Thiele/Small

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Thiele/Small commonly refers to a set of standard parameters that define how a loudspeaker driver performs. Developed by A. N. Thiele of the Australian Broadcasting Commission, and Richard H. Small from the University of Sydney. These serve as useful quantities for designing speakers because they are more easily determined experimentally than the fundamental mechanical parameters.

1 Fundamental small signal mechanical parameters
2 Small signal parameters
3 Large signal parameters
4 Other parameters
5 Qualitative Descriptions
6 See also
7 External links

[edit] Fundamental small signal mechanical parameters

These are the linearized physical parameters of a loudspeaker driver, as defined at small signal levels and modeled in the equivalent circuit. Some of these are not convenient to measure in a finished loudspeaker, so when designing speakers with off the shelf drive units, the more easily measured parameters below are more useful.

S_d - Projected area of the driver diaphragm, in square metres.
M_ms - Mass of the diaphragm, including acoustic load, in kilograms.
C_ms - Compliance of the driver's suspension, in metres per newton (the reciprocal of its stiffness).
R_ms - The mechanical resistance of a driver's suspension (lossiness) in N·s/m
L_e - Voice coil inductance measured in millihenries (mH).
R_e - DC resistance of the voice coil, measured in ohms.
Bl - The product of magnet strength and the length of wire in the magnetic field, in T·m (tesla·metres).

[edit] Small signal parameters

These parameters are determined by measuring the input impedance of the loudspeaker (especially near the resonance frequency) at small input levels where the mechanical behavior of the driver is largely linear - or proportional to the input.

F_s - Resonant frequency of the driver

$F_s = \frac{1}{2.\pi.\sqrt{C_{ms}.M_{ms}}}$

Q_es - Electrical Q of the driver at F_s

$Q_{es} = \frac{2.\pi.F_s.M_{ms}.R_e}{(Bl)^2}$

Q_ms - Mechanical Q of the driver at F_s

$Q_{ms} = \frac{2.\pi.F_s.M_{ms}}{R_{ms}}$

Q_ts - Total Q of the driver at F_s

$Q_{ts} = \frac{Q_{ms}.Q_{es}}{Q_{ms} + Q_{es}}$

V_as - Volume of air in cubic metres which, when acted upon by a piston of area S_d, has the same compliance as the driver's suspension. To get V_as in litres, multiply the result of the equation below by 1000.

$V_{as} = \rho.c^2.S_d^2.C_{ms}$

Where ρ is the density of air (1.184 kg/m³ at 25°C), and c is the speed of sound (346.3 m/s at 25°C).

[edit] Large signal parameters

These parameters are useful for predicting the approximate output capability of a driver in a particular configuration.

X_max - Maximum linear peak (or sometimes peak-to-peak) excursion (in mm) of the cone
X_mech - Maximum physical excursion of the driver before damage
P_e - Thermal capacity of the driver, in watts
V_d - Peak displacement volume, calculated by V_d = S_d·X_max

[edit] Other parameters

Z_max - The impedance of the loudspeaker at F_s, used when measuring Q_es and Q_ms.

$Z_{max} = R_e\left(1+\frac{Q_{ms}}{Q_{es}}\right)$

EBP - The Efficiency Bandwidth Product, an indicator of whether a driver should be in a vented or sealed enclosure.

$EBP = \frac{F_s}{Q_{es}}$

Z_nom - The nominal impedance of the loudspeaker, typically 4, 8 or 16 ohms.
η₀ - The reference or "power available" efficiency of the driver, in percent.

$\eta_0 = \left(\frac{9.614\times10^{-7} . F_s^3 . V_{as}}{Q_{es}}\right)\times100\ %$

[edit] Qualitative Descriptions

Cross-section of a dynamic cone loudspeaker. Image not to scale.

F_s
Is the point where the combination of the moving mass and suspension compliance causes the speaker to resonate. Usually it is less efficient to produce frequencies below Fs.

Q_ms
Describes the mechanical damping of the speaker, that is, the losses in the suspension (surround and spider.) A typical value is around 3. Higher Qms indicates fewer losses, and lower Qms indicates higher losses. The main effect of Qms is on the impedance of the driver, with high Qms drivers having a higher impedance peak.

Q_es
Describes the electrical damping of the loudspeaker. As the coil of wire moves through the magnetic field, it generates a current which opposes the motion of the coil, reducing cone movement. In most speakers, this is the dominant form of damping.

Q_ts
Describes the total electric and mechanical damping of the loudspeaker. Most speakers have a Qts in the range of 0.2 and 1.0.

Bl
Also known as the force factor. The higher the Bl value, the larger the force generated by a given current flowing through the voice coil. The forvce on the coil imposed by the magnet is Bl multiplied by the current through the coil. A typical value for Bl is about 10.0, larger values indicate powerful magnets or a lot of windings.

V_as
Describes the amount of resistance to motion there is when the speaker is mounted in free air. It represents the volume of air required to have the same stiffness as the speakers suspension when acted on by a piston of the same area (Sd) of the cone. Larger values mean less resistance, and generally they will require larger enclosures. This parameter is one of the most difficult to measure with precision. This value varies with the square of the diameter. If a 6” and 12” cone have the same resistance to motion in free air, the 12” cone will have a 4x higher Vas.

M_md
Means the mass of the cone, coil and other moving parts of the speaker. M_ms is the cone weight including the radiant mass, and is not to be mixed with the M_md. Some simulation softwares calculate the M_ms values when the M_md is entered.

S_d
The larger the cone, more air will it move. And because reproducing bass sound means moving air, the larger the cone the less it is required to move in order to displace the same amount of air.

X_max
This parameter can have many definitions. The most convenient is to represent it by the total height of the coil minus the upper polar piece height, divided by 2. A speaker with an 8mm X_max means it may move 8mm out and 8mm in while the coil still maintains the same number of windings in the magnetic gap, and approximately the same force on the coil. When the number of windings in the gap are reduced, nonlinearities and dynamic compression are introduced, and in extreme cases the speaker may be damaged. The coil may hit the end of the cap and deform itself, or the spider may hit the top plate and tear off.

V_d
If the point is moving big quantities of air in low frequencies, this is the parameter to be watched. That is because for producing sound it is necessary to move air and the lower the frequency to be reproduced, the higher the air quantity to be moved and the lower the frequency to be reproduced, the bigger the air quantity to be moved for such responses. One may achieve it through the use of smaller cones (smaller S_d), with the penalty of having more in and out movement as of larger cones. The larger cone area divided by the smaller cone area will give the need of displacement of the smaller compared to the larger to produce the same results. It is easy to calculate this and comparing V_d values will give an indication of the maximum output of a speaker.

η₀
Looking at the reference efficiency is more useful than looking at the sensibility (efficiency in dB) quoted by most of the manufacturers. Some values are not the same obtained by the listed values, being sometimes inflated. Others are quoted even without the other parameters listed. Speakers with high X_max values usually are inefficient (low sensibility), needing bigger amplifiers to play them. If the case is getting sound of smaller enclosures and playing with extreme powers, the solution is in using long inefficient coils, with high Xmax, with big and expensive amplifiers.

Dynamic compression
This is not an official T/S parameter, but it's certainly as important or more in the sound study. These values are quoted as an exception by the manufacturers, because it's the most hard one to get. This value gives the amount of loss in deciBels that a speaker will have because of heating the coil, which increases it's impedance and therefore the amplifier will provide less power to the speaker, even with a higher volume. Understanding it will allow one to play under the limits of the speaker, proving more sound in practice. The cause of this is the excessive displacement of the cone/coil, which causes less cooling because the coil is less in contact with the magnetic flow, passing the coil beyond the limit of the polar piece, where there is poor heat exchange, more than the circulating air because of ventilation improvements, and short rings in some cases. All speakers suffer of this, without exception, some more some less. A good indicator is the cone displacement where one should pay great attention.