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Thiele/Small parameters

  The works of Neville Thiele and Richard Small are considered to have the most impact on the loudspeaker design field as far as predictability of frequency responce at small excursions is concerned. A method was found, so that one could predict the frequency response performance of a loudspeaker system, based on its physical characteristics.

Understanding the response parameters allows calculation of predicted frequency response for a given speaker system in a uniform way. The formulas that accomplish this are rather lengthy and complex, and are best left to a computer. There are a number of computer programs and java applets that automate the design process of building an enclosure.

The three parameters that primarily determine the frequency response of a loudspeaker are compliance, free-air resonance, and Q.

The compliance, Vas, is a measure of the overall stiffness of the cone, surround (the part the attaches to front of the cone), and spider (the part that attaches to the rear of the cone). It is specified as the volume of air having the same compliance as the driver. A small number corresponds to a small volume of air, which is stiffer than a larger volume of air. Thus, compliance and stiffness are inversely proportional. Optimum enclosure volume is proportional to Vas.

Free-air resonance, Fs, is the resonant frequency of the driver's voice coil impedance with the driver suspended in free air (no enclosure). The -3 dB frequency (F3) of an enclosure is proportional to Fs.

The Q, Qts, is a measure of the sharpness of the driver's free-air resonance. It is defined as (Fh-Fl)/Fs, where Fh and Fl are the upper and lower -3 dB points of the driver's voice coil impedance in free air. Optimum enclosure volume is related to Qts but is not directly proportional. It is accurate to say that the volume gets larger as Qts gets larger. Likewise, F3 gets smaller as Qts gets larger, and for the sealed box enclosure, F3 is inversely proportional to Qts.

The Physical Characteristics of a speaker are:

Re: The D.C. resistance of the voice coil measured in Ohms.

Sd: The surface area of the speaker’s cone.

BL: The magnetic strength of the motor structure.

Mms: The total moving mass of the speaker including the small amount of air in front of and behind the cone.

Cms: The stiffness of the driver’s suspension.

Rms: The losses due to the suspension.

By understanding the relationship of these physical parameters and how to change them, we may alter the response parameters to fit the desired goal.

The Thiele/Small Response parameters are:

Re: The D.C. resistance of the voice coil measured in Ohms.

Sd: The surface area of the speaker.

Fs: The resonant frequency of the speaker.

Qes: The electrical “Q” of the speaker.

Qms: The mechanical “Q” of the speaker.

Qts: The total “Q” of the speaker.

Vas: The volume of air having the same acoustic compliance as the speaker’s suspension.

  Low end - how much air is displaced

in order to achive good reproduction of bass without excessive IM distorsion in mids and treble and retain capability of huge air displacements, ratio between excursion and effective cone area must be changed. Long throw chasis is not welcomed here, excursion must be as possibly short and cone area big (V=Sd*Xmax).

Note that most wideband drivers tend to have a rising response above about 1kHz (much depends on driver specifics) and that for example the FE208 will reach about 104db in the 2 - 4kHz range. This is a seperate issue to be dealt with. Some notes on that compiled by James from seperate post of myself and others are on the "single driver" webpages.

It is higly instructive to compare the kind of parameters found in Drivers traditionally used in sealed or vented Cabinets (Altec 755, Diatone 610A and similar) with those traditionally used in Horns (Fostex Sigma, Lowther, Pro Audio Drivers explicitly designed for Horns).

Ergo, Drivers with a Qt above 0.5 go into sealed or reflex Boxes, Drivers with a Qt below about 0.3 go into horns. Anything inbetween is not really happy in either...

Many modern Drivers use a very short phaseplug. Lowthers and similar use long Phaseplugs and longer Phaseplugs seem to improve smoothness at the cost of HF Extension. If in doubt get more cigars and use one set as long as you want and reduce the length in 5mm (or so) sections, noting the changes in sound. There will come a point where the sound does no longer improve but get's worse.