Thiele/Small parameters (commonly abbreviated T/S parameters, or TSP) are a set of
electromechanical
In engineering, electromechanics combines processes and procedures drawn from electrical engineering and mechanical engineering. Electromechanics focuses on the interaction of electrical and mechanical systems as a whole and how the two system ...
parameter
A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when ...
s that define the specified low frequency performance of a
loudspeaker driver
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 ...
. 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.
Rather than purchase off-the-shelf components, loudspeaker design engineers often define desired performance and work backwards to a set of parameters and manufacture a driver with said characteristics or order it from a driver manufacturer. This process of generating parameters from a target response is known as synthesis. Thiele/Small parameters are named after
A. Neville Thiele
Albert Neville Thiele, OAM (4 December 1920 – 1 October 2012), was an Australian audio engineer. Thiele was born in Brisbane, Australia. He was particularly noted for his work on electronic filters and on developing the Thiele/Small param ...
of the
Australian Broadcasting Commission
The Australian Broadcasting Corporation (ABC) is the national broadcaster of Australia. It is principally funded by direct grants from the Australian Government and is administered by a government-appointed board. The ABC is a publicly-own ...
, and
Richard H. Small
Richard H. Small (born 1935) is an American scientist, who has worked mainly in the field of electroacoustics. He is known for the commonly used Thiele/Small parameters for loudspeaker enclosure design, which are named after Small and his colleague ...
of the
University of Sydney
The University of Sydney (USYD), also known as Sydney University, or informally Sydney Uni, is a public university, public research university located in Sydney, Australia. Founded in 1850, it is the oldest university in Australia and is one o ...
, who pioneered this line of analysis for loudspeakers. A common use of Thiele/Small parameters is in designing
PA system
A public address system (or PA system) is an electronic system comprising microphones, amplifiers, loudspeakers, and related equipment. It increases the apparent volume (loudness) of a human voice, musical instrument, or other acoustic sound sou ...
and
hi-fi speaker enclosure
A loudspeaker enclosure or loudspeaker cabinet is an enclosure (often rectangular box-shaped) in which speaker drivers (e.g., loudspeakers and tweeters) and associated electronic hardware, such as crossover circuits and, in some cases, power ...
s; the TSP calculations indicate to the speaker design professionals how large a speaker cabinet will need to be and how large and long the
bass reflex
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. This port enables the sound fr ...
port (if it is used) should be.
History
The 1925 paper
of
Chester W. Rice Chester Williams Rice (December 16, 1888 – March 8, 1951) was an American electrical engineer who was the joint inventor in 1925 of the moving coil loudspeaker along with Edward W. Kellogg.
Career
Rice was born in Lynn, Massachusetts in 1 ...
and
Edward W. Kellogg
Edward Washburn Kellogg (February 20, 1883 – May 29, 1960) was an American inventor who invented the moving coil loudspeaker in 1925 along with Chester W. Rice at General Electric
Biography
He was born in Washington (state), Washington in 1883 ...
, fueled by advances in
radio
Radio is the technology of signaling and communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transm ...
and electronics, increased interest in direct radiator loudspeakers. In 1930,
A. J. Thuras
A is the first letter of the Latin and English alphabet.
A may also refer to:
Science and technology Quantities and units
* ''a'', a measure for the attraction between particles in the Van der Waals equation
* ''A'' value, a measure o ...
of
Bell Labs
Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984),
then AT&T Bell Laboratories (1984–1996)
and Bell Labs Innovations (1996–2007),
is an American industrial research and scientific development company owned by mult ...
patent
A patent is a type of intellectual property that gives its owner the legal right to exclude others from making, using, or selling an invention for a limited period of time in exchange for publishing an sufficiency of disclosure, enabling disclo ...
ed (US Patent No. 1869178) his "Sound Translating Device" (essentially a vented box) which was evidence of the interest in many types of
enclosure
Enclosure or Inclosure is a term, used in English landownership, that refers to the appropriation of "waste" or " common land" enclosing it and by doing so depriving commoners of their rights of access and privilege. Agreements to enclose land ...
design at the time.
Progress on loudspeaker enclosure design and analysis using
acoustic analogous circuits by academic acousticians like
Harry F. Olson
Harry Ferdinand Olson (December 28, 1901 – April 1, 1982) was a prominent engineer at RCA Victor and a pioneer in the field of 20th century acoustical engineering.
Biography
Harry F. Olson was born in Mount Pleasant, Iowa, to Swedish immigrant ...
continued until 1954 when
Leo L. Beranek of the
Massachusetts Institute of Technology
The Massachusetts Institute of Technology (MIT) is a Private university, private Land-grant university, land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern t ...
published ''Acoustics'',
a book summarizing and extending the
electroacoustics
Acoustical engineering (also known as acoustic engineering) is the branch of engineering dealing with sound and vibration. It includes the application of acoustics, the science of sound and vibration, in technology. Acoustical engineers are typica ...
of the era.
J. F. Novak
''J. The Jewish News of Northern California'', formerly known as ''Jweekly'', is a weekly print newspaper in Northern California, with its online edition updated daily. It is owned and operated by San Francisco Jewish Community Publications In ...
used novel simplifying assumptions in an analysis in a 1959 paper
which led to a practical solution for the response of a given loudspeaker in sealed and vented boxes, and also established their applicability by empirical measurement. In 1961, leaning heavily on Novak's work,
A. N. Thiele
Albert Neville Thiele, OAM (4 December 1920 – 1 October 2012), was an Australian audio engineer. Thiele was born in Brisbane, Australia. He was particularly noted for his work on electronic filters and on developing the Thiele/Small param ...
described a series of sealed and vented box "alignments" (i.e., enclosure designs based on electrical filter theory with well-characterized behavior, including frequency response, power handling, cone excursion, etc.) in a publication in an Australian journal.
This paper remained relatively unknown outside Australia until it was re-published in the ''
Journal of the Audio Engineering Society
The Audio Engineering Society (AES) is a professional body for engineers, scientists, other individuals with an interest or involvement in the professional audio industry. The membership largely comprises engineers developing devices or products ...
'' in 1971.
It is important to note that Thiele's work neglected enclosure losses and, although the application of filter theory is still important, his alignment tables now have little real-world utility due to neglecting enclosure losses.
Many others continued to develop various aspects of loudspeaker enclosure design in the 1960s and early 1970s. From 1968 to 1972,
J. E. Benson published three articles
in an Australian journal that thoroughly analyzed
sealed
Seal may refer to any of the following:
Common uses
* Pinniped, a diverse group of semi-aquatic marine mammals, many of which are commonly called seals, particularly:
** Earless seal, or "true seal"
** Fur seal
* Seal (emblem), a device to imp ...
,
vented and
passive radiator
In a radio antenna, a passive radiator or parasitic element is a conductive element, typically a metal rod, which is not electrically connected to anything else. Multielement antennas such as the Yagi–Uda antenna typically consist of a ...
designs, all using the same basic model, which included the effects of enclosure, leakage and port losses. Beginning in June 1972,
Richard H. Small
Richard H. Small (born 1935) is an American scientist, who has worked mainly in the field of electroacoustics. He is known for the commonly used Thiele/Small parameters for loudspeaker enclosure design, which are named after Small and his colleague ...
published a series of very influential articles on direct radiator loudspeaker system analysis,
including closed-box,
vented-box,
and passive-radiator
loudspeaker systems, in the ''Journal of the Audio Engineering Society'', restating and extending Thiele's work. These articles were also originally published in Australia, where he had attended graduate school, and where his thesis supervisor was J. E. Benson. The work of Benson and Small overlapped considerably, but differed in that Benson performed his work using computer programs and Small used
analog simulators. Small also analyzed the systems including enclosure losses. Richard H. Small and Garry Margolis, the latter of
JBL
JBL is an American audio equipment manufacturer headquartered in Los Angeles, California, United States. JBL serves the customer home and professional market. The professional market includes studios, installed/tour/portable sound, cars, music ...
, published an article in the ''Journal of the Audio Engineering Society'' (June 1981),
which recast much of the work that had been published up till then into forms suited to the programmable calculators of the time.
Fundamental parameters
These are the physical parameters of a loudspeaker driver, as measured at small signal levels, used in the equivalent electrical circuit models. Some of these values are neither easy nor convenient to measure in a finished loudspeaker driver, so when designing speakers using existing drive units (which is almost always the case), the more easily measured parameters listed under ''Small Signal Parameters'' are more practical.
*
– Equivalent piston area of the driver diaphragm, in square metres.
*
– Mass of the driver diaphragm and voice-coil assembly, including acoustic load, in kilograms. The mass of the driver diaphragm and voice-coil assembly alone is known as
.
*
– Compliance of the driver's suspension, in metres per newton (the reciprocal of its 'stiffness').
*
– The mechanical resistance of the driver's suspension (i.e., 'lossiness'), in N·s/m.
*
– Voice coil inductance, in henries (H) (typically measured at 1 kHz for woofers).
*
– DC resistance of the voice coil, in ohms.
*
– The product of magnetic flux density in the voice-coil gap and the length of wire in the magnetic field, in tesla-metres (T·m).
Small signal parameters
These values can be determined by measuring the
input impedance The input impedance of an electrical network is the measure of the opposition to current ( impedance), both static (resistance) and dynamic ( reactance), into the load network that is ''external'' to the electrical source. The input admittance (the ...
of the driver, near the resonance frequency, at small input levels for which the mechanical behavior of the driver is effectively linear (i.e., proportional to its input). These values are more easily measured than the fundamental ones above. The small signal parameters are:
*
– Resonance frequency of driver
:
*
– Driver
at
considering electrical resistance
only
:
*
– Driver
at
considering driver nonelectrical losses only
:
*
– Total driver
at
resulting from all driver resistances
:
*
– Volume of air having the same acoustic compliance as driver suspension
:
:where
is the
density of air
The density of air or atmospheric density, denoted '' ρ'', is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variation in atmospheric pressure, temperatur ...
(1.184 kg/m
3 at 25 °C), and
is the
speed of sound
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as ...
(346.1 m/s at 25 °C). Using
SI units
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
, the result will be in cubic metres. To convert
to
litre
The litre (international spelling) or liter (American English spelling) (SI symbols L and l, other symbol used: ℓ) is a metric unit of volume. It is equal to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubic metre (m3 ...
s, multiply by 1000.
Large signal parameters
These parameters are useful for predicting the approximate output of a driver at high input levels, though they are harder, sometimes extremely hard or impossible, to accurately measure. In addition, power compression, thermal, and mechanical effects due to high signal levels (e.g., high electric current and voltage, extended mechanical motion, and so on) all change driver behavior, often increasing distortion of several kinds.
*
– Maximum linear peak (or sometimes peak-to-peak) excursion (in mm) of the cone. Note that, because of mechanical issues, the motion of a driver cone becomes non-linear with large excursions, especially those in excess of this parameter.
*
– Maximum physical excursion of the driver before physical damage. With a sufficiently large electrical input, the excursion will cause damage to the voice coil or another moving part of the driver. In addition, arrangements for voice coil cooling (e.g., venting of the pole piece, or openings in the voice coil former above the coil itself, both allowing heat dissipation with air flow) will themselves change behaviors with large cone excursions.
*
– Thermal power handling capacity of the driver, in watts. This value is difficult to characterize and is often overestimated, by manufacturers and others. As the voice coil heats, it changes dimension to some extent, and changes electrical resistance to a considerable extent. The latter changes the electrical relationships between the voice coil and passive crossover components, changing the slope and crossover points designed into the speaker system.
*
– Peak displacement volume, calculated by
=
·
Other parameters
*
– The impedance of the driver at
, used when measuring
and
.
:
*
– The efficiency bandwidth product, a rough indicator measure. A common rule of thumb indicates that for
, a driver is perhaps best used in a vented enclosure, while
indicates a sealed enclosure. For