Thiele/Small parameters (commonly abbreviated T/S parameters, or TSP) 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.
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 of the Australian Broadcasting Commission, and Richard H. Small of the University of Sydney, who pioneered this line of analysis for loudspeakers. A common use of Thiele/Small parameters is in designing PA system and hi-fi speaker enclosures; 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 port (if it is used) should be.
History
The 1925 paper of Chester W. Rice and Edward W. Kellogg, fueled by advances in radio and electronics, increased interest in direct radiator loudspeakers. In 1930, A. J. Thuras of Bell Labs patented (US Patent No. 1869178) his "Sound Translating Device" (essentially a vented box) which was evidence of the interest in many types of enclosure design at the time.
Progress on loudspeaker enclosure design and analysis using acoustic analogous circuits by academic acousticians like Harry F. Olson continued in the 1940s. In 1952, Bart N. Locanthi developed equivalent electrical models of common loudspeaker configurations. In 1954 Leo L. Beranek of the Massachusetts Institute of Technology published Acoustics, a book summarizing and extending the electroacoustics of the era. J. F. Novak 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 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 in 1971. 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, vented and passive radiator designs, all using the same basic model, which included the effects of enclosure, leakage and port losses. Beginning in June 1972, Richard H. Small 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, 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 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 (1.184 kg/m3 at 25 °C), and is the speed of sound (346.1 m/s at 25 °C). Using SI units, the result will be in cubic metres. To convert to litres, multiply by 1000. – Mechanical resistance of driver suspension
– Mechanical compliance of driver suspension
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 , either enclosure may be used effectively.
– The nominal impedance of the loudspeaker, typically 4, 8 or 16 ohms. – The reference or "power available" efficiency of the driver, in percent.
The expression can be replaced by the value 5.445×10−4 m2·s/kg for dry air at 25 °C. For 25 °C air with 50% relative humidity the expression evaluates to 5.365×10−4 m2·s/kg. A version that is more easily calculated with typical published parameters is:
The expression can be replaced by the value 9.523×10−7 s3/m3 for dry air at 25 °C. For 25 °C air with 50% relative humidity the expression evaluates to 9.438×10−7 s3/m3. From the efficiency, we may calculate sensitivity, which is the sound pressure level a speaker produces for a given input: A speaker with an efficiency of 100% (1.0) would output a watt for every watt of input. Considering the driver as a point source in an infinite baffle, at one metre this would be distributed over a hemisphere with area m2 for an intensity of = 0.159155 W/m2. The auditory threshold is taken to be 10–12 W/m2 (which corresponds to a pressure level of 20×10−6 Pa). Therefore a speaker with 100% efficiency would produce an SPL equal to 10log(0.159155/10–12), which is 112.02 dB. The SPL at 1 metre for an input of 1 watt is then: dB(1 watt) = 112.02 + 10·log() The SPL at 1 metre for an input of 2.83 volts is then: dB(2.83 V) = dB(1 watt) + 10·log(8/) = 112.02 + 10·log() + 10·log(8/)
Qualitative descriptions
Resonance frequency of driver, measured in hertz (Hz). The frequency at which the combination of the energy stored in the moving mass and suspension compliance is maximum, and results in maximum cone velocity. A more compliant suspension or a larger moving mass will cause a lower resonance frequency, and vice versa. Usually it is less efficient to produce output at frequencies below , and input signals significantly below can cause large excursions, mechanically endangering the driver. Woofers typically have an in the range of 13–60 Hz. Midranges usually have an in the range of 60–500 Hz and tweeters between 500 Hz and 4 kHz. A typical factory tolerance for the value of is ±15%.
A unitless measurement, characterizing the combined electric and mechanical damping of the driver. In electronics, is the inverse of the damping ratio. The value of is proportional to the energy stored, divided by the energy dissipated, and is defined at resonance (). Most drivers have values between 0.2 and 0.5, but there are valid (if unusual) reasons to have a value outside this range.