Acoustics

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6.5. Thiele–Small parameters [5]

A complete low-frequency model of a loudspeaker drive unit can be defined by just six parameters known as the Thiele–Small parameters, which are

R_{E}, Q_{E S}, Q_{M S}, f_{S}, S_{D}, and V_{A S} .

$R_{E}, Q_{E S}, Q_{M S}, f_{S}, S_{D}, and V_{A S} .$

So far, we have introduced all of these except for V _AS. The parameters Q _ES, Q _MS, f _S, and S _D are defined by Eqs. (6.11), (6.12), (6.8), and (6.22), respectively. The parameter V _AS is the equivalent suspension volume. In other words, it is the volume of air having the same acoustic compliance as the suspension and is defined as

V_{A S} = C_{A S} ρ_{0} c^{2} = C_{M S} S_{D}^{2} ρ_{0} c^{2}

$V_{A S} = C_{A S} ρ_{0} c^{2} = C_{M S} S_{D}^{2} ρ_{0} c^{2}$

(6.26)

The use of this parameter will make more sense when we consider the performance of the loudspeaker with an enclosure of volume V _B, which in its simplest approximation is an extra compliance in the loop of Fig. 6.4b. Straight away, we can say that mounting the drive unit in a box of volume V _B = V _AS will result in a total compliance that is half that of the drive unit in free space or an infinite baffle. Hence, the suspension resonance frequency will be raised by a factor of

\sqrt{2}

$\sqrt{2}$

. From these six parameters, we can furnish our equivalent circuit of Fig. 6.4b with all the required element values:

C_{M S} = \frac{V_{A S}}{S_{D}^{2} ρ_{0} c^{2}}

$C_{M S} = \frac{V_{A S}}{S_{D}^{2} ρ_{0} c^{2}}$

(6.27)

Then from Eq. (6.8)

M_{M S} = \frac{1}{{(2 π f_{S})}^{2} C_{M S}}

$M_{M S} = \frac{1}{{(2 π f_{S})}^{2} C_{M S}}$

(6.28)

and from Eq. (6.12)

R_{M S} = \frac{1}{Q_{M S}} \sqrt{\frac{M_{M S}}{C_{M S}}}

$R_{M S} = \frac{1}{Q_{M S}} \sqrt{\frac{M_{M S}}{C_{M S}}}$

(6.29)

Inserting Eq. (6.28) into Eq. (6.11) yields

B l = \sqrt{\frac{R_{E}}{2 π f_{S} Q_{E S} C_{M S}}}

$B l = \sqrt{\frac{R_{E}}{2 π f_{S} Q_{E S} C_{M S}}}$

(6.30)

where we have ignored R _g because this is not a drive unit parameter. Finally, M _MD = M _MS − 2M _M1, where M _M1 is given by Eq. (6.5). Another parameter that is commonly found in loudspeaker data sheets, although it is not a Thiele–Small parameter, is the maximum (linear) displacement or x _max. It is a difficult parameter to specify in any meaningful way because it depends on how much distortion can be tolerated and varies with frequency [6].

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Table of Contents for Acoustics

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6.5. Thiele–Small parameters [5]

Table of Contents for
Acoustics