fit neatly within the cavity (anti node at terminus) remain largely captive (low acoustic output) while waves that do not (node or peak pressure at the terminus) exhibit high levels of energy transfer. Those that meet neither condition exactly produce output that is neither maximum nor minimum. There is no physical phenomenon that can cause "reflection". The electrical circuit analogy upon which the concept of "reflection" is based has no physical embodiment in an acoustical transmission line. As discussed below, the degree of acoustical coupling achieved and hence, loading, is determined by the difference between the distance from the driver to the terminus and the length of the quarter-wave peak of the fundamental wavefront (Fs) and its odd-ordered harmonics. The greater the difference, the lower the acoustical coupling. The smaller the difference, the greater the acoustical coupling and hence the lower the acoustical impedance.

Sound ducts as transmission lines

A duct for sound propagation also behaves like a transmission line (e.g. air conditioning duct, car muffler, ...). Its length may be similar to the wavelength of the sound passing through it, but the dimensions of its cross-section are normally smaller than one quarter the wavelength. Sound is introduced at one end of the tube by forcing the pressure across the whole cross-section to vary with time. An almost planar wavefront travels down the line at the speed of sound. When the wave reaches the end of the transmission line, behaviour depends on what is present at the end of the line. There are three possible scenarios:

1. The frequency of the pulse generated at the transducer results in a pressure peak at the terminus exit (odd ordered harmonic open pipe resonance) resulting in effectively low acoustic impedance of the duct and high level of energy transfer.
2. The frequency of the pulse generated at the transducer results in a pressure null at the terminus exit (even ordered harmonic open pipe anti -resonance) resulting in effectively high acoustic impedance of the duct and low level of energy transfer.
3. The frequency of the pulse generated at the transducer results in neither a peak or null in which energy transfer is nominal or in keeping with typical energy dissipation with distance from the source.

See also

• Frequency response
• Loudspeaker acoustics
• Loudspeaker measurement

External links

• Quarterwave loudspeakers – Martin J King, developer of TL modeling software
• Transmission Line Speakers Pages – TL projects, history & more
• Brines Acoustics Articles (Archived 2009-10-24) – Application, tips, essays
• Quarter Wave Tube - DiracDelta.co.uk - description of operation, equation and online calculation