LoudspeakerBuilder.ca - (Thiele-Small Audio Speaker Parameters)

A.N. Thiele and Richard H. Small defined most of the relationships and terms we now use to describe what happens in a audio speaker and between a audio speaker and a particular enclosure's type and size. Their work has become the standard for audio speaker measurement criteria and is known as the Thiele-Small parameters. All audio speaker manufactures use the Thiele-Small parameters in describing their products which allow you to do a direct characteristics comparison of different audio speakers as well as give your the necessary information for designing the crossover network and enclosure.

The most commonly used Thiele-Small parameters are listed below:

EBP - Is used loosely to decide what type of audio speaker enclosure will be best for any given audio speaker. It is calculated by dividing the Fs by the Qes. A result closer to 100 is usually best suited for an vented enclosure while an EBP closer to 50 will usually require a closed box design. This is just the "rule of thumb", some well designed high quality system violate this rule so use the EBP as a guide if the audio speaker manufacturer doesn't make a recommendation.

Fs - This is the free-air resonant of a speaker; it's the frequency that the audio speaker wants to vibrate at. This is a result of the weight of the moving parts (cone, etc) in balance with the stiffness of the audio speaker's suspension. At a speaker's Fs the speaker will over emphasize (make louder) that frequency and cause crossover points to change due to impedance variances. For accurate sound reproduction these frequency peaks must be controlled (kept flat).

Fb - The enclosure resonance (bass reflex).

Fc -The enclosure resonance (sealed enclosure systems).

Fp -Is the free-air resonant (Fs) frequency of a passive radiator.

F3 - Is the frequency where the response (loudness) is down from the reference level by 3 dB. Anything below this frequency is often too quiet to be useful; so F3 help defines a speaker's useful range. Look at the graph down below at the Qtc 0.707. The reference frequency is 90 dB, look along the line and look where it crosses the 87 db. The F3 for this audio speaker in a box with a Qtc of 0.707 is aprox 45 Hz

Lv - Is the length of the audio speaker enclosure's port.

Pe - Is defined as the maximum continuous (RMS) power-handling capability of a audio speaker.

Power Handling - Is rated on how much power a audio speaker can handle without causing damage. The most important consideration is the audio speakers ability to get rid of excessive heat. Factors that effect this include magnet and voice coil size and their ability to handle heat, venting, and the adhesives used in voice coil construction.

Mechanical factors are also considered, such as the power required to cause;

  1. The coil to hit the back plate or come out of the gap
  2. The cone buckling from too much outward movement.
  3. The spider bottoming on the top plate.

But still the most common cause of audio speaker failure is simple abuse; cranking it up beyond its power rating while asking the audio speaker to produce frequencies lower than it's frequency rating. So be sure to take into account the suggested usable frequency range and the Xmech parameter in conjunction with the power rating of the audio speaker to avoid such failures.

The Thiele-Small Q's - The control of those peaks at resonant frequency (Fs) is done with the audio speaker's suspension (spider, surround) balanced off against the opposing force of the voice coil and magnet. The measurements used in describing the control (dampening) the movement of the audio speaker's suspension are the Qms, Qes and Qts. If the manufacturer does this right they can often put the resonate frequency of the speaker outside; either above or below its intended frequency range use which helps results in a more "flat" frequency response audio speaker.

Q - The relative damping or system losses of a loudspeaker in an enclosure. The ratio of stored to dissipated energy

Qms - Is the measurement of control from the mechanical suspension system at resonance (Fs) which include the spider and the surround. They allow and control the movement of the audio speaker cone.

Qes - Is the measurement of control from the electrical suspension system at resonance (Fs) which include the voice coil and the magnet; the "engine" of the audio speaker.

Qts - The opposing forces from the mechanical and electrical suspensions acting against each other is the total Q of a audio speaker in free air at resonance (Fs).

Qmc - The Q of a audio speaker in a sealed box considering only the mechanical resistance.

Qec - The Q of a audio speaker in a sealed box considering only electrical resistance.

Qtc - Put a audio speaker into an enclosure and you then change how that audio speaker will act due to the resistance of the air pressure inside of the enclosure. When the audio speaker cone moves in or out the air pressure within the enclosure will put a resistance on its movements. The size and type of enclosure you build will depends upon the Qtc value you desire.

To decide upon your loudspeakers enclosure size you will need some loudspeaker software or good math skills and the math formulas; I prefer the software approach. In the software programs you will be asked to enter the required Thiele-Small parameters about the drivers such as the Q's, Fs, Vas, etc, some also ask enclosure type, number of drivers, etc. Then for the program to calculate the enclosure size it will want to know the Qtc value you want. The Qtc value you choose is a personal preference. A value of 0.707 is what most designers aim for, it will give you the flattest frequency response (accurate sound reproduction) and the lowest possible F3 (widest usable frequency range). Some people may not like this sound and want to enhanced base response so they may aim for 0.8 or higher.

In general high quality accurate audio loudspeakers Qtc are around 0.707, while loudspeakers that are designed to enhance the base may range from 0.8 to a max of 1.1. The more you move away from 0.707 anything over that will slowly start to sound boomy and unnatural and the base response will become more restricted.

If you want loud clean base go with larger audio drivers in larger enclosures, don't overwork a smaller audio speaker and try to increase the base by stuffing it in a small enclosure. Don't make the enclosures to big either; the more you oversize the enclosure (Qtc below 0.707) the more "tinny" it may sound, because you loose loudness (dB's) on the lower frequencies.

Thiele-Small QTC Comparison Chart

On this graph the vertical dB's represent how loud it is, the horizontal represents the frequencies. So looking at the chart you can compare the loudness of the various frequencies. Look at Qtc 1.500 and notice that all the frequencies below 60 Hz have been lost and then you have a huge (loud) peak at around 110 Hz and then it drops back rapidly, this is obviously not the desirable flat response that we want, unless all you want is single note boom box.

Now compare it to the Qtc 0.500 and note that there are no loud peaks, but now a lot of the frequencies below 50 Hz (F3 Value) will be too quiet. The best compromise is the Qtc of 0.707, no loud peaks and the loudness of the lower frequencies build quickly.

SPL (Sensitivity) - It is a representation of the efficiency and loudness that you can expect from a audio speaker relative to the input power. Keep in mind that it requires twice the power to increase the volume of a speaker by just 3dB. Don't look at efficiency alone; also consider that often there is a trade off between the low frequency reproduction capability and its sensitivity. Remember that lower frequencies require a lot of air to be moved and that requires a lot of power. So a audio speaker which is capable of doing very low frequencies will usually have lower SPL ratings.

Vap - Is defined as the volume of air that has the same compliance as the suspension of a passive radiator.

Vas/Cms - Represents the volume of air that when compressed to one cubic meter exerts the same force as the compliance (Cms) of the suspension in a particular speaker. The compliance or stiffness of the audio driver suspension is determined by the surround and the spider. It is simply a measurement of its stiffness.

Vb - The internal volume of a enclosure with a vent or passive radiator.

Vc - The total internal volume of a sealed enclosure.

Vd - No, it not that kind of VD. This Thiele-Small parameter is the Peak Diaphragm Displacement Volume which the total volume of air the cone will move. It is calculated by doubling Xmax then multiplying the result by Sd (Surface area of the cone). The higher the Vd figure is the better it is for use as a sub-bass driver.

Xmax/Xmech - (Maximum Linear Excursion) By definition it is the peak linear travel of a driver. Speaker output becomes non-linear when the voice coil begins to leave the magnetic gap. Non-linearity the point at which the number of turns in the magnetic gap which is exposed to the voice coil decrease. This excessive movement will increases audio speaker distortion.
Xmax is measured at the voice coil height minus top plate thickness, divided by 2. Xmech is expressed as the lowest of four potential failure condition measurement multiplied by 2. The four possible failures are;

  1. The spider crashing onto the top plate.
  2. The voice coil bottoming on back plate.
  3. The voice coil coming out of gap above core.
  4. The physical limitation of cone.

Take the lowest of these measurements then multiply it by two. This gives a distance that describes the maximum mechanical movement of the cone.

Zmax - This term represents the audio speaker's impedance at resonance.

Z - The total impedance, this includes the reactive and resistive resistance's