Full List: Thiele-Small Speaker Parameters W/ Descriptions


Speaker drivers and enclosures are quite complex in their design and functionality and can be measured in a wide variety of specifications and parameters.

What are Thiele-Small Parameters? Thiele-Small (T/S) Parameters are a series of measurements that define the mechanical, electrical and electromechanical properties of a loudspeaker. The TSPs apply particularly to individual drivers and enclosures (vented or ported) and give us specifics about how the speaker design and performance.

There are many Thiele-Small Parameters to be aware of. Some are more common (apply to more speakers) than others. In this article, I’ll emphasize the common parameters and describe all the potential TSPs we may find on a specifications sheet. I will also include examples when appropriate.


The Thiele-Small Parameters

Thiele-Small parameters are a subset of speaker specifications found on the data sheets of individual drivers and, sometimes, drivers with enclosures.

T/S parameters are named after Albert Neville Thiele of the Australian Broadcasting Commission and Richard H. Small of the University of Sydney, the two of whom pioneered these specifications for analyzing loudspeakers.

Many others have contributed to the list of T/S parameters since Thiele’s original series in 1961 and Small’s publishings beginning in 1972. Though many of the parameters are listed by manufacturers today, some manufacturers have created their own parameters to help describe their speakers.

In this article, we’ll discuss the universal parameters (fundamental, small-signal, large-signal and enclosure parameters) as well as the lesser-known parameters and even select manufacture-specific parameters.

These parameters are included by the manufacturer to present speaker designers with data that will aid in their producing speaker units with the driver.

Speaker units (as in the full-range 2-way and 3-way PA, bookshelf, studio monitor speakers, etc.) are generally built from ready-made drivers. The TSPs help the designed of such units choose the appropriate speaker driver for the speaker unit design.

So then, for a consumer or professional looking for a nice speaker (or set of speakers) for their studio; home entertainment system; live performance venue, etc., the Thiele-Small parameters are of little importance.

However, for those of us that design and build speaker units, either professionally or as an amateur hobbyist, the TSPs are very important!

In fact, loudspeaker designers may understand, by simply looking at the TSPs (or running them through simulators), the functionality of the driver in their theoretical or in-production unit design.

The TSPs will also give the designer a good idea of how large the enclosure ought to be and how long the bass-reflex port should be (if a bass-reflex port is to be included in the enclosure).

Many design engineers start with a goal of achieving certain parameters and work backward from there, choosing parts and design specs that will get them to their intended goal.

For the rest of us, these parameters may be a bit much but are nonetheless good specifications to understand when looking at a speaker driver’s data sheet.

By understanding the TSPs, we can better comprehend how a specific driver will perform in a unit. We can learn about the position, velocity and acceleration characteristics of the diaphragm; the impedance of the driver, and the overall sound.

It’s important to note that many of the parameters are measured and defined only at the speaker’s resonant frequency (Fs). That being said, some of these parameters will also apply to the frequency range in which the diaphragm motion (and therefore the sound) is linear.


Full List Of Thiele-Small Speaker Parameters

Below is a full list of the Thiele-Small parameters we may encounter on a speaker driver’s specifications sheet:

Note that no speaker will have values for every parameter. Note, too, that there are certain parameters that apply to most, if not all speaker drivers. We will get to each and every one of these parameters in this article.


Fundamental Thiele-Small Parameters

The fundamental TSPs refer to the physical parameters of the loudspeaker driver measured at small-signal levels.

Practically all electrodynamic “moving-coil” speaker drivers will have these parameters. The Rms parameter is the only one on this list that is frequently omitted from TSP data.


BL: BL Product (Force Factor)

Measured in Tesla-meters (T•m).

Force Factor (BL) = Flux Density (B) * Length Of Voice Coil (L)

The BL Product (aka Force Factor) measures the strength of the speaker motor. Stronger motors are more capable of moving larger diaphragms and, generally speaking, can handle more power.

This is not to say that a higher BL rating translates directly to efficiency or sensitivity. A stronger motor does not necessarily mean better handling power; higher efficiency, or more SPL.

The effectiveness of the BL Product is directly proportionate to the size of the speaker. Larger speakers demand higher BL factors. Therefore, a “high” rating on a small speaker may be average or even low if applied to a large speaker.

In general, high BL ratings yield better transient response in a speaker since the motor is capable of controlling the diaphragm with greater speed and accuracy.

Examples:


Cms: Mechanical Compliance Of Suspension

Measured in meters per Newton (m/N).

The Cms describes the compliance (inverse of stiffness) of the driver’s suspension which is made of the spider and surround. 

This parameter can be understood as the force exerted by the mechanical suspension of the speaker.

Cms is proportional to Compliance Equivalent Volume (Vas).

Speaking of resonance, the compliance of the driver is also linked to the resonant frequency (Fs) of the driver. As Cms goes up, the Fs goes down.

This is because stiffer suspension tends to allow shorter/faster vibrations while looser suspension tends to allows for longer/slower vibrations.

When producing a speaker driver, the Cms must be considered alongside the Qms parameter, which relates to the control of a transducer’s suspension when it reaches the resonant frequency (Fs).

Higher compliance means the driver is easier to move but will have an effect on the suspension’s ability to prevent lateral motion; absorb shock, and reduce the resonance of the driver.

Examples:


Le: Voice Coil Inductance

Measured in milliHenries (mH).

This TSP described the inductance of the voice coil. Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it.

This is important because audio signal are AC signals. Therefore, the current flowing through the voice coil is always changing.

When an alternating current is applied to the voice coil, the voice coil will resist the movement as the current alternates. This happens because a back EMF (electromotive force) is created that produces current flow in the opposite direction.

The applied audio signal tries to move the coil in one direction and the back EMF tries to move it in the opposite direction.

Because of inductance, impedance increases with frequency. This is because (assuming equal amplitude) higher frequencies have higher rates of change in their alternating currents.

Large Le values, then, typically yield poor high-end frequency response. This can be an issue for tweeters but is not a problem for woofers and subwoofers.

Inductance also causes the impedance to peak (Zmax) at the resonant frequency (Fs). This is because the driver will naturally want to oscillate at this frequency. The electromagnetic induction caused by the relative ease of movement causes a high impedance at the Fs.

Inductance is constant and is a property of the conductive voice coil. The inductance value is a function of the magnetic permeability of the coil material; the length of the coil (L); the area of the coil, and the number of turns in the coil.

Note that the back EMF varies with driver excursion as the voice coil moves relative to the stationary magnetic pole piece and, therefore, experiences a varying magnetic field. This inductance modulation causes some nonlinearity (distortion) in loudspeaker drivers. It is also the cause of the aforementioned impedance peak (Zmax) at the resonant frequency (Fs).

Examples:


Mmd: Diaphragm Mass

Measured in grams (g).

This TSP refers to the weight of the cone assembly (the voice coil, former, diaphragm, dust cap, half the surround, and half the spider).

Half the weight of the suspension is taken since the suspension connects the cone assembly to the basket/frame and the driver is not tasked with moving the diaphragm and not the entire suspension.

Examples:


Mms: Diaphragm Mass Including Air-Load

Measured in grams (g).

This TSP combines the Mmd mass with the air-load. The air-load (aka driver radiation mass load) is the weight of the air the driver cone must push to act properly as a transducer.

The driver radiation mass load is the weight of the air that coincides with the Volume Of Displacement (Vd) parameter.

As Mmd and Mms go up, the resonant frequency (Fs) goes down. Heavier cone assemblies have a tendency to want to oscillate more slowly than lighter cone assemblies (all else being equal).

As Mmd and Mms go up, the efficiency (η0) also drops. It takes more power to move heavier objects.

Examples:


Re: DC Resistance

Measured in ohms (Ω).

Sometimes called Revc: DC Voice Coil Resistance

The Re parameter refers entirely to the DC resistance (DCR) of the voice coil. Resistance is the resistance to direct electrical current in the voice coil.

DCR makes up a baseline in which the impedance (otherwise known as AC resistance) cannot drop below. The American EIA standard RS-299A specifies that Re (or DCR) should be at least 80% of the rated nominal impedance (Znom) of the driver.

It is rarely the case, at any frequency, that the driver will present a purely resistive load to its amplifier.

DC resistance is measured with a DC signal and with the cone prevented from moving.

When matching speakers, it’s better to use impedance values rather than resistance values. Resistance is a much more accurate measurement but nominal impedance gets us closer to the real story (the impedance graph gives us the real story).

Examples:


Rms: Mechanical Resistance (Lossiness)

Measured in kilograms per second (kg/s).

The Rms parameter is somewhat rare on TSP sheets. It refers to the mechanical resistance of the speaker, taking into account the driver’s suspension losses (damping). It acts as a measurement to the absorption qualities of the speaker suspension.

This parameter is the main factor in determining a driver’s Mechanical Q (Qms) and is defined by the suspension topology and material along with the former material that voice coil wraps around.

Examples:


Sd: Surface Area Of Cone

Measured in square metres (m2) or square centimetres (cm2).

The Sd parameter measures the effective projected area of the cone. In other words, the area of the cone that moves in order to produce sound.

Although a seemingly simple parameter, Sd can actually be quite difficult to measure since it largely depends on the shape and properties of the surround (including the Mechanical Compliance Of Suspension (Cms)).

The measurement typically ends up being the area calculated from the entire diameter of the diaphragm plus 1/3 to 1/2 the width of the surround. That is to say that drivers with equal diaphragm diameters can have significantly different Sd ratings depending on the width of their surrounds.

The Sd parameter along with the Maximum Linear Excursion (Xmax) parameter affect the potential maximum sound pressure level of the driver (before distortion). Sd and Maximum Physical Excursion (Xmech) affect the potential maximum sound pressure level (with significant distortion).

Examples:


Small-Signal Thiele-Small Parameters

The small-signal TSPs can be determined by measuring the impedance of the drive near the resonant frequency with small input levels.

“Small input levels” are defined as input signal levels at which the driver’s mechanical behaviour remains linear. In other words, these parameters are measured at levels that do not cause, or cause negligible amounts of, distortion.


Fs or F0: Resonant Frequency

Measured in Hertz (Hz).

Fs = 1 / (2π • (√CmsMms))

The resonant frequency Fs (sometimes labelled F0) refers to the free-air resonant frequency of the speaker driver. In other words, it’s the frequency at which the driver will move with minimal effort.

Put even differently, it is the point at which the weight of the moving parts of the speaker becomes balanced with the force of the speaker suspension when in motion.

A more compliant suspension (higher Cms) and a larger moving mass (higher Mms/Mmd) will cause a lower resonant frequency (lower Fs).

Without the help of a ported/vented enclosure, the speaker will be much less efficient at producing frequencies below Fs. Input signals well below the Fs rating may cause large excursions and physical damage to the speaker’s mechanical parts.

In other words, the Fs parameter marks the point at which the low-end frequency response of the driver begins to roll-off.

So although the Fs parameter applies to all drivers, it is really only of concern for woofers and subwoofers that are expected to actually produce frequencies near (and below) Fs.

All else being equal, a speaker with a lower Fs will be more capable of producing low-end than a speaker with a higher Fs. Of course, this is a generalization and there are other parameters that play a role in the speaker’s ultimate frequency response.

A typical factory tolerance for Fs spec is ±15%.

Examples:


Qes: Electrical Q @ Fs

Unitless.

Qes = (2π • FsMmsRe) / (BL)2

The Q measurements (Quality Factors) relate to the amount of relative damping in a loudspeaker. They describe how well the driver can control its movement at the resonant frequency.

Q is the inverse of the damping ratio and so lower Q values mean more control.

The Qes parameter more specifically refers to the electrical damping of the loudspeaker due to the voice coil and magnet motor.

As we’ve learned from our description of Inductance (Le), as the voice coil moves through the magnetic field, it produces a back EMF that opposes the current of the audio signal and, therefore, opposes the movement (damps) the driver.

This back EMF is proportional to the Force Factor (BL) times the velocity of the cone and is responsible for Qes and the increased impedance (Zmax) at the resonant frequency (Fs).

Ultimately, the electrical damping of a speaker driver relies on the damping of the driver and the damping of the connected amplifier. However, the Qes formula presented above assumes zero output impedance from the amplifier since the driver manufacturer does not know which amp will be used with its driver.

When an actual amplifier is used, its output impedance should be added to the DC resistance (Re) for calculations involving Qes.

Examples:


Qms: Mechanical Q @ Fs

Unitless.

Qms = (2π • FsMms) / Rms

Once again, the Q measurements (Quality Factors) relate to the amount of relative damping in a loudspeaker. They describe how well the driver can control its movement at the resonant frequency.

Q is the inverse of the damping ratio and so lower Q values mean more control.

The Qms parameter more specifically refers to the mechanical damping of the loudspeaker due to the losses in the suspension (spider and surround).

Higher Qms values mean lower mechanical losses and more control over the physical movement of the driver.

As discussed in the section on Induction (Le), the movement of the voice coil due to the AC audio signal causes an induced AC current in the opposite direction through the voice coil. So then, the mechanical Q (Qms) interacts with the driver electrically to resist movement and improve control.

A higher Qms value actually causes a higher peak impedance (Zmax) at the driver’s resonant frequency (Fs).

A predictor of the low versus high Qms values is when the former (the piece that the voice coil is wrapped around) is metallic or not, respectively. 

A metallic former will have its own magnetic field induced across during speaker movement on account of the voice coil and magnetic structure. The interaction with the voice coil will increase damping.

A non-metallic former will allow the voice and magnetic structure to interact with each other with no additional damping.

Examples:


Qts: Total Q @ Fs

Unitless.

Qts = (QesQms) / (Qes + Qms)

The Qts measurements (Total Quality Factor) is the inverse of the total damping ratio at the driver’s resonant frequency (Fs). It is defined as a combination of the mechanical Q (Qms) and the electrical Q (Qes).

Q is the inverse of the damping ratio and so lower Q values mean more control.

Though there are exceptions, Qts values can generally tell us the following:

  • Qts ≤ 0.4 indicate the driver is well-suited for a ported/vented enclosure.
  • 0.4 < Qts < 0.7 indicate the driver is well-suited for a sealed enclosure.
  • Qts ≥ 0.7 indicate the drive is well-suited for free-air of infinite baffle-type applications.

Examples:


Vas: Equivalent Compliance Volume

Measured in litres (L) or cubic feet (ft3).

Vas = ϱ • c2Sd2Cms

The Vas TSP measures the volume of air that has the same “stiffness” (inverse of compliance) as the driver’s suspension (Cms) when acted on by a piston of the same Surface Area Of Cone (Sd) as the driver.

What does this mean?

Well, the air inside an enclosure has its own compliance so that when we try to compress the air inside the enclosure (by moving the cone of the driver inward), there is resistance.

Smaller boxes have less volume and the air is harder to compress (less compliant). Larger boxes have more volume and the air is easier to compress (more compliant).

Vas describes the volume of air inside an enclosure that has the same compliance as the Mechanical Compliance Of Suspension (Cms) of the speaker.

So then, generally speaking, higher Vas values mean the speaker requires a larger enclosure.

Note that enclosures will have a volume less than Vas. Any enclosure with volume greater than Vas would act as an infinite baffle.

An infinite baffle is a driver with an, ideally (though impossible), infinite baffle. Imagine a driver in a wall that extends infinitely. In theory, this infinite wall would, by default, trap the rearward sound waves, making it a pseudo-sealed enclosure (though not necessarily so).

Examples:


Large-Signal Thiele-Small Parameters

Large-signal TSPs predict the approximate behaviour of a driver at high input signal levels.

These parameters are difficult to measure accurately due to the non-linear movement (distortion) the driver will experience at these high levels.


Pe: Thermal Power Handling

Measured in watts (W).

The Thermal Power Handling (Pe) T/S parameter refers to the maximum amount of electrical power a driver can handle before its voice coil assembly begins to melt, burn or otherwise sustain changes and damage.

Note that the thermal power handling limit is most often the overall power handling limit of a speaker. The exception is at low frequencies, where mechanical power handling comes into play. This is because lower frequencies cause large excursions relative to the applied power and drivers have limits to their movement: notably a maximum linear excursion (Xmax) and a maximum mechanical excursion (Xmech).

Power handling (include thermal power handling) is often given as two different ratings: “peak” and “RMS”.

The peak rating refers to the maximum power the driver is capable of withstanding for a very brief moment of time. Exceeding this limit will cause damage to the motor assembly.

The RMS (root mean square) power rating is not actually the technical RMS value (calculated as Ppeak / √2 for a sine wave). Rather it refers to the continuous power level a speaker can handle perpetually without burning-out.

For more information on speaker burn-out, check out my article Loudspeaker Blow-Out: Why It Happens & How To Avoid/Fix It.

Examples:


Vd: Volume Of Displacement

Measured in litres (L) or cubic feet (ft3).

Vd = Sd • Mmax

The Vd Thiele-Small parameter tells us the maximum volume of air a speaker is capable of displacing while maintaining linear movement. 

Vd values give us some indication as to how loud a speaker can get at low frequencies. The greater the volume of displaced air, the louder the bass.

Note that while the Vd is defined as the product of the Surface Area Of Cone (Sd) and the Maximum Linear Excursion (Xmax), the Sd is the more important of the two factors.

In theory, a small-diaphragm speaker with high excursion could produce as much Vd as a large-diaphragm speaker with a low excursion. However, a small-diaphragm, high-Xmax driver will likely be very inefficient since much of its voice coil will be outside the magnetic gap at any given time and contribute little to the diaphragm motion while producing distortion.

It bears repeating here that subwoofers would want require the highest Vd parameters.

Examples:


Xmax: Maximum Linear Excursion

Measured in millimetres (mm).

Maximum Linear Excursion (Xmax) = (height of voice coilheight of magnetic gap) / 2

The Xmax T/S parameter is the maximum distance a speaker can travel linearly without distorting the sound.

The voice coil has a certain height and oscillates up and down within the magnetic gap of the driver motor. If the coil is to travel too far a leave the magnetic gap, the AC audio signal will have much less control over system and the speaker will distort.

It’s important to note that, although it isn’t advised, exceeding Xmax will typically not damage the driver. Rather it will only cause distortion.

The Xmax and Surface Area Of Cone (Sd) parameters have a direct effect on how much sound pressure the driver will generate.

This parameter is different than the Maximum Mechanical Excursion (Xmech), which we’ll get to next.

To learn more about speaker distortion, check out my article Why Do Speakers Distort At High Sound/Audio Levels?

Examples:


Xmech: Maximum Mechanical Excursion

Measured in millimetres (mm).

The Xmech T/S parameter is the maximum distance a speaker can travel without damaging the driver. 

Unlike Maximum Linear Excursion (Mmax), which is threshold of distortion, Xmech is the physical limit of motion.

Exceeding Xmech will damage the driver by stretching its suspension on the way outward and smashing the voice coil against the back plate of the magnet on the way back. 

A damaged speaker will behave poorly, if at all.

Examples:


Thiele-Small Parameters For Enclosures

So we know that the T/S parameters will help us to decide what kind of driver would fit our enclosure and/or what size of enclosure would best suit the driver.

In the majority of cases, we only need to know a few key parameters to calculate an appropriate enclosure:

  • Resonant Frequency (Fs): knowing Fs helps us to lower the low-end cutoff (if necessary) by designing an appropriately-sized enclosure. It also warns us about choosing an enclosure with the same resonance to avoid excess ringing in the speaker unit.
  • Total Quality Factor (Qts):
    • Qts ≤ 0.4 indicate the driver is well-suited for a ported/vented enclosure.
    • 0.4 < Qts < 0.7 indicate the driver is well-suited for a sealed enclosure.
    • Qts ≥ 0.7 indicate the drive is well-suited for free-air of infinite baffle-type applications.
  • Equivalent Compliance Volume (Vas): Note that enclosures will have a volume less than Vas. Any enclosure with volume greater than Vas would act as an infinite baffle.

However, some manufacturers take it upon themselves to recommend certain enclosure parameters. These are listed below:

For more details about speakers and their enclosures, check out my article Why Do Loudspeakers Need Enclosures?


Fb: Resonance Frequency Of The Vented/Radiated Enclosure

Fb refers to the manufacturer-recommended resonant frequency of a ported/vented or radiated enclosure. It is ultimately up to the speaker unit designer to follow this parameter or not when using/designing a driver in a ported/vented or radiated enclosure.


Fc: Resonance Frequency Of The Sealed Enclosure

Fc refers to the manufacturer-recommended resonant frequency of a sealed/closed enclosure. It is ultimately up to the speaker unit designer to follow this parameter or not when using/designing a driver in a sealed/closed enclosure.


Vb: Volume Of The Vented/Radiated Enclosure

Vb refers to the manufacturer-recommended volume of a ported/vented or radiated enclosure. It is ultimately up to the speaker unit designer to follow this parameter or not when using/designing a driver in a ported/vented or radiated enclosure.


Vc: Volume Of The Sealed Enclosure

Vc refers to the manufacturer-recommended volume of a sealed/closed enclosure. It is ultimately up to the speaker unit designer to follow this parameter or not when using/designing a driver in a sealed/closed enclosure.


Other Thiele-Small Parameters

The above-listed TSPs (except the enclosure recommendations) are commonly found in TSP sheets for individual speaker drivers.

However, there are plenty of other T/S parameter that may or may not show up regularly. Some are constants or, at the very least, testing conditions. Others are required to calculate the more important TSPs. Some are duplicates of the big speaker specifications, and a select few are manufacturer-specific.

Without further ado, here are the lesser-known other Thiele-Small parameters:


B: Magnet Flux Density In Gap

Measured in Tesla (T).

The B parameter measures the magnetic flux density (magnetic field strength) in the driver’s gap. It is the magnetic field strength that causes the voice coil to oscillate as an AC audio signal passes through it.

This magnetic flux density is a function of the strength of the magnet; size of the magnet, and size of the gap.

The higher the B parameter, the more speaker motion the driver will produce for a given input signal.

B is used in calculating a fundamental TSP known as the BL Product or Force Factor (BL). The BL parameter of a driver is the product of the magnetic flux density in gap and the length of the voice coil.

For more information on how speakers use magnets, check out my article Why And How Do Speakers Use Magnets & Electromagnetism?


C: Propagation Velocity Of Sound

Measured in meters per second (m/s).

The C parameter is essentially the speed of sound in the driver manufacturer’s test. Typically this propagation velocity of sound is equal to approximately 343 m/s which is the speed of sound through air at STP (standard temperature and pressure).


Cas: Driver’s Acoustic Compliance

Measured in meters per Newton (m/N).

The Cas parameter is essentially the acoustic equivalent of the Mechanical Compliance Of Suspension (Cms).

Note that the Cms and Equivalent Compliance Volume (Vas) make the information of Cas redundant and that Cms is rarely found on TSP sheets.

Cms is the effective compliance (inverse of stiffness) of the air that the speaker pushes across its Surface Area Of Cone (Sd).


Cmes: Electrical Capacitance Including Air-Load

Measured in meters per farads (F).

Cmes = Mms / B2 • L2 

The Cmes parameter is a rare find in TSP sheets. It tells us the electrical capacitance representing the mechanical mass.

In other words, Cmes tells us how well the moving cone of the speaker can hold onto electric charge as a signal is applied to the voice coil.


D: Driver Diameter

Measured in meters (m) or inches (“).

The D parameter is the diameter of the diaphragm plus any part of the surround that moves with the diaphragm. It is not the same as the nominal diameter, which generally rounds the diameter up or down to nearest inch or half-inch.


EBP: Efficiency Bandwidth Product

Measured in Hertz (Hz).

EBP = Fs / Qes

The EPB parameter is a derived value that is used to help designers determine what kind of enclosure would best-suit the driver.

Though there are exceptions, EPB values can generally tell us the following:

  • EPB >100 indicates the driver is well-suited for a ported/vented enclosure.
  • EPB < 50 indicates the driver is well-suited for a sealed enclosure.
  • 50 ≤ EPB ≤ 100 indicates the drive is well-suited for either enclosure type

F3: -3 dB Cutoff Frequency

Measured in Hertz (Hz).

The F3 parameter is another one that rarely gets used.

It represents the frequency on the speaker’s frequency graph where the low-end roll-off passes -3 dB from average. The F3 of a driver is typically just below its resonant frequency (Fs).

This parameter helps us understand the limitations of the driver’s low-end response and whether it’s worth using in a speaker design.


L: Coil Length

Measured in meters (m).

The T/S parameter L tells us the length of the voice coil’s wire.

If the speaker is to perform linearly, this length of coil is to remain immersed in the magnetic field as the speaker moves.

The length of the coil is used to calculate other TSPs. The most notable is the BL Product Force Factor (BL) that multiplies the coil length (L) by the magnetic flux density of the gap (B).


Lces: Electrical Inductance Including Air-Load

Measured in milliHenries (mH).

Lces = Cms • B2 • L2 

The Lces parameter is a rare find in TSP sheets. It tells us the electrical inductance representing the Mechanical Compliance Of Suspension (Cms).

In other words, Lces tells us how well the suspension of the driver will resist the AC signal is applied to the voice coil as if the suspension was completely conductive.


Ms: Total Mass Of Moving Parts

Measured in grams (g).

The total mass of the speaker cone including the full weight of the surround and spider. 

A fairly useless measurement. Mmd and Mms are much more applicable.


η0: Reference Efficiency

Measured in percentage (%).

η0 = [(ϱBL2 • Sd2) / (2 • π • cMms2Re)] • 100%

or

η0 = [(4 • π2Fs3Vas) / (c3Qes)] • 100%

This parameter tells us the power efficiency of the driver as a percentage.

In other words, the η0 parameter tells us what percentage of the electrical power applied to the driver transducer is converted into acoustic power.

 η0 = Pa / Pamp

The reference efficiency can be used to calculate the sensitivity rating of the speaker driver as well. To do so, follow these equations:

  • dB SPL @ 1W/1m = 112.1 +10•log(η0)
  • dB SPL @ 2.83V/1m = 112.1 +10•log(η0) +10•log(8/Re)

A speaker driver with 100% efficiency would have a sensitivity rating of 112.1 SPL @ 1W/1m.

Note that speaker drivers are notoriously inefficient. Whatever electrical power is not converted to acoustic power (the vast majority of it) is dissipated as heat. This is why Thermal Power Handling (Pe) is a big deal in speakers.


ρ: Density Of Air

Measured in kilograms per cubic meter (kg/m3).

This parameter, which represents the density of air, is like the propagation velocity of sound (C) is a constant during testing.

Generally, ρ is given as the density of air at standard atmospheric temperature and pressure, which equals 1.18 kg/m3


Pa: Acoustic Power

Measured in watts (W).

The acoustic power parameter is another mostly-unused parameter. It tells us the acoustic power the speaker will output when 1 watt of electrical power is sent to it.

It is calculated with the efficiency rating of the speaker:

 η0 = Pa / Pamp


Qa: Q @ Fb Due To Absorption Losses

Unitless.

The Q measurements (Quality Factors) relate to the amount of relative damping in a loudspeaker. They describe how well the driver can control its movement at the resonant frequency.

Q is the inverse of the damping ratio and so lower Q values mean more control.

The Qa parameter more specifically refers to the additional damping of the loudspeaker due to the absorption losses if the manufacturer-recommended ported/vented enclosure with resonant frequency Fb is used.


Qec: Q @ Fc Due To Electrical Losses

Unitless.

The Q measurements (Quality Factors) relate to the amount of relative damping in a loudspeaker. They describe how well the driver can control its movement at the resonant frequency.

Q is the inverse of the damping ratio and so lower Q values mean more control.

The Qec parameter more specifically refers to the additional damping of the loudspeaker due to the electrical losses if the manufacturer-recommended sealed/closed enclosure with resonant frequency Fc is used.


Ql: Q @ Fb Due To Leakage Losses

Unitless.

The Q measurements (Quality Factors) relate to the amount of relative damping in a loudspeaker. They describe how well the driver can control its movement at the resonant frequency.

Q is the inverse of the damping ratio and so lower Q values mean more control.

The Ql parameter more specifically refers to the additional damping of the loudspeaker due to the leakage losses if the manufacturer-recommended ported/vented enclosure with resonant frequency Fb is used.


Qmc: Q @ Fc Due To Mechanical Losses

Unitless.

The Q measurements (Quality Factors) relate to the amount of relative damping in a loudspeaker. They describe how well the driver can control its movement at the resonant frequency.

Q is the inverse of the damping ratio and so lower Q values mean more control.

The Qmc parameter more specifically refers to the additional damping of the loudspeaker due to the mechanical losses if the manufacturer-recommended sealed/closed enclosure with resonant frequency Fc is used.


Qp: Q @ Fb Due To Port Losses

Unitless.

The Q measurements (Quality Factors) relate to the amount of relative damping in a loudspeaker. They describe how well the driver can control its movement at the resonant frequency.

Q is the inverse of the damping ratio and so lower Q values mean more control.

The Qp parameter more specifically refers to the additional damping of the loudspeaker due to the port losses if the manufacturer-recommended ported/vented enclosure with resonant frequency Fb is used.


Qtc: Pneumatic Q

Unitless.

The Q measurements (Quality Factors) relate to the amount of relative damping in a loudspeaker. They describe how well the driver can control its movement at the resonant frequency.

Q is the inverse of the damping ratio and so lower Q values mean more control.

The Qtc parameter refers to the manufacturer-recommended closed/sealed system’s Q at resonance (Fc), due to all losses.


Ras: Acoustic Losses

Measured in Newton-seconds per metre (N • s / m).

The Ras parameter is the acoustic resistance of the speaker, taking into account the acoustic losses around the driver.

It can be thought of as the acoustic equivalent of the Mechanical Resistance (Rms).


Res: Electrical Losses

Measured in ohms (Ω).

The Res parameter is the electrical resistance of the speaker, taking into account the electrical losses in the driver.

It can be thought of as the electrical equivalent of the Mechanical Resistance (Rms).


Rg: Amplifier Source Resistance

Measured in ohms (Ω).

The Rg parameter is incredibly rare because most drivers are standalone devices and are not combined with a specific amplifier.

However, in the case a driver is connected to a specific amp, the Rg parameter describes the source resistance (including leads, crossovers, etc.) of the amplifier.


SPLo: SPL From 1 Watt At 1 Meter

Measured in decibels sound pressure level (db SPL) with one watt (1 W) of power at a distance of 1 metre (1 m): dB SPL @ 1W/1m

The SPLo parameter is the same as the sensitivity rating of a speaker.

It tells us how loud (in dB SPL) the speaker will be at a distance of 1 metre when 1 watt of power is sent to it.

Speakers with higher sensitivities (SPLo) are more efficient than speakers with lower sensitivities. Sensitivity can be calculated from a speaker’s efficiency and vice versa via the equations below:

SPLo = 112.2 + 10 * log(n0)

n0 = 10(SPLo – 112.2)/10

To learn more about speaker sensitivity (and efficiency), check out my article Full Guide To Loudspeaker Sensitivity & Efficiency Ratings.


Xlim: Maximum Excursion Limitation

Measured in millimetres (mm).

The Xlim parameter is specific to Eminence speakers. The Eminence Delta-10A is listed in the examples below.

Xlim is expressed by Eminence as the lowest of four potential failure condition measurements:

  1. Spider crashing on top plate.
  2. Voice coil bottoming on back plate.
  3. Voice coil coming out of gap above core
  4. The physical limitation of cone.

A transducer exceeding the Xlim is certain to fail from one of these conditions.


Xvar: Usable Excursion/Variation

Measured in millimetres (mm).

The Xvar parameter is specific to B&C speakers. The B&C 8CX21 is listed in the examples below.

Xvar represents the excursion limit (beyond the Maximum Linear Excursion (Xmax)) in which the magnetic field seen by the voice coil (B); the total suspension compliance (Cms), or both, drops below 50% or their stated small-signal values.

At this point, high levels of distortion and power compression along with strong variations from small-signal behaviour are likely to occur.

The new technique yields different results from the standard measurement based on THD. B&C Speakers believes that this added information gives a more accurate and reliable description of loudspeakers behaviour in actual operating conditions.


Znom: Nominal Impedance

Measured in ohms (Ω).

The Znom T/S parameter is typically shared as a “regular” specification but sometimes makes an appearance in the parameters portion of a specs sheet.

Nominal impedance refers to the “rated impedance” of the speaker and is typical 2, 4, 6, 8, 12 or 16 Ω.

Of course, impedance changes wildly with frequency across the audible spectrum so Znom actually doesn’t tell us too much. Rather it is a standard to help users match the speaker to an appropriate amplifier.

Speaking of standards, the IEC states that the minimum impedance (which is close to, if not, the DC resistance of the speaker (Re)) should not drop below 80% of the nominal value across the speaker’s frequency range.


Zmax: Impedance At Resonance

Measured in ohms (Ω).

Zmax = Re [1 + (Qms/Qes)]

The impedance of a speaker is frequency-dependent and a spike in impedance happens at the resonant frequency (Fs) of the speaker.

This peak in impedance is represented by the Zmax value, which is used when calculating Qes and Qms.

The impedance (AC resistance, for all intents and purposes) spike at the Fs may seem counter-intuitive since it is precisely at this frequency that the driver moves the most ease.

However, it’s because the driver is so easy to move that the electrical impedance spikes. The ease of movement causes the speaker to move which produces a back EMF (through electromagnetic induction) in the coil the opposes the signal that would cause this movement.


Usable Frequency Range

Measured in Hertz (Hz).

The usable frequency range parameter is the manufacture-recommended crossover/filter points for the speaker.

Within this range, the speaker is expected to perform as per the other T/S parameters. Using a crossover (or another filter) to send audio frequencies only within this range from the audio signal will allow the speaker drive to perform as it should.

Tweeters, for example, are not designed to produce sub-bass and will likely get damaged if sub-bass frequencies are applied. This is reflected in the tweeter’s usable frequency response.

Subwoofer, as another example, are not designed to produce high-end frequencies and will likely get lose efficiency if high-end frequencies are applied. This is reflected in the subwoofer’s usable frequency response.

To learn more about speaker crossovers, check out my article What Is A Speaker Crossover Network? (Active & Passive).


Power Handling

Measured in watts (W).

Power handling is generally covered in the main specs of a speaker unit.

When dealing with individual drivers, the T/S parameter Thermal Power Handling (Pe) is more often used.

Pe is part of the overall power handling of a speaker. It deals with the maximum power a speaker can handle before it burns-out due to its voice coil and former melting, burning or becoming otherwise deformed.

But there is also a mechanical aspect to power handling that describes the power limit at which the speaker will become damaged due to over-excursion. This point coincides with the Maximum Mechanical Excursion (Xmech) of the speaker.

Power handling aims to cover both these aspects.

Generally speaking, a speaker will burn out due to thermal limitations before physical limitations. This holds true until we look at subwoofers.

Subwoofers have very large coils that can typically dissipate relatively large amounts of heat. At the same time, they must move lots of air and may be overloaded mechanically if too much excursion is demanded of them.


Voice Coil Height

Measured in millimetres (mm).

This is the measurement of the height of the driver’s voice coil.

Voice coil height is used to calculate the driver’s Maximum Linear Excursion (Xmax).

Maximum Linear Excursion (Xmax) = (voice coil height – magnetic gap height) / 2


Magnetic Gap Height

Measured in millimetres (mm).

This is the measurement of the height of the driver’s magnetic gap, in which the voice coil is suspended.

Magnetic gap height is used to calculate the driver’s Maximum Linear Excursion (Xmax).

Maximum Linear Excursion (Xmax) = (voice coil height – magnetic gap height) / 2


Speaker Examples

Here are a few speaker examples with their published Thiele-Small Parameters:


Jensen P8R

The Jensen P8R (link to compare prices at select retailers) is an 8″ 25 W Vintage Alnico Loudspeaker.

Jensen P8R

Link to the Jensen P8R specifications sheet.

T/S ParameterJensen P8R 4ΩJensen P8R 8Ω
Voice Coil DC Resistance (Re)3 Ω6.6 Ω
Resonance Frequency (Fs)129 Hz135 Hz
Mechanical Q Factor (Qms)8.678.67
Total Q Factor (Qts)1.432.28
Mechanical Moving Mass (Mms)9.3 g8.8 g
Mechanical Compliance (Cms)164 µm/N159 µm/N
Force Factor (BL)3.72 Wb/m3.99 Wb/m
Equivalent Acoustic Volume (Vas)10.5 L10.3 L
Maximum Linear Displacement (Xmax)±1 mm±1 mm
Reference Efficiency (η0)1.27 %0.95 %
Diaphragm Area (Sd)213.8 cm2213.8 cm2
Losses Electrical Resistance (Res)16 Ω27 Ω
Voice Coil Inductance @ 1kHz (Le)0.21 mH0.36 mH

Eminence Delta-10A

The Eminence Delta-10A (link to compare prices at select retailers) is a speaker recommended by Eminence for professional audio and bass guitar applications as a woofer/mid-bass or midrange in vented monitors, satellites and multi-way enclosures.

Eminence Delta-10A

Link to the Eminence Delta-10A specifications sheet.

  • Resonant Frequency (Fs): 66 Hz
  • DC Resistance (Re): 5.42 Ω
  • Coil Inductance (Le): 0.74 mH
  • Mechanical Q (Qms): 6.53
  • Electromagnetic Q (Qes): 0.35
  • Total Q (Qts): 0.33
  • Compliance Equivalent Volume (Vas): 30.5 liters / 1.08 cu.ft.
  • Peak Diaphragm Displacement Volume (Vd): 121 cc
  • Mechanical Compliance of Suspension (Cms): 0.18 mm/N
  • BL Product (BL): 14.4 T-M
  • Diaphragm Mass Inc. Airload (MMs): 32 grams
  • Efficiency Bandwidth Product (EBP): 189
  • Maximum Linear Excursion (Xmax): 3.5 mm
  • Surface Area of Cone (Sd): 344.9 cm2
  • Maximum Mechanical Limit (Xlim): 9.4 mm

Celestion BL15-300X

The Celestion BL15-300X (link to compare prices at select retailers) a steel 15″ inch bass guitar speaker that has industry-leading engineering built in.

Celestion BL15-300X

Link to the Celestion BL15-300X specifications sheet.

  • D: 0.33m/12.99in
  • Fs: 48.1Hz
  • Mair: 14.15g/0.499oz
  • Qms: 2.989
  • Qes: 1.004
  • Mmd: 68.24g/2.41oz
  • Qts: 0.751
  • Re: 3.15Ω
  • Vas: 137.69lt/4.86ft3
  • BL: 8.83Tm
  • Cms: 0.133mm/N
  • Rms: 8.327kg/s
  • Le (at 1kHz): 0.47mH

B&C 8CX21

The B&C 8CX21 (link to compare prices at select retailers) is an 8-ohm 8″ 25W/200W pro audio coaxial driver.

B&C 8CX21

Link to the B&C specifications sheet.

  • Resonance Frequency: 74 Hz
  • Re: 5.2 Ω
  • Qes: 0.39
  • Qms: 4.1
  • Qts: 0.36
  • Vas: 15.0 dm3 (0.55 ft3)
  • Sd: 220.0 cm2 (34.1 in2)
  • η: 1.5%
  • Xmax: 5.0mm
  • Xvar: 5.5mm
  • Mms: 21.0 g
  • Bl: 115 Txm
  • Le: 1.2 mH
  • EBP: 189 Hz

Dayton Audio RS225-8

The Dayton Audio RS225-8 (link to compare prices at select retailers) is an 8-ohm 8″ woofer.

Dayton Audio RS225-8

Link to the Dayton Audio RS225-8 specifications sheet.

  • DC Resistance (Re): 6.5 ohms
  • Voice Coil Inductance (Le): 0.86 mH @ 1 kHz
  • Resonant Frequency (Fs): 28.3 Hz
  • Mechanical Q (Qms): 1.46
  • Electromagnetic Q (Qes): 0.51
  • Total Q (Qts): 0.38
  • Diaphragm Mass Inc. Airload (Mms): 35.8g
  • Mechanical Compliance of Suspension (Cms): 0.88 mm/N
  • Surface Area Of Cone (Sd): 213.8 cm2
  • Volume Of Displacement (Vd): 149.7 cm3
  • BL Product (BL): 9.05 Tm
  • Compliance Equivalent Volume (Vas): 56.8 litres
  • Maximum Linear Excursion (Xmax): 7.0 mm

Peavey Lo Max 18” & 15”

The Peavey Lo Max 18” (link to compare prices at select online retailers) is an 8-ohm 18″ driver designed for subwoofer applications.

Peavey Lo Max 18”

Link to the Peavey Lo Max specifications sheet.

T/S ParameterPeavey Lo Max 15”Peavey Lo Max 18”
Znom (Ohms)88
Revc (Ohms)5.405.40
Sd (Square Meters)0.0890.118
BL (Tesla-meters)23.4023.40
Fo (Hz)38.531.5
Vas (Liters)124.0294.4
Cms (uM/N)110.8140.0
Mms (gm)146.00194.68
Qms11.0011.15
Qes0.3640.330
Qts0.3850.386
Mmax (mm)10.210.2
Le (mH)0.750.75
SPL (1 W 1m)95.595.5
η0 (%)2.202.20
Vd (cubic inches/milliliters)55.15 / 90473.06 / 1197
Pmax (Watts pgm.)24002400
Disp (inches3 / milliliters)242 / 3960310 / 5080

Scan Speak D2004/602000

The Scan Speak D2004/602000 (link to compare prices at select online retailers) is a 4-ohm 19mm dome tweeter.

Scan Speak D2004/602000

Link to the Scan Speak D2004/602000 specifications sheet.

  • Resonance Frequency [fs]: 600 Hz
  • Mechanical Q Factor [Qms]: 4.42
  • Electrical Q Factor [Qes]: 1.42
  • Total Q Factor [Qts]: 1.07
  • Force Factor [Bl]: 1.3 Tm
  • Mechanical Resistance [Rms]: 0.2 kg/s
  • Moving Mass [Mms]: 0.22 g
  • Suspension Compliance [Cms]: 0.32 mm/N
  • Effective Diaphragm Diameter [D]: 24 mm
  • Effective Piston Area [Sd]: 4.5 cm²
  • Equivalent Volume [Vas]: 0.01 L
  • Sensitivity (2.83V/1m): 88.4 dB
  • Ratio Bl/√Re: 0.78 N/√W
  • Ratio fs/Qts: 558 Hz

Accuton P220 (Passive Radiator)

The Accuton P220 (Passive Radiator) (link to check the price at select retailers) is a 220mm passive radiator driver designed for passive radiator speakers. It features no motor and acts to radiate along with an actual driver to increase precision and SPL within a single speaker enclosure,

Accuton P220 (Passive Radiator)

Link to the Accuton P220 specifications sheet.

  • Sensitivity (2.83V / 1m) [SPL]: 0 dB
  • DC Resistance [Re]: 0 Ω
  • Resonance Frequency [Fs]: 41 Hz
  • Equivalent Volume Of Air [Vas]: 26.5 L
  • Mechanical Q [Qms]: 0
  • Electrical Q [Qes]: 0
  • Total Q [Qts]: 0
  • Effective Piston Area [Sd]: 224 cm2
  • Moving Mass [Mms]: 23.4 g
  • Suspension Compliance [Cms]: 0.64 mm/N
  • Mechanical Resistance [Rms]: 0 kg•s

Seas Prestige H1794-08

The Seas Prestige H1794-08 (link to compare prices at select retailers) is a 6 1/2″ full-range driver with a large ferrite magnet system.

Seas Prestige H1794-08

Link to the Seas Prestige specifications sheet.

  • Nominal Impedance: 8 Ohms
  • Voice Coil Resistance: 5.7 Ohms
  • Recommended Frequency Range: 45 – 20000 Hz
  • Voice Coil Inductance: 0.49 mH
  • Short Term Power Handling: 110 W
  • Force Factor: 6.6 N/A
  • Long Term Power Handling: 40 W
  • Free Air Resonance: 42 Hz
  • Characteristic Sensitivity (2,83V, 1m): 89.7 dB
  • Moving Mass inc. air (Mms): 12.1 g
  • Voice Coil Diameter: 26 mm
  • Suspension Compliance: 1.19 mm/N
  • Voice Coil Height: 12 mm
  • Suspension Mechanical Resistance: 0.51 Ns/m
  • Air Gap Height: 6 mm
  • Effective Piston Area: 136 cm2
  • Linear Coil Travel (p-p): 6 mm
  • Vas: 31 Litres
  • Maximum Coil Travel (p-p): 14 mm
  • Qms: 6.29
  • Magnetic Gap Flux Density: 1.1 T
  • Qes: 0.42
  • Magnet Weight: 0.6 kg
  • Qts: 0.39
  • Total Weight: 1.8 kg

Dayton Audio AMT Mini-8

The Dayton Audio AMT Mini-8 (link to compare prices on Amazon and select retailers) is an air motion transformer (ribbon-type) tweeter. Because it does not have a moving-coil electrodynamic motor, it is without many of the T/S parameter listed in this article.

Dayton Audio AMT Mini-8

Dayton Audio AMT Mini-8 Specifications

  • Re: 7.92-Ohm
  • Le: N/A
  • Fs: N/A
  • Qms: 1.86
  • Qes: N/A
  • Qts: 1.84
  • Mms: N/A
  • Cms: N/A
  • Sd: 3.8 cm2
  • Vd: N/A
  • BL: N/A
  • Vas: N/A
  • VC Diameter: N/A

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