Thiele/Small parameters (commonly abbreviated T/S, 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.
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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 until 1954 when 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 a box, 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. It is important to note that Thiele's work neglected enclosure losses and, though a breakthrough at the time, his alignment tables now have little real-world utility.
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 June 1972, Richard H. Small published a series of very influential articles 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 did his work using computer programs and Small used analog simulators. Small also analyzed the systems including enclosure losses.
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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.
- Sd - Projected area of the driver diaphragm, in square metres.
- Mms - Mass of the diaphragm/coil, including acoustic load, in kilograms. Mass of the diaphragm/coil alone is known as Mmd
- Cms - Compliance of the driver's suspension, in metres per newton (the reciprocal of its 'stiffness').
- Rms - The mechanical resistance of a driver's suspension (i.e., 'lossiness') in N·s/m
- Le - Voice coil inductance measured in millihenries (mH) (measured at 1 kHz).
- Re - DC resistance of the voice coil, measured in ohms.
- Bl - The product of magnet field strength in the voice coil gap and the length of wire in the magnetic field, in tesla-metres (T·m).
- Vas - The volume of air which creates the same amount of compliance as the loudspeakers physical suspension.
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.
- Fs - Resonance frequency of the driver
- Qes - Electrical Q of the driver at Fs
- Qms - Mechanical Q of the driver at Fs
- Qts - Total Q of the driver at Fs
- Vas - Equivalent Compliance Volume, i.e. the volume of air which, when acted upon by a piston of area Sd, has the same compliance as the driver's 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.
- Xmax - 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.
- Xmech - 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.
- Pe - 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.
- Vd - Peak displacement volume, calculated by Vd = Sd·Xmax
Other parameters
- Zmax - The impedance of the driver at Fs, used when measuring Qes and Qms.
- EBP - The efficiency bandwidth product, a rough indicator measure. A common rule of thumb indicates that for EBP>100, a driver is perhaps best used in a vented enclosure, while EBP<50 indicates a sealed enclosure. For 50<EBP<100, either enclosure may be used effectively.
- Znom - The nominal impedance of the loudspeaker, typically 4, 8 or 16 ohms.
- ?0 - The reference or "power available" efficiency of the driver, in percent.
- A version more easily calculated with typical published parameters is:
- From the efficiency, we may calculate sensitivity, which is the sound pressure level a speaker produces for a given input:
Qualitative descriptions
Measurement notes--large signal behavior
Some caution is required when using and interpreting T/S parameters. It is important to mention that individual units may not match manufacturer specifications. Parameters values are almost never individually taken, but are at best averages across a production run, due to inevitable manufacturing variations. Driver characteristics will generally lie within a (sometimes specified) tolerance range. Cms is the least controllable parameter, but typical variations in Cms do not have large effects on the final response.
It is also important to understand that most T/S parameters are linearized small signal values. An analysis based on them is an idealized view of driver behavior, since the actual values of these parameters vary in all drivers according to drive level, voice coil temperature, over the life of the driver, etc. Cms decreases the farther the coil moves from rest. Bl is generally maximum at rest, and drops as the voice coil approaches Xmax. Re increases as the coil heats and the value will typically double by 270 °C (exactly 266 °C for Cu and 254 °C for Al), at which many voice coils are approaching (or have already reached) thermal failure.
As an example, Fs and Vas may vary considerably with input level, due to nonlinear changes in Cms. A typical 110 mm diameter full-range driver with an Fs of 95 Hz at 0.5 V signal level, might drop to 64 Hz when fed a 5 V input. A driver with a measured Vas of 7 L at 0.5 V, may show a Vas increase to 13 L when tested at 4 V. Qms is typically stable within a few percent, regardless of drive level. Qes and Qts decrease <13% as the drive level rises from 0.5 V to 4 V, due to the changes in Bl. Because Vas can rise significantly and Fs can drop considerably, with a trivial change in measured Mms, the calculated sensitivity value (?0) can appear to drop by >30% as the level changes from 0.5 V to 4 V. Of course, the driver's actual sensitivity has not changed at all, but the calculated sensitivity is correct only under some conditions. From this example, it is seen that the measurements to be preferred while designing an enclosure or system are those likely to represent typical operating conditions. Unfortunately, this level must be arbitrary, since the operating conditions are continually changing when reproducing music. Level-dependent nonlinearities typically cause lower than predicted output, or small variations in frequency response.
Level shifts caused by resistive heating of the voice coil are termed power compression. Design techniques which reduce nonlinearities may also reduce power compression, and possibly distortions not caused by power compression. There have been several commercial designs that have included cooling arrangements for driver magnetic structures, intended to mitigate voice coil temperature rise, and the attendant rise in resistance that is the cause of the power compression. Elegant magnet and coil designs have been used to linearize Bl and reduce the value and modulation of Le. Large, linear spiders can increase the linear range of Cms, but the large signal values of Bl and Cms must be balanced to avoid dynamic offset.
Lifetime changes in driver behavior
The mechanical components in typical speaker drivers may change over time. Paper, a popular material in cone fabrication, absorbs moisture easily and unless treated may lose some structural rigidity over time. This may be reduced by coating with water-impregnable material such as various plastic resins. Cracks compromise structural rigidity and if large enough are generally non-repairable. Temperature has a strong, generally reversible effect; typical suspension materials become stiffer at lower temperatures. The suspension experiences fatigue, and also undergoes changes from chemical and environmental effects associated with aging such as exposure to ultraviolet light, and oxidation which affect foam and natural rubber components badly, though butyl, nitrile, SBR rubber, and rubber-plastic alloys (such as Santoprene) are more stable. The polyester type of polyurethane foam is highly prone to disintegration after 10 to 15 years. The changes in behavior from aging may often be positive, though since the environment that they are used in is a major factor the effects are not easily predicted. Gilbert Briggs, founder of Wharfedale Loudspeakers in the UK, undertook several studies of aging effects in speaker drivers in the 1950s and 1960s, publishing some of the data in his books, notably Loudspeakers.
There are also mechanical changes which occur in the moving components during use. In this case, however, most of the changes seem to occur early in the life of the driver, and are almost certainly due to relaxation in flexing mechanical parts of the driver (e.g., surround, spider, etc.). Several studies have been published documenting substantial changes in the T/S parameters over the first few hours of use, some parameters changing as much as 15%+ over these initial periods. The proprietor of the firm GR Research has publicly reported several such investigations of several manufacturers' drivers. Other studies suggest little change, or reversible changes after only the first few minutes. This variability is largely related to the particular characteristics of specific materials, and reputable manufacturers attempt to take them into account. While there are a great many anecdotal reports of the audible effects of such changes in published speaker reviews, the relationship of such early changes to subjective sound quality reports is not completely clear. Some changes early in driver life are complementary (such as a reduction in Fs accompanied by a rise in Vas) and result in minimal net changes (small fractions of a dB) in frequency response. If the performance of speaker system is critical, as with high order (complex) or heavily equalized systems, it is sensible to measure T/S parameters after a period of run-in (some hours, typically, using program material), and to model the effects of normal parameter changes on driver performance.
Measurement techniques
There are numerous methods to measure T/S parameters, but the simplest use the input impedance of the driver, measured near resonance. The impedance may be measured in free air (with the driver unhoused and either clamped to a fixture or hanging from a wire, or sometimes resting on the magnet on a surface) and/or in test baffles, sealed or vented boxes or with varying amounts of mass added to the diaphragm. Noise in the measurement environment can have an effect on the measurement, so one should measure parameters in a quiet acoustic environment.
The most common (DIY-friendly) method before the advent of computer-controlled measurement techniques is the classic free air constant current method, described by Thiele in 1961. This method uses a large resistance (e.g., 500 to 1000 ohms) in series with the driver and a signal generator is used to vary the excitation frequency. The voltage across the loudspeaker terminals is measured and considered proportional to the impedance. It is assumed that variations in loudspeaker impedance will have little effect on the current through the loudspeaker. This is an approximation, and the method results in Q measurement errors for drivers with a high Zmax.
A second method is the constant voltage measurement, where the driver is excited by a constant voltage, and the current passing through the coil is measured. The excitation voltage divided by the measured current equals the impedance.
A common source of error using these first two methods is the use of inexpensive AC meters. Most inexpensive meters are designed to measure residential power frequencies (50-60 Hz) and are increasingly inaccurate at other frequencies (e.g., below 40 Hz or above a few hundred hertz). In addition, distorted or non-sine wave signals can cause measurement inaccuracies. Inexpensive voltmeters are also not very accurate or precise at measuring current and can introduce appreciable series resistance, which causes measurement errors.
A third method is a response to the deficiencies of the first two methods. It uses a smaller (e.g., 10 ohm) series resistor and measurements are made of the voltage across the driver, the signal generator, and/or series resistor for frequencies around resonance. Although tedious, and not often used in manual measurements, simple calculations exist which allow the true impedance magnitude and phase to be determined. This is the method used by many computer loudspeaker measurement systems. When this method is used manually, the result of taking the three measurements is that their ratios are more important than their actual value, removing the effect of poor meter frequency response
Source of the article : Wikipedia
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