TS Parameters (Thiele/Small Parameters)

[Sonnie]

"Thiele/Small" commonly refers to a set of electromechanical parameters that define how a loudspeaker driver performs. They are useful when designing speakers because they are more easily determined experimentally than more fundamental mechanical parameters. They are named after A. N. Thiele of the Australian Broadcasting Commission, and Richard H. Small of the University of Sydney, who pioneered this line of analysis for loudspeakers.

Fundamental small signal mechanical 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, including acoustic load, in kilograms.
• 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 (ie, 'lossiness') in N·s/m
• Le - Voice coil inductance measured in millihenries (mH).
• 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 T·m (tesla·metres).

Large signal parameters...

These parameters are useful for predicting the approximate output of a driver at high input levels.

• 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 enough inputs, ie those in excess of this parameter.
• Xmech - Maximum physical excursion of the driver before physical damage. With a sufficiently large input, the voice coil and cone will cause voice coil damage or to some mechanical part of the driver.
• Pe - Thermal power handling capacity of the driver, in watts. This value is difficult to characterize and is often overestimated, by manufacturers and others.
• Vd - Peak displacement volume, calculated by Vd = Sd·Xmax

Descriptions...

Fs
Also called F0, measured in hertz (Hz). The frequency at which the combination of the moving mass and suspension compliance maximally reinforces cone motion. 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 Fs, though motion below Fs can cause uncontrolled motion, mechanically endangering the driver. Woofers typically have an Fs in the range of 13–60 Hz. Midranges usually have an Fs in the range of 60–500 Hz and tweeters between 500 Hz and 4 kHz.


Qts
A unitless measurement, characterizing the combined electric and mechanical damping of the driver. In electronics, Q is the inverse of the damping ratio. The value of Qts is proportional to the energy stored, divided by the energy dissipated, and is defined at resonance (Fs). Most drivers have Qts values between 0.2 and 0.8.


Qms
A unitless measurement, characterizing the mechanical damping of the driver, that is, the losses in the suspension (surround and spider.) A typical value is around 3. High Qms indicates lower damping losses, and low Qms indicates higher. The main effect of Qms is on the impedance of the driver, with high Qms drivers displaying a higher impedance peak. One predictor for low Qms is a metallic voice coil former of a particular configuration. These act as eddy-current brakes and increase damping, reducing Qms. The same former, with an electrical break in the cylinder (so no conducting loop) avoids these losses.


Qes
A unitless measurement, describing 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. This so-called "Back-EMF" decreases the total current through the coil near the resonance frequency, reducing cone movement and increasing impedance. In most drivers, Qes is the dominant factor in the voice coil damping.


Bl
Measured in tesla-metres (T·m). Technically this is B x l (vector cross product or B * l * sin(θ)), but the standard geometry of a circular coil in an annular voice coil gap gives sin(θ)=1. Bl is also known as the 'force factor' because the force on the coil imposed by the magnet is Bl multiplied by the current through the coil. The higher the Bl value, the larger the force generated by a given current flowing through the voice coil. Bl has a very strong effect on Qes.


Vas
Measured in litres (L), is a measure of the free air 'stiffness' of the suspension -- the driver must be mounted in free air. It represents the volume of air that has the same stiffness as the driver's suspension when acted on by a piston of the same area (Sd) as the cone. Larger values mean lower stiffness, and generally require larger enclosures. Vas varies with the square of the diameter.


Mms
Measured in grams (g), this is the mass of the cone, coil and other moving parts of a driver, including the acoustic load imposed by the air in contact with the driver cone. Mmd is the cone mass without the acoustic load, and the two should not be confused. Some simulation software calculates Mms when Mmd is entered.


Rms
Units are not usually given for this parameter, but it is in mechanical 'ohms'. Rms is a measurement of the losses, or damping, in a driver's suspension and moving system. It is the main factor in determining Qms. Rms is influenced by suspension topology, materials, and by the voice coil former (bobbin) material.


Cms
Measured in metres per Newton (m/N). Describes the compliance (ie, the inverse of stiffness) of the suspension. The more compliant a suspension system is, the lower its stiffness, so the higher the Vas will be.


Re
Measured in ohms (Ω), this is the DC resistance of the voice coil. American EIA standard RS-299A specifies that DCR should be at least 80% of the rated driver impedance, so an 8-ohm rated driver will have a DC resistance of at least 6.4 ohms, and a 4-ohm unit should measure 3.2 ohms minimum. Advertised values are often approximate at best.


Le
Measured in millihenries (mH), this is the inductance of the voice coil. The coil is an inductor in part due to losses in the pole piece, so the apparent inductance changes with frequency. Large Le values limit the high frequency output of the driver and cause response changes near cutoff. Simple modeling software often neglects the effects of Le, and so does not include its consequences. Building a copper cap into the magnet structure can reduce this effect.


Sd
Measured in square metres (m²). The effective area of the cone or diaphragm. It varies with the conformation of the cone, and details of the surround. Generally accepted as the cone body diameter plus half the width of the annulus (surround). Wide roll surrounds can have significantly less Sd than conventional types.


Xmax
Specified in millimeters (mm). In the simplest form, subtract the height of the voice coil winding from the height of the magnetic gap, take the absolute value and divide by 2. This technique was suggested by JBL's Mark Gander in a 1981 AES paper, as an indicator of a loudspeaker motor's linear range. Although easily determined, it neglects non-linearities and limitations introduced by the suspension. Subsequently, a combined mechanical/acoustical measure was suggested, in which a driver is progressively driven to high levels at low frequencies, with Xmax determined at 10% THD. This method better represents actual driver performance, but is harder and more time-consuming to determine.


Vd
Specified in litres (L). The volume displaced by the cone, equal to the cone area (Sd) multiplied by Xmax. Any particular value may be achieved in any of several ways. For instance, by having a small cone with a large Xmax, or a large cone with a small Xmax. Comparing Vd values will give an indication of the maximum output of a driver at low frequencies. High Xmax, small cone diameter drivers are likely to be inefficient, since much of the voice coil winding will be outside the magnetic gap at any one time and will therefore contribute little or nothing to cone motion. Likewise, large cone diameter high Xmax drivers are likely to be more efficient as they will not need, and so may not have, long voice coils.

η0
Specified in percent (%). Comparing drivers by their reference efficiency is more useful than using 'sensitivity' since manufacturer sensitivity figures are too often overly optimistic.


Reference: Wikipedia

[anidabi]

Finally someone did this! Good work, although I already knew these and you can find these from winISD help. Still it's good to have driver paprameters explained as forum sticky, so it's easier for the newbies. I do remember how frustrating it was at first to try to find explanations for the parameters.

[thekl0wn]

Hmmm.... This needs to be printed out, laminated, and put up on the wall. Great quick reference with nice brief, but very informative descriptions.

Great work Sonnie!

[Endless Lasers]

When measuring the T/S parameters of a new driver, how many hours should this driver be run to get reliable numbers. Should this be done with music or just a one frequency sinewave?

[Mike P.]

I'll assume you referring to a subwoofer. I've read to use a frequency around the Fs of the sub. Apply enough power to exercise the suspension using no more then 3/4 of the xmax. Some say for 10 minutes, others say for a full day. I would think a couple of hours would be sufficient.

[Anthony]

Don't just use a sine wave, as they can heat up the voice coil quite a bit if left on for a long time. Use warble tones or pink noise, or just general music or movies to do a quick break-in.

That being said, I don't know how long, but I imagine a couple of solid hours of use or a couple of days of casual use should suffice to loosen the suspension and shake anything else into place.

[Mike P.]

Using sine waves at the resonant frequency is fine since the speaker moves significantly with very little power applied. The combination of very high impedance and significant cone movement eliminates any chance of overheating the voice coil.

In my experience, to make a nice jig for measuring thielsmall parameters is a must.
There r difference of opinion among experts regarding measuring thiel small parameters.
I discussed this matter with few experts in the field.
They hv different approach. 1) LMS hv 3 approches. 1 st one is old. But the other two LTS & TSL r used by Vance Dickson in voice coil magazine. Dr. Eart Geddles suggest his own patented method for TS parameters.
Now what is the experience of the members here?
By which testing method they got better results in the final product?

[slyv12]

now i understand

[aNomad]

It was my understanding that when a woofer driver breaks in, the only parameter that changes is the compliance, which though it affects Vas directly, it also affects Fs indirectly, and when doing enclosure calculations, those cancel to a degree that the difference in response (in most cases) is negligible. Has anybody heard this before? It seems to make sense, because if it didn't, every loudspeaker made would need a redesigned cabinet after a year or so.

[Mindaudio]

aNomad,

all TSPs are interlinked. I've written a small program called TSPcheck that checks, whether a set of TSP is consistent. Often manufacturers claim a high efficiency which is far aways from the half space referecne efficiency you can calculate out of the TSPs.

The screenshot of the program shows all formulas on the right side:



Pico