What do Thiele Small (T/S) parameters mean ?

The Thiele Small parameters, or TS values for short, are all very confusing and difficult to understand and remember. I’m going to try to make it as easy as possible to understand them. Firstly, why do I even need these parameters ? Ever heard this scenario : “I got a 300W 10″ subwoofer and I want to make an enclosure for it” ? Without the TS values, you are blindfolded. Your best bet is to make an average sized sealed box and call it a day.

Secondly, why do they call them thiele small ( what the hell is a thiele? )? Well, they’re actually names : Neville Thiele and Richard Small. Basically, Mr. Thiele wrote a paper about various parameters that affect the performance of infinite baffle and bass reflex loudspeakers. Mr. Small (have fun with that name in school) completed the paper after some time. Of course, many others have their contribution, but they are the ones who got the most credit, thus the name.

Let’s round up most of the Thiele Small parameters, try to explain them and give real world examples :

Fs or F0 (Hertz) 

This is the resonance frequency in free air. It is the frequency where the driver moves with minimal effort. If you tap a speaker (or any object for that matter), it will make a sound, which has the same frequency as its resonant frequency. When the driver reaches the resonance frequency, its response starts to roll off. Below F0, the frequency response starts to thiele small fs resonant frequencydegrade and rolls off. This means that the lower the F0 , the better the bass response. Of course this is only valid for woofers. For midrange drives and tweeters, the resonance frequency will be significantly higher, and there is no better or worse values, it depends on your project.

  • The lower the Fs , the better.
  • A woofer with Fs of 40 Hz will not play well at 30 Hz.
  • A woofer with Fs of 40 Hz will play well at 45 Hz.
  • Woofers can have resonant frequencies of 20 Hz or even lower. While you can’t hear those frequencies, you can feel them, if that is your thing.
  • Fs for midrange drivers and tweeters is irrelevant, as they will probably play above that frequency anyway.

Q (Unitless)

Also called quality factor or  damping factor. When I say damp, I don’t refer to humidity or sound damping. It’s more like car dampers, like a suspension. The damping of the speaker, is a characteristic that helps it resume its rest state. Without adequate damping, a speaker would move uncontrollably at resonance frequency. Q actually stands for quality factor and is the inverse of damping. As damping goes up, Q goes down, but it is widely accepted that Q is a measurement of damping. Speaker damping is of 3 types : mechanical, electrical and pneumatic.

Qms

Also called mechanical Q – The damping made by the suspension of the driver : the surround and the spider of the speaker.

Qes

Also called electrical Q – The damping made by the coil – magnet assembly. When the coil moves through the magnetic field, it generates a current which opposes this motion (hence the electrical damping). Another factor which contributes to the electrical damping is the amplifier. This depends on your particular amplifier. The Qes provided by the speaker manufacturer does not include amplifier damping, for he does not know which amplifier you are going to use.

Qts

Also called total Q  – The damping made by Qms and Qes combined. They don’t literally add up, instead use this formula :  1/Qts = 1/Qms + 1/Qes . This is the Q you should look for if you plan to use it in free air

Qtc

This is the pneumatic damping i was talking abut. This parameter exists only when there is a box in the equation. You will not find this parameter quoted by the manufacturer of the speaker, because he doesn’t know inside which box you will place the speaker. Depending on the size of the box, the air inside it will act like a spring and contribute to the damping of the speaker. You can say that Qtc = Qts + Qof the box. This is the Q you should look for if you plan to use a sealed box.thiele small q resonant frequency

  • Qts does not give much information, as you will probably put the speaker into a box and the value will change, depending on your box
  • However, Qts of values of 0.6 or higher, will demand a very large box. This can be good if you plan to go free air or bad if space is an issue.
  • You can use predefined bass-reflex alignments for Qts values lower than 0.7.
  • Higher Qes values suggests that the woofer is more suitable for sealed enclosures. Lower values recommends the bass-reflex.

How to design loudspeakers - video courses

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Acoustics 101 : Speaker design basics and enclosure design
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Acoustics 201 : Loudspeaker measurements
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Cms (Meters per Newton)

The compliance of the speaker. The suspension of the speaker (the surround and the spider) has a certain stiffness. If the suspension is stiff, the driver is not compliant. So, the easy it is to move the speaker, the more compliant it is. A higher Cms will yield a lower Fs.

  • Compliance affects the resonant frequency. If Cms goes up => Fs goes down (Imagine a ball on a spring. The stiffness of the spring determines the compliance. If the spring is stiff, then it is less compliant and the ball will bounce at a higher frequency (short and fast bounces). If the spring is not stiff, or more compliant, the ball will make long bounces (reduced frequency) ).

Vas (Liters) 

The air inside the cabinet has its own compliance. When you try to compress the air inside a box, you will encounter resistance. If the box is small, the air is harder to compress and therefore less compliant, and if the box is larger, the air is easier to compress, therefore more compliant. In conclusion, Vas describes the volume of the air inside the cabinet, where the compliance of the speaker matches the compliance of the air inside the box.

  • If you are making an acoustic suspension box, you can tell that the volume of the box will be something less than Vas .
  • If it’s larger than Vas, it would be an infinite baffle.

Re (Ohms)

The DC resistance. Not to be confused with the impedance of the driver. The driver impedance depends on frequency anyway. DC resistance is like taking the voice coil of the speaker and pretend it’s a resistor. Measure how many ohms it got … Boom! That’s Re !

  • Re will have a lower value than the impedance of the driver. A speaker with an impedance of 4 ohms will have Re = 2.6 – 3.8 ohms.

Impedance (Ohms)

This is the AC resistance. This is not a fixed value. Because the speaker is moving, the impedance varies with frequency. Impedance will have a high value at resonance frequency. Usually the manufacturer will quote one number, like 4 ohms or 8 ohms, but that is just to make things simple. A 8 ohm speaker can have impedance vary from 6 ohms to 25 ohms or more, but for the most frequencies it will be around 8 ohms.

  • In the graph below you can see a typical 4 ohm woofer impedance chart.
  • At around 32 Hz, the resonant frequency, the impedance spikes.
  • As the frequency rises, so does the impedance, but that is not important because the woofer doesn’t need to play that high anyway (for wide band drivers is important though).
  • Not including the resonant frequency, the speaker impedance is mostly around 4 ohms. That’s why the manufacturer quotes that number.
  • At resonant frequency, the woofer needs more power from the amplifier to move (because of the increased impedance), but that is countered by the fact that the woofers tends to move easily at resonance anyway.

frequency vs impedance

Le (Millihenries)

This is the inductance of the voice coil. When you apply an AC current to the voice coil, it will resist the movement as the current alternates. When current is applied to the voice coil, at the same time, an additional current flow is created, in the opposite direction of the current flow, called back EMF, which is short for electromotive force. As current flows through the voice coil, it moves it into a certain direction, and back EMF tries to move it in the opposite direction. That is why the impedance spikes at resonance frequency. At that frequency the speaker easily reaches high excursions and back EMF is working hard to pull it back.

  • Inductance causes the impedance to rise as the frequency goes up (see the graph above).
  • Large Le values will translate into poor high frequency response (not a problem for subwoofers).
  • To improve high frequency response, a technique called shorting ring or Faraday loop can be used.

Bl (Tesla * Meters)

Bl is actually B * l. Which is (the flux density) x (the length of the voice coil). This measures the motor’s strength. A higher Bl will translate in higher efficiency. Of course, efficiency is determined by lots of factors, so a higher Bl doesn’t necessarily mean a higher SPL. To make it more blunt : bigger magnet and bigger coil equals bigger motor. Try not to get fooled by small magnets, as neodymium magnets are stronger than normal ferrite magnets and don’t need to be as large.

  • You shouldn’t get too preoccupied by the Bl factor. The strength of the motor is in direct correlation with the size / weight of the cone, size of the coil, size of the magnet, size of the basket. If you modify Bl, you have to change a lot of things. The manufacturer will take care of this, and this number should not tell you much. However …
  • A high Bl speaker will be suitable for loaded horn applications.
  • A high Bl will translate into better transients (sudden sounds). The motor has enough oomph to move the cone with a fast reaction time.
  • Bl is in accordance with the size of the speaker, so it’s hard to give an estimate of which is high and which is low. Bl of around 10 is pretty average. While, for a 12″ woofer, a Bl of 20 or more is considered a high number.

How to design loudspeakers - video courses

acoustics image

Acoustics 101 : Speaker design basics and enclosure design
speaker image

Acoustics 201 : Loudspeaker measurements
minichip image

Loudspeaker engineering : How to design speaker crossovers

Xmax (Millimeters)

Is the maximum distance a speaker can travel without distorting. The coil has a certain length and moves up and down inside the magnetic gap of the motor. If the coil travels too far and leaves the magnetic gap, the speaker will distort, as the magnet has a reduced control on the voice coil. Don’t confuse this thiele small parameter with Xmech.

  • Xmax = ( (height of the voice coil) – (height of the magnetic gap)  ) / 2
  • Xmax  (together with Sd) is going to directly affect how much sound pressure the woofer will generate.
  • Exceeding Xmax, although not recommended, will not damage the woofer (most of the time), it will only introduce distortion.

Xmax explained

Xmech (Millimeters)

Is the maximum distance a speaker can travel without damaging the driver. When a driver is exceeding the quoted Xmax, distortion is introduced into the sound. However, if the driver exceeds the quoted Xmech, the mechanical limits of the driver are reached and damage can occur to the driver. When the driver travels forward, it will stretch the surround until it can’t move forward. It looks and sounds disturbing. On the way back, the voice coil will hit the back plate of the magnet and will sound like loud bangs / knocks.

  • Don’t exceed the Xmech of the speaker! It can damage it.

Sd (Square meters)

The effective area of the cone. This is important, if you want to reach high pressure levels (Xmax also). You are probably wandering why 2 speakers of the same quoted dimensions have different Sd ? It is because only half of the surround is considered cone area, so larger surrounds will yield a smaller Sd.

  • The surface area of the cone (together with Xmax) is going to directly affect how much sound pressure the woofer will generate. Don’t get hung up too much on this. Just looking at the quoted diameter will tell you enough.

Mms and Mmd (grams)

This is the total moving mass. If you place on a scale the cone, the coil, half of the surround and half of the spider, you got yourself the value of Mmd. If you add to this equation the weight of the air in front of the speaker, then you will get the Mms  value. When the speaker is moving, the pocket of air directly in front of it, will move with the cone. This air has its own mass and has to be accounted for, when calculating the total moving mass (Mms).

  • If Mms goes up => Fs goes down (Imagine a ball hanging on a spring. If the ball is heavier, the ball will bounce at a lower frequency).
  • If Mms goes up => Efficiency goes down (More amplifier power is needed to push the cone).

SPL (decibels)

SPL stands for sound pressure level. The higher the number, the higher the efficiency. Good SPL rating is around 88 – 90 db, at 1 W / 1 m. This means that the manufacturer picks a certain frequency (depending on the type of the driver : woofer, midrange, tweeter), places a microphone at 1 meter from the speaker, and plays a 1 W tone at that frequency. How many decibels the microphone picks up is the actual SPL.

  • The higher the efficiency, the better. No need for big amplifiers.
  • Careful with SPL ratings at 2.83 V / 1 m. This takes impedance into account. At 8 ohms there is no difference. So 90 db measured at 2.83 V / 1 m are the same as 90 db measured at 1 W / 1 m. But if the speaker is 4 ohms, 90 db measured at 2.83 V / 1 m is equal to 90 db measured at 2 W / 1 m, which is equivalent to 87 db 1 W / 1m.
  • For a 2 ohm speaker 90 db 2.83 V / 1 m is equivalent to 84 db 1 W / 1 m and so on.

Conclusion

There are many parameters that describe how a speaker will function and some of them are not in this list. If you want to build an enclosure, you don’t need to know all of the Thiele Small parameters. Most of the time, you will only need Fs, Qts and Vas.  Sometimes, when the manufacturer is recommending some type of box, you will encounter some of these acronyms :

  • Vc – Volume of closed box.
  • Vb – Volume of bass reflex box.
  • Fc – Resonance frequency of the closed box.
  • Fb – Resonance frequency of the bass reflex box.

Today, software applications do most of the work for us when it comes to interpreting Thiele Small parameters and making calculations. But it is much easier to comprehend when you know how they work. If you want to dig deeper, try the T/S parameters equations article, and see how they interact with one another

References

  1. Newnes Audio and Hi-Fi Engineer’s Pocket Book by Vivian Capelm (Elsevier, 2016). (Amazon affiliate link)
  2. The Audio Expert: Everything You Need to Know About Audio by Ethan Winer (Focal Press, 2012). (Amazon affiliate link)
  3. Image source : link.